Para Titi Letty - University of Floridaufdcimages.uflib.ufl.edu/UF/E0/04/57/61/00001/MIRO_A.pdf ·...

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GENETIC AND GEOGRAPHIC PERSPECTIVES ON HUMAN MIGRATION AND IMPLICATIONS FOR PREHISTORIC DEMOGRAPHIC RECONSTRUCTIONS

By

AIDA T MIRÓ

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA

2013

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© 2013 Aida T. Miró

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Para Titi Letty

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ACKNOWLEDGMENTS

I would first like to thank my mom, dad and sister for their unconditional support

and love in all of my endeavors. I would like to thank Professor Connie Mulligan for her

encouragement, mentorship, and guidance throughout my graduate career. I would also

like to thank Professors David Reed, Michael Miyamoto, and Steve Brandt for their

insight and guidance throughout this learning process. I thank current and former

postdoctoral researchers and graduate students in the Mulligan lab, Dr. David Hughes,

Dr. Laurel Pearson, Dr. Andrew Kitchen, Dr. Amy Non, and Tamar Carter for their

support and helpful insight during the past six years. I thank all my undergraduate

assistants, especially Alex Wang, Shannon McNulty, Timothy Scott, and Nubiana Todd,

whose tireless work has greatly contributed to my dissertation research and with whom I

have learned how to be a mentor. I’m grateful for the Yemenite individuals who

participated in the study that is part of this dissertation. I thank my extended family for

always rooting for me, especially, Titi Letty, Jenny, mamamama, Tití and abuelitita. I

thank my friends for their continuous support, for making me laugh, and for helping me

keep a balance during graduate school, particularly Teresa Szakos and Dr. Yaraimé

Colón-Cales.

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TABLE OF CONTENTS

page

ACKNOWLEDGMENTS .................................................................................................. 4

LIST OF TABLES ............................................................................................................ 7

LIST OF FIGURES .......................................................................................................... 8

ABSTRACT ..................................................................................................................... 9

CHAPTER

1 INTRODUCTION .................................................................................................... 11

2 HUMAN DEMOGRAPHIC PROCESSES AND GENETIC VARIATION AS REVEALED BY MTDNA SIMULATIONS ................................................................ 24

Materials and Methods............................................................................................ 27

Models .............................................................................................................. 27

Simulations ....................................................................................................... 28

Summary Statistics ........................................................................................... 28

Statistical Analysis ............................................................................................ 29

Results .................................................................................................................... 29

Partitioning of Genetic Variation by Demographic Parameters......................... 29

Comparison of Summary Statistics .................................................................. 30

Comparison of Evolutionary Scenarios ............................................................ 31

Discussion .............................................................................................................. 33

Demographic Parameters................................................................................. 33

Summary Statistics ........................................................................................... 34

Relevance to Human Evolution ........................................................................ 35

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3 HUMAN MIGRATION PATTERNS IN YEMEN AND IMPLICATIONS FOR RECONSTRUCTING PREHISTORIC POPULATION MOVEMENTS .................. 107

Methods ................................................................................................................ 109

Samples and Data .......................................................................................... 109

Estimation of Migration ................................................................................... 110

Results .................................................................................................................. 112

Discussion ............................................................................................................ 115

Patrilocality and Genetic Signals .................................................................... 115

Patterns of Migration ...................................................................................... 117

Empirical Estimates of Migration .................................................................... 118

Application of Migration Estimates in Prehistoric Demographic Modeling ...... 121

4 CONCLUSION ...................................................................................................... 134

LIST OF REFERENCES ............................................................................................. 147

BIOGRAPHICAL SKETCH .......................................................................................... 159

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LIST OF TABLES

Table page

2-1 Summary statistics analyzed and their definitions .................................................. 40

2-2 Partitioning of genetic variation by demographic parameter for each summary statistic. ................................................................................................................... 41

2-3 Recommendation of optimal summary statistic to use for each parameter of interest. ................................................................................................................... 42

2-4 Demographic scenarios compared in Tukey’s tests and p-values for each summary statistic. ................................................................................................... 43

2-5 Percent of simulated scenarios that agree with empirical Fst estimates separated by CS and GF categories. .................................................................... 102

3-1 Summary statistics for migration distances. .......................................................... 125

3-2 Best model to explain probability of migration. ...................................................... 126

3-3 Estimates for the direction of migration in each collection site across all three generation groups. ................................................................................................ 127

3-4 Directional means estimates for each group by collection site. ............................. 128

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LIST OF FIGURES

Figure page

2-1 Alternative scenarios for initial colonization of modern humans out of Africa........ 103

2-2 Box plots of estimates of 5 summary statistics that partition genetic variation more equally between CS, GF, and CSxGF than seen in the other summary statistics. ............................................................................................................... 104

2-3 Box plots of estimates of 4 summary statistics that partition genetic variation primarily by CS, compared to the other summary statistics. ................................. 105

2-4 Box plots of estimates of 3 summary statistics that partition genetic variation similar to summary statistics in Figure 2-3.. .......................................................... 106

3-1 Proportion of migrants by sex for each generation group.. ................................... 129

3-2 Density plots combining migration distance and frequency of the distance for each group. ........................................................................................................... 130

3-3 Plot of migration distances for marital pairs. ......................................................... 131

3-4 Migration direction vectors and mean migration direction by collection site over all three generations. ............................................................................................ 132

3-5 Migration direction vectors and mean migration direction for each collection site by generation group.. ............................................................................................ 133

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

GENETIC AND GEOGRAPHIC PERSPECTIVES ON HUMAN MIGRATION AND

IMPLICATIONS FOR PREHISTORIC DEMOGRAPHIC RECONSTRUCTIONS

By

Aida T Miró

August 2013

Chair: Connie J. Mulligan Major: Genetics and Genomics

This dissertation integrates simulated genetic data with empirical non-genetic

data to develop a framework for reconstructing human demographic processes. In the

first study, I simulate mitochondrial DNA for demographic scenarios representing the

initial dispersal of modern humans out of Africa. Summary statistics are estimated for

the simulated datasets to calculate the percent of explained variation by each parameter

and to identify which parameter combinations generate distinct differences in genetic

variation. I also identify the informativeness of different summary statistics at

summarizing genetic variation. The results show that colonization size and gene flow

have the largest effects on genetic variation, suggesting that defining these migration

parameters with more realistic values would allow a more accurate reconstruction of the

migration out of Africa.

In the second study, I analyze migration patterns through four generations in

Yemen. I compare the proportion of migrants, and the distance and directionality of

migration across the generations and identify factors that influence the migration

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patterns. The results suggest that the proportion of migrants and migration distance is

significantly lower in the grandparents’ generation and more likely represents realistic

values for prehistoric processes. I describe how the values for these migration

parameters calculated for the grandparents’ generation can be used to generate more

informative hypothesis models for prehistoric demographic reconstructions. The results

from both studies are combined to develop a more realistic and geographically explicit

model for the migration out of Africa that increases the possibility of accurately inferring

the process and estimating values for parameters that have thus far been a challenge.

This dissertation illustrates the importance of using interdisciplinary approaches from

genetic and non-genetic disciplines in the continued efforts of reconstructing

evolutionary histories.

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CHAPTER 1 INTRODUCTION

Human evolutionary history has been characterized by a series of population

growths and contractions, population fissions, and migration, in addition to mutation

events. Each of these events has had an effect on patterns of human genetic variation.

Mutations in the DNA of individuals increase the genetic variation of a population as,

over generations, the mutations accumulate and become fixed or extinct in the

population. However, different demographic processes have varying effects on the

fixation of mutations. Population growth increases genetic variation in a population, with

each new individual increasing the opportunity for mutation and fixation. Population

contractions and population fissions tend to decrease the genetic variation as mutations

can be lost from a population when individuals die off or leave the population.

Population fissions can further create founder effects, where the individuals that leave a

population carry only a subset of the genetic diversity of the original population

(Joblinget al. 2004). Over time, the original population and the new population

accumulate mutations independently, increasing the genetic difference between the

populations. This difference can be further increased by subsequent population growths

or contractions. In contrast, migration can reduce the genetic difference between

populations through the exchange of different genetic mutations (gene flow), while

increasing the genetic diversity within each population. As can be seen, the effects of

simple demographic processes on genetic variation, such as the effect of population

fission, are well understood and can be accurately inferred. However, the effects of

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more complex scenarios, as would occur from combinations of these processes, are

less clear.

Humans have expanded into almost every region of the world, creating a

complex evolutionary history. Anatomically modern human arose in Africa around 100-

200 thousand years ago (kya) (Forster 2004; Garrigan and Hammer 2006; Pakendorf

and Stoneking 2005). Humans migrated out of Africa into Eurasia 60-80kya from

somewhere in northeast Africa (Forster 2004; Macaulayet al. 2005; Soareset al. 2012).

They colonized Europe 40-50kya (Forster 2004; Lell and Wallace 2000). The

colonization of Asia occurred most likely through a coastal route to southern Asia and

southeast Asia around 50-66kya (Barkeret al. 2007; Macaulayet al. 2005) arriving in

Oceania by 48-63kya (Macaulayet al. 2005; Turneyet al. 2001). The Americas were

colonized by ~15kya from a group that migrated from southeast Asia (Kitchenet al.

2008). After these initial colonizations, some areas of the world underwent major

recolonization processes. For example, 35-45 kya there was a major migration from a

population in southern Asia back to northern Africa (Gonzalezet al. 2007; Olivieriet al.

2006). Another notable example includes the recolonization of Europe around 10kya

from a population somewhere in southwest Asia, introducing agriculturalists that

admixed with the existing hunter-gatherer populations (Pinhasiet al. 2012; Rasteiro and

Chikhi 2013). The combination of demographic processes that has occurred in each

region has generated an elaborate pattern of genetic variation in the current population

of the region.

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Genetic anthropologists interpret the patterns of genetic variation within and

between populations in order to reconstruct the demographic processes that have

characterized human evolutionary history. Until recent advances in sequencing

technology allowed for economical sequencing of autosomal DNA, mitochondrial

(mtDNA) and Y chromosome (NRY) DNA have been the genetic markers primarily used

to reconstruct demographic processes. Both markers are uniparentally inherited and

have little or no recombination (Heinet al. 2005; Pakendorf and Stoneking 2005). This

allows researchers to directly trace genetic mutations (or combinations of mutations

known as haplotypes) from parents to offspring over time. Using this framework, the

presence of a mutation in two populations suggests that one population is descended

from the other, both populations share a common ancestor, or gene flow has moved the

mutation from one population to the other. Thus, the number of mutations and

differences in mutations between individuals and populations can be used to infer

estimates of population parameters, such as the timing of population fissons or levels of

gene flow between populations. Genetic summary statistics, such as Φst, which

measures the proportion of genetic diversity due to haplotype differences among

populations (Excoffieret al. 1992), are used to infer the historic connectivity between

populations (Holsinger and Weir 2009). Large Φst values indicate that populations are

highly differentiated and suggest little gene flow. Small Φst values indicate similarity

between populations and suggest much more gene flow. Median networks and

phylogenetic trees, which show the connectivity between individuals (Bandeltet al. 1999;

Felsenstein 1983) are also used to describe individual and population relationships.

Individuals (or haplotypes) who lie close together in the network or tree are more

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genetically similar (and more related) than individuals who lie far from each other.

Furthermore, “rooted” phylogenetic trees, in which the ancestral haplotype is known, are

used to chronologically order and date the population fissions (Felsenstein 1981).

Individuals with shorter branch lengths indicate fewer mutations, suggesting population

fissions occurred more recently, whereas individuals with long branch lengths suggest

population fissions occurred longer ago.

Traditionally, the values for individual parameters in a demographic process are

estimated from the genetic diversity and the estimates are jointly interpreted in a post-

hoc manner to describe a process that is consistent with other sources of evidence (e.g.

archaeological or geological data). A notable example is the reconstruction of the

process of anatomically modern human out of Africa. Rooted phylogenetic trees from

individuals from Africa, Europe, and Asia show that European and Asian populations

are descendants of African populations (Bowcocket al. 1991; Garrigan and Hammer

2006; Liet al. 2008). Furthermore, European populations lie intermediate to African and

Asians in the trees (Garrigan and Hammer 2006; Liet al. 2008). Fst estimates (which is

similar to Φst , but for allele differences) are smaller between Africa and Europe (0.141)

than between Africa and Asia (0.235) and smallest between Asia and Europe (0.093)

(Bowcocket al. 1991), suggesting that Europeans are most closely related to Asians and

more closely related to Africans than Asians are related to Africans. Bowcock et al

(1991) proposed a model to explain these findings, in which Europeans were the

product of admixture between Africans and Asians, each contributing 35% and 65%

respectively. However, the similarity between Africans and Europeans could be caused

by other demographic processes as well. Gene flow between African and European

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populations after the European and Asian fission could lead Europeans to be more

genetically similar to Africans (Cerezoet al. 2012; McEvoyet al. 2011). Thus the

confounding nature of demographic processes can lead to different processes having a

similar effect on patterns of genetic variation.

A major drawback of post-hoc interpretation is that there is no possibility to test

the interpretation against other alternative interpretations that may provide better

explanations for the observed data. Model-based methods of demographic

reconstruction present a solution to post-hoc interpretations by explicitly testing

competing hypothesis through the simulation of genetic variation representing

alternative models and comparisons of these hypothesis models to the empirical data

(Beaumontet al. 2002; Tavaréet al. 1997). Approximation approaches (i.e. maximum

likelihood approximations and Bayesian approximations) have been particularly

successful model-based methods for estimating parameter values (Beaumont 2010;

Beaumontet al. 2002; Garrigan and Hammer 2006; Marjoram and Tavaré 2006). For

these methods, different hypothesis models that can represent a demographic process

are created to explain the observed patterns of genetic variation. The models are

generated by defining exact values or ranges of values for different parameters of

interest. These values are then used in simulations that generate DNA data with

patterns of genetic variation reflecting the demographic processes of the models.

Each model is represented by multiple (i.e. thousands) simulated datasets. Each

simulated dataset reflects both the pattern of genetic variation generated by the

specified demographic scenario and the stochasticity of the mutation process. Thus,

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each simulated dataset for a specific model has a slightly different pattern of genetic

variation that is still representative of the model. Each dataset is then compared to the

empirical data to test which model “best” explains the observed data.

In order to compare the simulated datasets to the empirical data, the genetic

variation of each dataset must be summarized. Summary statistics provide quick and

easy ways to calculate values to summarize genetic variation. The summary statistics

calculated for each simulated dataset generate a distribution of summary statistic

estimates for each model that represents all the possible patterns of genetic variation

generated by the model. The summary statistics of each simulated dataset are

compared to summary statistics of the empirical data. The summary statistics that are

most similar (i.e. that have the smallest absolute difference after being subtracted),

represent the model(s) that best explain the empirical data. A cutoff value (e.g. 1%) is

selected to determine the number of simulations that will be used to select the best

model(s). The model(s) with the most support from the simulations within the cutoff

value represents the best model(s). This model contains the values for each

demographic parameter that best represents the empirical data.

In the method described above, the values for each demographic parameter are

jointly inferred from the best model. This presents an advantage of model-based

methods over traditional methods, where parameters are individually estimated.

Explicitly accounting for parameter combinations when generating the simulated genetic

variation and jointly inferring the values of the parameters from the best model, at least

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partially, accounts for the confounding effects of combinations of parameters on genetic

variation, which might not be detected through traditional approaches.

Since different demographic processes (i.e. parameter combinations) can lead to

similar patterns of genetic variation, the confounding effects of parameter combinations

on genetic variation nonetheless limit inferences from model-based methods, despite

the improvement over traditional methods. Oftentimes more than one model can “best”

explain the empirical data. Even within one model, such as the single origin out of Africa

model explaining modern human expansion, there can be multiple parameter

combinations that realistically represent the model. Parameter combinations with similar

patterns of genetic variation are likely to all be selected as the best explanation to the

empirical genetic data. Multiple “best” demographic scenarios decrease the probability

of accurately inferring the values for the individual parameters because each parameter

will comprise the range of values for all the scenarios included as “best”. Therefore, in

order to generate informative hypothesis models (or parameter combinations), it is

important to determine if the parameter combinations produce patterns of genetic

variation that are distinguishable from each other.

Additionally, different summary statistics can summarize different aspects of the

genetic variation. Thus, a specific summary statistic might more accurately reflect the

portion of genetic variation generated by a specific parameter than another summary

statistic. In order to select the summary statistics that most effectively identify the best

model, it is necessary to ascertain which summary statistics are more informative for

summarizing the genetic variation and differentiating the parameter combinations.

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A further advantage of model-based methods is that they allow the inclusion of

data from multiple disciplines. Data from genetic and non-genetic sources, such as

archaeological evidence, can be directly incorporated to inform the values for the

demographic parameters. Incorporating data from across disciplines to fix or set ranges

on specific parameters offers multiple benefits. Prior knowledge is explicitly

incorporated, instead of having to find post-hoc explanations for the empirical genetic

evidence that will be consistent with the other sources of evidence. The values for the

parameters are more realistic and thus, more likely to be accurate, allowing for more

informative hypothesis models. Realistic hypothesis models increase the overall

probability of selecting the “best” model. Establishing values for specific parameters

also offers the possibility of testing more values for parameters with unknown prior

estimates.

The inclusion of prior data from both genetic and non-genetic sources can greatly

enhance a study that is using a model-based approach. However, finding useful

estimates to define parameter values can sometimes pose a challenge. For example,

data are more readily available for some parameters to describe the migration of

modern humans out of Africa, than for other parameters. The timing of modern humans

out of Africa can be delimited by combining the dates established on archaeological

remains out of Africa and the divergence dates of African and non-African haplotypes

estimated from previous genetic studies. Thermoluminescence and electron spin

resonance dating of archaic human remains found in Qafzeh and Skhul (modern day

Israel) place archaic humans in the Levant 90-120kya (Grün and Stringer 1991;

Mercieret al. 1993; Valladaset al.). These data suggest that the successful migration of

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modern humans out of Africa could not have happened before then. Alternatively,

archaeological remains in Europe and Asia place modern human’s arrival 45kya-50kya

(Mellars 2006). Analyses of mitochondrial DNA (mtDNA) suggest that the L3

haplogroup, which is ancestral to all non-African haplogroups, diverged between 60 and

90 kya (Forster 2004; Gonderet al. 2007; Soareset al. 2012). The most ancestral non-

African haplogroups, M and N, which gave rise to all other non-African haplogroups,

diverged as late as 50kya-65kya (Atkinsonet al. 2008; Beharet al. 2008; Macaulayet al.

2005). These data narrow the time during which modern humans could have migrated

of Africa to a range of about 50 thousand years.

Some parameters, such as the possible size of the population that migrated out

of Africa, must rely primarily on genetic data because of the lack of non-genetic data.

Values for the population size of non-Africans have been estimated as low as 1% of the

African population (Atkinsonet al. 2008; Fagundeset al. 2007), and as high as 33%

(Relethford and Harpending 1995; Tenesaet al. 2007). Other studies have found more

intermediate values of 10-20% (Gronauet al. 2011). Data on population movement

acquired from a demographic approach would provide a more realistic value that could

further delimit the possible size of the population migrating out of Africa.

Still for other parameters, such as the migration rate between adjacent

populations after the migration out of Africa, it is difficult to identify values that are

informative for demographic reconstruction using model-based methods. Current

empirical estimates of migration based on ethnographic studies include short time

frames of the seasonal movement of hunters and gatherers (Hahnet al. 1966; Marlowe

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2010) or migrant workers (de Haan and Rogaly 2002). These data lack the information

on movement across generations that is needed to define gene flow in the developed

demographic scenarios. Demographic studies from birth certificates and census data

provide data that allow us to trace movement over longer periods of time (i.e. between

individuals and their parents), but these studies have generally focused on a limited

analysis of migration, such as distance moved or proportion moved, and have been

performed in developed countries (Boattiniet al. 2007; Gray and Bilsborrow 2013;

Mielkeet al. 1994; Mortonet al. 1971). The focus on developed countries probably

makes the values unrealistically high for prehistoric demographic processes. Genetic

studies have estimated migration rates between Africa and Eurasia (Coxet al. 2008;

Gravelet al. 2011), but the values were estimated from samples located very distant

from each other, so it is uncertain how informative the values are to describe the

movement between adjacent populations. Migration rates estimated in a developing

country from a demographic approach could provide a source of more informative data

to define the values for the migration rate that occurred immediately after the migration

out of Africa.

Additionally, spatial patterns of migration from demographic data could show

whether there is a pattern in the direction that individuals, and the population as a

whole, are moving. These type of data would also allow to determine whether

geographic features, or other factors, have an effect on the patterns of migration (e.g. if

people are moving to areas with particular geographic characteristics). Currently, it is

very difficult to identify the exact geographic location where a demographic process

occurred from DNA data (Epperson 2003). For example, it is unclear whether the

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divergence of mtDNA haplotypes L3 and M/N, which characterize African and non-

African populations respectively, occurred before the new population migrated out of

Africa, or after (i.e.in the Middle East) and L3 was lost from the new population out of

Africa due to genetic drift (Forester 2004). Knowledge on spatial patterns of migration

could help elucidate the geographic area where a demographic process occurred by

allowing more geographically explicit hypothesis models to be developed.

In this dissertation, I attempt to fill some of the gaps of model-based methods for

their use in human demographic reconstruction. In Chapter 2, simulations characteristic

of model-based methods are generated under a simplified model of modern human out

of Africa that includes multiple values for population size, gene flow and time of the

population fission and movement out of Africa (Miró-Herrans and Mulligan 2013). I

develop a framework to identify demographic scenarios that generate distinguishable

differences in patterns of genetic variation and that offer informative hypothesis against

which to compare empirical genetic data. Multiple summary statistics are calculated for

each demographic scenario to identify the informativeness of different summary

statistics in summarizing genetic variation. Based on the results, I provide specific

recommendations about the summary statistics to use according to the specific

demographic parameter under study. Additionally, I identify the contribution of each

demographic parameter to the patterns of genetic variation.

In Chapter 3, I use GPS coordinates from the place of residence of individuals

sampled in Yemen, their birthplaces and their parents’ and grandparents’ birthplaces to

evaluate patterns of human migration. With the geographic coordinates, the direction of

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migration is identified to detect whether geographic features, or other factors, have an

effect on the patterns of migration. I calculate the proportion of migrants and the

distance of migration across generations. Comparisons of these migration parameters

across generations offers the possibility of identifying if and how the migration

parameters change over time and assess whether the values in one generation provide

more informative estimates than another generation. The results indicate that the

grandparents’ generation provides parameter values that more realistically represent

estimates for prehistoric demographic processes. Specifically, my results provide

empirical estimates for migration parameters that can be used to generate more

informative and geographically explicit hypothesis models for prehistoric human

processes.

This dissertation illustrates the advantages of taking an interdisciplinary approach

to address human evolution. Through the use of simulated genetic data, I identify the

significant effect migration has had on human genetic variation and how our limited

knowledge on human migration constrains the accurate reconstruction of demographic

processes and estimation of other demographic parameters. I then address the

challenges posed by the effects of migration by estimating empirical values for migration

parameters from non-genetic data to generate more realistic hypothesis demographic

scenarios and increase the probability of accurately reconstructing demographic

processes. Specifically, by integrating data from genetic, geographic and demographic

approaches, I provide a framework to develop more realistic and geographically explicit

scenarios for the migration out of Africa that should allow for the accurate estimation of

some of the demographic parameters that have thus far been a challenge to estimate.

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More generally, this dissertation contributes to the understanding of human evolution in

various fields of study and provides a general framework for creating informative models

that can be used for reconstructing the evolutionary history of many different species.

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CHAPTER 2 HUMAN DEMOGRAPHIC PROCESSES AND GENETIC VARIATION AS REVEALED

BY MTDNA SIMULATIONS

Evolutionary history can be described as a series of sequential demographic

events that created the genetic complexity observed in the organism under study.

Reconstructing evolutionary history requires identifying the relevant demographic

processes and understanding how these processes have affected patterns of existing

genetic variation. To make inferences about human evolutionary processes, such as the

first migration of humans out of Africa, it is important to know whether different

hypothesized demographic processes are distinguishable based on the genetic

variation of the present human population. For instance, can we distinguish between a

large and small colonizing population for the initial migration out of Africa? Furthermore,

different combinations of demographic parameters, such as population size and gene

flow, can interact to generate similar patterns of genetic variation. By looking at small

changes in demographic parameters, in combination with each other, we can determine

the influence of these parameters on patterns of genetic variation.

With the growth in computational power, simulations now allow us to generate

multiple sets of genetic data for complex evolutionary processes. We can compare the

simulated datasets to each other to determine how genetic variation changes as

demographic parameters change (Carvajal-Rodríguez 2008) and identify which

parameter interactions cause detectable differences in genetic variation. Although many

studies have compared simulations of evolutionary processes to empirical data to make

inferences about the empirical data (Deshpandeet al. 2009; Fagundeset al. 2007;

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Gronauet al. 2011; Lohmuelleret al. 2009; Veeramahet al. 2012), few studies have used

simulations to investigate the effects of demographic parameters and their interactions

on genetic variation (Calafellet al. 2001). Comparing simulated demographic scenarios

can help us determine which demographic parameters merit more attention because of

their increased effect on genetic variation and can direct the investigation to questions

focused on the parameters with greatest effect. Comparisons of simulated scenarios

also allow identification of the parameter combinations (and by inference, the

demographic scenarios) that can be distinguished from each other based on the genetic

variation of each scenario.

For instance, comparing simulated scenarios could improve our understanding of

the critical period in human history when anatomically modern humans left Africa and

colonized the rest of the planet. Although many studies have focused on estimating

specific values for parameters of interest for the colonization of humans out of Africa,

e.g. (DeGiorgioet al. 2009; Fagundeset al. 2007; Gronauet al. 2011), the large

variances for some of these estimates suggest it would be useful to better understand

how specific values for each parameter, and their interactions, affect genetic variation.

Three parameters of particular interest for the colonization of humans out of Africa are i)

the size of the colonizing population, ii) the timing of the event and iii) the amount of

subsequent gene flow into and out of Africa. Examining the interaction of these primary

parameters using estimates drawn from the literature should give insight into which of

the parameters has a larger effect on genetic variation and whether increased efforts to

refine the value will lead to increased resolution of other parameters of interest.

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Demographic parameters have generally been inferred from statistics that

summarize the patterns of genetic variation. Although Lohse and Kelleher (2009) show

that likelihood methods provide better estimates of demographic parameters, recent

studies show that it is still common practice to use summary statistics (Bustamante and

Ramachandran 2009; Deshpandeet al. 2009; Keinanet al. 2008). The use of summary

statistics has become increasingly popular in methods of Bayesian inference, such as

approximate Bayesian computation (ABC) (Beaumont 2010; Beaumontet al. 2002;

Marjoram and Tavaré 2006). In brief, the ABC approach compares summary statistics

calculated from an empirical data set with summary statistics calculated from simulated

scenarios that serve as hypotheses to explain the empirical data. For ABC, and other

approaches, it is necessary to know whether different demographic scenarios lead to

different summary statistic values, thus reflecting the effect of different demographic

parameter combinations on genetic variation. Furthermore, it is essential to determine,

and is largely lacking in the current literature, which summary statistics are most

informative for a parameter or evolutionary process of interest (Hickersonet al. 2006).

In this study, we simulate mitochondrial DNA (mtDNA) nucleotide sequences for

42 alternative demographic scenarios describing the colonization of modern humans out

of Africa. The diverse set of parameter combinations allows us to evaluate the influence

of these parameters on genetic variation. Three parameters of primary interest were

varied in these scenarios; colonization size (CS), rate of gene flow between African and

non-African populations (GF), and the time of the colonization event (TC). Values for

these parameters were chosen from the literature to represent realistic demographic

scenarios that could have produced the current human genetic variation. Twelve

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summary statistics were calculated for each of 1,000 simulated datasets produced for

42 different demographic scenarios. The summary statistics were used to 1) detect

differences between demographic scenarios and determine which scenarios could be

distinguished from each other, 2) determine the effects of particular demographic

parameters (CS, GF, and TC) on genetic variation, and 3) identify the informativeness

of different summary statistics on genetic variation.

Materials and Methods

Models

Forty-two scenarios were modeled to describe the demographic process for the

initial colonization of modern humans out of Africa. In this model (Figure 2-1), two

populations split at one of two possible colonization times, with the colonizing population

having one of three possible sizes, followed by seven possible proportions of

bidirectional gene flow between the populations. The values for colonization time (TC)

were 100,000 and 50,000 years ago, the earliest and most recent estimates for

movement of modern humans out of Africa, respectively (Beharet al. 2008; Gonderet al.

2007; Klein 1998; Macaulayet al. 2005; Mellars 2006; Salaset al. 2002). The values for

colonization size (CS) were estimated as a proportion of the African population and set

at 1% , the lowest estimated value of migrants (Atkinsonet al. 2008; Fagundeset al.

2007), 30%, the highest estimated value (Relethford and Harpending 1995; Tenesaet

al. 2007), and 10% as an intermediate value (Gronauet al. 2011). The values for gene

flow (GF) were 10-6, 10-5, 10-4, 10-3, 10-2, 0.1, and 0.5 proportion of migrants from each

population per effective individual per generation. These values for GF were selected to

begin at Nem<<1 and increase by single orders of magnitude until Nem>>1 to reflect

28

highly structured populations and highly panmictic populations, respectively. The initial

population size was fixed at 10,000 (Atkinsonet al. 2008; Fagundeset al. 2007) with

constant population size.

Simulations

One thousand coalescent simulations for each of the 42 demographic scenarios

were generated using SIMCOAL2 (Laval and Excoffier 2004). One hundred sequences

of human mtDNA data were simulated for each population with a coding region of

15,446 nucleotides (nt) and a substitution rate of 1.7 x 10-8 substitutions per site per

year (Atkinsonet al. 2008; Ingmanet al. 2000) and a control region of 1123 nt and a

substitution rate of 4.7 x 10-7 substitutions per site per year (Howellet al. 2003).

Summary Statistics

Twelve summary statistics (Table 2-1) were calculated for each of the 42,000

simulated mtDNA datasets to capture the genetic variation of the 42 different scenarios.

Fst and Φst were calculated between the two populations with ARLEQUIN 3.11

(Excoffieret al. 2005). Tau-hat )τ̂( was calculated from the mismatch distribution of the

simulated mtDNA coding region with R (R Development Core Team 2010). Number of

segregating sites (S), Watterson’s θ (θW), nucleotide diversity (π), Ramos-Onsins and

Rozas’ R2, Tajima’s D (TD), number of singleton sites (NSS), number of haplotypes (#

Hap), number of singletons (# Single), and homozygosity (Hmzy) were calculated with

Sample_stats3, a version of the Sample_stats utility distributed with Hudson’s MS

(2002), modified for DNA sequence data (available at

http://github.com/ryanraaum/samplestats). The code to calculate Ramos-Onsins and

29

Rozas’ R2 was incorporated with permission from Mlcoalsim (Ramos-Onsins and

Mitchell-Olds 2007).

Statistical Analysis

A multi-factorial analysis of variance (ANOVA) including all three parameters of

interest (CS, GF, and TC) was performed for each summary statistic using R (R

Development Core Team 2010). The percent of variation explained by each parameter

and parameter interaction was estimated from the additive component of variance,

which was in turn calculated from the expected mean square value. Pair-wise

comparisons (Tukey’s tests) were performed for each pair of the 42 demographic

scenarios, for a total of 861 comparisons for each of the 12 summary statistics.

Results

Partitioning of Genetic Variation by Demographic Parameters

ANOVAs were used to partition the genetic variation summed across all 42,000

simulated datasets into the tested parameters and their interactions and to determine

which parameters and interactions had a significant effect in explaining differences

between the 42 demographic scenarios as reflected in each summary statistic (Table 2-

2). For parameters and interactions that were significant in explaining variation, the

actual value of explained variance was then calculated to identify how variation was

partitioned among the parameters and interactions within each summary statistic.

All parameters and interactions were significant (p-value<1.0 x 10-6) in explaining

the differences in genetic variation between the 42 demographic scenarios using the

following summary statistics: Fst, Φst, S, θW, π, TD, R2, and τ̂ (Table 2-2). TC and TC

30

interactions (i.e. TCxCS and TCxGF) were not significant for NSS, # Hap, # Single, and

Hmzy.

CS, GF and their interaction (i.e. CSxGF) were significant across all summary

statistics and yielded the highest percent of explained variance. CS explained the most

variation, ranging from 2.4% to 96.4%, depending on the summary statistic. This was

followed by the interaction between CS and GF (3.1- 43.5%) and then GF (0.8- 86.8%).

TC and its interactions with GF and CS explained only a small percent of the variation

(TC: 0.1-1.9%, TCxGF: 0.4-5.3%, and TCxCS: 0.1-0.8%).

Comparison of Summary Statistics

Percent of explained variation was also compared across summary statistics to

determine how each summary statistic partitioned variation into the investigated

parameters and interactions (Table 2-2). Fst and Φst partitioned more variation in GF

relative to the other summary statistics, with percent of explained variance of 85.6% and

86.8% respectively. ,τ̂ # Hap, # Single, and Hmzy partitioned the most variation for CS

relative to the other summary statistics, with values of 84.3%, 96.4%, 96.1%, and

77.5%, respectively. While TC contributed little to the explained variation, Fst and Φst

reflected more variation due to TC (1.0% and 1.9%) than any other summary statistic.

S, θW, π, TD, R2, and NSS had more similar patterns of partitioning the variation among

each parameter and their interactions, with the variation more equally distributed

between CS, GF, and CSxGF than in the other summary statistics.

31

Comparison of Evolutionary Scenarios

Pair-wise comparisons were performed on all 42 parameter combinations for a

total of 861 t-tests to determine which of the 42 demographic scenarios could be

distinguished from each other (Table 2-4). Significant differences in the summary

statistic estimates indicate a distinguishable difference in genetic variation between the

parameter combinations and suggest we could distinguish between the represented

demographic scenarios. Four summary statistics ( ,τ̂ # Hap, # Single, Hmzy) partitioned

the variation primarily into a single parameter (CS) and are not discussed later, as the

pair-wise comparisons and box plots mainly showed a pattern where the demographic

scenarios differed by CS category (Table 2-4 and Figure 2-3). It is worth noting,

however, that the pair-wise comparisons and box plots of τ̂ have similar trends to those

of the summary statistics discussed later, particularly π, although differences in τ̂

between demographic scenarios are less distinct, despite τ̂ being developed as a

measure to estimate time of a demographic event (Rogers 1995). Although Φst and Fst

also partition the majority of variation into a single category (GF), these summary

statistics show more representation by TC and TC interactions (i.e. TCxCS and TCxGF)

than the other summary statistics; box plots depicting the range of estimates of eight

summary statistics for all 42 demographic scenarios are discussed later (Figures 2-2

and 2-4).

Fst and Φst, which measure similar aspects of genetic variation, have similar

trends in the box plots, where Φst has smaller differences between the demographic

scenarios. Interestingly, estimates of both Fst and Φst, significantly decrease in value as

32

GF increases within each CS category (Figures 2-2a and 2-4a and Table 2-4). GF

categories of moderate levels of GF (10-4 and 10-3) are significantly different from each

other, whereas TC is significantly different for low GF categories (10-6 and 10-5). S and

θW are related measurements that also show similar trends in the box plots. Within the

CS category of 1%, high and low levels of GF are clearly differentiated (Figures 2-2b

and 2-4b and Table 2-4), but the difference between GF categories diminishes with

increasing CS. With respect to TC, 50kya and 100kya produce significantly different

estimates from each other when CS=10% for GF>10-3 and when CS=1% + GF=10-3.

Estimates of π show a similar pattern as S and θW estimates (Figure 2-2c), with smaller

differences in π estimates between the scenarios, except that TC produces significantly

different π estimates for GF categories of low values within CS=1%. Estimates of R2

and TD show similar patterns in the box plots (Figure 2-2d and 2-4c). For CS=10%,

categories of GF>10-3 produce significantly greater estimates than categories of GF of

10-3 and less, whereas TC produces differences similar to those of π (Table 2-4).

Estimates of NSS are significantly different for high and low levels of GF for CS=1% and

CS=10% (Figure 2-2e and Table 2-4). TC only produces significantly different estimates

for CS=1% for GF=10-3.

Most of the discussed summary statistics (except Fst and Φst) show that low GF

categories (<10-4) for CS=1% and CS=10% have similar summary statistics relative to

high GF categories for CS=30%. Fst and Φst show a different pattern, thus providing

insight into the effects of gene flow by reflecting the diversity between two migrating

populations instead of the overall diversity among the two populations, which the other

summary statistics reflect. Fst and Φst show a similar pattern for the three CS categories

33

where Fst and Φst estimates decrease as GF category values increase. The discussed

summary statistics also show that, in general, TC produced significantly different

estimates for GF categories equal or less than 10-5, but not for high GF categories. The

demographic scenarios with CS=1% and GF=10-3 were generally distinct from each

other and all other scenarios.

Discussion

Demographic Parameters

Our results illustrate that migration, whether represented as colonization size

(CS) or gene flow (GF), shows the largest effect on human genetic variation over the

time period in which humans colonized the planet. Specifically, our simulations indicate

that CS has the largest influence on patterns of genetic variation (percent of variance

explained averaged over all summary statistics) and CS, GF and CS x GF explain most

of the genetic variation that has arisen in humans, as simulated in this study.

Interactions between CS and GF have varying effects on patterns of genetic variation.

For example, the majority of box plots (Figures 2-2 and 2-4) reveal that low to moderate

levels of GF (< 10-3) create similar patterns of genetic variation across all CS categories.

This supports findings such as those of Kitchen et al. (2008), where reducing gene flow

as low as zero produced a much larger colonization size for peopling of the Americas, in

contrast to Hey’s (2005) results where colonization size was one hundred fold smaller

with much higher levels of gene flow. However, the extreme values tested here show

that large CS with low GF (less than 10-4) creates a very different effect relative to small

CS and high GF. This can be explained because large CS with low GF leads to high

genetic variation as it increases the difference between the populations, whereas small

34

CS and high GF lowers genetic variation as it decreases the difference between the

migrating populations.

Summary Statistics

This is one of the first studies to investigate the informativeness of specific

summary statistics in the inference and comparison of demographic processes

(Hickersonet al. 2006; Sefcet al. 2007). Specifically, we were interested in determining

the extent to which different summary statistics can distinguish between the modeled

scenarios. Although one summary statistic alone cannot distinguish between all of the

scenarios, our results suggest that combining several summary statistics, selected

based on the parameters of interest, will allow better resolution when comparing

empirical data with simulated data.

Our results clearly show that the summary statistics differentially explain variance

depending on the demographic parameter (Table 2-2). In general, summary statistics in

which percent of explained variation is distributed across multiple parameters and

interactions (such as S, θW, π, TD, R2, and NSS) are able to distinguish between more

demographic scenarios. In contrast, summary statistics where the majority of variation is

concentrated in one main parameter (such as ,τ̂ # Hap, # Single, and Hmzy) are useful

for studies that focus on one parameter, but have more limited utility to distinguish

between different demographic scenarios. It is important to note that some demographic

scenarios produce genetically similar results that cannot be differentiated regardless of

the summary statistic used. This similarity suggests that some evolutionary processes

35

and specific questions, such as the timing of the first human migration out of Africa, may

not be resolved based on mitochondrial DNA data.

A limitation in methods that compare empirical data with simulated data, such as

ABC approaches, is that the analyses require a small number of summary statistics to

avoid the situation in which so many simulated scenarios are rejected that it is

impossible to make any conclusions about the empirical data (Beaumontet al. 2002;

Hamilton 2005; Wegmannet al. 2009). Our results show similarity in box plot profiles

across some pairs of summary statistics, most likely because they reflect a similar

aspect of the genetic variation, for example, S and θW. This similarity offers the

possibility to reduce the number of summary statistics used when comparing empirical

and simulation data. We make specific recommendations on the optimal summary

statistics to use based on the parameters and questions of interest for studies of

evolutionary history where CS and GF have played a dominant role, such as in the

current analysis (Table 2-3).

Relevance to Human Evolution

A goal in evolutionary studies is to identify changes in demographic parameters

given the observed genetic variation. In most cases, it is unclear how small changes in

the parameters of interest will influence genetic variation, for example, how will small

changes in gene flow influence observed levels of genetic variation. We use a model of

modern human migration out of Africa, with changes in colonization size (CS), time of

colonization (TC) and gene flow (GF), to investigate the effect of demographic changes

on genetic variation.

36

To address the extent of gene flow between African and non-African populations

after the initial migration out of Africa, values for GF were selected such that GF<10-4

represents population substructure, GF=10-4 represents migration equilibrium (Nem≈1),

and GF>10-4 represents panmixia. The box plots of the demographic scenarios (Figures

2- 2 and 2-4) illustrate that when CS=1% (and in some cases when CS=10%), GF=10-3

appears as a transition point where genetic variation decreases significantly (in a

sigmoidal curve) as GF increases. Our pair-wise comparisons (Table S-4) show that

summary statistic estimates when GF<10-3 are similar to each other, but have

significantly greater estimates when GF>10-3, which also have similar estimates to each

other. The sharp transition in genetic variation from GF of 10-4 to 10-3 reveals a rapid

breakdown of population substructure to panmixia within only an order of magnitude

increase in gene flow. Thus, it should be possible to distinguish between scenarios on

either side of the transition point, i.e. GF=10-3, but much more difficult to distinguish

scenarios within high or low GF, i.e. GF>10-3 or GF<10-3.

Fst has been commonly used to measure genetic differences between

populations as a means to reflect gene flow. Our results allow us to assess the amount

of gene flow required to generate different Fst estimates. When we compare our

simulated Fst estimates with Fst estimates of African populations versus European

populations (0.141) or versus Asian populations (0.235) (Bowcocket al. 1991), we

observe areas of overlap between the simulated and empirical estimates of Fst (0.141-

0.235) (Figures 2-2a and Table 2-5). For CS categories of 1% and 10%, we observe the

most overlap with empirical Fst estimates at GF=10-3, whereas for CS=30%, the

maximum overlap occurs at GF=10-4. Simulations of bottlenecks show that a CS of 30%

37

is not accompanied by a reduction in genetic diversity as we see empirically between

African and non-African populations (Ramachandranet al. 2005; Relethford 2001),

suggesting that CS=1% and CS=10% are better estimates of the size of the colonizing

population. Our results show that there is almost twice as much overlap with empirical

Fst estimates when CS=1% (Figures 2-2a and Table 2-5), providing the strongest

support for a scenario in which the migrating population carried 1% of existing African

mitochondrial genetic variation (i.e. CS=1%) and both African and non-African

populations experienced bidirectional GF of 10-3.

It is interesting to speculate on what these values mean in terms of actual

individuals, particularly with respect to GF and CS. A GF of 10-3 represents 10

individuals moving per generation in both directions. Although this value seems large, it

may not be unreasonable that an average of ten individuals per generation migrated

between African and non-African populations, particularly immediately after migration

out of Africa when the populations were still geographically close. Deshpande et al.

(2009) modeled a serial founder population history for migration out of Africa and

colonization of Eurasia and they identified 0.01 (100 individuals) as the maximum

bidirectional exchange rate between adjoining populations. Furthermore, 1% of the

population leaving Africa (CS=1%) to colonize the world seems reasonable under our

model of a panmictic population. However, Africa was potentially highly structured

before the exit of modern humans out of Africa (Campbell and Tishkoff 2008;

Veeramahet al. 2012). A high degree of structure could imply that East Africa, where

humans first emigrated to the rest of the world, was a distinct sub-population, and the

colonization size leaving from this area could be larger than 1%, reflecting published

38

colonization sizes of 9-18% (Deshpandeet al. 2009; Gronauet al. 2011). Future studies

should address the effect of African population substructure on the genetic variation of

non-African populations, specifically how African sub-structure affects our ability to

accurately model the evolutionary processes that gave rise to non-African genetic

diversity.

Although changes in colonization size (CS) and gene flow (GF) create detectable

differences in genetic variation in our study, time of colonization (TC) shows relatively

little effect on patterns of genetic variation. For most of the simulations, demographic

scenarios of 50kya are not distinguishable from those of 100kya.This result is probably

due to the relatively recent times chosen in the current analysis, i.e. 50kya and 100kya,

which were chosen to reflect relevant times for human migration. Although time is an

important factor affecting genetic diversity in general, anatomically modern human’s

short existence likely explains why colonization time has not played an important role in

human genetic diversity. Notably, for values that may most accurately reflect human

demographic history (CS=1% and GF=10-3), six summary statistics can distinguish

between TC of 50kya and 100kya (Figures 2-2b-e and 2-4b-c), suggesting time is only

distinguishable under particular conditions.

Our findings demonstrate the utility of comparing simulated demographic

scenarios to understand the effect of demographic parameters on genetic variation. Our

results show that different demographic parameters have varying effects on

contemporary genetic variation. The parameters that generate a larger difference in

genetic variation obscure the differences in genetic variation caused by other

39

parameters, such that scenarios with differences in the lesser effect parameters cannot

be distinguished from one another. In the case of humans, our comparisons reveal that

migration (CS or GF) has such a large effect on genetic variation that scenarios with

different times for an event are less likely to be distinguishable, particularly with mtDNA.

A better understanding of the three particular parameters addressed in this study (CS,

GF, and TC) allows other demographic parameters to be addressed. For example, by

narrowing potential values of colonization size to 1% and gene flow to 10-3, new

scenarios can be generated to assess the effect of other parameters of interest, such as

population growth or the occurrence of gene flow at specific times. In a similar fashion,

comparisons of simulated scenarios can provide insight into the evolutionary history of

any system. With increased understanding of the effects of demographic parameters on

genetic variation, more accurate inferences about evolutionary histories will be possible.

40

Table 2-1. Summary statistics analyzed and their definitions

Summary statistic Reference Notation Definition

Fst (Wright 1951) Fst Proportion of genetic diversity due to allele differences among populations

Φst (Excoffieret al. 1992)

Φst Proportion of genetic diversity due to haplotype differences among populations

Segregating sites (Fu 1995) S Number of polymorphic sites

Watterson’s theta (Watterson 1975) θW S corrected for number of samples

Nucleotide diversity (Nei 1987) π Average number of nucleotide differences per site

Ramos-Onsin’s and Rozas’ R2

(Ramos-Onsins and Rozas 2002)

R2 Test of neutrality based on difference between number of singleton mutations and π

Tajima’s D (Tajima 1989) TD Test of neutrality based on difference between S and pair-wise differences

Number of singleton sites

(Baldinget al. 2003)

NSS Number of sites where only one individual has a different allele

Tau hat (Rogers 1995) τ̂ Estimate of time measured in mutational units

Number of haplotypes


# Hap Number of different unique allele combinations

Number of singletons


# Single Number of haplotypes that appear only once in the sample

Homozygosity (Baldinget al. 2003)

Hmzy Probability of two samples in a population having the same haplotype

41

Table 2-2. Partitioning of genetic variation by demographic parameter for each summary statistic.

For each summary statistic, variation is partitioned by the parameters of interest (CS,GF,TC) and their interactions and is presented as percent of variation explained. aInteractions between parameters *p-value <1.0x10-6

Parameter Fst Φst S θW π R2 TD NSS τ̂ # Hap # Single Hmzy

Colonization size (CS) 6.5* 2.4* 38.3* 38.3* 52.3* 44.4* 44.4* 10.1* 84.3* 96.4* 96.1* 77.5*

Gene flow (GF) 85.6* 86.8* 28.8* 28.8* 19.1* 14.4* 14.6* 46.2* 5.4* 1.4* 0.8* 6.1* Time of colonization (TC) 1.0* 1.9* 0.1* 0.1* 0.1* 0.2* 0.2* 0 0.1* 0 0 0

CSxGFa 4.1* 3.1* 31.9* 31.9* 26.4* 36.9* 36.7* 43.5* 8.2* 2.2* 3.1* 16.4*

CSxTCa 0.3* 0.3* 0.1* 0.1* 0.2* 0.3* 0.3* 0 0.8* 0 0 0

GFxTCa 2.0* 5.3* 0.4* 0.4* 1.3* 2.4* 2.5* 0.1 0.8* 0 0 0 CSxGFxTCa 0.5* 0.4* 0.4* 0.4* 0.6 1.4* 1.4* 0 0.4* 0 0.4 0

42

Table 2-3. Recommendation of optimal summary statistic to use for each parameter of

interest.

aSummary statistics were chosen based on an assessment that identified the statistic with the highest percent of variation explained (Table 2-2) and most extreme differentiation of parameter combinations (Figures 2-2, 2-3, and 2-4).

Parameter of interest Optimal summary statistica Colonization size # Single Gene flow Fst Time Fst Colonization size x gene flow S, θW, R2, TD Gene flow x time Fst, R2, TD

43

Table 2-4. Demographic scenarios compared in Tukey’s tests and p-values for each summary statistic.

Parameter combination comparison (GF:TC:CS)

Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.001:100:1 vs 0.001:50:1 0.88663 0.00029 0 0 0 0 0 0.00218 1 1 1 1 0.001:100:1 vs 0.01:50:1 0 1.15E-11 0 0 0 0.02903 0.5498 0 0.99986 0 0 1 0.001:100:1 vs 0.1:50:1 0 4.68E-13 0 0 0 0 0 0 0 0 0 1 0.001:100:1 vs 0.5:50:1 0 4.61E-13 0 0 0.00014 0 0 0 0 0 0 0.49813 0.001:100:1 vs 1e-04:100:1 0 0 0 0 0 0 0 0 5.06E-11 0.50251 0 0 0.001:100:1 vs 1e-04:50:1 0 0 0 0 0 0 0 0 5.79E-13 0.11624 0 0 0.001:100:1 vs 1e-05:100:1 0 0 0 0 0 0 0 0 3.82E-13 0.00923 0 0 0.001:100:1 vs 1e-05:50:1 0 0 0 0 0 0 0 0 9.95E-11 0.20124 3.63E-13 0 0.001:100:1 vs 1e-06:100:1 0 0 0 0 0 0 0 0 5.43E-13 0.08961 0 0 0.001:100:1 vs 1e-06:50:1 0 0 0 0 0 0 0 0 4.41E-13 0.01389 0 0 0.001:100:10 vs 0.001:100:1 0 1 0 0 0 0 0 0 0 0 0 0 0.001:100:10 vs 0.001:50:1 0 3.08E-05 0 0 0 0 0 5.24E-13 0 0 0 0 0.001:100:10 vs 0.001:50:10 1 0.99999 0 0 0 4.02E-13 4.02E-13 0.00325 1 1 1 0 0.001:100:10 vs 0.01:100:1 0.00141 3.68E-11 0 0 0 0 0 0 0 0 0 0

44

Table 2-4. Continued.


Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.001:100:1 vs 0.001:50:1 0.88663 0.00029 0 0 0 0 0 0.00218 1 1 1 1 0.001:100:1 vs 0.01:50:1 0 1.15E-11 0 0 0 0.02903 0.5498 0 0.99986 0 0 1 0.001:100:1 vs 0.1:50:1 0 4.68E-13 0 0 0 0 0 0 0 0 0 1 0.001:100:1 vs 0.5:50:1 0 4.61E-13 0 0 0.00014 0 0 0 0 0 0 0.49813 0.001:100:1 vs 1e-04:100:1 0 0 0 0 0 0 0 0 5.06E-11 0.50251 0 0 0.001:100:1 vs 1e-04:50:1 0 0 0 0 0 0 0 0 5.79E-13 0.11624 0 0 0.001:100:1 vs 1e-05:100:1 0 0 0 0 0 0 0 0 3.82E-13 0.00923 0 0 0.001:100:1 vs 1e-05:50:1 0 0 0 0 0 0 0 0 9.95E-11 0.20124 3.63E-13 0 0.001:100:1 vs 1e-06:100:1 0 0 0 0 0 0 0 0 5.43E-13 0.08961 0 0 0.001:100:1 vs 1e-06:50:1 0 0 0 0 0 0 0 0 4.41E-13 0.01389 0 0 0.001:100:10 vs 0.001:100:1 0 1 0 0 0 0 0 0 0 0 0 0 0.001:100:10 vs 0.001:50:1 0 3.08E-05 0 0 0 0 0 5.24E-13 0 0 0 0 0.001:100:10 vs 0.001:50:10 1 0.99999 0 0 0 4.02E-13 4.02E-13 0.00325 1 1 1 0 0.001:100:10 vs 0.01:100:1 0.00141 3.68E-11 0 0 0 0 0 0 0 0 0 0 0.001:100:10 vs 0.01:50:1 0.00013 2.78E-10 0 0 0 0 0 0 0 0 0 0

45



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.001:100:10 vs 0.01:50:10 0 1.21E-09 0 0 0.00015 0 0 0 0 0 1 6.45E-12 0.001:100:10 vs 0.1:100:1 0 1.74E-12 0 0 0 0 0 0 0 0 0 0 0.001:100:10 vs 0.1:50:1 0 1.96E-12 0 0 0 0 0 0 0 0 0 0 0.001:100:10 vs 0.1:50:10 0 5.67E-12 0 0 1.70E-11 0 0 0 0 0 1 0 0.001:100:10 vs 0.5:100:1 0 1.51E-12 0 0 0 0.99977 0.99743 0 0 0 4.75E-13 0 0.001:100:10 vs 0.5:50:1 0 1.83E-12 0 0 0 0 0 0 0 0 4.29E-13 0 0.001:100:10 vs 0.5:50:10 0 3.84E-12 0.99998 0.99998 0 0 0 0 0 0 1 0 0.001:100:10 vs 1e-04:100:1 0 0 0 0 4.39E-13 0.98808 0.99314 8.52E-08 0 0 0 0 0.001:100:10 vs 1e-04:100:10 0 0 0 0 0 3.16E-13 3.42E-13 6.72E-12 1.96E-12 0 1 0 0.001:100:10 vs 1e-04:50:1 0 0 0 0 4.17E-13 0.99586 0.9978 0.00288 0 0 0 0 0.001:100:10 vs 1e-04:50:10 0 0 0 0 0 5.00E-13 5.66E-13 1.55E-11 4.12E-13 0 1 0 0.001:100:10 vs 1e-05:100:1 0 0 0 0 0 0 0 3.85E-13 0 0 0 2.16E-09 0.001:100:10 vs 1e-05:100:10 0 0 0 0 0 0 0 0 4.36E-13 0 1 0 0.001:100:10 vs 1e-05:50:1 0 0 0 0 0 5.35E-13 5.89E-13 4.27E-13 0 0 0 0.9404 0.001:100:10 vs 1e-05:50:10 0 0 0 0 0 0 0 4.08E-13 3.02E-13 0 1 0

46



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.001:100:10 vs 1e-06:100:1 0 0 0 0 0 0 0 4.15E-13 0 0 0 3.44E-13 0.001:100:10 vs 1e-06:100:10 0 0 0 0 0 0 0 3.98E-13 3.70E-13 0 1 0 0.001:100:10 vs 1e-06:50:1 0 0 0 0 0 4.88E-13 5.24E-13 1.47E-08 0 0 0 0.99994 0.001:100:10 vs 1e-06:50:10 0 0 0 0 0 0 0 1.94E-12 3.21E-13 0 1 0 0.001:100:30 vs 0.001:100:1 0 0.78442 0 0 0 0 0 0 0 0 0 0 0.001:100:30 vs 0.001:100:10 0 0.97029 0 0 0 0 0 4.90E-13 0 0 1 0 0.001:100:30 vs 0.001:50:1 0 6.05E-12 0 0 0 0 0 0 0 0 0 0 0.001:100:30 vs 0.001:50:10 0 0.06322 0 0 0 2.36E-06 2.91E-06 0.00024 0 0 1 0 0.001:100:30 vs 0.001:50:30 1 1 0.99993 0.99993 0.29182 0.56511 0.5592 0.99728 1 1 1 0.00412 0.001:100:30 vs 0.01:100:1 5.28E-13 0.00011 0 0 0 0 0 0 0 0 0 0 0.001:100:30 vs 0.01:100:10 6.53E-14 0.00054 0 0 0 0.95964 0.98616 0 0 0 1 0 0.001:100:30 vs 0.01:50:1 3.72E-13 0.00045 0 0 0 0 0 0 0 0 0 0 0.001:100:30 vs 0.01:50:10 5.60E-14 0.00122 0 0 0 1.24E-07 7.69E-08 0 0 0 1 0 0.001:100:30 vs 0.01:50:30 0 0.00016 0.00167 0.00167 1 0.03597 0.03653 7.65E-08 0.84174 0.00167 1 0.48128 0.001:100:30 vs 0.1:100:1 0 9.90E-06 0 0 0 0 0 0 0 0 0 0

47



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.001:100:30 vs 0.1:100:10 0 1.89E-05 0 0 0 4.93E-13 5.03E-13 0 1.49E-13 0 1 0 0.001:100:30 vs 0.1:50:1 0 1.11E-05 0 0 0 0 0 0 0 0 0 0 0.001:100:30 vs 0.1:50:10 0 2.94E-05 0 0 0 0 0 0 4.07E-13 0 1 0 0.001:100:30 vs 0.1:50:30 0 2.36E-05 0.00167 0.00167 0.91289 4.37E-05 4.99E-05 4.22E-13 0.21063 4.47E-07 1 0.08323 0.001:100:30 vs 0.5:100:1 0 8.51E-06 0 0 0 0 0 0 0 0 1.21E-13 0 0.001:100:30 vs 0.5:100:10 0 2.01E-05 0 0 3.84E-13 7.62E-13 9.18E-13 0 1 1 1 0 0.001:100:30 vs 0.5:50:1 0 1.04E-05 0 0 0 0.98564 0.99112 0 0 0 0 0 0.001:100:30 vs 0.5:50:10 0 2.03E-05 0 0 6.52E-05 0 0 0 1 1 1 5.07E-13 0.001:100:30 vs 0.5:50:30 0 2.18E-05 0.00102 0.00102 0.06706 0.97502 0.97359 0.87869 0.01178 6.72E-12 1 4.24E-13 0.001:100:30 vs 1e-04:100:1 0 0 0 0 0 0 0 0.34141 0 0 0 0 0.001:100:30 vs 1e-04:100:10 0 0 0.50244 0.50244 2.12E-08 4.51E-07 4.13E-07 0.99832 0 0 0.9989 0 0.001:100:30 vs 1e-04:100:30 0 0 7.90E-05 7.90E-05 0.0265 0.94783 0.95041 0.9091 1 0.88561 1 0.00315 0.001:100:30 vs 1e-04:50:1 0 0 3.98E-13 3.98E-13 0 0 0 0.00027 0 0 0 0 0.001:100:30 vs 1e-04:50:10 0 0 0.00034 0.00034 4.03E-13 7.48E-11 6.04E-11 0.99516 0 0 0.99823 0 0.001:100:30 vs 1e-04:50:30 0 0 0.00399 0.00399 0.80317 1 1 0.99986 1 0.79828 1 0.80178

48



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.001:100:30 vs 1e-05:100:1 0 0 0.02396 0.02396 0.68619 1 1 1 0 0 0 0 0.001:100:30 vs 1e-05:100:10 0 0 1 1 1 1 1 0.99996 0 0 0.99678 0 0.001:100:30 vs 1e-05:100:30 0 0 3.33E-06 3.33E-06 8.85E-06 0.02366 0.02465 0.86836 0.99996 0.63273 1 0.08667 0.001:100:30 vs 1e-05:50:1 0 0 4.98E-13 4.95E-13 5.02E-13 5.73E-11 5.36E-11 1 0 0 0 0 0.001:100:30 vs 1e-05:50:10 0 0 0.98819 0.98819 0.02793 0.12307 0.1148 1 0 0 0.99819 0 0.001:100:30 vs 1e-05:50:30 0 0 0.00044 0.00044 0.10254 0.99558 0.99606 0.97542 0.99991 0.50527 1 0.93678 0.001:100:30 vs 1e-06:100:1 0 0 0.3622 0.3622 0.99992 1 1 1 0 0 0 0 0.001:100:30 vs 1e-06:100:10 0 0 1 1 0.99991 0.99974 0.99973 1 0 0 0.99488 0 0.001:100:30 vs 1e-06:100:30 0 0 2.57E-12 2.57E-12 7.36E-13 3.54E-06 3.69E-06 0.46882 0.9981 0.17981 1 7.54E-06 0.001:100:30 vs 1e-06:50:1 0 0 3.49E-13 3.48E-13 4.48E-13 8.74E-11 8.41E-11 0.55738 0 0 0 0 0.001:100:30 vs 1e-06:50:10 0 0 0.99977 0.99977 0.00327 0.0186 0.01744 0.99983 0 0 0.99729 0 0.001:100:30 vs 1e-06:50:30 0 0 5.37E-07 5.37E-07 0.00074 0.66763 0.68201 0.80593 0.99997 0.62177 1 0.001 0.001:50:1 vs 1e-04:50:1 0 0 0 0 0 0 0 0 2.56E-11 0.21171 1.21E-13 0 0.001:50:1 vs 1e-05:50:1 0 0 0 0 0 0 0 0 1.24E-08 0.33648 3.33E-13 0 0.001:50:1 vs 1e-06:50:1 0 0 0 0 0 0 0 0 3.74E-13 0.03156 0 0

49



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.001:50:10 vs 0.001:100:1 0 1 0 0 0 0 0 0 0 0 0 0 0.001:50:10 vs 0.001:50:1 0 0.04412 0 0 0 0 0 0 0 0 0 0 0.001:50:10 vs 0.01:100:1 0.00264 5.28E-13 0 0 0 0 0 0 0 0 0 0 0.001:50:10 vs 0.01:50:1 0.00026 3.17E-13 0 0 0 0 0 0 0 0 0 0 0.001:50:10 vs 0.1:100:1 0 3.39E-13 0 0 0 0 0 0 0 0 0 0 0.001:50:10 vs 0.1:50:1 0 3.47E-13 0 0 0 0 0 0 0 0 0 0 0.001:50:10 vs 0.5:100:1 0 3.28E-13 0 0 0 1.01E-12 3.42E-12 0 0 0 4.74E-13 0 0.001:50:10 vs 0.5:50:1 0 3.43E-13 0 0 0 0.08214 0.07518 0 0 0 4.25E-13 0 0.001:50:10 vs 1e-04:100:1 0 0 3.82E-13 3.84E-13 0.55455 1.12E-11 6.88E-12 0.99909 0 0 0 0 0.001:50:10 vs 1e-04:50:1 0 0 3.56E-13 3.56E-13 0.61015 4.67E-12 3.09E-12 1 0 0 0 0 0.001:50:10 vs 1e-04:50:10 0 0 0 0 0.01133 0.99999 0.99998 0.47556 3.66E-13 0 1 1 0.001:50:10 vs 1e-05:100:1 0 0 0 0 3.41E-13 0.00144 0.00167 0.00107 0 0 0 4.29E-08 0.001:50:10 vs 1e-05:50:1 0 0 0 0 0.44136 0.99999 0.99998 0.05665 0 0 0 0 0.001:50:10 vs 1e-05:50:10 0 0 0 0 3.36E-13 0.96551 0.97624 0.00137 2.77E-13 0 1 0.89561 0.001:50:10 vs 1e-06:100:1 0 0 0 0 1.40E-13 6.34E-06 7.74E-06 0.00147 0 0 0 0.00096

50



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.001:50:10 vs 1e-06:50:1 0 0 0 0 0.51228 1 0.99999 0.9893 0 0 0 0 0.001:50:10 vs 1e-06:50:10 0 0 0 0 6.30E-13 0.99976 0.99988 0.24781 2.93E-13 0 1 0.86979 0.001:50:30 vs 0.001:100:1 0 0.77075 0 0 0 0 0 0 0 0 0 0 0.001:50:30 vs 0.001:100:10 0 0.96651 0 0 0 0 0 0 0 0 1 0 0.001:50:30 vs 0.001:50:1 0 5.24E-12 0 0 0 0 0 0 0 0 0 0 0.001:50:30 vs 0.001:50:10 0 0.05924 0 0 0 2.92E-13 3.05E-13 1.00E-09 0 0 1 0 0.001:50:30 vs 0.01:100:1 4.69E-13 0.00012 0 0 0 0 0 0 0 0 0 0 0.001:50:30 vs 0.01:100:10 3.85E-13 0.00059 0 0 0 8.99E-05 0.0002 0 0 0 1 0 0.001:50:30 vs 0.01:50:1 4.43E-13 0.0005 0 0 0 0 0 0 0 0 0 0 0.001:50:30 vs 0.01:50:10 4.01E-13 0.00133 0 0 0 0.21534 0.18082 0 0 0 1 0 0.001:50:30 vs 0.1:100:1 0 1.11E-05 0 0 0 0 0 0 0 0 0 0 0.001:50:30 vs 0.1:100:10 0 2.10E-05 0 0 0 5.97E-05 6.68E-05 0 0 0 1 0 0.001:50:30 vs 0.1:50:1 0 1.24E-05 0 0 0 0 0 0 0 0 0 0 0.001:50:30 vs 0.1:50:10 0 3.27E-05 0 0 0 0 0 0 3.93E-13 0 1 0 0.001:50:30 vs 0.5:100:1 0 9.51E-06 0 0 0 0 0 0 0 0 1.12E-13 0

51



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.001:50:30 vs 0.5:100:10 0 2.24E-05 0 0 0 0.00017 0.00022 0 1 1 1 0 0.001:50:30 vs 0.5:50:1 0 1.16E-05 0 0 0 0.0002 0.00027 0 0 0 0 0 0.001:50:30 vs 0.5:50:10 0 2.26E-05 0 0 3.51E-13 4.14E-13 4.51E-13 0 1 1 1 0 0.001:50:30 vs 1e-04:100:1 0 0 0 0 0 0 0 0.00014 0 0 0 0 0.001:50:30 vs 1e-04:100:10 0 0 0.00171 0.00171 3.36E-13 4.88E-13 4.80E-13 0.04806 0 0 0.99878 0 0.001:50:30 vs 1e-04:50:1 0 0 0 0 0 0 0 1.21E-09 0 0 0 0 0.001:50:30 vs 1e-04:50:10 0 0 1.41E-08 1.41E-08 0 4.20E-13 3.86E-13 0.03232 0 0 0.99805 0 0.001:50:30 vs 1e-04:50:30 0 0 0.66255 0.66255 1 0.99934 0.9992 1 0.99987 0.48876 1 0.99932 0.001:50:30 vs 1e-05:100:1 0 0 5.91E-06 5.91E-06 6.74E-07 0.02012 0.01983 0.97037 0 0 0 0 0.001:50:30 vs 1e-05:100:10 0 0 1 1 0.82373 0.99667 0.99628 1 0 0 0.99647 0 0.001:50:30 vs 1e-05:50:1 0 0 3.15E-13 3.15E-13 0 3.88E-13 3.80E-13 0.34895 0 0 0 0 0.001:50:30 vs 1e-05:50:10 0 0 0.06514 0.06514 1.32E-10 3.30E-08 2.70E-08 0.95922 0 0 0.99801 0 0.001:50:30 vs 1e-05:50:30 0 0 0.28421 0.28421 1 1 1 1 0.99841 0.2244 1 0.99098 0.001:50:30 vs 1e-06:100:1 0 0 0.00075 0.00075 0.00045 0.42371 0.41897 0.95552 0 0 0 0 0.001:50:30 vs 1e-06:100:10 0 0 1 1 0.99997 1 1 0.99999 0 0 0.99443 0

52



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.001:50:30 vs 1e-06:50:1 0 0 3.58E-13 3.58E-13 0 4.47E-13 4.35E-13 0.00053 0 0 0 0 0.001:50:30 vs 1e-06:50:10 0 0 0.20982 0.20982 3.00E-12 7.45E-10 6.29E-10 0.09233 0 0 0.99703 0 0.001:50:30 vs 1e-06:50:30 0 0 0.00474 0.00474 0.99998 1 1 1 0.99928 0.31098 1 1 0.01:100:1 vs 0.001:100:1 0 1.90E-12 0 0 0 4.52E-13 4.76E-09 0 1 0 0 1 0.01:100:1 vs 0.001:50:1 0 0 0 0 0 0 0 0 0.99852 0 0 1 0.01:100:1 vs 0.01:50:1 1 1 0.01902 0.01902 0.99959 0.00859 0.05214 1 0.55582 0.99979 0.98176 1 0.01:100:1 vs 0.1:50:1 0 1 0 0 1 0 0 0 0 0 1.16E-11 1 0.01:100:1 vs 0.5:50:1 0 1 0.99243 0.99243 1.21E-13 0 0 0 0 0 0 0.94464 0.01:100:1 vs 1e-04:100:1 0 0 0 0 0 0 0 0 3.34E-13 0 0 0 0.01:100:1 vs 1e-04:50:1 0 0 0 0 0 0 0 0 3.46E-13 0 0 0 0.01:100:1 vs 1e-05:100:1 0 0 0 0 0 0 0 0 4.24E-13 0 0 0 0.01:100:1 vs 1e-05:50:1 0 0 0 0 0 0 0 0 3.58E-13 0 0 0 0.01:100:1 vs 1e-06:100:1 0 0 0 0 0 0 0 0 3.36E-13 0 0 0 0.01:100:1 vs 1e-06:50:1 0 0 0 0 0 0 0 0 4.04E-13 0 0 0 0.01:100:10 vs 0.001:100:1 0 1.50E-11 3.48E-13 3.48E-13 0 0 0 0 0 0 0 0

53



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.01:100:10 vs 0.001:100:10 0 3.60E-10 0 0 6.50E-06 0 0 0 0 0 1 0.0133 0.01:100:10 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.01:100:10 vs 0.001:50:10 0 3.18E-13 0 0 0 0.13299 0.09045 0 0 0 1 0 0.01:100:10 vs 0.01:100:1 0 1 0 0 0 0 0 0 0 0 0 0 0.01:100:10 vs 0.01:50:1 0 1 0 0 0 0 0 0 0 0 0 0 0.01:100:10 vs 0.01:50:10 1 1 0 0 3.17E-13 3.35E-13 3.59E-13 1 1 1 1 0 0.01:100:10 vs 0.1:100:1 1 1 0 0 0 0 0 0 0 0 0 0 0.01:100:10 vs 0.1:50:1 1 1 0 0 0 0 0 0 0 0 0 0 0.01:100:10 vs 0.1:50:10 0.73425 1 7.46E-08 7.46E-08 0 0 0 0 1.59E-05 5.29E-13 1 0 0.01:100:10 vs 0.5:50:1 0.62743 1 0 0 0 1 1 0 0 0 3.77E-13 0 0.01:100:10 vs 0.5:50:10 0.45014 1 0 0 0 0 0 0 0 0 1 0 0.01:100:10 vs 1e-04:100:1 0 0 0 0 0 0 0 0 0 0 0 6.09E-10 0.01:100:10 vs 1e-04:100:10 0 0 0 0 0 0.0565 0.03021 0 0 0 1 0 0.01:100:10 vs 1e-04:50:1 0 0 0 0 0 0 0 0 0 0 0 6.97E-13 0.01:100:10 vs 1e-04:50:10 0 0 0 0 0 0.00024 8.80E-05 0 0 0 1 0

54



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.01:100:10 vs 1e-05:100:1 0 0 0 0 0 1 1 0 0 0 0 7.46E-14 0.01:100:10 vs 1e-05:100:10 0 0 0 0 0 0.29932 0.4251 0 0 0 1 0 0.01:100:10 vs 1e-05:50:1 0 0 0 0 0 0.0002 8.09E-05 0 0 0 0 0.99931 0.01:100:10 vs 1e-05:50:10 0 0 0 0 0 1 1 0 0 0 1 0 0.01:100:10 vs 1e-06:100:1 0 0 0 0 0 0.98673 0.99653 0 0 0 0 0 0.01:100:10 vs 1e-06:100:10 0 0 0 0 0 0.02396 0.0432 0 0 0 1 0 0.01:100:10 vs 1e-06:50:1 0 0 0 0 0 0.00026 0.00011 0 0 0 0 0.85815 0.01:100:10 vs 1e-06:50:10 0 0 0 0 0 0.99942 0.9963 0 0 0 1 0 0.01:100:30 vs 0.001:100:1 0 3.14E-12 0 0 0 0 0 0 0 0 0 0 0.01:100:30 vs 0.001:100:10 0 6.79E-11 0 0 0 0 0 0 0 0 0.99999 0 0.01:100:30 vs 0.001:100:30 0 0.00017 5.10E-12 5.09E-12 1 0.01462 0.01397 8.06E-09 0.75022 0.00056 1 1 0.01:100:30 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.01:100:30 vs 0.001:50:10 0 2.76E-13 0 0 0 3.81E-13 3.97E-13 0 0 0 0.99999 0 0.01:100:30 vs 0.001:50:30 0 0.00019 3.59E-13 3.59E-13 0.64956 1 1 0.00104 0.89517 0.00334 1 0.09071 0.01:100:30 vs 0.01:100:1 0 1 0 0 0 0 0 0 0 0 0 0

55



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.01:100:30 vs 0.01:100:10 0.99749 1 0 0 0 4.29E-08 1.15E-07 9.59E-13 0 0 1 0 0.01:100:30 vs 0.01:50:1 0 1 0 0 0 0 0 0 0 0 0 0 0.01:100:30 vs 0.01:50:10 0.998 1 0 0 0 0.98613 0.97856 3.41E-13 0 0 1 0 0.01:100:30 vs 0.01:50:30 1 1 0.47422 0.47422 1 1 1 1 1 1 1 0.97299 0.01:100:30 vs 0.1:100:1 1 1 0 0 0 0 0 0 0 0 0 0 0.01:100:30 vs 0.1:100:10 1 1 0 0 0 0.02283 0.02516 0 0 0 1 0 0.01:100:30 vs 0.1:50:1 1 1 0 0 0 0 0 0 0 0 0 0 0.01:100:30 vs 0.1:50:10 1 1 0 0 0 0 0 0 0 0 1 0 0.01:100:30 vs 0.1:50:30 1 1 0.47387 0.47387 0.99539 1 1 0.07003 1 1 1 0.57872 0.01:100:30 vs 0.5:100:1 1 1 0 0 0 0 0 0 0 0 6.53E-14 0 0.01:100:30 vs 0.5:100:10 1 1 0 0 1.87E-13 0.04614 0.05717 0 0.59462 7.66E-05 1 0 0.01:100:30 vs 0.5:50:1 1 1 0 0 0 1.20E-07 1.67E-07 0 0 0 0 0 0.01:100:30 vs 0.5:50:10 1 1 0 0 5.40E-06 4.20E-10 7.14E-10 0 0.42396 1.00E-05 1 3.59E-13 0.01:100:30 vs 0.5:50:30 1 1 0 0 0.2438 0.99787 0.99739 0.01308 0.99999 0.6995 1 4.03E-13 0.01:100:30 vs 1e-04:100:1 0 0 0.05191 0.05191 0 0 0 4.70E-13 0 0 0 0

56



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.01:100:30 vs 1e-04:100:10 0 0 0.00143 0.00143 9.79E-10 4.07E-13 3.87E-13 3.34E-13 0 0 0.99696 0 0.01:100:30 vs 1e-04:100:30 0 0 0 0 0.11881 0.9993 0.99912 0.01003 0.02212 5.65E-11 1 0.07466 0.01:100:30 vs 1e-04:50:1 0 0 0.56006 0.56006 0 0 0 0 0 0 0 0 0.01:100:30 vs 1e-04:50:10 0 0 0.74643 0.74643 2.84E-13 0 0 3.13E-13 0 0 0.99541 0 0.01:100:30 vs 1e-04:50:30 0 0 0 0 0.97779 0.44606 0.4283 0.00029 0.01432 1.84E-11 1 0.9991 0.01:100:30 vs 1e-05:100:1 0 0 0.10057 0.10057 0.3227 4.99E-05 4.77E-05 9.60E-10 0 0 0 0 0.01:100:30 vs 1e-05:100:10 0 0 1.21E-12 1.20E-12 1 0.3245 0.31283 0.00019 0 0 0.99224 0 0.01:100:30 vs 1e-05:100:30 0 0 0 0 0.0001 1 1 0.01416 0.00788 4.05E-12 1 0.5896 0.01:100:30 vs 1e-05:50:1 0 0 1 1 4.12E-13 0 0 1.16E-12 0 0 0 0 0.01:100:30 vs 1e-05:50:10 0 0 1.29E-05 1.29E-05 0.00464 3.62E-12 2.88E-12 6.59E-10 0 0 0.99532 0 0.01:100:30 vs 1e-05:50:30 0 0 0 0 0.33198 0.98339 0.98034 0.00368 0.00596 1.61E-12 1 0.99997 0.01:100:30 vs 1e-06:100:1 0 0 0.00315 0.00315 0.99081 0.00736 0.00704 5.91E-10 0 0 0 0 0.01:100:30 vs 1e-06:100:10 0 0 3.05E-13 3.04E-13 1 0.92032 0.9163 1.65E-07 0 0 0.98837 0 0.01:100:30 vs 1e-06:100:30 0 0 0 0 8.67E-12 0.99996 0.99997 0.09187 0.00193 4.34E-13 1 0.00059 0.01:100:30 vs 1e-06:50:1 0 0 1 1 3.55E-13 0 0 4.40E-13 0 0 0 0

57



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.01:100:30 vs 1e-06:50:10 0 0 1.27E-06 1.27E-06 0.0004 4.60E-13 4.42E-13 3.93E-13 0 0 0.99333 0 0.01:100:30 vs 1e-06:50:30 0 0 0 0 0.00564 1 1 0.02128 0.00812 3.71E-12 1 0.03147 0.01:50:1 vs 0.001:50:1 0 0 0 0 0 0 0 0 1 0 0 1 0.01:50:1 vs 1e-04:50:1 0 0 0 0 0 0 0 0 5.27E-08 0 0 0 0.01:50:1 vs 1e-05:50:1 0 0 0 0 0 0 0 0 1.05E-05 0 0 0 0.01:50:1 vs 1e-06:50:1 0 0 0 0 0 0 0 0 3.90E-11 0 0 0 0.01:50:10 vs 0.001:100:1 0 5.38E-11 0 0 0 0 0 0 0 0 0 0 0.01:50:10 vs 0.001:50:1 0 0 7.11E-05 7.11E-05 0 0 0 0 0 0 0 0 0.01:50:10 vs 0.001:50:10 0 3.66E-13 0 0 4.72E-07 0 0 0 0 0 1 5.84E-06 0.01:50:10 vs 0.01:100:1 0 1 0 0 0 0 0 0 0 0 0 0 0.01:50:10 vs 0.01:50:1 0 1 0 0 0 0 0 0 0 0 0 0 0.01:50:10 vs 0.1:100:1 1 1 0 0 0 0 0 0 0 0 0 0 0.01:50:10 vs 0.1:50:1 1 1 0 0 0 0 0 0 0 0 0 0 0.01:50:10 vs 0.5:100:1 0.55749 1 0 0 0 0 0 0 0 0 4.19E-13 0 0.01:50:10 vs 0.5:50:1 0.64697 1 0 0 0 3.77E-13 3.78E-13 0 0 0 3.96E-13 0

58



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.01:50:10 vs 1e-04:100:1 0 0 0 0 0.36286 0 0 0 0 0 0 0 0.01:50:10 vs 1e-04:50:1 0 0 0 0 0.31532 0 0 0 0 0 0 0 0.01:50:10 vs 1e-04:50:10 0 0 0 0 3.65E-13 0 0 0 0 0 1 1.29E-09 0.01:50:10 vs 1e-05:100:1 0 0 0 0 0 2.73E-11 1.61E-11 0 0 0 0 1 0.01:50:10 vs 1e-05:50:1 0 0 0 0 4.25E-13 0 0 0 0 0 0 3.84E-13 0.01:50:10 vs 1e-05:50:10 0 0 0 0 0 4.88E-13 4.11E-13 0 0 0 1 5.37E-13 0.01:50:10 vs 1e-06:100:1 0 0 0 0 0 4.13E-08 2.56E-08 0 0 0 0 1 0.01:50:10 vs 1e-06:50:1 0 0 0 0 4.62E-13 0 0 0 0 0 0 3.73E-13 0.01:50:10 vs 1e-06:50:10 0 0 0 0 0 3.84E-13 4.19E-13 0 0 0 1 6.11E-13 0.01:50:30 vs 0.001:100:1 0 2.98E-12 0 0 0 0 0 0 0 0 0 0 0.01:50:30 vs 0.001:100:10 0 6.40E-11 0 0 0 0 0 0 0 0 0.99999 0 0.01:50:30 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.01:50:30 vs 0.001:50:10 0 2.76E-13 0 0 0 3.60E-13 3.79E-13 0 0 0 0.99999 0 0.01:50:30 vs 0.001:50:30 0 0.00018 1.23E-07 1.23E-07 0.99657 1 1 0.00481 0.9462 0.00899 1 1 0.01:50:30 vs 0.01:100:1 0 1 0 0 0 0 0 0 0 0 0 0

59



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.01:50:30 vs 0.01:100:10 0.99801 1 0 0 0 2.00E-07 5.71E-07 4.43E-13 0 0 1 0 0.01:50:30 vs 0.01:50:1 0 1 0 0 0 0 0 0 0 0 0 0 0.01:50:30 vs 0.01:50:10 0.99843 1 0 0 0 0.93872 0.91017 3.94E-13 0 0 1 0 0.01:50:30 vs 0.1:100:1 1 1 0 0 0 0 0 0 0 0 0 0 0.01:50:30 vs 0.1:100:10 1 1 0 0 0 0.00889 0.00926 0 0 0 1 0 0.01:50:30 vs 0.1:50:1 1 1 0 0 0 0 0 0 0 0 0 0 0.01:50:30 vs 0.1:50:10 1 1 0 0 0 0 0 0 0 0 1 0 0.01:50:30 vs 0.5:100:1 1 1 0 0 0 0 0 0 0 0 7.46E-14 0 0.01:50:30 vs 0.5:100:10 1 1 0 0 0 0.01923 0.02298 0 0.70731 0.00025 1 0 0.01:50:30 vs 0.5:50:1 1 1 0 0 0 5.39E-07 8.16E-07 0 0 0 0 0 0.01:50:30 vs 0.5:50:10 1 1 0 0 2.15E-08 7.34E-11 1.13E-10 0 0.5379 3.66E-05 1 0 0.01:50:30 vs 1e-04:100:1 0 0 2.54E-09 2.54E-09 0 0 0 4.79E-13 0 0 0 0 0.01:50:30 vs 1e-04:100:10 0 0 0.99992 0.99992 1.82E-12 3.67E-13 3.60E-13 4.54E-13 0 0 0.99712 0 0.01:50:30 vs 1e-04:50:1 0 0 1.16E-06 1.16E-06 0 0 0 0 0 0 0 0 0.01:50:30 vs 1e-04:50:10 0 0 1 1 4.22E-13 0 0 3.99E-13 0 0 0.99563 0

60



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.01:50:30 vs 1e-04:50:30 0 0 4.48E-13 4.48E-13 1 0.64731 0.64235 0.0015 0.02426 1.03E-10 1 1 0.01:50:30 vs 1e-05:100:1 0 0 1 1 0.0216 0.00018 0.00018 1.00E-08 0 0 0 0 0.01:50:30 vs 1e-05:100:10 0 0 0.0005 0.0005 1 0.51356 0.51293 0.00101 0 0 0.99259 0 0.01:50:30 vs 1e-05:50:1 0 0 0.12725 0.12725 2.98E-13 0 0 9.21E-12 0 0 0 0 0.01:50:30 vs 1e-05:50:10 0 0 0.86499 0.86499 6.29E-05 1.93E-11 1.67E-11 7.01E-09 0 0 0.99555 0 0.01:50:30 vs 1e-05:50:30 0 0 4.79E-13 4.79E-13 0.94463 0.99775 0.99755 0.0151 0.01052 6.72E-12 1 1 0.01:50:30 vs 1e-06:100:1 0 0 0.99999 0.99999 0.5521 0.01919 0.01958 6.32E-09 0 0 0 0 0.01:50:30 vs 1e-06:100:10 0 0 5.10E-06 5.10E-06 1 0.9799 0.98065 1.34E-06 0 0 0.98886 0 0.01:50:30 vs 1e-06:50:1 0 0 0.03902 0.03902 1.87E-13 0 0 3.64E-13 0 0 0 0 0.01:50:30 vs 1e-06:50:10 0 0 0.5732 0.5732 3.26E-06 7.44E-13 7.13E-13 6.43E-13 0 0 0.99364 0 0.01:50:30 vs 1e-06:50:30 0 0 4.15E-13 4.15E-13 0.13839 1 1 0.07065 0.01413 1.88E-11 1 0.99976 0.1:100:1 vs 0.001:100:1 0 4.60E-13 0 0 0 0 0 0 0 0 0 1 0.1:100:1 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 1 0.1:100:1 vs 0.01:100:1 0 1 0 0 1 0 0 0 0 0 1.83E-08 1 0.1:100:1 vs 0.01:50:1 0 1 0 0 0.90829 0 0 0 0 0 3.00E-13 1

61



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.1:100:1 vs 0.1:50:1 1 1 1 1 1 0.99802 0.99846 1 1 1 1 1 0.1:100:1 vs 0.5:50:1 0.99936 1 0 0 0 0 0 0.86402 0 0 0 0.93151 0.1:100:1 vs 1e-04:100:1 0 0 0 0 0 0 0 0 0 0 0 0 0.1:100:1 vs 1e-04:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.1:100:1 vs 1e-05:100:1 0 0 0 0 0 0 0 0 0 0 0 0 0.1:100:1 vs 1e-05:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.1:100:1 vs 1e-06:100:1 0 0 0 0 0 0 0 0 0 0 0 0 0.1:100:1 vs 1e-06:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.1:100:10 vs 0.001:100:1 0 5.50E-13 0.99929 0.99929 0 0 0 0 0 0 0 0 0.1:100:10 vs 0.001:100:10 0 3.53E-12 0 0 0.28411 0 0 0 0 0 1 1 0.1:100:10 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.1:100:10 vs 0.001:50:10 0 3.81E-13 0 0 0 0 0 0 0 0 1 0 0.1:100:10 vs 0.01:100:1 0 1 0 0 0 0 0 0 0 0 0 0 0.1:100:10 vs 0.01:100:10 0.65153 1 1.58E-11 1.58E-11 0.92459 3.96E-13 4.10E-13 0 0.00027 7.38E-13 1 0.65483 0.1:100:10 vs 0.01:50:1 0 1 0 0 0 0 0 0 0 0 0 0

62



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.1:100:10 vs 0.01:50:10 0.67078 1 0 0 3.96E-13 0.99812 0.99926 0 0.00017 6.24E-13 1 4.98E-13 0.1:100:10 vs 0.1:100:1 0.99954 1 0 0 0 0 0 0 0 0 0 0 0.1:100:10 vs 0.1:50:1 0.99459 1 0 0 0 0 0 0 0 0 0 0 0.1:100:10 vs 0.1:50:10 1 1 0 0 3.45E-13 2.84E-13 2.93E-13 0.98952 1 1 1 0 0.1:100:10 vs 0.5:100:1 1 1 0 0 0 0 0 0 0 0 3.74E-13 0 0.1:100:10 vs 0.5:50:1 1 1 0 0 0 3.93E-13 3.92E-13 0 0 0 1.40E-13 0 0.1:100:10 vs 0.5:50:10 1 1 0 0 0 0.45254 0.4927 0 4.08E-13 0 1 0 0.1:100:10 vs 1e-04:100:1 0 0 0 0 0 0 0 0 0 0 0 4.80E-13 0.1:100:10 vs 1e-04:100:10 0 0 0 0 0 0 0 0 0 0 1 0 0.1:100:10 vs 1e-04:50:1 0 0 0 0 0 0 0 0 0 0 0 2.05E-13 0.1:100:10 vs 1e-04:50:10 0 0 0 0 0 0 0 0 0 0 0.99999 0 0.1:100:10 vs 1e-05:100:1 0 0 0 0 0 3.35E-13 3.43E-13 0 0 0 0 4.73E-13 0.1:100:10 vs 1e-05:100:10 0 0 0 0 0 1.26E-10 1.35E-10 0 0 0 0.99998 0 0.1:100:10 vs 1e-05:50:1 0 0 0 0 0 0 0 0 0 0 0 1 0.1:100:10 vs 1e-05:50:10 0 0 0 0 0 0 0 0 0 0 0.99999 0

63



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.1:100:10 vs 1e-06:100:1 0 0 0 0 0 4.00E-13 4.10E-13 0 0 0 0 4.33E-13 0.1:100:10 vs 1e-06:100:10 0 0 0 0 0 3.94E-08 4.37E-08 0 0 0 0.99996 0 0.1:100:10 vs 1e-06:50:1 0 0 0 0 0 0 0 0 0 0 0 1 0.1:100:10 vs 1e-06:50:10 0 0 0 0 0 0 0 0 0 0 0.99999 0 0.1:100:30 vs 0.001:100:1 0 6.53E-13 0 0 0 0 0 0 0 0 0 0 0.1:100:30 vs 0.001:100:10 0 5.51E-12 0 0 0 0 0 0 0 0 0.99999 0 0.1:100:30 vs 0.001:100:30 0 2.88E-05 3.24E-13 3.24E-13 1 0.05056 0.05307 4.33E-13 0.28668 1.43E-06 1 1 0.1:100:30 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.1:100:30 vs 0.001:50:10 0 4.06E-13 0 0 0 4.10E-13 4.38E-13 0 0 0 0.99999 0 0.1:100:30 vs 0.001:50:30 0 3.20E-05 3.89E-13 3.89E-13 0.12009 1 1 4.43E-13 0.46698 1.35E-05 1 0.21712 0.1:100:30 vs 0.01:100:1 0 1 0 0 0 0 0 0 0 0 0 0 0.1:100:30 vs 0.01:100:10 0.6213 1 0 0 0 3.68E-07 1.10E-06 0.00481 0 0 1 0 0.1:100:30 vs 0.01:100:30 1 1 1 1 1 1 1 0.13295 1 1 1 1 0.1:100:30 vs 0.01:50:1 0 1 0 0 0 0 0 0 0 0 0 0 0.1:100:30 vs 0.01:50:10 0.64091 1 0 0 0 0.90204 0.85846 2.60E-06 0 0 1 0

64



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.1:100:30 vs 0.01:50:30 1 1 0.0294 0.0294 0.99996 1 1 0.04492 1 1 1 0.99764 0.1:100:30 vs 0.1:100:1 0.9993 1 0 0 0 0 0 0 0 0 0 0 0.1:100:30 vs 0.1:100:10 1 1 0 0 0 0.00593 0.00593 0 0 0 1 0 0.1:100:30 vs 0.1:50:1 0.99267 1 0 0 0 0 0 0 0 0 0 0 0.1:100:30 vs 0.1:50:10 1 1 0 0 0 0 0 0 0 0 1 0 0.1:100:30 vs 0.1:50:30 1 1 0.02936 0.02936 0.70639 0.99999 0.99999 1 1 1 1 0.81601 0.1:100:30 vs 0.5:100:1 1 1 0 0 0 0 0 0 0 0 6.53E-14 0 0.1:100:30 vs 0.5:100:10 1 1 0 0 4.10E-13 0.01316 0.01523 0 0.17666 1.27E-07 1 0 0.1:100:30 vs 0.5:50:1 1 1 0 0 0 9.77E-07 1.56E-06 0 0 0 0 0 0.1:100:30 vs 0.5:50:10 1 1 0 0 0.00037 3.57E-11 5.12E-11 0 0.09795 1.12E-08 1 3.41E-13 0.1:100:30 vs 0.5:50:30 1 1 0 0 0.02018 0.99997 0.99997 3.58E-12 1 0.99982 1 6.61E-13 0.1:100:30 vs 1e-04:100:1 0 0 0.6099 0.6099 0 0 0 0 0 0 0 0 0.1:100:30 vs 1e-04:100:10 0 0 7.88E-06 7.88E-06 1.89E-07 4.33E-13 4.31E-13 0 0 0 0.99638 0 0.1:100:30 vs 1e-04:100:30 0 0 0 0 0.00698 0.99999 0.99999 2.36E-12 0.00193 3.90E-13 1 0.1851 0.1:100:30 vs 1e-04:50:1 0 0 0.99675 0.99675 0 0 0 0 0 0 0 0

65



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.1:100:30 vs 1e-04:50:10 0 0 0.09057 0.09057 7.06E-13 0 0 0 0 0 0.99459 0 0.1:100:30 vs 1e-04:50:30 0 0 0 0 0.5363 0.7251 0.72807 3.53E-13 0.00115 3.44E-13 1 0.99998 0.1:100:30 vs 1e-05:100:1 0 0 0.00215 0.00215 0.90216 0.00029 0.00031 4.21E-13 0 0 0 0 0.1:100:30 vs 1e-05:100:10 0 0 2.75E-13 2.75E-13 1 0.59599 0.60371 3.29E-13 0 0 0.99097 0 0.1:100:30 vs 1e-05:100:30 0 0 0 0 1.22E-06 1 1 4.09E-12 0.00057 2.97E-13 1 0.82411 0.1:100:30 vs 1e-05:50:1 0 0 1 1 4.01E-13 0 0 0 0 0 0 0 0.1:100:30 vs 1e-05:50:10 0 0 2.79E-08 2.79E-08 0.08855 3.98E-11 3.71E-11 4.21E-13 0 0 0.99449 0 0.1:100:30 vs 1e-05:50:30 0 0 0 0 0.0332 0.99918 0.99919 7.61E-13 0.00041 5.49E-13 1 1 0.1:100:30 vs 1e-06:100:1 0 0 2.11E-05 2.11E-05 1 0.02766 0.02925 3.96E-13 0 0 0 0 0.1:100:30 vs 1e-06:100:10 0 0 3.99E-13 3.99E-13 0.996 0.99009 0.99122 3.48E-13 0 0 0.98661 0 0.1:100:30 vs 1e-06:100:30 0 0 0 0 4.07E-13 0.99767 0.99751 1.85E-10 0.00011 3.46E-13 1 0.00246 0.1:100:30 vs 1e-06:50:1 0 0 1 1 3.73E-13 0 0 0 0 0 0 0 0.1:100:30 vs 1e-06:50:10 0 0 1.88E-09 1.88E-09 0.01347 1.06E-12 1.06E-12 0 0 0 0.99222 0 0.1:100:30 vs 1e-06:50:30 0 0 0 0 0.00014 1 1 8.09E-12 0.00059 2.93E-13 1 0.08923 0.1:50:1 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 1

66



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.1:50:1 vs 0.01:50:1 0 1 0 0 0.99998 0 0 0 0 0 3.74E-13 1 0.1:50:1 vs 1e-04:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.1:50:1 vs 1e-05:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.1:50:1 vs 1e-06:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.1:50:10 vs 0.001:100:1 0 6.60E-13 0 0 0 0 0 0 0 0 0 0 0.1:50:10 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.1:50:10 vs 0.001:50:10 0 4.13E-13 0 0 0.08099 0 0 0 0 0 1 0.99431 0.1:50:10 vs 0.01:100:1 0 1 0 0 0 0 0 0 0 0 0 0 0.1:50:10 vs 0.01:50:1 0 1 0 0 0 0 0 0 0 0 0 0 0.1:50:10 vs 0.01:50:10 0.7518 1 3.25E-13 3.27E-13 0.92991 3.94E-13 4.11E-13 0 9.69E-06 5.02E-13 1 0.09243 0.1:50:10 vs 0.1:100:1 0.99988 1 0 0 0 0 0 0 0 0 0 0 0.1:50:10 vs 0.1:50:1 0.99792 1 0 0 0 0 0 0 0 0 0 0 0.1:50:10 vs 0.5:100:1 1 1 0 0 0 0 0 0 0 0 4.18E-13 0 0.1:50:10 vs 0.5:50:1 1 1 0 0 0 0 0 0 0 0 1.21E-13 0 0.1:50:10 vs 1e-04:100:1 0 0 0 0 1 0 0 0 0 0 0 0

67



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.1:50:10 vs 1e-04:50:1 0 0 0 0 1 0 0 0 0 0 0 0 0.1:50:10 vs 1e-04:50:10 0 0 0 0 1.15E-12 0 0 0 0 0 0.99999 0.26954 0.1:50:10 vs 1e-05:100:1 0 0 0 0 0 0 0 0 0 0 0 0.00468 0.1:50:10 vs 1e-05:50:1 0 0 0 0 4.89E-09 0 0 0 0 0 0 0 0.1:50:10 vs 1e-05:50:10 0 0 0 0 0 0 0 0 0 0 0.99999 0.00332 0.1:50:10 vs 1e-06:100:1 0 0 0 0 0 0 0 0 0 0 0 0.72667 0.1:50:10 vs 1e-06:50:1 0 0 0 0 8.74E-09 0 0 0 0 0 0 0 0.1:50:10 vs 1e-06:50:10 0 0 0 0 0 0 0 0 0 0 0.99998 0.00316 0.1:50:30 vs 0.001:100:1 0 6.01E-13 0 0 0 0 0 0 0 0 0 0 0.1:50:30 vs 0.001:100:10 0 4.60E-12 0 0 0 0 0 0 0 0 0.99999 0 0.1:50:30 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.1:50:30 vs 0.001:50:10 0 3.90E-13 0 0 0 0 0 0 0 0 0.99999 0 0.1:50:30 vs 0.001:50:30 0 2.62E-05 1.23E-07 1.23E-07 1 0.9178 0.92943 3.61E-13 0.36642 4.56E-06 1 1 0.1:50:30 vs 0.01:100:1 0 1 0 0 0 0 0 0 0 0 0 0 0.1:50:30 vs 0.01:100:10 0.49755 1 0 0 0 6.69E-12 2.73E-11 0.01144 0 0 1 0

68



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.1:50:30 vs 0.01:50:1 0 1 0 0 0 0 0 0 0 0 0 0 0.1:50:30 vs 0.01:50:10 0.51734 1 0 0 0 1 1 8.70E-06 0 0 1 0 0.1:50:30 vs 0.01:50:30 1 1 1 1 1 1 1 0.02106 1 1 1 1 0.1:50:30 vs 0.1:100:1 0.99688 1 0 0 0 0 0 0 0 0 0 0 0.1:50:30 vs 0.1:100:10 1 1 0 0 0 0.61412 0.60556 0 0 0 1 0 0.1:50:30 vs 0.1:50:1 0.97833 1 0 0 0 0 0 0 0 0 0 0 0.1:50:30 vs 0.1:50:10 1 1 0 0 0 0 0 0 0 0 1 0 0.1:50:30 vs 0.5:100:1 1 1 0 0 0 0 0 0 0 0 5.60E-14 0 0.1:50:30 vs 0.5:100:10 1 1 0 0 0 0.76772 0.78652 0 0.12363 3.72E-08 1 0 0.1:50:30 vs 0.5:50:1 1 1 0 0 0 2.19E-11 4.22E-11 0 0 0 0 0 0.1:50:30 vs 0.5:50:10 1 1 0 0 4.27E-12 1.45E-06 1.82E-06 0 0.06541 3.06E-09 1 0 0.1:50:30 vs 1e-04:100:1 0 0 2.53E-09 2.53E-09 0 0 0 0 0 0 0 0 0.1:50:30 vs 1e-04:100:10 0 0 0.99992 0.99992 5.05E-13 0 0 0 0 0 0.99617 0 0.1:50:30 vs 1e-04:50:1 0 0 1.15E-06 1.15E-06 0 0 0 0 0 0 0 0 0.1:50:30 vs 1e-04:50:10 0 0 1 1 3.08E-13 0 0 0 0 0 0.99428 0

69



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.1:50:30 vs 1e-04:50:30 0 0 4.45E-13 4.45E-13 1 0.01045 0.01107 2.99E-13 0.00063 2.98E-13 1 1 0.1:50:30 vs 1e-05:100:1 0 0 1 1 8.89E-05 3.04E-08 3.64E-08 3.95E-13 0 0 0 0 0.1:50:30 vs 1e-05:100:10 0 0 0.0005 0.0005 0.99959 0.00541 0.00587 2.85E-13 0 0 0.99051 0 0.1:50:30 vs 1e-05:50:1 0 0 0.1271 0.1271 0 0 0 0 0 0 0 0 0.1:50:30 vs 1e-05:50:10 0 0 0.86521 0.86521 4.97E-08 5.49E-13 5.43E-13 3.45E-13 0 0 0.99418 0 0.1:50:30 vs 1e-05:50:30 0 0 4.81E-13 4.81E-13 1 0.23389 0.24073 4.85E-13 0.00022 4.53E-13 1 1 0.1:50:30 vs 1e-06:100:1 0 0 1 1 0.01952 1.72E-05 1.99E-05 3.17E-13 0 0 0 0 0.1:50:30 vs 1e-06:100:10 0 0 5.11E-06 5.11E-06 1 0.11237 0.12129 3.83E-13 0 0 0.98597 0 0.1:50:30 vs 1e-06:50:1 0 0 0.03896 0.03896 0 0 0 0 0 0 0 0 0.1:50:30 vs 1e-06:50:10 0 0 0.57356 0.57356 1.39E-09 3.11E-13 3.15E-13 0 0 0 0.99181 0 0.1:50:30 vs 1e-06:50:30 0 0 4.14E-13 4.14E-13 0.93431 0.86045 0.8641 2.13E-12 0.00031 5.23E-13 1 1 0.5:100:1 vs 0.001:100:1 0 4.48E-13 0 0 0 0 0 0 0 0 0 0.01013 0.5:100:1 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0.04094 0.5:100:1 vs 0.01:100:1 0 1 0 0 0.00744 0 0 0 0 0 0 0.11284 0.5:100:1 vs 0.01:50:1 0 1 0 0 0.85995 0 0 0 0 0 0 0.01282

70



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.5:100:1 vs 0.1:100:1 0.99802 1 4.02E-13 4.02E-13 0.00031 0 0 0.97831 0 0 0 0.09962 0.5:100:1 vs 0.1:50:1 0.98438 1 3.25E-13 3.28E-13 0.01711 0 0 0.94921 0 0 0 0.06586 0.5:100:1 vs 0.5:50:1 1 1 3.39E-13 3.39E-13 1.17E-08 0 0 1 0.82029 0.63273 1 1 0.5:100:1 vs 1e-04:100:1 0 0 0 0 0 1 1 0 0 0 0 0 0.5:100:1 vs 1e-04:50:1 0 0 0 0 0 1 1 0 0 0 0 0 0.5:100:1 vs 1e-05:100:1 0 0 0 0 0 0 0 0 0 0 0 0 0.5:100:1 vs 1e-05:50:1 0 0 0 0 0 5.08E-08 2.80E-07 0 0 0 0 0 0.5:100:1 vs 1e-06:100:1 0 0 0 0 0 0 0 0 0 0 0 0 0.5:100:1 vs 1e-06:50:1 0 0 0 0 0 3.50E-08 1.91E-07 0 0 0 0 0 0.5:100:10 vs 0.001:100:1 0 5.59E-13 0 0 0 0 0 0 0 0 0 0 0.5:100:10 vs 0.001:100:10 0 3.79E-12 3.66E-13 3.65E-13 0 0 0 0 0 0 1 0 0.5:100:10 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.5:100:10 vs 0.001:50:10 0 3.85E-13 0 0 0.98721 0 0 0 0 0 1 3.75E-13 0.5:100:10 vs 0.01:100:1 0 1 0 0 0 0 0 0.99997 0 0 0 0 0.5:100:10 vs 0.01:100:10 0.49807 1 0 0 0 4.32E-13 4.37E-13 0 0 0 1 0

71



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.5:100:10 vs 0.01:50:1 0 1 0 0 0 0 0 0.97686 0 0 0 0 0.5:100:10 vs 0.01:50:10 0.51786 1 0 0 4.89E-13 0.99979 0.99996 0 0 0 1 0 0.5:100:10 vs 0.1:100:1 0.9969 1 0 0 0 0 0 0 0 0 0 0 0.5:100:10 vs 0.1:100:10 1 1 0 0 0 1 1 0 4.04E-13 0 1 0 0.5:100:10 vs 0.1:50:1 0.97842 1 0 0 0 0 0 0 0 0 0 0 0.5:100:10 vs 0.1:50:10 1 1 0 0 2.52E-06 4.97E-13 5.02E-13 0 4.45E-13 0 1 3.74E-13 0.5:100:10 vs 0.5:100:1 1 1 0 0 0 0 0 0 0 0 1.21E-13 0 0.5:100:10 vs 0.5:50:1 1 1 0 0 0 3.92E-13 3.48E-13 0 0 0 0 0 0.5:100:10 vs 0.5:50:10 1 1 1.66E-09 1.66E-09 0.0001 0.30498 0.3129 1 1 1 1 3.28E-13 0.5:100:10 vs 1e-04:100:1 0 0 0 0 0.00021 0 0 0 0 0 0 0 0.5:100:10 vs 1e-04:100:10 0 0 0 0 0.03885 0 0 0 0 0 0.99896 4.93E-13 0.5:100:10 vs 1e-04:50:1 0 0 0 0 0.00029 0 0 0 0 0 0 0 0.5:100:10 vs 1e-04:50:10 0 0 0 0 0.98988 0 0 0 0 0 0.99834 2.20E-10 0.5:100:10 vs 1e-05:100:1 0 0 0 0 4.64E-12 4.09E-13 4.32E-13 0 0 0 0 0 0.5:100:10 vs 1e-05:100:10 0 0 0 0 0 5.14E-10 7.14E-10 0 0 0 0.99695 0.57067

72



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.5:100:10 vs 1e-05:50:1 0 0 0 0 1 0 0 0 0 0 0 0 0.5:100:10 vs 1e-05:50:10 0 0 0 0 3.87E-08 0 0 0 0 0 0.9983 1.02E-06 0.5:100:10 vs 1e-06:100:1 0 0 0 0 2.85E-13 5.15E-13 5.67E-13 0 0 0 0 0 0.5:100:10 vs 1e-06:100:10 0 0 0 0 0 1.39E-07 1.93E-07 0 0 0 0.99514 0.99969 0.5:100:10 vs 1e-06:50:1 0 0 0 0 1 0 0 0 0 0 0 0 0.5:100:10 vs 1e-06:50:10 0 0 0 0 1.08E-06 0 0 0 0 0 0.99744 3.85E-06 0.5:100:30 vs 0.001:100:1 0 5.81E-13 0 0 0 0 0 0 0 0 0 0 0.5:100:30 vs 0.001:100:10 0 4.26E-12 0 0 0 0 0 0 0 0 0.99998 0 0.5:100:30 vs 0.001:100:30 0 2.21E-05 0.00022 0.00022 0.00011 0.09797 0.09865 0.86226 0.0057 1.06E-12 1 3.73E-13 0.5:100:30 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.5:100:30 vs 0.001:50:10 0 3.85E-13 0 0 0 3.00E-13 3.15E-13 1.13E-11 0 0 0.99998 0 0.5:100:30 vs 0.001:50:30 0 2.47E-05 0.20036 0.20036 0.99788 1 1 1 0.01514 1.12E-11 1 1.47E-06 0.5:100:30 vs 0.01:100:1 0 1 0 0 0 0 0 0 0 0 0 0 0.5:100:30 vs 0.01:100:10 0.45654 1 0 0 0 1.28E-06 3.43E-06 0 0 0 1 0 0.5:100:30 vs 0.01:100:30 1 1 0 0 0.00101 1 1 0.01481 0.99989 0.43475 1 4.70E-13

73



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.5:100:30 vs 0.01:50:1 0 1 0 0 0 0 0 0 0 0 0 0 0.5:100:30 vs 0.01:50:10 0.47596 1 0 0 0 0.78676 0.73159 0 0 0 1 0 0.5:100:30 vs 0.01:50:30 1 1 3.91E-13 3.91E-13 0.04062 1 1 0.05168 0.99941 0.26548 1 6.23E-11 0.5:100:30 vs 0.1:100:1 0.99513 1 0 0 0 0 0 0 0 0 0 0 0.5:100:30 vs 0.1:100:10 1 1 0 0 0 0.00244 0.00258 0 0 0 1 0 0.5:100:30 vs 0.1:100:30 1 1 0 0 1.76E-05 1 1 4.42E-12 1 0.99461 1 3.70E-13 0.5:100:30 vs 0.1:50:1 0.9702 1 0 0 0 0 0 0 0 0 0 0 0.5:100:30 vs 0.1:50:10 1 1 0 0 0 0 0 0 0 0 1 0 0.5:100:30 vs 0.1:50:30 1 1 3.94E-13 3.94E-13 0.71666 0.99985 0.99989 1.28E-12 1 0.99915 1 9.28E-09 0.5:100:30 vs 0.5:100:1 1 1 0 0 0 0 0 0 0 0 0 0 0.5:100:30 vs 0.5:100:10 1 1 0 0 0 0.00571 0.00702 0 0.00245 4.28E-13 1 0 0.5:100:30 vs 0.5:50:1 1 1 0 0 0 3.29E-06 4.82E-06 0 0 0 0 0 0.5:100:30 vs 0.5:50:10 1 1 0 0 4.03E-13 7.82E-12 1.23E-11 0 0.00095 3.12E-13 1 0 0.5:100:30 vs 0.5:50:30 1 1 1 1 1 1 1 1 1 1 1 1 0.5:100:30 vs 1e-04:100:1 0 0 0 0 0 0 0 4.75E-06 0 0 0 0

74



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.5:100:30 vs 1e-04:100:10 0 0 7.13E-13 7.14E-13 0 3.71E-13 3.68E-13 0.00439 0 0 0.99475 0 0.5:100:30 vs 1e-04:100:30 0 0 1 1 1 1 1 1 4.40E-06 3.83E-13 1 2.13E-06 0.5:100:30 vs 1e-04:50:1 0 0 0 0 0 0 0 1.38E-11 0 0 0 0 0.5:100:30 vs 1e-04:50:10 0 0 3.73E-13 3.73E-13 0 1.21E-13 1.03E-13 0.00268 0 0 0.99231 0 0.5:100:30 vs 1e-04:50:30 0 0 1 1 0.85507 0.86036 0.85589 1 2.27E-06 4.32E-13 1 3.53E-12 0.5:100:30 vs 1e-05:100:1 0 0 4.56E-13 4.56E-13 9.71E-13 0.00078 0.0008 0.64461 0 0 0 0 0.5:100:30 vs 1e-05:100:10 0 0 0.00075 0.00075 0.00297 0.75865 0.75659 1 0 0 0.98753 0 0.5:100:30 vs 1e-05:100:30 0 0 1 1 1 1 1 1 9.37E-07 3.45E-13 1 8.51E-09 0.5:100:30 vs 1e-05:50:1 0 0 0 0 0 9.33E-14 9.33E-14 0.06546 0 0 0 0 0.5:100:30 vs 1e-05:50:10 0 0 2.51E-10 2.51E-10 4.18E-13 1.78E-10 1.52E-10 0.60012 0 0 0.99218 0 0.5:100:30 vs 1e-05:50:30 0 0 1 1 0.99998 0.99994 0.99993 1 6.23E-07 1.49E-13 1 8.49E-13 0.5:100:30 vs 1e-06:100:1 0 0 4.94E-13 4.89E-13 2.95E-09 0.0567 0.05733 0.58728 0 0 0 0 0.5:100:30 vs 1e-06:100:10 0 0 0.02902 0.02902 0.146 0.99838 0.99844 0.98986 0 0 0.98191 0 0.5:100:30 vs 1e-06:100:30 0 0 0.72921 0.72921 0.62517 0.98692 0.98736 1 1.25E-07 0 1 0.00117 0.5:100:30 vs 1e-06:50:1 0 0 0 0 0 1.31E-13 1.31E-13 2.17E-05 0 0 0 0

75



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.5:100:30 vs 1e-06:50:10 0 0 4.15E-09 4.15E-09 4.03E-13 3.30E-12 3.01E-12 0.01012 0 0 0.98916 0 0.5:100:30 vs 1e-06:50:30 0 0 1 1 1 1 1 1 9.77E-07 3.17E-13 1 9.18E-06 0.5:50:1 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0.79308 0.5:50:1 vs 0.01:50:1 0 1 3.11E-07 3.11E-07 4.13E-13 0 0 0 0 0 0 0.54774 0.5:50:1 vs 0.1:50:1 0.9931 1 0 0 3.92E-13 0 0 0.77643 0 0 0 0.87616 0.5:50:1 vs 1e-04:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.5:50:1 vs 1e-05:50:1 0 0 0 0 0 8.71E-05 5.93E-05 0 0 0 0 0 0.5:50:1 vs 1e-06:50:1 0 0 0 0 0 0.00012 8.20E-05 0 0 0 0 0 0.5:50:10 vs 0.001:100:1 0 5.61E-13 0 0 0 0 0 0 0 0 0 0 0.5:50:10 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.5:50:10 vs 0.001:50:10 0 3.80E-13 0 0 7.90E-11 0 0 0 0 0 1 0 0.5:50:10 vs 0.01:100:1 0 1 0 0 0 0 0 0.99541 0 0 0 0 0.5:50:10 vs 0.01:50:1 0 1 0 0 0 0 0 0.81507 0 0 0 0 0.5:50:10 vs 0.01:50:10 0.46949 1 0 0 0 0.00034 0.00067 0 0 0 1 0 0.5:50:10 vs 0.1:100:1 0.99479 1 0 0 0 0 0 0 0 0 0 0

76



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.5:50:10 vs 0.1:50:1 0.96872 1 0 0 0 0 0 0 0 0 0 0 0.5:50:10 vs 0.1:50:10 1 1 0 0 9.33E-14 3.59E-06 3.79E-06 0 3.61E-13 0 1 0 0.5:50:10 vs 0.5:100:1 1 1 0 0 0 0 0 0 0 0 1.31E-13 0 0.5:50:10 vs 0.5:50:1 1 1 0 0 0 0 0 0 0 0 0 0 0.5:50:10 vs 1e-04:100:1 0 0 0 0 4.21E-13 0 0 0 0 0 0 0 0.5:50:10 vs 1e-04:50:1 0 0 0 0 3.74E-13 0 0 0 0 0 0 0 0.5:50:10 vs 1e-04:50:10 0 0 0 0 0.41232 0 0 0 0 0 0.99844 0 0.5:50:10 vs 1e-05:100:1 0 0 0 0 0.88695 0 0 0 0 0 0 0 0.5:50:10 vs 1e-05:50:1 0 0 0 0 0.00979 0 0 0 0 0 0 0 0.5:50:10 vs 1e-05:50:10 0 0 0 0 1 0 0 0 0 0 0.99841 0 0.5:50:10 vs 1e-06:100:1 0 0 0 0 0.10614 0 0 0 0 0 0 0 0.5:50:10 vs 1e-06:50:1 0 0 0 0 0.00688 0 0 0 0 0 0 0 0.5:50:10 vs 1e-06:50:10 0 0 0 0 1 0 0 0 0 0 0.9976 0 0.5:50:30 vs 0.001:100:1 0 5.77E-13 0 0 0 0 0 0 0 0 0 0 0.5:50:30 vs 0.001:100:10 0 4.18E-12 0 0 0 0 0 0 0 0 0.99998 0

77



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.5:50:30 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 0.5:50:30 vs 0.001:50:10 0 3.91E-13 0 0 0 6.59E-13 7.48E-13 1.43E-11 0 0 0.99998 0 0.5:50:30 vs 0.001:50:30 0 2.43E-05 0.41239 0.41239 1 1 1 1 0.0295 1.19E-10 1 0.00131 0.5:50:30 vs 0.01:100:1 0 1 0 0 0 0 0 0 0 0 0 0 0.5:50:30 vs 0.01:100:10 0.43881 1 0 0 0 0.00293 0.00619 0 0 0 1 0 0.5:50:30 vs 0.01:50:1 0 1 0 0 0 0 0 0 0 0 0 0 0.5:50:30 vs 0.01:50:10 0.45801 1 0 0 0 0.02177 0.01582 0 0 0 1 0 0.5:50:30 vs 0.01:50:30 1 1 3.33E-13 3.33E-13 0.89416 0.99986 0.99985 0.04638 0.99994 0.50527 1 3.61E-07 0.5:50:30 vs 0.1:100:1 0.99413 1 0 0 0 0 0 0 0 0 0 0 0.5:50:30 vs 0.1:100:10 1 1 0 0 0 1.00E-06 1.03E-06 0 0 0 1 0 0.5:50:30 vs 0.1:50:1 0.96595 1 0 0 0 0 0 0 0 0 0 0 0.5:50:30 vs 0.1:50:10 1 1 0 0 0 0 0 0 0 0 1 0 0.5:50:30 vs 0.1:50:30 1 1 3.28E-13 3.28E-13 1 0.40302 0.41511 1.10E-12 1 0.99999 1 2.29E-05 0.5:50:30 vs 0.5:100:1 1 1 0 0 0 0 0 0 0 0 0 0 0.5:50:30 vs 0.5:100:10 1 1 0 0 0 3.19E-06 4.08E-06 0 0.00529 8.02E-13 1 0

78



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.5:50:30 vs 0.5:50:1 1 1 0 0 0 0.00583 0.0079 0 0 0 0 0 0.5:50:30 vs 0.5:50:10 1 1 0 0 4.83E-13 4.89E-13 5.14E-13 0 0.00216 4.09E-13 1 0 0.5:50:30 vs 1e-04:100:1 0 0 0 0 0 0 0 5.70E-06 0 0 0 0 0.5:50:30 vs 1e-04:100:10 0 0 3.40E-12 3.40E-12 3.62E-13 4.23E-13 4.21E-13 0.00503 0 0 0.99503 0 0.5:50:30 vs 1e-04:50:1 0 0 0 0 0 0 0 1.75E-11 0 0 0 0 0.5:50:30 vs 1e-04:50:10 0 0 3.92E-13 3.92E-13 0 4.78E-13 4.70E-13 0.00309 0 0 0.9927 0 0.5:50:30 vs 1e-04:50:30 0 0 1 1 1 1 1 1 6.35E-06 4.01E-13 1 2.76E-08 0.5:50:30 vs 1e-05:100:1 0 0 2.86E-13 2.95E-13 2.38E-08 0.20421 0.21078 0.67043 0 0 0 0 0.5:50:30 vs 1e-05:100:10 0 0 0.00325 0.00325 0.40857 1 1 1 0 0 0.98811 0 0.5:50:30 vs 1e-05:50:1 0 0 0 0 0 4.52E-13 4.58E-13 0.07255 0 0 0 0 0.5:50:30 vs 1e-05:50:10 0 0 2.40E-09 2.40E-09 3.08E-12 2.88E-06 2.64E-06 0.62656 0 0 0.99257 0 0.5:50:30 vs 1e-05:50:30 0 0 1 1 1 1 1 1 1.81E-06 4.29E-13 1 4.41E-09 0.5:50:30 vs 1e-06:100:1 0 0 1.24E-12 1.24E-12 2.97E-05 0.92753 0.93112 0.61383 0 0 0 0 0.5:50:30 vs 1e-06:100:10 0 0 0.08597 0.08597 0.99027 1 1 0.99209 0 0 0.98268 0 0.5:50:30 vs 1e-06:50:1 0 0 0 0 0 4.93E-13 4.92E-13 2.58E-05 0 0 0 0

79



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

0.5:50:30 vs 1e-06:50:10 0 0 3.52E-08 3.52E-08 4.55E-13 9.49E-08 9.04E-08 0.01149 0 0 0.98967 0 0.5:50:30 vs 1e-06:50:30 0 0 1 1 1 1 1 1 2.80E-06 4.12E-13 1 0.00531 1e-04:100:1 vs 0.001:50:1 0 0 0 0 0 0 0 0 6.70E-09 0.68381 0 0 1e-04:100:1 vs 0.01:50:1 0 0 0 0 0 0 0 0 6.22E-06 0 0 0 1e-04:100:1 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:100:1 vs 0.5:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:100:1 vs 1e-04:50:1 1 1 1 1 1 1 1 0.99932 1 1 1 1 1e-04:100:1 vs 1e-05:100:1 0 0 2.55E-11 2.55E-11 0 0 0 0.59095 0.99881 1 1 0 1e-04:100:1 vs 1e-05:50:1 0 0 0.26424 0.26424 8.73E-07 6.30E-07 5.55E-07 0.99701 1 1 0.57183 2.76E-13 1e-04:100:1 vs 1e-06:100:1 0 0 4.18E-13 4.19E-13 0 0 0 0.6482 1 1 1 0 1e-04:100:1 vs 1e-06:50:1 0 0 0.54336 0.54336 1.46E-06 4.43E-07 3.81E-07 1 0.99978 1 1 4.55E-13 1e-04:100:10 vs 0.001:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:100:10 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:100:10 vs 0.001:50:10 0 0 0 0 6.78E-07 1 1 0.38532 1.02E-12 0 1 1 1e-04:100:10 vs 0.01:100:1 0 0 0 0 0 0 0 0 0 0 0 0

80



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-04:100:10 vs 0.01:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:100:10 vs 0.01:50:10 0 0 0 0 0 0 0 0 0 0 1 1.39E-06 1e-04:100:10 vs 0.1:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:100:10 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:100:10 vs 0.1:50:10 0 0 0 0 3.79E-13 0 0 0 0 0 1 0.96688 1e-04:100:10 vs 0.5:100:1 0 0 0 0 0 4.42E-12 3.37E-11 0 0 0 4.44E-13 0 1e-04:100:10 vs 0.5:50:1 0 0 0 0 0 0.03243 0.02435 0 0 0 3.03E-13 0 1e-04:100:10 vs 0.5:50:10 0 0 0 0 1 0 0 0 0 0 0.99904 0 1e-04:100:10 vs 1e-04:100:1 0 9.42E-09 3.58E-13 3.55E-13 5.13E-13 8.55E-11 7.65E-11 1 0 0 0 0 1e-04:100:10 vs 1e-04:50:1 0 8.58E-05 8.45E-12 8.45E-12 5.53E-13 3.29E-11 2.99E-11 0.40647 0 0 0 0 1e-04:100:10 vs 1e-04:50:10 0.00814 0.85967 0.99662 0.99662 0.99937 1 1 1 1 1 1 1 1e-04:100:10 vs 1e-05:100:1 0 0 1 1 0.06328 0.00039 0.00036 0.99996 0 0 0 8.50E-09 1e-04:100:10 vs 1e-05:100:10 0 0 0.30629 0.30629 1.81E-10 6.05E-10 5.66E-10 0.14281 1 0.99641 1 5.70E-05 1e-04:100:10 vs 1e-05:50:1 0 0 8.99E-05 8.99E-05 0.51958 1 1 1 0 0 0 0 1e-04:100:10 vs 1e-05:50:10 0 0 1 1 0.84955 0.86653 0.87134 0.99998 1 0.99978 1 0.97115

81



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-04:100:10 vs 1e-06:100:1 0 0 1 1 0.00047 1.27E-06 1.16E-06 0.99999 0 0 0 0.00029 1e-04:100:10 vs 1e-06:100:10 0 0 0.02219 0.02219 4.78E-13 1.76E-12 1.61E-12 0.94598 0.99789 0.53575 1 4.22E-08 1e-04:100:10 vs 1e-06:50:1 0 0 1.23E-05 1.23E-05 0.44841 1 1 1 0 0 0 0 1e-04:100:10 vs 1e-06:50:10 0 0 1 1 0.99298 0.99566 0.99575 1 1 1 1 0.95923 1e-04:100:30 vs 0.001:100:1 4.34E-13 0 0 0 0 0 0 0 0 0 0 0 1e-04:100:30 vs 0.001:100:10 0 0 0 0 0 0 0 0 0 0 1 0 1e-04:100:30 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:100:30 vs 0.001:50:10 0 0 0 0 0 5.20E-13 5.71E-13 2.34E-11 0 0 1 0 1e-04:100:30 vs 0.001:50:30 0 0 0.11659 0.11659 1 1 1 1 0.99997 0.61627 1 1 1e-04:100:30 vs 0.01:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:100:30 vs 0.01:100:10 0 0 0 0 0 0.00181 0.00393 0 0 0 1 0 1e-04:100:30 vs 0.01:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:100:30 vs 0.01:50:10 0 0 0 0 0 0.03225 0.02374 0 0 0 1 0 1e-04:100:30 vs 0.01:50:30 0 0 4.69E-13 4.69E-13 0.72896 0.99997 0.99997 0.03676 0.03662 3.10E-10 1 0.99999 1e-04:100:30 vs 0.1:100:1 0 0 0 0 0 0 0 0 0 0 0 0

82



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-04:100:30 vs 0.1:100:10 0 0 0 0 0 1.89E-06 1.95E-06 0 4.74E-13 0 1 0 1e-04:100:30 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:100:30 vs 0.1:50:10 0 0 0 0 0 0 0 0 4.69E-13 0 1 0 1e-04:100:30 vs 0.1:50:30 0 0 4.66E-13 4.66E-13 0.99998 0.4894 0.50214 8.44E-13 0.00107 3.39E-13 1 1 1e-04:100:30 vs 0.5:100:1 0 0 0 0 0 0 0 0 0 0 1.59E-13 0 1e-04:100:30 vs 0.5:100:10 0 0 0 0 0 5.92E-06 7.53E-06 0 1 0.98782 1 0 1e-04:100:30 vs 0.5:50:1 0 0 0 0 0 0.00369 0.00506 0 0 0 0 0 1e-04:100:30 vs 0.5:50:10 0 0 0 0 3.71E-13 5.36E-13 2.69E-13 0 1 0.99966 1 0 1e-04:100:30 vs 0.5:50:30 0 0 1 1 1 1 1 1 1.21E-05 4.22E-13 1 0.00174 1e-04:100:30 vs 1e-04:100:1 0 0 0 0 0 0 0 8.33E-06 0 0 0 0 1e-04:100:30 vs 1e-04:100:10 0 6.26E-13 4.80E-13 4.78E-13 3.74E-13 3.81E-13 3.75E-13 0.00666 0 0 0.99936 0 1e-04:100:30 vs 1e-04:50:1 0 0 0 0 0 0 0 2.87E-11 0 0 0 0 1e-04:100:30 vs 1e-04:50:10 0 1.36E-05 3.67E-13 3.67E-13 0 4.14E-13 4.01E-13 0.00412 0 0 0.99893 0 1e-04:100:30 vs 1e-04:50:30 0 2.24E-12 1 1 1 1 1 1 1 1 1 0.99868 1e-04:100:30 vs 1e-05:100:1 0 0 3.78E-13 3.78E-13 3.96E-09 0.15347 0.15885 0.72285 0 0 0 0

83



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-04:100:30 vs 1e-05:100:10 0 0 0.00029 0.00029 0.22637 1 1 1 0 0 0.99798 0 1e-04:100:30 vs 1e-05:100:30 0 0 1 1 0.99996 0.99985 0.99985 1 1 1 1 1 1e-04:100:30 vs 1e-05:50:1 0 0 0 0 0 3.98E-13 4.00E-13 0.08956 0 0 0 0 1e-04:100:30 vs 1e-05:50:10 0 0 6.08E-11 6.08E-11 8.06E-13 1.53E-06 1.41E-06 0.68097 0 0 0.99891 0 1e-04:100:30 vs 1e-05:50:30 0.72414 1 1 1 1 1 1 1 1 1 1 0.98564 1e-04:100:30 vs 1e-06:100:1 0 0 3.94E-13 3.90E-13 6.71E-06 0.8825 0.8875 0.66867 0 0 0 0 1e-04:100:30 vs 1e-06:100:10 0 0 0.01385 0.01385 0.94522 1 1 0.99547 0 0 0.99669 0 1e-04:100:30 vs 1e-06:100:30 0 0 0.85816 0.85816 0.02546 0.18308 0.18193 1 1 1 1 1 1e-04:100:30 vs 1e-06:50:1 0 0 0 0 0 4.25E-13 4.30E-13 3.70E-05 0 0 0 0 1e-04:100:30 vs 1e-06:50:10 0 0 1.08E-09 1.08E-09 3.56E-13 4.77E-08 4.55E-08 0.01494 0 0 0.99832 0 1e-04:100:30 vs 1e-06:50:30 4.00E-05 0.30463 1 1 1 1 1 1 1 1 1 1 1e-04:50:1 vs 1e-05:50:1 0 0 0.92943 0.92943 1.30E-06 2.83E-07 2.53E-07 0.06203 1 1 0.93972 4.82E-13 1e-04:50:1 vs 1e-06:50:1 0 0 0.99352 0.99352 2.16E-06 1.98E-07 1.72E-07 0.99134 1 1 1 4.05E-13 1e-04:50:10 vs 0.001:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:50:10 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0

84



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-04:50:10 vs 0.01:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:50:10 vs 0.01:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:50:10 vs 0.1:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:50:10 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:50:10 vs 0.5:100:1 0 0 0 0 0 4.02E-08 2.53E-07 0 0 0 4.64E-13 0 1e-04:50:10 vs 0.5:50:1 0 0 0 0 0 0.00011 6.46E-05 0 0 0 3.18E-13 0 1e-04:50:10 vs 1e-04:100:1 0 4.04E-13 2.40E-08 2.40E-08 2.76E-10 5.04E-07 5.03E-07 1 0 0 0 0 1e-04:50:10 vs 1e-04:50:1 0 2.89E-12 8.08E-06 8.08E-06 4.43E-10 2.26E-07 2.29E-07 0.49821 0 0 0 0 1e-04:50:10 vs 1e-05:100:1 0 0 1 1 1.07E-05 2.92E-07 2.38E-07 0.99982 0 0 0 4.10E-12 1e-04:50:10 vs 1e-05:50:1 0 0 0.30049 0.30049 1 1 1 1 0 0 0 0 1e-04:50:10 vs 1e-05:50:10 0 0 0.6292 0.6292 0.00592 0.06729 0.06607 0.99991 1 1 1 1 1e-04:50:10 vs 1e-06:100:1 0 0 0.99944 0.99944 6.92E-09 2.58E-10 2.08E-10 0.99993 0 0 0 7.49E-07 1e-04:50:10 vs 1e-06:50:1 0 0 0.1151 0.1151 1 1 1 1 0 0 0 0 1e-04:50:10 vs 1e-06:50:10 0 0 0.30985 0.30985 0.04563 0.3127 0.30421 1 1 1 1 1 1e-04:50:30 vs 0.001:100:1 0.025 0 0 0 0 0 0 0 0 0 0 0

85



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-04:50:30 vs 0.001:100:10 0 0 0 0 0 0 0 0 0 0 1 0 1e-04:50:30 vs 0.001:50:1 0.99999 0 0 0 0 0 0 0 0 0 0 0 1e-04:50:30 vs 0.001:50:10 0 0 0 0 0 1.36E-09 1.88E-09 6.16E-09 0 0 1 0 1e-04:50:30 vs 0.01:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:50:30 vs 0.01:100:10 0 0 0 0 0 0.20373 0.31006 0 0 0 1 0 1e-04:50:30 vs 0.01:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:50:30 vs 0.01:50:10 0 0 0 0 0 0.0001 6.46E-05 0 0 0 1 0 1e-04:50:30 vs 0.1:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:50:30 vs 0.1:100:10 0 0 0 0 0 3.97E-10 4.09E-10 0 3.10E-13 0 1 0 1e-04:50:30 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-04:50:30 vs 0.1:50:10 0 0 0 0 0 0 0 0 5.26E-13 0 1 0 1e-04:50:30 vs 0.5:100:1 0 0 0 0 0 0 0 0 0 0 1.59E-13 0 1e-04:50:30 vs 0.5:100:10 0 0 0 0 0 1.58E-09 2.10E-09 0 1 0.96629 1 0 1e-04:50:30 vs 0.5:50:1 0 0 0 0 0 0.29948 0.35173 0 0 0 0 0 1e-04:50:30 vs 0.5:50:10 0 0 0 0 1.27E-12 3.98E-13 4.41E-13 0 1 0.9982 1 0

86



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-04:50:30 vs 1e-04:100:1 0 0 0 0 0 0 0 0.00051 0 0 0 0 1e-04:50:30 vs 1e-04:100:10 0 0 2.82E-11 2.82E-11 4.08E-13 1.93E-10 1.88E-10 0.11189 0 0 0.9994 0 1e-04:50:30 vs 1e-04:50:1 0 0 0 0 0 0 0 7.41E-09 0 0 0 0 1e-04:50:30 vs 1e-04:50:10 0 0 3.22E-13 3.22E-13 1.03E-13 3.83E-13 3.75E-13 0.07903 0 0 0.999 0 1e-04:50:30 vs 1e-05:100:1 0 0 3.65E-13 3.65E-13 2.96E-05 0.96647 0.96912 0.99587 0 0 0 0 1e-04:50:30 vs 1e-05:100:10 0 0 0.0115 0.0115 0.9965 1 1 1 0 0 0.9981 0 1e-04:50:30 vs 1e-05:50:1 0 0 0 0 0 3.67E-13 3.76E-13 0.56106 0 0 0 0 1e-04:50:30 vs 1e-05:50:10 0 0 1.85E-08 1.85E-08 1.28E-08 0.00147 0.00138 0.99347 0 0 0.99898 0 1e-04:50:30 vs 1e-05:50:30 0 4.08E-13 1 1 1 1 1 1 1 1 1 1 1e-04:50:30 vs 1e-06:100:1 0 0 7.62E-12 7.63E-12 0.00866 1 1 0.9926 0 0 0 0 1e-04:50:30 vs 1e-06:100:10 0 0 0.2038 0.2038 1 1 1 1 0 0 0.99687 0 1e-04:50:30 vs 1e-06:50:1 0 0 0 0 0 3.91E-13 3.89E-13 0.00182 0 0 0 0 1e-04:50:30 vs 1e-06:50:10 0 0 2.42E-07 2.42E-07 3.23E-10 9.51E-05 9.20E-05 0.1958 0 0 0.99842 0 1e-04:50:30 vs 1e-06:50:30 0 8.39E-14 0.99996 0.99996 0.98047 0.99985 0.99987 1 1 1 1 0.98769 1e-05:100:1 vs 0.001:50:1 0 0 0 0 0 0 0 0 3.31E-13 0.02165 0 0

87



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-05:100:1 vs 0.01:50:1 0 0 0 0 0 0 0 0 1.33E-11 0 0 0 1e-05:100:1 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:100:1 vs 0.5:50:1 0 0 0 0 0 1 1 0 0 0 0 0 1e-05:100:1 vs 1e-04:50:1 0 0 2.03E-08 2.03E-08 0 0 0 0.00121 1 1 0.99827 0 1e-05:100:1 vs 1e-05:50:1 0 0 0.01408 0.01408 5.53E-09 2.33E-07 2.16E-07 1 0.99704 1 0.00932 3.86E-13 1e-05:100:1 vs 1e-06:100:1 0.11212 0.12746 1 1 1 1 1 1 1 1 0.79573 0.99987 1e-05:100:1 vs 1e-06:50:1 0 0 0.00305 0.00305 3.08E-09 3.33E-07 3.16E-07 0.79947 1 1 1 3.54E-13 1e-05:100:10 vs 0.001:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:100:10 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:100:10 vs 0.001:50:10 0 0 0 0 0 4.09E-09 5.41E-09 1.09E-08 3.82E-13 0 1 1.51E-05 1e-05:100:10 vs 0.01:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:100:10 vs 0.01:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:100:10 vs 0.01:50:10 0 0 0 0 0 4.33E-05 2.82E-05 0 0 0 1 0 1e-05:100:10 vs 0.1:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:100:10 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0

88



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-05:100:10 vs 0.1:50:10 0 0 0 0 0 0 0 0 0 0 0.99997 1.24E-11 1e-05:100:10 vs 0.5:100:1 0 0 0 0 0 0 0 0 0 0 4.97E-13 0 1e-05:100:10 vs 0.5:50:1 0 0 0 0 0 0.41692 0.4727 0 0 0 3.34E-13 0 1e-05:100:10 vs 0.5:50:10 0 0 0 0 1.35E-06 3.67E-13 4.14E-13 0 0 0 0.99714 0 1e-05:100:10 vs 1e-04:100:1 0 0 0 0 0 0 0 0.00077 0 0 0 0 1e-05:100:10 vs 1e-04:50:1 0 0 2.52E-13 2.52E-13 0 0 0 1.30E-08 0 0 0 0 1e-05:100:10 vs 1e-04:50:10 0 0 9.41E-05 9.41E-05 4.89E-13 4.50E-13 4.37E-13 0.10258 1 1 1 0.00924 1e-05:100:10 vs 1e-05:100:1 0 1.07E-05 0.00889 0.00889 0.18188 0.98859 0.98928 0.99812 0 0 0 0 1e-05:100:10 vs 1e-05:50:1 1 4.10E-13 3.76E-13 3.74E-13 3.81E-13 4.27E-13 4.31E-13 0.63154 0 0 0 0 1e-05:100:10 vs 1e-05:50:10 0 0 0.94145 0.94145 0.00163 0.00302 0.00278 0.99687 1 1 1 0.44653 1e-05:100:10 vs 1e-06:100:1 0 4.30E-13 0.20058 0.20058 0.95537 1 1 0.9964 0 0 0 3.83E-13 1e-05:100:10 vs 1e-06:100:10 4.34E-13 2.91E-09 1 1 1 1 1 1 1 1 1 1 1e-05:100:10 vs 1e-06:50:1 1 5.48E-13 2.86E-13 2.86E-13 4.07E-13 4.59E-13 4.54E-13 0.00266 0 0 0 0 1e-05:100:10 vs 1e-06:50:10 0 0 0.99645 0.99645 0.00012 0.00022 0.0002 0.24198 1 1 1 0.58482 1e-05:100:30 vs 0.001:100:1 0 0 0 0 0 0 0 0 0 0 0 0

89



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-05:100:30 vs 0.001:100:10 0 0 0 0 0 0 0 0 0 0 1 0 1e-05:100:30 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:100:30 vs 0.001:50:10 0 0 0 0 0 4.79E-13 3.25E-13 1.23E-11 0 0 1 0 1e-05:100:30 vs 0.001:50:30 0 0 0.01646 0.01646 0.93901 1 1 1 0.99922 0.32013 1 1 1e-05:100:30 vs 0.01:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:100:30 vs 0.01:100:10 0 0 0 0 0 9.67E-08 2.93E-07 0 0 0 1 0 1e-05:100:30 vs 0.01:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:100:30 vs 0.01:50:10 0 0 0 0 0 0.96787 0.94761 0 0 0 1 0 1e-05:100:30 vs 0.01:50:30 0 0 3.94E-13 3.94E-13 0.00688 1 1 0.0497 0.01374 2.08E-11 1 1 1e-05:100:30 vs 0.1:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:100:30 vs 0.1:100:10 0 0 0 0 0 0.01408 0.01427 0 3.58E-13 0 1 0 1e-05:100:30 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:100:30 vs 0.1:50:10 0 0 0 0 0 0 0 0 2.80E-13 0 1 0 1e-05:100:30 vs 0.1:50:30 0 0 3.88E-13 3.88E-13 0.3424 1 1 1.21E-12 0.0003 5.31E-13 1 1 1e-05:100:30 vs 0.5:100:1 0 0 0 0 0 0 0 0 0 0 1.68E-13 0

90



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-05:100:30 vs 0.5:100:10 0 0 0 0 0 0.02951 0.03416 0 1 0.89639 1 0 1e-05:100:30 vs 0.5:50:1 0 0 0 0 0 2.65E-07 4.21E-07 0 0 0 0 0 1e-05:100:30 vs 0.5:50:10 0 0 0 0 1.87E-13 1.70E-10 2.47E-10 0 1 0.98812 1 0 1e-05:100:30 vs 0.5:50:30 0 0 1 1 0.99891 0.99944 0.99945 1 2.68E-06 4.23E-13 1 2.13E-05 1e-05:100:30 vs 1e-04:100:1 0.05123 0 0 0 0 0 0 5.07E-06 0 0 0 0 1e-05:100:30 vs 1e-04:100:10 0 0 2.88E-13 2.97E-13 0 4.17E-13 4.10E-13 0.00462 0 0 0.99945 0 1e-05:100:30 vs 1e-04:50:1 0.52556 0 0 0 0 0 0 1.50E-11 0 0 0 0 1e-05:100:30 vs 1e-04:50:10 0 0 3.96E-13 3.96E-13 0 0 0 0.00282 0 0 0.99908 0 1e-05:100:30 vs 1e-04:50:30 0 0 1 1 0.50515 0.55099 0.5515 1 1 1 1 1 1e-05:100:30 vs 1e-05:100:1 0 0 3.32E-13 3.32E-13 3.93E-13 9.71E-05 0.0001 0.65401 0 0 0 0 1e-05:100:30 vs 1e-05:100:10 0 0 1.42E-05 1.42E-05 0.00034 0.41926 0.42395 1 0 0 0.99824 0 1e-05:100:30 vs 1e-05:50:1 0 0.01392 0 0 0 0 0 0.06795 0 0 0 0 1e-05:100:30 vs 1e-05:50:10 1 6.54E-10 1.31E-12 1.31E-12 4.46E-13 8.19E-12 7.46E-12 0.60972 0 0 0.99906 0 1e-05:100:30 vs 1e-05:50:30 0 0 1 1 0.99594 0.99367 0.99357 1 1 1 1 1 1e-05:100:30 vs 1e-06:100:1 0 0 5.27E-13 5.27E-13 1.12E-10 0.01227 0.01286 0.59692 0 0 0 0

91



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-05:100:30 vs 1e-06:100:10 0 0 0.00119 0.00119 0.03301 0.95884 0.96165 0.99073 0 0 0.99709 0 1e-05:100:30 vs 1e-06:100:30 0.00028 0.00599 0.99558 0.99558 0.92152 0.99978 0.99977 1 1 1 1 0.99681 1e-05:100:30 vs 1e-06:50:1 0 0.00042 0 0 0 0 0 2.31E-05 0 0 0 0 1e-05:100:30 vs 1e-06:50:10 0.08667 5.69E-05 1.71E-11 1.71E-11 4.24E-13 5.56E-13 5.52E-13 0.0106 0 0 0.99855 0 1e-05:100:30 vs 1e-06:50:30 0 0 1 1 1 1 1 1 1 1 1 1 1e-05:50:1 vs 1e-06:50:1 0.99999 1 1 1 1 1 1 0.99985 0.99933 1 0.53299 1 1e-05:50:10 vs 0.001:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:50:10 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:50:10 vs 0.01:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:50:10 vs 0.01:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:50:10 vs 0.1:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:50:10 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:50:10 vs 0.5:100:1 0 0 0 0 0 3.52E-13 4.16E-13 0 0 0 4.71E-13 0 1e-05:50:10 vs 0.5:50:1 0 0 0 0 0 1 0.99999 0 0 0 3.19E-13 0 1e-05:50:10 vs 1e-04:100:1 0.40667 2.35E-07 3.37E-13 3.37E-13 0 3.20E-13 3.25E-13 0.63561 0 0 0 0

92



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-05:50:10 vs 1e-04:50:1 0.97175 6.11E-12 3.61E-13 3.67E-13 0 4.09E-13 4.10E-13 0.00155 0 0 0 0 1e-05:50:10 vs 1e-05:100:1 0 0 0.99795 0.99795 1 0.92261 0.91221 1 0 0 0 5.41E-13 1e-05:50:10 vs 1e-05:50:1 0 0 4.76E-07 4.76E-07 1.49E-05 0.05971 0.06267 1 0 0 0 0 1e-05:50:10 vs 1e-06:100:1 0 0 1 1 0.94598 0.19719 0.18483 1 0 0 0 1.53E-10 1e-05:50:10 vs 1e-06:50:1 0 0 4.68E-08 4.68E-08 9.20E-06 0.07208 0.07647 0.8333 0 0 0 0 1e-05:50:10 vs 1e-06:50:10 0.5389 0.99974 1 1 1 1 1 1 1 1 1 1 1e-05:50:30 vs 0.001:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:50:30 vs 0.001:100:10 0 0 0 0 0 0 0 0 0 0 1 0 1e-05:50:30 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:50:30 vs 0.001:50:10 0 0 0 0 0 1.82E-12 2.41E-12 1.36E-10 0 0 1 0 1e-05:50:30 vs 0.01:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:50:30 vs 0.01:100:10 0 0 0 0 0 0.00837 0.01697 0 0 0 1 0 1e-05:50:30 vs 0.01:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:50:30 vs 0.01:50:10 0 0 0 0 0 0.00825 0.00574 0 0 0 1 0 1e-05:50:30 vs 0.1:100:1 0 0 0 0 0 0 0 0 0 0 0 0

93



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-05:50:30 vs 0.1:100:10 0 0 0 0 0 2.20E-07 2.22E-07 0 3.80E-13 0 1 0 1e-05:50:30 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-05:50:30 vs 0.1:50:10 0 0 0 0 0 0 0 0 3.01E-13 0 1 0 1e-05:50:30 vs 0.5:100:1 0 0 0 0 0 0 0 0 0 0 1.68E-13 0 1e-05:50:30 vs 0.5:100:10 0 0 0 0 0 7.34E-07 9.28E-07 0 1 0.81334 1 0 1e-05:50:30 vs 0.5:50:1 0 0 0 0 0 0.01582 0.02122 0 0 0 0 0 1e-05:50:30 vs 0.5:50:10 0 0 0 0 5.51E-13 3.77E-13 3.96E-13 0 1 0.96695 1 0 1e-05:50:30 vs 1e-04:100:1 0 0 0 0 0 0 0 3.14E-05 0 0 0 0 1e-05:50:30 vs 1e-04:100:10 0 7.38E-09 1.24E-12 1.24E-12 3.77E-13 6.14E-13 6.05E-13 0.01736 0 0 0.99946 0 1e-05:50:30 vs 1e-04:50:1 0 0 0 0 0 0 0 1.65E-10 0 0 0 0 1e-05:50:30 vs 1e-04:50:10 0 0.01434 4.70E-13 4.70E-13 0 3.56E-13 3.53E-13 0.01114 0 0 0.99909 0 1e-05:50:30 vs 1e-05:100:1 0 0 5.21E-13 5.21E-13 5.73E-08 0.36189 0.37389 0.87678 0 0 0 0 1e-05:50:30 vs 1e-05:100:10 0 0 0.00147 0.00147 0.51883 1 1 1 0 0 0.99826 0 1e-05:50:30 vs 1e-05:50:1 0 0 0 0 0 3.42E-13 3.47E-13 0.17883 0 0 0 0 1e-05:50:30 vs 1e-05:50:10 0 0 6.98E-10 6.98E-10 7.26E-12 1.18E-05 1.11E-05 0.84802 0 0 0.99907 0

94



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-05:50:30 vs 1e-06:100:1 0 0 6.51E-13 6.48E-13 6.14E-05 0.9831 0.98468 0.83916 0 0 0 0 1e-05:50:30 vs 1e-06:100:10 0 0 0.04813 0.04813 0.9969 1 1 0.99961 0 0 0.99712 0 1e-05:50:30 vs 1e-06:50:1 0 0 0 0 0 3.64E-13 3.63E-13 0.00013 0 0 0 0 1e-05:50:30 vs 1e-06:50:10 0 0 1.09E-08 1.09E-08 5.69E-13 4.45E-07 4.35E-07 0.0364 0 0 0.99856 0 1e-05:50:30 vs 1e-06:50:30 0.80769 0.999 1 1 1 1 1 1 1 1 1 0.93329 1e-06:100:1 vs 0.001:50:1 0 0 0 0 0 0 0 0 2.02E-11 0.16899 4.46E-13 0 1e-06:100:1 vs 0.01:50:1 0 0 0 0 0 0 0 0 4.28E-08 0 0 0 1e-06:100:1 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:100:1 vs 0.5:50:1 0 0 0 0 0 0.9964 0.99801 0 0 0 0 0 1e-06:100:1 vs 1e-04:50:1 0 0 3.12E-11 3.12E-11 0 0 0 0.00167 1 1 1 0 1e-06:100:1 vs 1e-05:50:1 0 0 0.00022 0.00022 1.48E-12 1.99E-10 1.85E-10 1 1 1 0.99995 1.49E-13 1e-06:100:1 vs 1e-06:50:1 0 0 3.25E-05 3.25E-05 9.88E-13 3.01E-10 2.88E-10 0.84236 1 1 1 3.56E-13 1e-06:100:10 vs 0.001:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:100:10 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:100:10 vs 0.001:50:10 0 0 0 0 0 1.03E-11 1.33E-11 2.09E-05 4.81E-13 0 1 8.35E-09

95



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-06:100:10 vs 0.01:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:100:10 vs 0.01:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:100:10 vs 0.01:50:10 0 0 0 0 0 0.00261 0.00188 0 0 0 1 0 1e-06:100:10 vs 0.1:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:100:10 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:100:10 vs 0.1:50:10 0 0 0 0 0 0 0 0 0 0 0.99994 3.07E-13 1e-06:100:10 vs 0.5:100:1 0 0 0 0 0 0 0 0 0 0 5.27E-13 0 1e-06:100:10 vs 0.5:50:1 0 0 0 0 0 0.04261 0.05281 0 0 0 3.54E-13 0 1e-06:100:10 vs 0.5:50:10 0 0 0 0 1.38E-09 5.13E-13 3.11E-13 0 0 0 0.99541 0 1e-06:100:10 vs 1e-04:100:1 0 0 0 0 0 0 0 0.10309 0 0 0 0 1e-06:100:10 vs 1e-04:50:1 0 0 0 0 0 0 0 2.42E-05 0 0 0 0 1e-06:100:10 vs 1e-04:50:10 0 0 7.10E-07 7.10E-07 3.56E-13 4.62E-13 4.48E-13 0.9059 1 0.99607 1 2.69E-05 1e-06:100:10 vs 1e-05:100:1 0.00039 1 0.00017 0.00017 0.00422 0.58043 0.58203 1 0 0 0 0 1e-06:100:10 vs 1e-05:50:1 3.41E-13 0 3.74E-13 3.73E-13 0 4.50E-13 4.44E-13 0.99991 0 0 0 0 1e-06:100:10 vs 1e-05:50:10 0 0 0.34659 0.34659 6.81E-06 5.16E-05 4.51E-05 1 1 1 1 0.0116

96



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-06:100:10 vs 1e-06:100:1 3.49E-13 0.95548 0.01122 0.01122 0.24816 0.99824 0.99824 1 0 0 0 0 1e-06:100:10 vs 1e-06:50:1 8.29E-10 0 4.40E-13 4.40E-13 0 4.72E-13 4.67E-13 0.21805 0 0 0 0 1e-06:100:10 vs 1e-06:50:10 0 0 0.67176 0.67176 2.85E-07 2.25E-06 2.02E-06 0.98434 1 0.99927 1 0.02407 1e-06:100:30 vs 0.001:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:100:30 vs 0.001:100:10 0 0 0 0 0 0 0 0 0 0 1 0 1e-06:100:30 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:100:30 vs 0.001:50:10 0 0 0 0 0 0 0 6.69E-13 0 0 1 0 1e-06:100:30 vs 0.001:50:30 0 0 3.66E-07 3.66E-07 0.00088 0.62804 0.6396 1 0.98536 0.05544 1 1 1e-06:100:30 vs 0.01:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:100:30 vs 0.01:100:10 0 0 0 0 0 6.73E-13 1.29E-12 0 0 0 1 0 1e-06:100:30 vs 0.01:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:100:30 vs 0.01:50:10 0 0 0 0 0 1 1 0 0 0 1 0 1e-06:100:30 vs 0.01:50:30 0 0 0 0 5.35E-09 0.99915 0.99917 0.23782 0.00356 6.30E-13 1 0.80355 1e-06:100:30 vs 0.1:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:100:30 vs 0.1:100:10 0 0 0 0 0 0.91114 0.91415 0 4.93E-13 0 1 0

97



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-06:100:30 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:100:30 vs 0.1:50:10 0 0 0 0 0 0 0 0 3.57E-13 0 1 0 1e-06:100:30 vs 0.1:50:30 0 0 0 0 1.00E-05 1 1 4.01E-11 5.67E-05 4.91E-13 1 0.99717 1e-06:100:30 vs 0.5:100:1 0 0 0 0 0 0 0 0 0 0 1.77E-13 0 1e-06:100:30 vs 0.5:100:10 0 0 0 0 0 0.96871 0.9764 0 0.99979 0.4374 1 0 1e-06:100:30 vs 0.5:50:1 0 0 0 0 0 1.22E-12 1.74E-12 0 0 0 0 0 1e-06:100:30 vs 0.5:50:10 0 0 0 0 0 1.92E-05 2.61E-05 0 0.99999 0.74243 1 0 1e-06:100:30 vs 0.5:50:30 0 0 0.46602 0.46602 0.00901 0.13642 0.13553 1 3.78E-07 6.53E-14 1 0.15031 1e-06:100:30 vs 1e-04:100:1 1 0 0 0 0 0 0 2.09E-07 0 0 0 0 1e-06:100:30 vs 1e-04:100:10 0 0 3.64E-13 3.64E-13 0 0 0 0.0004 0 0 0.99951 0 1e-06:100:30 vs 1e-04:50:1 0.9937 0 0 0 0 0 0 7.32E-13 0 0 0 0 1e-06:100:30 vs 1e-04:50:10 0 0 0 0 0 0 0 0.00023 0 0 0.99917 0 1e-06:100:30 vs 1e-04:50:30 0 0 0.2476 0.2476 3.14E-05 0.00151 0.00148 1 1 1 1 0.48351 1e-06:100:30 vs 1e-05:100:1 0 0 0 0 2.89E-13 1.46E-09 1.56E-09 0.2452 0 0 0 0 1e-06:100:30 vs 1e-05:100:10 0 3.07E-13 1.43E-11 1.43E-11 5.03E-11 0.00071 0.00072 1 0 0 0.99841 0

98



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-06:100:30 vs 1e-05:50:1 0 1 0 0 0 0 0 0.0097 0 0 0 0 1e-06:100:30 vs 1e-05:50:10 0.009 0 4.62E-13 4.62E-13 0 3.53E-13 3.39E-13 0.21477 0 0 0.99915 0 1e-06:100:30 vs 1e-05:50:30 0 0 0.61424 0.61424 0.00514 0.06385 0.06262 1 1 1 1 0.27804 1e-06:100:30 vs 1e-06:100:1 0 0 1.40E-13 1.40E-13 4.04E-13 1.29E-06 1.36E-06 0.20657 0 0 0 0 1e-06:100:30 vs 1e-06:100:10 0 0 6.83E-09 6.83E-09 7.71E-08 0.0249 0.02567 0.82967 0 0 0.99735 0 1e-06:100:30 vs 1e-06:50:1 0 1 0 0 0 0 0 1.09E-06 0 0 0 0 1e-06:100:30 vs 1e-06:50:10 1 4.14E-13 5.06E-13 5.06E-13 0 4.76E-13 4.68E-13 0.00105 0 0 0.99868 0 1e-06:100:30 vs 1e-06:50:30 0 0 0.99983 0.99983 0.31672 0.52445 0.5153 1 1 1 1 1 1e-06:50:10 vs 0.001:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:50:10 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:50:10 vs 0.01:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:50:10 vs 0.01:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:50:10 vs 0.1:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:50:10 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:50:10 vs 0.5:100:1 0 0 0 0 0 4.01E-13 3.24E-13 0 0 0 4.84E-13 0

99



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-06:50:10 vs 0.5:50:1 0 0 0 0 0 0.99698 0.99385 0 0 0 3.27E-13 0 1e-06:50:10 vs 1e-04:100:1 1 1.06E-12 3.56E-13 3.56E-13 8.39E-14 3.63E-13 3.53E-13 1 0 0 0 0 1e-06:50:10 vs 1e-04:50:1 1 3.35E-13 2.72E-13 2.72E-13 1.31E-13 3.14E-13 3.13E-13 0.26448 0 0 0 0 1e-06:50:10 vs 1e-05:100:1 0 0 0.95731 0.95731 0.9998 0.54766 0.53086 1 0 0 0 2.79E-13 1e-06:50:10 vs 1e-05:50:1 0 3.07E-13 3.78E-08 3.78E-08 0.00025 0.28826 0.29341 1 0 0 0 0 1e-06:50:10 vs 1e-06:100:1 0 0 1 1 0.62887 0.03494 0.03278 1 0 0 0 2.10E-10 1e-06:50:10 vs 1e-06:50:1 0 3.47E-13 3.24E-09 3.24E-09 0.00016 0.32753 0.33578 1 0 0 0 0 1e-06:50:30 vs 0.001:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:50:30 vs 0.001:100:10 0 0 0 0 0 0 0 0 0 0 1 0 1e-06:50:30 vs 0.001:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:50:30 vs 0.001:50:10 0 0 0 0 0 3.18E-13 3.39E-13 5.60E-12 0 0 1 0 1e-06:50:30 vs 0.01:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:50:30 vs 0.01:100:10 0 0 0 0 0 0.00017 0.00042 0 0 0 1 0 1e-06:50:30 vs 0.01:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:50:30 vs 0.01:50:10 0 0 0 0 0 0.15533 0.11939 0 0 0 1 0

100



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-06:50:30 vs 0.1:100:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:50:30 vs 0.1:100:10 0 0 0 0 0 3.08E-05 3.02E-05 0 3.51E-13 0 1 0 1e-06:50:30 vs 0.1:50:1 0 0 0 0 0 0 0 0 0 0 0 0 1e-06:50:30 vs 0.1:50:10 0 0 0 0 0 0 0 0 2.86E-13 0 1 0 1e-06:50:30 vs 0.5:100:1 0 0 0 0 0 0 0 0 0 0 1.68E-13 0 1e-06:50:30 vs 0.5:100:10 0 0 0 0 0 8.74E-05 0.0001 0 1 0.89031 1 0 1e-06:50:30 vs 0.5:50:1 0 0 0 0 0 0.00038 0.00056 0 0 0 0 0 1e-06:50:30 vs 0.5:50:10 0 0 0 0 4.67E-13 3.77E-13 3.87E-13 0 1 0.9869 1 0 1e-06:50:30 vs 1e-04:100:1 0 0 0 0 0 0 0 2.74E-06 0 0 0 0 1e-06:50:30 vs 1e-04:100:10 0 0.00061 4.70E-13 4.70E-13 0 5.47E-13 5.50E-13 0.00291 0 0 0.99944 0 1e-06:50:30 vs 1e-04:50:1 0 3.36E-13 0 0 0 0 0 6.85E-12 0 0 0 0 1e-06:50:30 vs 1e-04:50:10 0 0.95528 8.39E-14 8.39E-14 0 4.20E-13 4.13E-13 0.00176 0 0 0.99907 0 1e-06:50:30 vs 1e-05:100:1 0 0 4.45E-13 4.45E-13 9.24E-12 0.03175 0.03423 0.56567 0 0 0 0 1e-06:50:30 vs 1e-05:100:10 0 0 2.47E-06 2.47E-06 0.01476 0.99902 0.99915 1 0 0 0.99822 0 1e-06:50:30 vs 1e-05:50:1 0 0 0 0 0 3.92E-13 3.99E-13 0.0477 0 0 0 0

101



Fst p-value

φst p-value

S p-value

θW p-value

π p-value

R2 p-value

TD p-value

NSS p-value

# Hap p-value

# Single p-value

Hmzy p-value

Tau-hat p-value

1e-06:50:30 vs 1e-05:50:10 0 0 5.07E-13 5.10E-13 2.85E-13 7.33E-08 7.06E-08 0.5206 0 0 0.99905 0 1e-06:50:30 vs 1e-06:100:1 0 0 3.91E-13 3.91E-13 3.89E-08 0.52511 0.54102 0.50779 0 0 0 0 1e-06:50:30 vs 1e-06:100:10 0 0 0.00027 0.00027 0.37211 1 1 0.97998 0 0 0.99706 0 1e-06:50:30 vs 1e-06:50:1 0 0 0 0 0 4.41E-13 4.51E-13 1.28E-05 0 0 0 0 1e-06:50:30 vs 1e-06:50:10 0 0 2.19E-12 2.19E-12 3.59E-13 1.76E-09 1.78E-09 0.00687 0 0 0.99853 0

102

Table 2-5. Percent of simulated scenarios that agree with empirical Fst estimates separated by CS and GF categories.

Fst estimates for simulations were compared to empirical Fst estimates for Africa vs European (0.141) or Asian (0.235) populations (Bowcock et al. 1991). ‘% overlap’ reflects simulated Fst estimates that fall between 0.141 and 0.235 for each GF x CS category. ‘% Total overlap’ shows simulated Fst estimates that fall between 0.141 and 0.235 for each CS category for 42,000 simulations. The small values for % total overlap indicate that the majority of tested parameter combinations do not fit the empirical data well.

CS=1% CS=10% CS=30%

GF category % overlap



10-06 0 10-06 3.1 10-06 26.8

10-05 0 10-05 4.2 10-05 29.5 10-04 1.4 10-04 20.0 10-04 63.5 10-03 82.0 10-03 35.6 10-03 6.6 0.01 23.8 0.01 0.1 0.01 0 0.1 0 0.1 0 0.1 0 0.5 0 0.5 0 0.5 0

% Total overlap 2.6 1.5 3.0

103

Figure 2-1. Alternative scenarios for initial colonization of modern humans out of Africa. Scenarios include all combinations for time of colonization (TC) and colonization size (CS). Each scenario is modeled with seven values of bidirectional gene flow (where GF=10-6, 10-5, 10-4, 10-3, 10-2, 0.1, and 0.5 proportion of migrants per generation).

104

Figure 2-2. Box plots of estimates of 5 summary statistics that partition genetic variation more equally between CS, GF, and CSxGF than seen in the other summary statistics. Panels A) Fst. B) S. C) π. D) R2. E) NSS. Each panel shows the distribution of 42,000 estimates of the summary statistic calculated for each of 1,000 datasets simulated under 42 parameter combinations as listed at the bottom of the figure. The gray bar in panel A) shows the range of empirical Fst

values (0.141-0.235) between African populations vs European and Asian populations (Bowcocket al. 1991).

105

Figure 2-3. Box plots of estimates of 4 summary statistics that partition genetic variation primarily by CS, compared to the other summary statistics. A) B) #Hap. C) #Single. D) Hmzy. Each box plot represents a demographic scenario described by the parameter values at the bottom of the figure.

.τ̂

A

B

C

D

106

Figure 2-4. Box plots of estimates of 3 summary statistics that partition genetic variation similar to summary statistics in Figure 2-3. A) Φst. B) θW. C) TD. have similar box plot profiles to Fst, S, and R2, respectively . Each box plot represents a demographic scenario described by the parameter values at the bottom of the figure.

107

CHAPTER 3 HUMAN MIGRATION PATTERNS IN YEMEN AND IMPLICATIONS FOR

RECONSTRUCTING PREHISTORIC POPULATION MOVEMENTS

Humans’ facility for dispersal has played a large role in our evolutionary history,

yet how and why humans have moved throughout history is unclear. Most data on

human movement come from ethnographic studies, comparisons of birthplaces from

birth certificates, and census data. While ethnographic studies offer insight into social

and environmental factors that influence human movement, they generally involve

seasonal or temporary movements, as in the case of migrant workers (de Haan and

Rogaly 2002) or hunters and gatherers (Hahnet al. 1966; Marlowe 2010). In order to

understand how migration has influenced our evolutionary history, it is necessary to

address migration as the movement to a new location for permanent settlement. Birth

certificate and census data allow us to trace movement across longer periods of time

(i.e. between generations), but studies using these data generally focus either on the

proportion of migrants or the distance moved, do not usually use multi-generational

families, and can typically only be studied in developed countries (Boattiniet al. 2007;

Daviset al. 2013; Gray and Bilsborrow 2013; Levy 2010; Mielkeet al. 1994; Mortonet al.

1971). A deeper understanding of migration over multiple generations in a developing

country offers the possibility of describing more general patterns of human migration

and of identifying factors that may have influenced migration throughout human

evolution.

Since human migration has had the largest effect on genetic variation (Miró-

Herrans and Mulligan 2013), a better understanding of human migration patterns would

allow more accurate reconstructions of demographic processes. Comparisons of

108

empirical genetic data to simulated genetic variation generated from models that

realistically represent the demographic process under study offer the possibility of

reconstructing prehistoric demographic processes (Beaumontet al. 2002). Values for

migration parameters estimated from human migration patterns, such as the proportion

of the population that is moving, could define some model parameters to generate more

realistic demographic scenarios. The ability to include empirically-informed values to fix

or set ranges on migration parameters increases the probability of identifying the best

model to explain the data.

Evaluating migration patterns in a developing country could provide migration

estimates that are similar to prehistoric population movements. Yemen is a developing

country (Malik 2013) that has a heterogeneous landscape with coastal plains on the

west and south, mountain ranges in the west and desert in the north, thus providing a

fertile setting in which to investigate environmental factors that may have influenced

prehistoric population movements. It also has a patrilocal and patrilineal society with a

primarily shared language and religion (Dresch 1989), which are social factors that

could play a role in migration as well. The migration within a population of mostly

agriculturalists and pastoralists could provide more realistic values of distance and

proportion of migration for prehistoric movements since the advent of agriculture. The

values could also provide informative lower limits for describing the migration of

prehistoric hunter-gatherers, who typically exhibit more movement than agriculturalists

(Hazelwood and Steele 2004).

In this study, we use GPS coordinates from birthplaces and places of residence

across four generations in Yemen to calculate the proportion, the distance and the

109

direction of migration between each generation. We test for differences in these values

between the groups, we identify factors that influence migration patterns, and we

discuss possible effects of the migration patterns on genetic variation. Based on our

results, we provide estimates for the proportion and distance of migration in a

developing country, which can serve to define parameter values for demographic

models against which to test genetic data to reconstruct prehistoric demographic

processes. Our use of empirical data on population movements over four generations in

Yemen provides knowledge that will allow for more accurate reconstruction of

prehistoric processes of migration.

Methods

Samples and Data

In 2007, saliva samples were collected throughout mainland Yemen for genetic

analysis. Data were also collected from each study participant on place of residence,

place of birth, parents’ place of birth and grandparents’ place of birth. Since all sampled

individuals were adults, their current residence was assumed to be a proxy for the

location of the next generation, i.e. their children, therefore providing data for residence

patterns for a fourth generation in the study. For the purposes of this study, the

individuals in each generation were considered independent samples. Location names

for all birthplaces (and place of residence) were translated from Arabic and GPS

coordinates were obtained using Geonames.org. In instances where a town name was

not identifiable in the Geonames database, but the larger district could be identified, a

GPS coordinate was obtained for the centroid of the district. Samples for which town or

district locations could not be determined were removed. Ultimately, the resulting

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dataset contained GPS coordinates for the sampled individual’s place of residence and

place of birth, mother’s and father’s places of birth, and maternal-grandmother’s,

maternal-grandfather’s, paternal grandmother’s, and paternal grandfather’s places of

birth for 351 sampled individuals.

Estimation of Migration

The occurrence of migration was determined by the difference in birthplace or

residence location between generations. A migration event occurred in the sampled

individual’s generation (G1) if the place of residence was different from the birthplace. A

migration in the parental generation (G2) occurred if the parent’s offspring was born in a

different location than the parent’s birthplace (i.e. if the sampled individual’s birthplace

was different from their mother’s or father’s birthplace). Similarly, a migration event in

the grandparental generation (G3) occurred if the parent’s birthplace was different from

the grandparent’s birthplace. Migration events were determined for eight different

groups: female sampled individuals (G1fem), male sampled individuals (G1male), mothers

(G2fem), fathers (G2male), maternal-grandmothers (G3mfem), maternal-grandfathers

(G3mmale), paternal-grandmothers (G3pfem), paternal-grandfathers (G3pmale). The

frequency of migration events was calculated for each of the eight groups (sample sizes

were 70 in G1fem, 281 in G1male, and 351 in each group in G2 and in G3. The observed

frequencies were compared through goodness-of-fit tests.

The age of the sampled individuals ranged from 13 to 69, which meant that each

generation group (G1, G2, G3) essentially included two generation time periods. To

account for the possibility of migration events occurring over different generation time

periods within each generation group, the eight groups were further divided into two age

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groups with a 25 year generation time between them, based on the ages of the sampled

individuals (under and over 40 years old). Only 10% of the samples in any generation

were in the over 40 years old sub-group, suggesting that any difference in migration

event frequencies could be due instead, to the unbalanced sample size; thus no further

analyses were performed with the groups partitioned by age over and under 40 years.

Migration distance was calculated from the geographic distance between

birthplaces/residences in two different generations using the GPS coordinates. G1

migration distances were calculated as the geographic distance between the sampled

individual’s birthplace and place of residence. G2 migration distances were calculated

from the parent’s birthplace and the sampled individual’s birthplace. Migration distances

were calculated for G3 from the difference in grandparent’s birthplace and parent’s

birthplace. The migration distances were compared between sex in each generation

and between generations using Wilcoxon Rank tests and Kruskal-Wallis analysis of

variance.

Different models including generation group, sex, birthplace location (latitude and

longitude) and residence location were tested in logistic regressions to see which model

(and parameters) best explained migration. AIC (Akaike information criterion) were used

to select the best model. Additionally, the migration events were plotted geographically

and the mean direction of the migrations was calculated for each collection site (to

account for sampling) using ESRI ArcMap10.

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Results

The proportion of migrants was calculated from the frequency of migration events

for females and males in three generations (G1fem= 0.314, G1male= 0.267,G2fem= 0.376,

G2male= 0.311, G3mfem= 0.120, G3mmale= 0.111, G3pfem= 0.097,G3pmale= 0.080). Within

each generation, the proportion of migrants between male and female groups was not

significantly different (Figure 3-1). However, more recent generations G1 and G2 had a

significantly larger proportion of migrants than G3 (p=0.0005). The proportion of

migrants for each generation group (males and females combined) was G1=0.276,

G2=0.343, G3=0.102. We calculated a multi-generation proportion of migrants for G3 to

correct for back migration events by determining the number of migration events in

which the grandparents’ birthplace was different than the residence location. This

produced a multi-generation proportion of migrants for G3 of 0.086.

The distance of migration was also calculated for each of the eight groups. G1

and G2 migration distances were significantly larger than G3 (p<2.2x10-16). Density

plots combining the migration distance (including non-migrants) and the frequency of

these distances revealed that G1fem not only had the largest migration distance, but had

more migrations at longer distances (>250km), than the other groups (Figure 3-2).

However, when compared by sex within generations, female distances were not

significantly different from male distances. Summary statistics on migration distances

were calculated on all the individuals and on only migrating individuals (Table 3-1).

Correlation analyses were performed on marital pairs in G2 and G3 to determine

whether marital pairs were moving together and should be considered each a single

group (instead of female and male groups) in further analyses. A low correlation

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coefficient (<0.1) would suggest the marital pair migrations were completely

independent from each other and a high correlation coefficient (>0.9) would suggest that

the marital pairs were moving together and could be treated as one group. G2 had a

significant (p= 2.2x10-16) Spearman’s rho correlation coefficient of 0.589. Maternal

grandparents (G3M) had a rho coefficient of 0.782 (p= 2.2x10-16) and paternal

grandparents (G3P) had a rho coefficient of 0.623 (p= 2.2x10-16). The results showed

there was a moderate and significant correlation between all the marital pairs. These

coefficients suggest that a portion of the marital pairs are moving together, but the

correlations are not high enough to consider the marital pairs as a single group.

Furthermore, the moderate correlation coefficients suggest these values could be due to

post-marital residence dynamics (i.e. females moving with their husbands). Female and

male marital pair distances were plotted and showed that correlated migrations were of

the same distance, which is consistent with marital pairs moving to the same place

(Figure 3-3). These results suggest that many of the marital pairs are moving together.

Out of the 121 migration events in G3, 56% are of marital pairs moving together.

Logistic regression models including different combinations of generation, sex,

birthplace coordinates and residence location coordinates were performed to explain

presence or absence of migration. The model with the lowest AIC included generation,

sex, birth latitude and longitude and residence latitude (Table 3-2). This best model

demonstrated that the probability of migration decreased in G3, decreased in males

(consistent with females moving with their husbands’ family) and decreased with a more

eastern birthplace, in comparison to G1fem. The probability of migration increased in G2

and increased with more northern birthplaces and places of residence. However, of

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these factors, only G3 had a coefficient above one, suggesting that G3 contributes the

most to the probability of migration, and specifically, belonging to the G3 generation

decreases the probability of migration.

While birthplace latitude, birth place longitude and residence location latitude had

small coefficients, their statistically significant contribution to migration probability

suggests that there could be factors “pushing” and “pulling” individuals to move (Lee

1966). The birthplace and residence coordinates were used to plot the directionality of

migration and assess whether or not there was a pattern in directionality that could

explain the “pushing” and “pulling” effects (Figure 3-4). The mean migration direction

was calculated from these migration vectors for each sample collection site (to account

for the effect of sampling). While the mean migration directions seem to have a

southbound tendency, the circular variance (which describes the variation associated

with the directional mean, where values close to 0 represent a similar direction for all

migration vectors and values close to 1 correspond to vectors in all compass directions)

was moderate to high for all collection sites, ranging from 0.675 to 0.867 (Table 3-3),

suggesting movement in all directions.

The mean migration directions were further calculated by collection site for each

generation group (Figure 3-5 and Table 3-4). Within generation groups G2 and G3,

female and male migration directions were similar in many collection sites, supporting

the idea that marital pairs moved together. The mean migration lengths were generally

larger for G1 and G2 than for G3, reflecting the decreased migration distance in G3. For

each collection site, the mean migration directions varied greatly between generation

groups, suggesting a level of stochasticity to the migration directions. When the mean

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migration directions were spatially compared to geographic features (i.e. elevation, land

use/land cover, and watershed), no pattern arose (data not shown), further supporting

stochasticity in the directionality of migrations.

Discussion

Our study helps elucidate human migration patterns using empirical population

movement data across multiple generations in Yemen. Our results show that the

proportion and distance of migration increased in recent generations. While movement

in the recent generations may reflect social and political changes that have occurred in

the last 50 years (Federal-Research-Division 2008), the reduced movement in the

oldest generation most likely reflects a lack of technology and associated mobility (Lee

1966), suggesting that this generation may be most representative of prehistoric

movements. The correlated distance and directionality of migrations within marital pairs

illustrate the prevalence of post-marital residence dynamics. The significance of

birthplace and residence locations in the probability of migration, but lack of pattern in

the direction of migration, suggest a degree of stochasticity in terms of human

movements. These cultural factors affecting modern movement have most likely played

important roles in prehistoric migrations as well, suggesting that the migration patterns

and estimates described in our results provide information to make more accurate

prehistoric inferences.

Patrilocality and Genetic Signals

Moderate correlation coefficients for G2 and G3 marital pairs and the plot of

migration distances in marital pairs suggests that pairs are moving together and the

correlation seems to strengthen with increasing distance (Figure 3-4). Our best fit

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model, which shows that females are more likely to move than males when accounting

for other contributing variables, suggests that patrilocality (females moving to their

husbands’ family) may be driving the movement. This is supported by ethnographic

accounts that ~90% of the Yemeni population is patrilocal (Weir 2007). However, the

coefficient of the effect that being male has on the probability of migration is low (-0.240)

and within each generation the migration distance is not significantly different between

females and males. This suggests that males are only slightly less likely to migrate than

females and that males are travelling similar distances compared to females. In a

perfect patrilocal post-marital residence dynamic, males move short distances and stay

close to their family, while females move longer distances to be near their husbands’

family. The similar migration distances between females and males suggest there is not

strict patrilocality in Yemen and that other factors are influencing male movement. This

interpretation is supported by ethnographic data showing that males may occasionally

migrate large distances from their birthplace for socioeconomic or political reasons

(Dresch 1989; Weir 2007). Our data show that male migration has occurred more often

in the last 50 years (as shown by the increase in dispersal in G1 and G2 relative to G3).

The similar migration distances between females and males and consequent

imperfect patrilocality may be the principal contributor to the lack of association

observed between geographic and genetic distance in male lineages (i.e. Y

chromosome) in Yemen (Raaumet al. 2013). Females moving with their husbands

(Figure 3-3) may also explain why shared mitochondrial DNA (mtDNA) haplotypes have

been found between east and west Yemen, over 750km apart (Cernyet al. 2008).

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Patterns of Migration

Logistic regressions were used to test the effect of birthplace and residence

locations on the probability of migration in order to assess whether there were factors

“pushing” or “pulling”, respectively, individuals to a new location. Birthplace latitude and

longitude and residence latitude were significant parameters in explaining the probability

of migration. Given this result, birthplace and residence coordinates were used to plot

migration directions and determine whether a pattern could be observed that could

account for the effects of birthplace and residence locations. Mean migration directions

were calculated by collection site (to account for sampling bias) to summarize the

overall migration direction patterns (Figures 3-4 and 3-5 and Table 3-3). While the mean

migration directions had a southbound trend, the circular variances were large,

suggesting overall dispersal in multiple directions. Additionally, mean migration

directions calculated by collection site for each generation showed that the collection

sites had different mean directions between generations, further supporting migration in

multiple directions. We also spatially compared the migration directions with different

geographic features (i.e. elevation, land use/land cover, and watershed) to identify

environmental factors that may influence migration direction. We found no pattern

associated with the migration directions and the geographic features. These results

suggest that while there may be factors “pushing” and “pulling” individuals to move, the

overall direction of migration has little or no pattern. These results contrast with island

migration patterns (e.g. Polynesia) where migration direction has a pattern from larger

islands to smaller islands (Clarket al. 2006; Joblinget al. 2004; Kirch 1980). Given that

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continental migrations are less limited by the carrying capacity of new colonization sites

than islands, this result is not surprising.

While island migrations have been well described by ethnographic and

archaeological data (Clarket al. 2006; Kirch 1980), continental migration patterns have

been primarily addressed through genetic data. Genetic evidence has suggested that

overall continental migrations have a linear pattern, such that increasing distance from

Africa is correlated with decreasing genetic diversity (Liet al. 2008; Ramachandranet al.

2005). Our data suggest that the smaller scale migrations (Figures 3-4 and 3-5) that led

to this continental pattern may have been less directed. Our results are consistent with

the idea that smaller migrations, which consider the movement of individuals, tend to be

more random, while larger scale movements focused on populations have more

directionality associated with them (Hazelwood and Steele 2004; Skellam 1951).

Empirical Estimates of Migration

Comparisons of proportion of migrants and migration distances across four

generations showed that migration was significantly lower around fifty years ago (G3).

Furthermore, the best fit model to explain the probability of migration shows that G3 has

not only the biggest effect, but a negative effect on the probability of migration (i.e.

belonging to G3 decreases the probability of a migration event). Spatial patterns of

migration in G3 (Figure 3-5c) show, that while there are some long migration distances,

on average, the distances are short. Yemen’s less-developed state and poor

transportation infrastructure (Federal-Research-Division 2008) combined with the

significantly reduced migration in G3, suggests that our data from the G3 generation

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can provide empirically-based estimates of migration frequency and distance that are

reflective of prehistoric movements.

We calculated the mean and median migration distances for G3 (Table 3-1). The

mean migration distance for all individuals (i.e. including both individuals who migrated

and those who did not) was 10km. The mean and median distances for migrating

individuals were 96km and 26km, respectively. The shorter migration distance values

(10km and 26km) are within the range of previously reported average migration

distances (Ammerman and Cavalli-Sforza 1984; Markset al. 2012; Wijsman and Cavalli-

Sforza 1984). These mean migration distances potentially demarcate the distances

within which post-marital residence patterns (patrilocality in the case of Yemen) have a

distinguishable effect on genetic structure (Markset al. 2012; Raaumet al. 2013).

Beyond the mean distance is probably where sex-biased migration is less detectable.

The median value (26km) is within the range of 10-30km that Ammerman and

Cavalli-Sforza (1984) believe is plausible for migration distance in agriculturalist

societies. Dividing 26km by a generation time of 25 years results in a migration speed of

1.04km/year. This value is comparable to the 1km/year migration speed for the Neolithic

transition estimated from archeological data (Hazelwood and Steele 2004; Pinhasiet al.

2005). These similarities suggest that the median distance is representative of migration

distances of agriculturalist groups.

A migration speed (3.84km/year) from the mean value for migrating individuals

(96km) falls within the broad range of hunter-gatherer migration speeds calculated from

archeological evidence. Fort et al (2004) estimated the speed of the hunter-gatherers’

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recolonization of northern Europe after the last glacial maxima between 0.7 and

1.4km/year. Hamilton and Buchanan (2007) estimated a speed of 5-8km/year for the

colonization of North America, while Hazelwood and Steele (2004) obtained estimates

of 6-10km/year. Because our value is intermediate from the values of these studies, it

provides a distance that may be more generally applicable to other migration processes,

particularly de novo colonization migration distances by hunter-gatherers. This can be

seen when we compare our estimate with Macaulay et al’s (2005) inferred migration

speed for the colonization of Southeast Asia. Based on founder time estimates from

Eurasian and Australasian mtDNAs and the distance between India and Australasia,

Macaulay et al infer a migration speed of 4km/year. Our empirical estimate of 3.84

km/year supports that the migration process they proposed, is in fact plausible.

While migration distance has been estimated through different approaches, few

studies have estimated the proportion of migrants (Boattiniet al. 2007; Markset al. 2012;

Mortonet al. 1971; Woodet al. 1985). We calculated the proportion of migrants for G3 to

be 0.102 (or 0.086 when adjusting for back migration in the four generations). These

values are smaller than the 0.4 proportion of migrants that we calculated from Wood et

al’s (1985) dataset from migration between parishes in Papua New Guinea and the

0.366 estimate obtained from the calculation of individuals that were not born in the

same parishes as their parents in La Cabrera, Spain (Boattiniet al. 2007). These

differences from our estimates seem reasonable as Wood et al’s estimates are from a

more recent population (and are closer to our G1 and G2 estimates) and Boatinni et al’s

estimates are from a more developed country. Our estimates are somewhat larger than

the 0.032 proportion of migrants into the island of Pingelap in Micronesia by Morton et al

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(1971). However Morton et al’s value is close to our adjusted proportion of migrants

(0.087). We also calculated the maximum and average number of individuals moving

between the same locations, for a proportion of migrants of 0.0036 and 0.0011,

respectively. These lower values are consistent with findings by Deshpande et al

(2009), where the genetic estimates of proportion of migrants (i.e. migration rates) for a

world-wide colonization model is less than 0.01. Our values are similar to findings by

Miró-Herrans and Mulligan (2013), where the proportion of migrants exchanged

between African and non-Africans populations was 0.001 and similar to the migration

rate for non-African populations (1.5x10-3) obtained by Cox et al (2008). The similarity of

our estimates with those of other migration studies, suggests that our values can be

used to generate testable models for prehistoric reconstruction.

Application of Migration Estimates in Prehistoric Demographic Modeling

Model-based approaches for inferring prehistoric processes from genetic

variation are becoming increasingly popular (Marjoram and Tavaré 2006). These

approaches, such as approximate Bayesian computation (Beaumontet al. 2002), require

the generation of explicit demographic models to compare to empirical data. Including

specific values for known parameters and informative ranges of values for unknown

parameters increases the probability of identifying the best model to explain the data.

The results from our study provide estimates that can be used to fix or set ranges on

parameters related to migration, such as gene flow or founding population size, so that

other parameters of interest can be addressed in greater depth, e.g. time of a

demographic event. For example, the maximum and average proportion of individuals

moving between the same locations (0.0036 and 0.0011) can be used to define gene

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flow (or migration rates) between populations stretching from southern Asia to northern

Africa to create simulated DNA for models that address the back-migration into Africa.

The larger migration values (0.102 or 0.086) could be used to define the founding

population sizes for each new population. Defining these parameters would allow for an

in-depth exploration of the timing of the back-migration.

Additionally, our results provide estimates to generate more geographically

explicit models. Our mean and median migration distances (96km and 26km) provide

estimates for the distance between populations, particularly for large scale movements,

such as the back-migration from southern Asia. The migration distance between each

population would define the number of populations to be simulated for the region under

study. For example, a distance of 100km between each population would require ~70

populations between southern Asia and northern Africa (approx. 7,000km).

Understanding the possible distances involved in large scale movements also helps us

determine how rapidly a migration could have occurred and how levels of gene flow

may have been affected between the populations.

The lack of migration directionality in our results suggests that explicitly including

stochasticity or multidirectionality when describing the movement between populations

might more accurately reflect the large-scale migration process. For example, the back-

migration to Africa probably included movement through established populations, where

the migrants settled in some of the established populations, but not in others. Therefore,

a lattice stepping-stone migration model, that includes some randomness in when a

migration occurs and between which populations, might better reflect this migration

process.

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Our results show there is over a 58% correlation between female and male

movement in marital pairs, in which more pairs move together with increasing distance.

Additionally, we show that 56% of migration events in G3 were by marital pairs. This

means that at least 50% of the migrants have a 1:1 female to male ratio. Even if the

remaining 50% of migrants are only female or male, the ratio is at most 3:1. These

results argue for, at most, a 3:1 ratio (for either sex) of sex-biased migration for

migrations at short distances, where post-marital residence has a larger effect on

population structuring (Markset al. 2012; Raaumet al. 2013). Alternatively, for longer

migrations, such as the migration from southern Asia to northern Africa, a female to

male ratio closer to 1:1 may more accurately model demographically balanced

populations that would have been reproductively self-sustaining.

In this study, we have analyzed empirical data on migration patterns over four

generations of human populations in Yemen in order to gain insight into the factors that

influence migration, and specifically may have affected prehistoric movements

throughout human evolution. We have addressed the effect of these factors on genetic

variation and provided empirical estimates for migration-related parameters that can be

used to generate demographic models in model-based methods of prehistoric

reconstruction. Our empirical estimates of generation G3 have provided values for

proportion of migrants, with values ranging from 0.102 or 0.086 proportion of overall

migration, to 0.0036 or 0.0011 proportion of migrants between two specific populations.

We have also provided migration distances (96km and 26km, mean and median,

respectively) that can be used define the distance between populations and therefore

the number of populations for the area under study. The findings from this study shed

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light on human migration patterns and are intended to enable more accurate

reconstruction of the demographic processes that characterized human evolution.

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Table 3-1. Summary statistics for migration distances.

Median and mode for “All individuals” was zero for all groups. Values in parenthesis represent sample size

All individuals Mean ±SD Median Mode G1 (351) 69 249 0 0 G1Female (70) 156 405 . . G1Male (251) 48 186 . . G2 (702) 72 265 . . G2Female (351) 73 269 . . G2Male (351) 72 262 . . G3 (1404) 10 66 . . G3Female (702) 9 61 . . G3Male (702) 10 71 . .

Migrating individuals Mean ±SD Median Mode G1 (97) 251 424 81 103 G1Female (22) 497 601 103 103 G1Male (75) 179 328 75 103 G2 (241) 211 419 29 103 G2Female (132) 193 411 23 103 G2Male (109) 232 430 44 103 G3 (143) 96 188 26 26 G3Female (76) 82 169 24 17 G3Male (67) 111 208 28 26

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Table 3-2. Best model to explain probability of migration.

p<0.04 for all factors. The probability of migration decreases in G3, decreases in males, and decreased with a more eastern birthplace, in comparison to G1fem. The probability of migration increases in G2 and increases with more northern birthplaces and places of residence.

Factor Coefficient Intercept -1.924 Generation:G2 0.256 Generation:G3 -1.244 Sex:Male -0.240 Birth Latitude 0.221 Birth Longitude -0.121 Residence Latitude 0.225

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Table 3-3. Estimates for the direction of migration in each collection site across all three generation groups.

aMean directional angle is measured clockwise from due North. bMean distance is measured in decimal degrees.cCircular variance describes the variation associated with the directional mean, where values close to 0 represent a similar direction for all migration vectors and values close to 1 correspond to vectors in all compass directions

Collection site Mean directional anglea Mean distanceb Circular

variancec

Abyan 103.19 1.659 0.676 Al Bayda 107.87 1.405 0.806 Al Hudaydah 321.06 1.814 0.867 Al Mahra 161.96 2.282 0.833 Amran 120.51 0.995 0.704 Dhamar 62.78 0.370 0.758 Hadramout 171.57 3.953 0.675

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Table 3-4. Directional means estimates for each group by collection site.

aMean directional angle is measured clockwise from due North. bMean distance is measured in decimal degrees.

Group Generation Collection site Mean directional anglea

Circular variance

Mean distanceb

G1female G1 Al Bayda 20.676 0.045 0.174 G1female G1 Al Hudaydah 171.328 0.471 5.307 G1female G1 Al Mahra 149.404 0.714 3.869 G1female G1 Hadramout 153.945 0.023 9.225 G1male G1 Abyan 93.105 0.513 3.115 G1male G1 Al Bayda 282.164 0.914 3.400 G1male G1 Al Hudaydah 98.593 0.603 1.960 G1male G1 Al Mahra 213.058 0.494 0.956 G1male G1 Amran 151.418 0.640 1.382 G1male G1 Dhamar 79.936 0.522 0.515 G1male G1 Hadramout 155.123 0.430 2.441 G2female G2 Abyan 93.264 0.675 1.525 G2female G2 Al Bayda 94.257 0.773 1.335 G2female G2 Al Hudaydah 329.910 0.795 1.620 G2female G2 Al Mahra 230.602 0.853 3.961 G2female G2 Amran 112.443 0.645 0.931 G2female G2 Dhamar 251.241 0.781 0.290 G2female G2 Hadramout 179.180 0.895 4.442 G2male G2 Abyan 116.708 0.539 2.298 G2male G2 Al Bayda 83.530 0.827 2.226 G2male G2 Al Hudaydah 6.450 0.765 2.635 G2male G2 Al Mahra 285.254 0.926 3.355 G2male G2 Amran 109.280 0.400 0.675 G2male G2 Dhamar 243.264 0.895 0.540 G2male G2 Hadramout 284.876 0.952 3.493 G3female G3 Abyan 106.306 0.522 0.200 G3female G3 Al Bayda 135.958 0.631 0.255 G3female G3 Al Hudaydah 264.634 0.643 0.148 G3female G3 Al Mahra 114.916 0.698 0.973 G3female G3 Amran 294.408 0.765 1.258 G3female G3 Dhamar 48.563 0.530 0.232 G3female G3 Hadramout 181.400 0.006 3.917 G3male G3 Abyan 281.966 0.846 0.479 G3male G3 Al Bayda 141.926 0.633 0.371 G3male G3 Al Hudaydah 303.292 0.583 0.339 G3male G3 Al Mahra 126.886 0.757 1.427 G3male G3 Amran 252.032 0.689 1.334 G3male G3 Dhamar 61.057 0.557 0.292 G3male G3 Hadramout 181.400 0.006 3.917

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Figure 3-1. Proportion of migrants by sex for each generation group. P-values are

shown for goodness-of-fit tests between groups.

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Figure 3-2. Density plots combining migration distance and frequency of the distance for each group. Wilcoxon Rank tests were performed for G1 and G2 within generation comparisons and Kruskal-Wallis tests were performed for G3 within generation comparison and between generation comparisons. P-values are shown for the respective tests.

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Figure 3-3. Plot of migration distances for marital pairs. G2 (red circle), G3M (green triangle), G3P (blue cross). The solid line shows a theoretical 1:1 relationship, where females and males have the same dispersal distance. The inner box shows a close-up of the relationship for distances less than 250km.

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Figure 3-4. Migration direction vectors and mean migration direction (large arrows) by

collection site over all three generations.

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Figure 3-5. Migration direction vectors and mean migration direction (females – light

gray arrows, males – dark gray arrows) for each collection site by generation group. A) G1. B) G2. C) G3.

A

B

C

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CHAPTER 4 CONCLUSION

Humans’ facility for dispersal and continuous movement has generated elaborate

evolutionary histories throughout different regions of the planet. Some regions have

experienced greater amounts and more intensive migration than others. The region

from northeast Africa, ranging from the Horn of Africa (includes Ethiopia, Somalia,

Djibouti, and Eritrea) to Egypt, through the Arabian Peninsula to western Asia

(somewhere around Iran) has been the center of various major migrations in human

evolutionary history. East Africa (including the Horn of Africa) is argued to have been a

refugia ~70kya (Compton 2011; Scholzet al. 2007) and the area of origin of mtDNA

haplogroup L3 (Atkinsonet al. 2009; Soareset al. 2012). L3 arose in east Africa 60-

80kya and was quickly followed by population growth (Atkinsonet al. 2009) and

migrations out of Africa and within Africa (Soareset al. 2012). Haplogroups M and N,

which are non-African branches of L3, arose during the process out of Africa, or

immediately thereafter somewhere in western Asia, 40-70kya (Forster 2004). The

presence of haplogroup M1 in northern Africa supports a migration back to Africa from

southern Asia 35-45kya (Gonzalezet al. 2007; Olivieriet al. 2006). This “out of Africa”

region (OAR) is posited to have had various local refugia during the latter part of the

Last Glacial Maxima (LGM) from which a local expansion occurred starting 12-15kya

(Al-Abriet al. 2012; Cernyet al. 2011; Roseet al. 2013). Commercial exchange may have

led to local migrations between Ethiopia and the southern part of the Arabian Peninsula

since ~9kya, as well as between Ethiopia and the Levant (which includes countries off

the east coast of the Mediterranean Sea) since ~3kya (Boattiniet al. 2013; Paganiet al.

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2012). A more recent migration occurred in the 7th century AD, with the expansion of

Islam in the Arabian Peninsula and North Africa (Hennet al. 2012; Nebelet al. 2002).

Each of these demographic processes generated a unique pattern of genetic

variation in the existing population. Every new migration wave introduced the new

genetic variation into the OAR. After about 70ky of modern human occupation of this

region, the combination of these demographic processes has created a very complex

pattern of genetic variation. Reconstructing human evolutionary history in this region

from the genetic data presents the challenge of inferring different ancient processes

from the genetic variation generated by the combined demographic processes. The

challenge is greatest when trying to reconstruct older processes, such as the migration

out of Africa, from current patterns of genetic variation.

The complexity of the processes that have occurred in the region can be

disentangled, in part, by generating simulated patterns of genetic variation for

demographic scenarios that might realistically represent the demographic processes

under study and testing genetic data against these models (i.e. approximation model-

based methods). Hypothesis models can be developed to describe a single process,

such as the migration of modern humans out of Africa, or multiple processes (e.g.

including numerous migrations). To generate informative hypothesis models that will

allow clear interpretation of the empirical data, it’s critical to identify which hypothesis

models generate distinguishable differences in the genetic variation and how each

demographic parameter is contributing to the genetic variation.

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The proportion of genetic variation explained by each parameter informs on how

accurately the parameters can be estimated. A parameter that explains a larger portion

of the genetic variation is more likely to be accurately estimated, than a parameter that

explains much less of the variation. A parameter that explains a large portion of the

genetic variation can cause many of the demographic scenarios to generate similar

patterns of genetic variation, reducing the probability of accurately estimating the value

for the parameters that explain less of the genetic variation. The individual contribution

of each demographic parameter to the total genetic variation can be calculated through

the comparison of demographic scenarios. It is important to identify the parameters that

explain more of the variation to determine the type of additional data (i.e. genetic or

non-genetic) that would improve the estimation of the less contributing parameters.

Defining a range of realistic values, calculated from these additional sources of data, for

parameters that explain a larger proportion of the genetic variation can reduce the

number of demographic scenarios tested against the empirical genetic data and lead to

the selection of only one hypothesis model that “best” explains the data. This, in turn,

leads to the improved estimation of parameters that explain less of the genetic variation.

My results show that for the migration of modern humans out of Africa the

colonization size and rate of gene flow explain most of the genetic variation (Miró-

Herrans and Mulligan 2013). Therefore, changes in the values of these parameters can

cause significant changes on the patterns of genetic variation. The range of values that

has been proposed for the size of the migrating population, from 1% to 33% (Atkinsonet

al. 2008; Deshpandeet al. 2009; Tenesaet al. 2007), can have vastly different effects on

genetic variation. A population that is 1% of the original population can have a

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significant reduction in genetic variation and can quickly become genetically dissimilar

to the original population. A population that is 30% of the original population can

maintain similar levels of genetic variation as the original population. While the effects of

the extreme values for colonization size are fairly well understood, the effects of more

intermediate, and probably more realistic, values on genetic variation are less obvious.

My results show that scenarios with colonization size greater than 10% usually don’t

generate distinguishable patterns of genetic variation, so the values for other

parameters can’t be accurately estimated. Similarly, scenarios with migration rates

greater than 10-3 or less than 10-3 generate similar patterns of genetic variation, limiting

the inference of other parameter values. Therefore, it becomes a priority to identify

whether a realistic value for colonization size is around 10% and for migration rate is

around 10-3, in order to generate hypothesis scenarios in which the values for the other

parameters, such as the time for the migration out of Africa, can be estimated.

The comparison of patterns of migration across four generations in Yemen

(Chapter 3), show that the grandparents’ generation had the lowest levels and most

restricted patterns of migration. This suggests that values for migration parameters

estimated for this generation are most representative of migration parameter values for

prehistoric demographic processes. Therefore, the empirical values calculated for the

proportion of migrants can serve to narrow migration related parameters in hypothesis

models of prehistoric processes, and more specifically for the model of migration out of

Africa. The overall proportion of migrants for the grandparents’ generation was 0.102 (or

0.086 when adjusting for back migration in the four generations) and the maximum and

average number of individuals moving between the same locations was 0.0036 and

138

0.0011, respectively. The overall proportion of migrants (0.102 or 0.086) could reflect

the number of individuals moving at a given time, such as might occur during a

colonization event. Although in my study the most supported colonization size was 1%,

when comparing Fst values for the simulated scenarios with Fst values of African versus

European and African versus Asian, a colonization size of 10% also had strong support.

Furthermore, using model-based methods with a serial founder event model for out of

Africa and nuclear data, Deshpande et al (2009) found the colonization size to be 0.09

to 0.18 of the population. The number of individuals moving between the same locations

(0.0036 and 0.0011) could represent the migration rate between adjacent populations.

Cox et al (2008) report a rate of 1.5x10-3 for non-African populations and 2.7x10-4 for

African populations and Gravel et al (2011) suggest a rate of 1.5x10-4 between the

African population and the non-African population that gave rise to European and Asian

populations. In contrast, Deshpande et al report a higher rate of migration between

adjacent populations of up to 10-2. The results from my simulated demographic

scenarios support a rate of 10-3, which was also shown to be a transition point from

which it should be possible to distinguish between scenarios on either side (GF>10-3 or

GF<10-3). Together the results from my studies suggest, that for human demographic

reconstructions, migration parameters can be narrowed to a colonization size of (or

around) 0.08-0.1 and migration rate of 10-4-10-2 between adjacent populations. These

values for migration parameters offer the best possibility of accurately accounting for the

effects of migration and identifying the values for other parameters of interest.

The demographic scenarios for the model out of Africa included two values for

the timing of the migration out of Africa (50kya and 100kya), representing the most

139

extreme values reflected in the literature, with the largest difference between the values

(Miró-Herrans and Mulligan 2013). The timing of the population fission and migration

out of Africa is of great interest in many fields. The wide range of values for when

humans left Africa estimated from mtDNA and NRY overlap with multiple climate

stages. These stages, as defined by oxygen isotopes, have alternating cool and warm

climates (McDermott 2004). The state of the climate when humans left Africa has

implications for human behavior, suggesting, for example, whether humans migrated to

new areas while the climate made movement easier or whether they migrated in search

of new areas because the climate was unsuitable. Accurately identifying the timing for

the migration out of Africa, thus, has implications for understanding human behavior.

The result of the comparisons of the demographic scenarios showed that

scenarios of 50kya could not generally be distinguished from scenarios of 100kya based

on the genetic variation of mtDNA. This inability to distinguish between 50kya and

100kya occurs most likely because of the small effects of time on the genetic variation

of human mtDNA (Miró-Herrans and Mulligan 2013). These results suggest that

additional genetic and non-genetic data could improve the ability to estimate the time of

the migration of humans out of Africa. In a recent study of the population history of the

KhoeSan in Africa, Veeramah et al (2012) calculated the time of population fission

between non-Pygmies, Eastern Pygmies and Western Pygmies and found the non-

Pygmy/Pygmy population split occurred at ~49kya and the Eastern/Western split

occurred at ~32kya. The identification of times of two population fissions within a 17ky

window of time demonstrates that time can be more accurately estimated with the use

of multiple genetic markers. Advances in sequencing technology are now allowing us to

140

generate large quantities of genetic markers for multiple individuals at affordable prices.

The increase in genetic data, along with the incorporation of demographic data, such as

the migration estimates previously described, increase the possibility of more accurate

estimates of realistic time values from demographic reconstructions. This will allow the

identification of critical time points in human evolution and contribute to the overall

understanding of human behavior.

The identification of the most informative summary statistics also contributes to

the improvement of demographic reconstructions. Approximation approaches using

summary statistics require a small number of informative summary statistics to avoid the

situation where the comparison of simulated datasets to the empirical dataset for each

summary statistic excludes so many simulated scenarios that it is impossible to make

inferences about the empirical data (Beaumontet al. 2002; Hamilton 2005; Wegmannet

al. 2009). Through the comparison of the developed demographic scenarios by multiple

summary statistics, I have identified summary statistics that are informative at

summarizing genetic variation of specific parameters (Miró-Herrans and Mulligan 2013).

Fst summarizes the individual effects of gene flow and time and the combined effect of

gene flow and time, while number of singletons optimally summarizes the effect of

colonization time (Table 2-3). Tajima’s D summarizes the combined effects of

colonization size and gene flow, as well as the combined effects of gene flow and time.

These results suggest that the combined use of these three summary statistics (i.e. Fst,

number of singletons and Tajima’s D) offers the possibility of more accurate

reconstructions of human demographic processes.

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The results presented suggest that the out of Africa model developed for this

dissertation, while simple, provides a useful model that can be refined to further

investigate the process of modern humans out of Africa. By incorporating the results

from the empirical patterns of migration, a more geographically explicit model can be

generated that can serve to address the specific route humans took during their

migration out of Africa. Using the framework presented in this dissertation, different

demographic scenarios can be compared to determine whether demographic scenarios

with different routes can be distinguished and which scenarios present informative

hypotheses to compare to empirical data.

In addition to the complexity described thus far, the expansion out of Africa is

further debated as to whether it occurred in one migration wave or two waves and which

route was used. Using traditional approaches of demographic inference from uni-

parentally inherited markers (i.e. mtDNA and NRY), those who propose two routes

suggest one wave went South through the Horn of Africa, across the Red Sea, and

across the Arabian Peninsula 59-69kya, possibly giving rise to the Asian population,

and one wave went North through the Levant 39-53kya, possibly giving rise to the

European population (Luiset al. 2004; Maca-Meyeret al. 2003). Those who propose

one migration posit either a Southern route 60-80kya (Forster 2004; Metspaluet al.

2004) or a Northern route 40-50kya (Rowoldet al. 2007). Additionally, it is unclear

whether the haplotypes that characterize non-African populations, and are lacking in

African populations, diverged in Africa right at the time of departure or after the new

population migrated out of Africa (Forster 2004).

142

Multiple other studies have addressed the migration out of Africa using

approximation model-based methods (Deshpandeet al. 2009; Gravelet al. 2011;

Gutenkunstet al. 2009; Liuet al. 2006; Ramachandranet al. 2005). Two main models

have been used among these studies, a serial founder event model (Deshpandeet al.

2009; Liuet al. 2006; Ramachandranet al. 2005) and a three population model (Gravelet

al. 2011; Gutenkunstet al. 2009). The serial founder event models have described a

one-dimensional stepping stone model for the movement from Eastern Africa. They

assume a land-based movement, leading to a colonization through the Levant and then

linearly across Asia and to the Americas. An advantage of this approach is that it offers

the possibility of incorporating some ecological parameters such as the size of each

population and the carrying capacity for each population (i.e. the size of the population

before a new colonization occurs). These studies demonstrate that a serial founder

event model best explains the migration out of Africa. The three population models

assumes a population fission between African and non-African populations and a

second fission between European and Asian populations. An advantage of this

approach is that it offers the possibility of two dimensions of movement, thus the

migration between the three populations can be estimated. The goal of these migration

studies has been to describe models for humans’ world-wide colonization, not the

specific process of humans moving from Eastern Africa to Western Asia. Therefore,

they assume a single migration wave out of Africa and do not consider the demographic

scenarios that test the one wave and two wave models for the migration out of Africa.

By integrating the findings from these studies and the results from my analyses,

a geographically explicit model can be developed that allows the comparison of a single

143

northern migration (NM), a single southern migration (SM), and a two wave northern

and southern migration (NSM) out of Africa. The use of a two-dimensional stepping-

stone model (Kimura and Weiss 1964) allows for serial founder events to occur in two

dimensions and offers the advantages of the two out of Africa models previously

described. This two-dimensional model creates a lattice of populations that can be

overlayed onto geographic boundaries extending from eastern Africa (from the Horn of

Africa to Egypt), across the Arabian Peninsula, and to Western Asia.

The empirical distance calculated for mean distance of migrating individuals

(96km) was identified as a reasonable distance for migration of hunter-gatherers in

Chapter 3. Thus, if hunter-gatherers move ~100km to a new population, the size of each

population can be defined as being 100x100km. The distance also defines the number

of populations that might have realistically been colonized across the geographic

boundaries. Starting the migration from Addis Ababa, Ethopia (Deshpandeet al. 2009;

Liuet al. 2006; Ramachandranet al. 2005) and ending somewhere in Iran, a northern

migration would require more population colonizations, than a southern migration. The

number of populations can serve as a parameter that distinguishes the NM from the

SM.

Programs such as SPLATCHE (Curratet al. 2004) allow a cost to be defined

across the geographic boundaries to define the difficulty, and therefore the probability,

of a specific area to be traversed during migration. Alternative demographic scenarios

with different geographic costs would allow the same geographic model to be tested for

the different hypothesized routes. For example, to define the NM, a high cost can be

assigned to the area of the Red Sea, such that the migration occurs through the North.

144

Alternatively, the populations North of Addis Ababa can be assigned a cost that requires

the migration to cross the Bab-el Mandeb Strait, which was the narrowest part of the

Red Sea (Baileyet al. 2007), to design an SM route. Additionally, costs could be

assigned to the northern populations and the Red Sea area to generate patterns of

genetic variation for the NSM two wave demographic scenarios. The cost map can also

be used to describe the Arabian Peninsula to define the more likely path.

The results of the migration patterns in Chapter 3 illustrate that there is some

stochasticity in the direction of migration. This stochasticity can be incorporated in the

geographic model to account for movement across large continental areas, such as the

Arabian Peninsula. By defining a number of migrants, based on realistic migration rates

identified as optimal in this dissertation (10-4-10-2), in a migration model that draws from

a multinomial distribution to assign those migrants to the adjacent populations (also

available in SPLATCHE), each adjacent population receives a different number of

migrants per generation that is representative of the realistic migration rates. This

approach, along with the cost map, would generate demographic scenarios that account

for the uncertainty of the migration process across the Arabian Peninsula.

The ability to define additional demographic and ecological parameters increases

the possibility of estimating the time of the migration out of Africa, particularly as it

applies to the two migration waves. The realistic colonization rates identified in this

dissertation (0.08-0.10) can be incorporated. The population growth rate can be defined

as a logistic growth rate with a rate of 1.8 (Deshpandeet al. 2009; Liuet al. 2006;

Ramachandranet al. 2005). The optimal carrying capacity has been estimated to be

between 600 and 1200 (Deshpandeet al. 2009; Liuet al. 2006).

145

The time of migration(s) out of Africa is of great interest, as the timing primarily

defines the two migration waves. Analyses of nuclear data have estimated the migration

out of Africa at ~50kya, with a 95% confidence interval of 40-70kya (Fagundeset al.

2007; Gravelet al. 2011; Gronauet al. 2011). Hypothesis scenarios with different time

intervals for each route can be defined in which the NM occurs between 40-55kya, the

SM occurs 50-80kya, and the NSM has two time intervals of 40-55kya and 50-80kya

(50kya is incorporated into all scenarios to include the fact that 50kya is the most likely

time that has been estimated for the migration out of Africa). The overlap in time

intervals suggests that estimating the time of the migration out of Africa, particularly if

there were two migrations at different times, presents the biggest challenge for

reconstructing the migration out of Africa. The combination of different time intervals,

geographically distinct scenarios, and realistic demographic parameters offers the

greatest possibility of generating distinct hypothesis scenarios for the NM, SM, and

NSM routes that are informative for accurately reconstructing the migration out of Africa.

The considerations described above offer the possibility of generating

demographic scenarios that most accurately represent the different scenarios for the

migration out of Africa. Future studies comparing these scenarios will allow us to identify

whether the patterns of genetic variation generated from migration through the Northern

and Southern routes can be distinguished, as well as identify which scenarios are

distinguishable and most informative. Following the approaches in Liu et al (2006),

where they compared data from simulated populations with data from empirical

populations that corresponded to the same geographical locations, the informative

146

hypothesis scenarios can then be compared to the empirical data to test which

migration scenario (NM, SM, or NSM) best explains the migration out of Africa.

The revised model presented for the migration out of Africa illustrates how

genetic and non-genetic data can be incorporated to improve human demographic

reconstruction. Overall, this dissertation demonstrates how integrating data from non-

genetic disciplines can enhance our ability to make inferences from genetic data and

improve our interpretations of prehistoric demographic processes. Interdisciplinary

approaches, such as I have described in this dissertation, will be essential as we

continue to move forward to unravel the evolutionary history of different species.

147

LIST OF REFERENCES

Al-Abri A, Podgorna E, Rose JI, Pereira L, Mulligan CJ, Silva NM, Bayoumi R, Soares P, Cerny V 2012. Pleistocene-Holocene Boundary in Southern Arabia from the Perspective of Human Mtdna Variation. Am J Phys Anthropol 149: 291-298.

Ammerman AJ, Cavalli-Sforza LL. 1984. The Neolithic Transition and the Genetics of Populations in Europe. Princeton, New Jersey: Princeton University Press.

Atkinson QD, Gray RD, Drummond AJ 2009. Bayesian Coalescent Inference of Major Human Mitochondrial DNA Haplogroup Expansions in Africa. Proc Biol Sci 276: 367-373.

Atkinson QD, Gray RD, Drummond AJ 2008. Mtdna Variation Predicts Population Size in Humans and Reveals a Major Southern Asian Chapter in Human Prehistory. Molecular Biology and Evolution 25: 468-474.

Bailey GN, Flemming NC, King GCP, Lambeck K, Momber G, Moran LJ, Al-Sharekh A, Vita-Finzi C 2007. Coastlines, Submerged Landscapes, and Human Evolution: The Red Sea Basin and the Farasan Islands. The Journal of Island and Coastal Archaeology 2: 127-160.

Balding DJ, Bishop M, Cannings C. 2003. Handbook of Statistical Genetics. In. West Sussex, England: John Wiley & Sons, Ltd.

Bandelt H-J, Forster P, Röhl A 1999. Median-Joining Networks for Inferring Intraspecific Phylogenies. Molecular Biology and Evolution 16: 37–48.

Barker G, Barton H, Bird M, Daly P, Datan I, Dykes A, Farr L, Gilbertson D, Harrisson B, Hunt C, Higham T, Kealhofer L, Krigbaum J, Lewis H, McLaren S, Paz V, Pike A, Piper P, Pyatt B, Rabett R, Reynolds T, Rose J, Rushworth G, Stephens M, Stringer C, Thompson J, Turney C 2007. The 'Human Revolution' in Lowland Tropical Southeast Asia: The Antiquity and Behavior of Anatomically Modern Humans at Niah Cave (Sarawak, Borneo). J Hum Evol 52: 243-261.

Beaumont MA 2010. Approximate Bayesian Computation in Evolution and Ecology. Annual Review of Ecology, Evolution, and Systematics 41: 379-406.

Beaumont MA, Wenyang Z, Balding DJ 2002. Approximate Bayesian Computation in Population Genetics. Genetics 162: 2025–2035.

148

Behar DM, Villems R, Soodyall H, Blue-Smith J, Pereira L, Metspalu E, Scozzari R, Makkan H, Tzur S, Comas D, Bertranpetit J, Quintana-Murci L, Tyler-Smith C, Wells RS, Rosset S 2008. The Dawn of Human Matrilineal Diversity. The American Journal of Human Genetics 82: 1130-1140.

Boattini A, Blanco Villegas MJ, Pattener D 2007. Genetic Structure of La Cabrera,Spain, from Surnames and Migration Matrices. Human Biology 79: 649-666.

Boattini A, Castri L, Sarno S, Useli A, Cioffi M, Sazzini M, Garagnani P, De Fanti S, Pettener D, Luiselli D 2013. Mtdna Variation in East Africa Unravels the History of Afro-Asiatic Groups. Am J Phys Anthropol 150: 375-385.

Bowcock AM, Kidd JR, Mountain JL, Hebert JM, Carotenuto L, Kidd KK, Cavalli-Sforza LL 1991. Drift, Admixture, and Selection in Human Evolution: A Study with DNA Polymorphisms. Proc Natl Acad Sci U S A 88: 839-843.

Bustamante CD, Ramachandran S 2009. Evaluating Signatures of Sex-Specific Processes in the Human Genome. Nature Genetics 41: 8-10.

Calafell F, Grigorenkob EL, Chikani AA, Kidd KK 2001. Haplotype Evolution and Linkage Disequilibrium: A Simulation Study. Human Heredity 51: 85-96.

Campbell MC, Tishkoff SA 2008. African Genetic Diversity: Implications for Human Demographic History, Modern Human Origins, and Complex Disease Mapping. Annual Review of Genomics and Human Genetics 9: 403-433.

Carvajal-Rodríguez A 2008. Simulation of Genomes: A Review. Current Genomics 9: 155-159.

Cerezo M, Achilli A, Olivieri A, Perego UA, Gomez-Carballa A, Brisighelli F, Lancioni H, Woodward SR, Lopez-Soto M, Carracedo A, Capelli C, Torroni A, Salas A 2012. Reconstructing Ancient Mitochondrial DNA Links between Africa and Europe. Genome Res 22: 821-826.

Cerny V, Mulligan CJ, Fernandes V, Silva NM, Alshamali F, Non A, Harich N, Cherni L, El Gaaied AB, Al-Meeri A, Pereira L 2011. Internal Diversification of Mitochondrial Haplogroup R0a Reveals Post-Last Glacial Maximum Demographic Expansions in South Arabia. Mol Biol Evol 28: 71-78.

149

Cerny V, Mulligan CJ, Ridl J, Zaloudkova M, Edens CM, Hajek M, Pereira L 2008. Regional Differences in the Distribution of the Sub-Saharan, West Eurasian, and South Asian Mtdna Lineages in Yemen. Am J Phys Anthropol 136: 128-137.

Clark G, Anderson A, Wright D 2006. Human Colonization of the Palau Islands, Western Micronesia. The Journal of Island and Coastal Archaeology 1: 215-232.

Compton JS 2011. Pleistocene Sea-Level Fluctuations and Human Evolution on the Southern Coastal Plain of South Africa. Quaternary Science Reviews 30: 506-527.

Cox MP, Woerner AE, Wall JD, Hammer MF 2008. Intergenic DNA Sequences from the Human X Chromosome Reveal High Rates of Global Gene Flow. BMC Genet 9: 76.

Currat M, Ray N, Excoffier L 2004. Splatche: A Program to Simulate Genetic Diversity Taking into Account Environmental Heterogeneity. Molecular Ecology Notes 4: 139-142.

Davis KF, D'Odorico P, Laio F, Ridolfi L 2013. Global Spatio-Temporal Patterns in Human Migration: A Complex Network Perspective. PLoS One 8: e53723.

de Haan A, Rogaly B 2002. Introduction: Migrant Workers and Their Role in Rural Change. Journal of Development Studies 38: 1-14.

DeGiorgio M, Jakobsson M, Rosenberg NA 2009. Out of Africa: Modern Human Origins Special Feature: Explaining Worldwide Patterns of Human Genetic Variation Using a Coalescent-Based Serial Founder Model of Migration Outward from Africa. Proceedings of the National Academy of Sciences 106: 16057-16062.

Deshpande O, Batzoglou S, Feldman M, Cavalli-Sforza L 2009. A Serial Founder Effect Model for Human Settlement out of Africa. Proceedings of the Royal Society B: Biological Sciences 276: 291-300.

Dresch P. 1989. Tribes, Government, and History in Yemen. New York: Clarendon Press.

Epperson BK. 2003. Geographical Genetics. Princeton, New Jersey: Princeton University Press.

150

Excoffier L, Laval G, Schneider S 2005. Arlequin (Version 3.0): An Integrated Software Package for Population Genetics Data Analysis. Evolutionary Bioinformatics Online 2005: 47-50.

Excoffier L, Smouse PE, Quattro JM 1992. Analysis of Molecular Variance Inferred from Metric Distances among DNA Haplotypes: Application to Human Mitochondrial DNA Restriction Data. Genetics 131: 479-491.

Fagundes NJR, Ray N, Beaumont M, Neuenschwander S, Salzano FM, Bonatto SL, Excoffier L 2007. Statistical Evaluation of Alternative Models of Human Evolution. Proceedings of the National Academy of Sciences 104: 17614-17619.

Federal-Research-Division. 2008. Country Profile: Yemen. Published:Congress Lo. http://lcweb2.loc.gov/frd/cs/profiles/Yemen.pdf

Felsenstein J 1981. Evolutionary Trees from DNA Sequences: A Maximum Likelihood Approach. Journal of Molecular Evolution 17: 368-376.

Felsenstein J 1983. Statistical Inference of Phylogenies. Journal of the Royal Statistical Society. Series A (General) 146.

Forster P 2004. Ice Ages and the Mitochondrial DNA Chronology of Human Dispersals: A Review. Philosophical Transactions of the Royal Society B: Biological Sciences 359: 255-264.

Fort J, Pujol T, Cavalli-Sforza LL 2004. Palaeolithic Populations and Waves of Advance. Cambridge Archaeological Journal 14: 53-61.

Fu YX 1995. Statistical Properties of Segregating Sites. Theor Popul Biol 48: 172-197.

Garrigan D, Hammer MF 2006. Reconstructing Human Origins in the Genomic Era. Nat Rev Genet 7: 669-680.

Gonder MK, Mortensen HM, Reed FA, de Sousa A, Tishkoff SA 2007. Whole-Mtdna Genome Sequence Analysis of Ancient African Lineages. Molecular Biology and Evolution 24: 757-768.

http://lcweb2.loc.gov/frd/cs/profiles/Yemen.pdf�

151

Gonzalez AM, Larruga JM, Abu-Amero KK, Shi Y, Pestano J, Cabrera VM 2007. Mitochondrial Lineage M1 Traces an Early Human Backflow to Africa. BMC Genomics 8: 223.

Gravel S, Henn BM, Gutenkunst RN, Indap AR, Marth GT, Clark AG, Yu F, Gibbs RA, Genomes P, Bustamante CD 2011. Demographic History and Rare Allele Sharing among Human Populations. Proc Natl Acad Sci U S A 108: 11983-11988.

Gray C, Bilsborrow R 2013. Environmental Influences on Human Migration in Rural Ecuador. Demography.

Gronau I, Hubisz MJ, Gulko B, Danko CG, Siepel A 2011. Bayesian Inference of Ancient Human Demography from Individual Genome Sequences. Nature Genetics 43: 1031-1034.

Grün R, Stringer CB 1991. Electron Spin Resonance Dating and the Evolution of Modern Humans. Archaeometry 33: 153-199.

Gutenkunst RN, Hernandez RD, Williamson SH, Bustamante CD 2009. Inferring the Joint Demographic History of Multiple Populations from Multidimensional Snp Frequency Data. PLoS Genet 5: e1000695.

Hahn CHL, Vedder H, Fourie L. 1966. Native Tribes of South West Africa: Frank Cass and Company.

Hamilton G 2005. Bayesian Estimation of Recent Migration Rates after a Spatial Expansion. Genetics 170: 409-417.

Hamilton MJ, Buchanan B 2007. Spatial Gradients in Clovis-Age Radiocarbon Dates across North America Suggest Rapid Colonization from the North. Proc Natl Acad Sci U S A 104: 15625-15630.

Hazelwood L, Steele J 2004. Spatial Dynamics of Human Dispersals. Journal of Archaeological Science 31: 669-679.

Hein J, Schierup MH, Wiuf C. 2005. Gene Genealogies, Variation and Evolution: A Primer in Coalescent Theory. New York: Oxford University Press.

152

Henn BM, Botigue LR, Gravel S, Wang W, Brisbin A, Byrnes JK, Fadhlaoui-Zid K, Zalloua PA, Moreno-Estrada A, Bertranpetit J, Bustamante CD, Comas D 2012. Genomic Ancestry of North Africans Supports Back-to-Africa Migrations. PLoS Genet 8: e1002397.

Hey J 2005. On the Number of New World Founders: A Population Genetic Portrait of the Peopling of the Americas. PLOS Biology 3: 0965-0975.

Hickerson MJ, Dolman G, Moritz C 2006. Comparative Phylogeographic Summary Statistics for Testing Simultaneous Vicariance. Molecular Ecology 15: 209-223.

Holsinger KE, Weir BS 2009. Genetics in Geographically Structured Populations: Defining, Estimating and Interpreting Fst. Nature Reviews Genetics 10: 639-650.

Howell N, Smejkal CB, Mackey DA, Chinnery PF, Turnbull DM, Herrnstadt C 2003. The Pedigree Rate of Sequence Divergence in the Human Mitochondrial Genome. There Is a Difference between Phylogenetic and Pedigree Rates. Am J Hum Genet 72: 659-670.

Hudson RR 2002. Generating Samples under a Wright–Fisher Neutral Model of Genetic Variation Bioinformatics 18: 337-338.

Ingman M, Kaessmann H, Pääbo S, Gyllensten U 2000. Mitochondrial Genome Variation and the Origin of Modern Humans. Nature 408: 708-713.

Jobling MA, Hurles ME, Tyler-Smith C. 2004. Human Evolutionary Genetics: Origins, Peoples & Disease. New York: Garland Science.

Keinan A, Mullikin JC, Patterson N, Reich D 2008. Accelerated Genetic Drift on Chromosome X During the Human Dispersal out of Africa. Nature Genetics 41: 66-70.

Kirch P 1980. Society Polynesian Prehistory: Cultural Adaptation in Island Ecosystems: Oceanic Islands Serve Asarchaeological Laboratories for Studying the Complex Dialectic between Human Populations and Their Environments. American Scientist 68: 39-48.

Kitchen A, Miyamoto MM, Mulligan CJ 2008. A Three-Stage Colonization Model for the Peopling of the Americas. PLoS One 3: e1596.

153

Klein RG. 1998. Why Anatomically Modern People Did Not Disperse from Africa 100,000 Years Ago. In: Akazawa T, Aoki K, Bar-Yosef O, editors. Neandertals and Modern Humans in Western Asia. New York: Plenum Press. p. 509-521.

Laval G, Excoffier L 2004. Bioinformatics 20: 2485–2487.

Lee E 1966. A Theory of Migration. Demography 3: 47-57.

Lell JT, Wallace DC 2000. The Peopling of Europe from the Maternal and Paternal Perspectives. American Journal of Human Genetics 67: 1376–1381.

Levy M 2010. Scale-Free Human Migration and the Geography of Social Networks. Physica A: Statistical Mechanics and its Applications 389: 4913-4917.

Li JZ, Absher DM, Tang H, Southwick AM, Casto AM, Ramachandran S, Cann HM, Barsh GS, Feldman M, Cavalli-Sforza LL, Myers RM 2008. Worldwide Human Relationships Inferred from Genome-Wide Patterns of Variation. Science 319: 1100-1104.

Liu H, Prugnolle F, Manica A, Balloux F 2006. A Geographically Explicit Genetic Model of Worldwide Human-Settlement History. Am J Hum Genet 79: 230-237.

Lohmueller KE, Bustamante CD, Clark AG 2009. Methods for Human Demographic Inference Using Haplotype Patterns from Genomewide Single-Nucleotide Polymorphism Data. Genetics 182: 217-231.

Lohse K, Kelleher J 2009. Measuring the Degree of Starshape in Genealogies – Summary Statistics and Demographic Inference. Genetics Research 91: 281.

Luis JR, Rowold DJ, Regueiro M, Caeiro B, Cinnioglu C, Roseman C, Underhill PA, Cavalli-Sforza LL, Herrera RJ 2004. The Levant Versus the Horn of Africa: Evidence for Bidirectional Corridors of Human Migrations. Am J Hum Genet 74: 532-544.

Maca-Meyer N, González AM, Pestano J, Flores C, Larruga JM, Cabrera VM 2003. Mitochondrial DNA Transit between West Asia and North Africa Inferred from U6 Phylogeography. BMC Genetics 4.

154

Macaulay V, Hill C, Achilli A, Rengo C, Clarke D, Meehan W, Blackburn J, Semino O, Scozzari R, Cruciani F, Taha A, Shaari NK, Raja JM, Ismail P, Zainuddin Z, Goodwin W, Bulbeck D, Bandelt HJ, Oppenheimer S, Torroni A, Richards M 2005. Single, Rapid Coastal Settlement of Asia Revealed by Analysis of Complete Mitochondrial Genomes. Science 308: 1034-1036.

Malik K. 2013. Human Development Report 2013. In: United Nations Development Program.

Marjoram P, Tavaré S 2006. Modern Computational Approaches for Analysing Molecular Genetic Variation Data. Nature Reviews Genetics 7: 759-770.

Marks SJ, Levy H, Martinez-Cadenas C, Montinaro F, Capelli C 2012. Migration Distance Rather Than Migration Rate Explains Genetic Diversity in Human Patrilocal Groups. Mol Ecol 21: 4958-4969.

Marlowe FW. 2010. The Hadza: Hunter-Gatherers of Tanzania. Berkeley, CA: University of California Press.

McDermott F 2004. Palaeo-Climate Reconstruction from Stable Isotope Variations in Speleothems: A Review. Quaternary Science Reviews 23: 901-918.

McEvoy BP, Powell JE, Goddard ME, Visscher PM 2011. Human Population Dispersal "out of Africa" Estimated from Linkage Disequilibrium and Allele Frequencies of Snps. Genome Res 21: 821-829.

Mellars P 2006. Going East: New Genetic and Archaeological Perspectives on the Modern Human Colonization of Eurasia. Science 313: 796-800.

Mercier N, Valladas H, Bar-Yosef O, Vandermeersch B, Stringer C, Joron JL 1993. Thermoluminescence Date for the Mousterian Burial Site of Es-Skhul, Mt. Carmel. Journal of Archaeological Science 20: 169-174.

Metspalu M, Kivisild T, Metspalu E, Parik J, Hudjashov G, Kaldma K, Serk P, Karmin M, Behar DM, Gilbert MT, Endicott P, Mastana S, Papiha SS, Skorecki K, Torroni A, Villems R 2004. Most of the Extant Mtdna Boundaries in South and Southwest Asia Were Likely Shaped During the Initial Settlement of Eurasia by Anatomically Modern Humans. BMC Genet 5: 26.

155

Mielke J, Relethford JH, Eriksson A 1994. Temporal Trends in Migration in the Aland Islands: Effects of Population Size and Geographic Distance. Human Biology 66: 399-410.

Miró-Herrans AT, Mulligan CJ 2013. Human Demographic Processes and Genetic Variation as Revealed by Mtdna Simulations. Mol Biol Evol 30: 244-252.

Morton N, Harris D, Yee S, Lew R 1971. Pingelap and Mokil Atolls: Migration. American Journal of Human Genetics 23: 339-349.

Nebel A, Landau-Tasseron E, Filon D, Oppenheim A, Faerman M 2002. Genetic Evidence for the Expansion of Arabian Tribes into the Southern Levant and North Africa. American Journal of Human Genetics 70: 1594–1596.

Nei M. 1987. Molecular Evolutionary Genetics. New York: Columbia Univ. Press.

Olivieri A, Achilli A, Pala M, Battaglia V, Fornarino S, Al-Zahery N, Scozzari R, Cruciani F, Behar DM, Dugoujon JM, Coudray C, Santachiara-Benerecetti AS, Semino O, Bandelt HJ, Torroni A 2006. The Mtdna Legacy of the Levantine Early Upper Palaeolithic in Africa. Science 314: 1767-1770.

Pagani L, Kivisild T, Tarekegn A, Ekong R, Plaster C, Gallego Romero I, Ayub Q, Mehdi SQ, Thomas MG, Luiselli D, Bekele E, Bradman N, Balding DJ, Tyler-Smith C 2012. Ethiopian Genetic Diversity Reveals Linguistic Stratification and Complex Influences on the Ethiopian Gene Pool. Am J Hum Genet 91: 83-96.

Pakendorf B, Stoneking M 2005. Mitochondrial DNA and Human Evolution. Annu Rev Genomics Hum Genet 6: 165-183.

Pinhasi R, Fort J, Ammerman AJ 2005. Tracing the Origin and Spread of Agriculture in Europe. PLoS Biol 3: e410.

Pinhasi R, Thomas MG, Hofreiter M, Currat M, Burger J 2012. The Genetic History of Europeans. Trends Genet 28: 496-505.

R Development Core Team. 2010. R: A Language and Environment for Statistical Computing. Version 2.11.1. Vienna, Austria: R Development Core Team.

156

Raaum RL, Al-Meeri A, Mulligan CJ 2013. Culture Modifies Expectations of Kinship and Sex-Biased Dispersal Patterns: A Case Study of Patrilineality and Patrilocality in Tribal Yemen. Am J Phys Anthropol 150: 526-538.

Ramachandran S, Deshpande O, Roseman CC, Rosenberg NA, Feldman MW, Cavalli-Sforza LL 2005. Support from the Relationship of Genetic and Geographic Distance in Human Populations for a Serial Founder Effect Originating in Africa. Proceedings of the National Academy of Sciences 102: 15942-15947.

Ramos-Onsins SE, Mitchell-Olds T 2007. Mlcoalsim: Multilocus Coalescent Simulations. Evolutionary Bioinformatics Online 3: 41-44.

Ramos-Onsins SE, Rozas J 2002. Statistical Properties of New Neutrality Tests against Population Growth. Molecular Biology and Evolution 19: 2092-2100.

Rasteiro R, Chikhi L 2013. Female and Male Perspectives on the Neolithic Transition in Europe: Clues from Ancient and Modern Genetic Data. PLoS One 8: e60944.

Relethford J. 2001. Genetics and the Search for Modern Human Origins. New York: Wiley-Liss.

Relethford JH, Harpending HC 1995. Ancient Differences in Population Size Can Mimic a Recent African Origin of Modern Humans. Current Anthropology 36: 667-674.

Rogers A 1995. Genetic Evidence for a Pleistocene Population Explosion. Evolution 49: 608-615.

Rose JI, Cerny V, Bayoumi R 2013. Tabula Rasa or Refugia? Using Genetic Data to Assess the Peopling of Arabia. Arabian archaeology and epigraphy 2013 95–101.

Rowold DJ, Luis JR, Terreros MC, Herrera RJ 2007. Mitochondrial DNA Geneflow Indicates Preferred Usage of the Levant Corridor over the Horn of Africa Passageway. J Hum Genet 52: 436-447.

Salas A, Richards M, De la Fe T, Lareu M-V, Sobrino B, Sánchez-Diz P, Macaulay V, Carracedo Á 2002. The Making of the African Mtdna Landscape. The American Journal of Human Genetics 71: 1082-1111.

157

Scholz CA, Johnson TC, Cohen AS, King JW, Peck JA, Overpeck JT, Talbot MR, Brown ET, Kalindekafe L, Amoako PY, Lyons RP, Shanahan TM, Castaneda IS, Heil CW, Forman SL, McHargue LR, Beuning KR, Gomez J, Pierson J 2007. East African Megadroughts between 135 and 75 Thousand Years Ago and Bearing on Early-Modern Human Origins. Proc Natl Acad Sci U S A 104: 16416-16421.

Sefc KM, Payne RB, Sorenson MD 2007. Genetic Differentiation after Founder Events: An Evaluation of Fst Estimators with Empirical and Simulated Data. Evolutionary Ecology Research 9: 21-39.

Skellam JG 1951. Random Dispersal in Theoretical Populations. Biometrika 38: 196-218.

Soares P, Alshamali F, Pereira JB, Fernandes V, Silva NM, Afonso C, Costa MD, Musilova E, Macaulay V, Richards MB, Cerny V, Pereira L 2012. The Expansion of Mtdna Haplogroup L3 within and out of Africa. Mol Biol Evol 29: 915-927.

Tajima F 1989. Statistical Method for Testing the Neutral Mutation Hypothesis by DNA Polymorphism. Genetics 123: 585-595.

Tavaré S, Balding DJ, Griffiths RC, Donnlly P 1997. Inferring Coalescence Times from DNA Sequence Data. Genetics 145 505-518.

Tenesa A, Navarro P, Hayes BJ, Duffy DL, Clarke GM, Goddard ME, Visscher PM 2007. Recent Human Effective Population Size Estimated from Linkage Disequilibrium. Genome Research 17: 520-526.

Turney CSM, Kershaw AP, Moss P, Bird MI, Fifield LK, Cresswell RG, Santos GM, Di Tada ML, Hausladen PA, Zhou Y 2001. Redating the Onset of Burning at Lynch's Crater (North Queensland): Implications for Human Settlement in Australia. Journal of Quaternary Science 16: 767-771.

Valladas H, Reyss JL, Joron JL, Valladas G, Bar-Yosef O, Vandermeersch B Thermoluminescence Dating of Mousterian Troto-Cro-Magnon'remains from Israel and the Origin of Modern Man. Nature 331: 614 - 616.

Veeramah KR, Wegmann D, Woerner A, Mendez FL, Watkins JC, Destro-Bisol G, Soodyall H, Louie L, Hammer MF 2012. An Early Divergence of Khoesan Ancestors from Those of Other Modern Humans Is Supported by an Abc-Based Analysis of Autosomal Resequencing Data. Molecular Biology and Evolution 29: 617-630.

158

Watterson GA 1975. On the Number of Segregating Sites in Genetical Models without Recombination. Theoretical Population Biology 7: 256-276.

Wegmann D, Leuenberger C, Excoffier L 2009. Efficient Approximate Bayesian Computation Coupled with Markov Chain Monte Carlo without Likelihood. Genetics 182: 1207-1218.

Weir B. 2007. A Tribal Order: Politics and Law in the Mountains of Yemen. Austin, TX: The University of Texas Press.

Wijsman EM, Cavalli-Sforza LL 1984. Migration and Genetic Popoulation Structure with Special Reference to Humans. Annual Review of Ecology and Systematics 15: 279-301.

Wood JW, Smouse PE, Long JC 1985. Sex-Specific Dispersal Patterns in Two Human Populations of Highland New Guinea. The American Naturalist 125: 747-768.

Wright S 1951. The Genetical Structure of Populations. Annals of Eugenics 15: 323–354.

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BIOGRAPHICAL SKETCH

Aida T. Miró graduated from Colegio Rosa-Bell in Guaynabo, Puerto Rico in

Spring 2001. She then attended the University of Puerto Rico, Rio Piedras from Fall

2001 to Fall 2006 and graduated in December 2006 with a Bachelor of Science degree

in biology and a Bachelor of Science degree in anthropology. She interned at Walt

Disney World during Spring 2007. She then began graduate school at the University of

Florida in August 2007 and received a Doctor of Philosophy degree in genetics and

genomics in August 2013. She began a postdoctorate fellowship at the University of

Texas, Austin in January 2014.

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