Lecture 11: Genetic Drift and Effective Population Size

October 1, 2012

Last Time Introduction to genetic drift

Fisher-Wright model of genetic drift

Diffusion model of drift

Effects within and among subpopulations

Simple Model of Genetic Drift

Many independent subpopulations

Subpopulations are of constant size

Random mating within subpopulations

N=16 N=16N=16

N=16N=16

N=16 N=16

N=16N=16N=16

N=16N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16N=16N=16 N=16N=16 N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16 N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

N=16

Effects of Drift

Within subpopulations

Changes allele frequencies

Degrades diversity

Reduces variance

Does not cause deviations from HWE

Among subpopulations (if there are many)

Does NOT change allele frequencies

Does NOT degrade diversity

Increases variance in allele frequencies

Causes a deficiency of heterozygotes compared to Hardy-Weinberg expectations (if the existence of subpopulations is ignored) (to be covered in more detail later)

Today

Interactions of drift and selection

Effective population size

Exams!

Effects of DriftSimulation of 4 subpopulations with 20 individuals, 2 alleles

Random changes through time

Fixation or loss of alleles

Little change in mean frequency

Increased variance among subpopulations

Example: Drift and Flour Beetle Color Tribolium castaneum

experiment with lab populations of different sizes

Frequency of body color polymorphisms: single locus, black, red, brown

Why does frequency of wild-type allele increase over time?

Why does this depend on population size?

Conner and Hartl 2004

N=10

N=20

N=50

N=100

Effects of Selection on Allele Frequency Distributions

No Selection

N=20

s=0.1, h=0.5

Selection pushes A1 toward fixation

A2 still becomes fixed by chance 3.1% of the time

Genetic drift versus directional selection

s=0.1,h=0.5, p0=0.5 Drift eventually leads to

fixation and loss of alleles

Drift and selection combined push fit alleles to fixation more quickly than drift or selection alone

Some “unfit” alleles do become fixed

What happens without drift?

No populations are fixed for A1 after 20 generations

How long until these become fixed?

Drift can counter selection in very small populations

Problem 4 in Wednesday’s lab exercise contrasts two cases that fall on the middle curve

N=10, s=0.25

N=100, s=0.25

Fixation as a Function of Ns and Starting Allele Frequency

Combined Effects of Drift and Selection

Probability of fixation of a favorable allele will be a function of initial allele frequency, selection coefficient, heterozygous effect, and population size

Favorable alleles won’t necessarily go to fixation when drift is involved

Drift reduces efficiency of selection in the sense that unfavorable alleles may not be purged from population

Favorable alleles do increase in frequency more quickly when drift is involved over ALL subpopulations

Can be simulated by allowing selection to alter allele frequencies prior to effects of drift

Nuclear Genome Size Size of nuclear genomes

varies tremendously among organisms: C-value paradox

No association with organismal complexity, number of chromosomes, or number of genes

Arabidopsis thaliana 120 MbpPoplar 460 MbpRice 450 Mbp Maize 2,500

Mbp Barley 5,000

MbpHexaploid wheat 16,000

MbpFritillaria (lilly family) >87,000

Mbp

Noncoding DNA is part of Answer

Fugu: 365 MbpHuman: 3500 Mbp

opossum ~ 52% rice ~ 35%

Arabidopsis ~ 14% Drosophila ~ 15%

pufferfish ~ 2%

barley ~ 55%

wheat ~ 80% corn ~ 70%

Human ~ 45%

mouse ~ 40%

Why is there so much variation in genome size?

Why do microbes have so much simpler genomes than eukaryotes?

Why do trees have such huge genomes?

The importance of Genetic Drift and Selection in Determining Genome Size

Large effective population sizes mean selection more effective at wiping out variations with even minor effects on fitness

Transposable elements and introns eliminated from finely-tuned populations, persist where drift can overwhelm selection

Lynch and Conery 2004 Science 302:1401

Historical View on Drift Fisher

Importance of selection in determining variation

Selection should quickly homogenize populations (Classical view)

Genetic drift is noise that obscures effects of selection

Wright

Focused more on processes of genetic drift and gene flow

Argued that diversity was likely to be quite high (Balance view)

Controversy raged until advent of molecular markers showed diversity was quite high

Neutral theory revived controversy almost immediately

Effective Population Size

Census population size often inappropriate for population genetics calculations

Breeding population size often smaller

For genetic drift, historical events or nonrandom mating patterns might reduce EFFECTIVE size of the population

Effective Population Size is an ideal population of size N in which all parents have an equal probability of being the parents of any individual progeny.

also

The size of a theoretically ideal population that would have the same observed level of genetic drift

Factors Reducing Effective Population Size

Unequal number of breeding males and females

Unequal reproductive success

Changes in population size through time

Bottlenecks

Founder Effects

Table courtesy of K. Ritland

Effective Population Size: Effects of Different Numbers of Males and Females

See Hedrick (2011) page 213 for

derivation

Effect of Proportion of Males in the Population on Effective Population Size

Small population size in one generation can cause drastic reduction in diversity for many future generations

Effect is approximated by harmonic mean

Variation of population size in different generations

i

e

N

tN

1

te NNNNtN

1...

11111

321

See Hedrick (2011) page 219 for

derivation

Effective Population Size: The bottleneck effect

“Alleles” in original population

“Alleles” remaining after bottleneck

The Founder effect Outlying populations

founded by a small number of individuals from source population

Analogous to bottleneck

Expect higher drift, lower diversity in outlying populations

Exam Issues

Genotype frequency versus allele frequency (problem 2A, 7)

Meaning of the chi-square: larger than critical value, reject null hypothesis

Recessive alleles and fitness (Multiple choice problem 3; problem 5)