Disentangling the Effects of Ecological and Environmental ...m044k0952/... · models developed for...

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Disentangling the Effects of Ecological and Environmental Processes on the Spatial Structure of

Metacommunities

by Sarah L. Salois

B.S. in Biology, Eastern Connecticut State University

A dissertation submitted to

The Faculty of

the College of Science of Northeastern University

in partial fulfillment of the requirements for the degree of Doctor of Philosophy

June 12, 2019

Dissertation directed by

Tarik C. Gouhier Professor of Marine and Environmental Sciences

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Dedication

To the memory of John and Noella Young who believed in me always and to my husband, Caleb, and our two children who inspire me daily.

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Acknowledgements

Let me start by acknowledging that this body of work could not have been achieved

without the support of my mentors, colleagues, friends and family both within and outside of

academia. I am forever grateful for all the encouragement and enthusiasm I have received from

the community of people I have grown to know along this journey.

I’d first like to thank Tarik Gouhier (my adviser) who guided me along this process and

whose standards and encouragement have been integral to my success. To the members of my

committee, Brian Helmuth, Jon Grabowski, Steve Vollmer and Ron Etter who have kept me on

track, I am grateful for all of your unique perspectives, insights and encouraging feedback which

have been fundamental to this dissertation as well as my professional development.

Thank you to my lab mates whose laughter and support I could not have survived

without. Thank you for being such great friends, always there to exchange ideas, lend a hand in

the field(ish) or with help with code. Each one of you contributes to the perfect equilibrium that

is the Gouhier lab, thank you all for keeping me sane and reminding me not to take myself too

seriously. May we continue to share pop-culture themed RColorBrewer palettes until the end of

days.

I’d like to express my gratitude to the Marine Science Center community, staff and

faculty both past and present. Each one of you has played a part in getting me to the finish line

and I truly value the hard work that goes into facilitating all the great research and education

coming out of the MSC that I have been so grateful to be a part of.

Finally, my deepest gratitude to my husband who has been patient and endlessly

supportive throughout the trials and tribulations that come along with a dissertation. I promise I

won’t do this again.

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Abstract of Dissertation

Identifying the relative influence of ecological and environmental processes on ecosystem

structure remains a challenge. This is partly because the inherent stochasticity and complexity of

nature, the product of multiple processes operating at different temporal and spatial scales, have

made it difficult to identify general rules that govern the assembly and dissolution of ecosystems.

Conversely, these same attributes have inspired a vast amount of theoretical and empirical

investigations of these natural systems, spanning multiple temporal and spatial scales. This

project is motivated by such seminal work and aims to combine both theoretical and empirical

tools to add to our understanding of the drivers of spatiotemporal dynamics in a changing world.

Through a combination of mathematical models, computer simulations and statistical analyses on

long-term ecological time series, this body of work aims to understand the nonlinearities of

marine systems across spatial scales. Specifically, this project investigates the mechanisms

governing community structure across spatial scales and examines the effects of interacting

ecological processes in complex and interconnected ecosystems in an era of global change. The

models developed for this thesis reveal the relative importance of dispersal, species interactions,

environmental heterogeneity as well as highlight the potential vulnerability of ecosystems to

climate change, and thus be a valuable extension to current forecasting methods and may provide

useful implications for the conservation and management of marine ecosystems.

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Table of Contents

Dedication 2

Acknowledgements 3

Abstract of Dissertation 4

Table of Contents 5

List of Figures 7

List of Tables 8

Introduction: The complexity of natural systems 9

Literature Cited 13

Chapter 1: Multifactorial effects of dispersal in an environmentally forced 18

metacommunity

Abstract 18

Introduction 19

Materials and Methods 23

Results 29

Discussion 36

Literature Cited 43

Tables 49

Figures 50

Chapter 2: Coexistence mechanisms collide across scales 54

Abstract 54

Introduction 55


Results 62

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Table of Contents (continued)

Discussion 65

Literature Cited 69

Figures 73

Chapter 3: Coastal upwelling generates cryptic temperature refugia 76

Abstract 76

Introduction 77


Results 87

Discussion 92

Literature Cited 98

Tables 104

Figures 106

Conclusions and Recommendations 111

Literature cited 114

Appendices 115

Appendix 1.1: Mechanistic schematics

Appendix 1.2: Robustness of metacommunity model results to 116

environmental stochasticity

Appendix 1.3: Robustness of metacommunity model results to 121

covariation in advection and diffusion rates

Appendix 3.1: Wavelet analysis 125

Appendix 3.2: Permutation-based ANCOVA tables 133

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ListofFigures

Chapter 1: Multifactorial effects of dispersal in an environmentally forced metacommunity

1.1. Metacommunity species richness at multiple spatial scales as a function of dispersal advection (a) and diffusion (b) for different environmental gradients

1.2 Species rank abundance as a function of dispersal advection rate (a) and diffusion rate (b)

1.3 Variation partitioning of community structure as a function of dispersal advection rate (a-c) and diffusion rate (d-f)

1.4 Variation partitioning results for an intertidal metacommunity

Chapter 2: Coexistence Mechanisms collide across scales

2.1 Schematic diagram of the spatially-explicit metacommunity model

2.2 Metacommunity species richness at multiple spatial scales as a function of dispersal diffusion and recruitment facilitation 2.3 Species extinction risk as function of dispersal rate

Chapter 3: Coastal upwelling generates cryptic temperature refugia

3.1 Hierarchicalclusteringofcorrelationsofwatertemperaturefrom timeseriesacross16sites 3.2 Hierarchicalclusteringofcorrelationsofwaveletpowerextracted fromwaveletanalysisacross16sites. 3.3 Timeseriesandscaleaveragedwaveletpowerfordailymicrohabitat watertemperatureforallsites. 3.4 Correlationasafunctionofdistance.Pairwisecomparisonsbetween siteswithintheCanaryCurrentSystem. 3.5 Coherenceandphasedifferenceasafunctionofdistance.

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ListofTables

Chapter 1: Multifactorial effects of dispersal in an environmentally forced metacommunity

1.1. ANOVA:effectsofpelagiclarvalduration(PLD)andzone onthespatialfraction

Chapter 3: Coastal upwelling generates cryptic temperature refugia

3.1 Kendall’scoefficientofconcordance(W)measuringdegreeof synchronybetweensites

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INTRODUCTION

Thecomplexityofnaturalsystems Complexity and variability are quasi-ubiquitous features of natural ecosystems that make it

difficult to link patterns and processes across scales. This inherent ecological complexity is the

product of multiple processes operating at different temporal and spatial scales. A central goal of

ecology is to reduce this complexity by partitioning the relative importance of processes

occurring at regional scales (e.g., landscape connectivity) and local scales (e.g., species

interactions)(Levins and Culver 1971, Peres-Neto and Legendre 2010, Dray et al. 2012).

Although abiotic processes are often thought to act at larger scales than biotic processes

(Chase and Leibold 2003, Boulangeat et al. 2012, Vellend et al. 2014), mapping abiotic and

biotic processes to specific spatial scales remains a hotly debated issue (Levin 1992, Cowen and

Sponaugle 2009, Christian Hof et al. 2011, Araújo and Rozenfeld 2014). Some theories suggest

that hierarchical or scale-dependent approaches are most useful for mechanistically linking

ecological patterns and processes(Willis and Whittaker 2002, Pearson and Dawson 2003, McGill

2010), while others advocate for the use of metacommunity theory to examine the interactions

between local and regional processes (Menge and Olson 1990, Leibold et al. 2004, Guichard

2005, Gotelli 2010, Gouhier et al. 2010).

Disentangling the effects of ecological and environmental drivers is even more complicated

in an era of global change because intensifying exogenous pressures can alter key processes and

cause both non-stationary and non-linear responses in ecosystems (Fridley et al. 2007, Baskett et

al. 2010, Amarasekare and Savage 2012, White et al. 2013, Andrello et al. 2015). For instance,

changes in climate are expected to have pronounced effects on seawater temperature leading to

changes in seasonality and patterns of connectivity in marine systems (Munday et al. 2009,

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Schiffers et al. 2013, Gerber et al. 2014, Andrello et al. 2015). Even slight fluctuations of this

type could create phenological mismatches, often resulting in deleterious ecological

consequences such as the observed seasonal disparity between larval release and resource

availability (Harley et al. 2006, Kordas et al. 2011, Francis et al. 2012). Anthropogenic impacts,

such as overharvesting or coastal development will only exacerbate these anticipated

consequences (Halpern et al. 2007, Condon et al. 2011, Roux et al. 2013, Watson et al. 2015,

Scyphers et al. 2015).

This dissertation aims to gain fundamental understanding of the mechanisms driving

biodiversity (chapter 1), coexistence (chapter 2) and environmental refugia (chapter 3) across

spatiotemporal scales. Together, these chapters provide critical insights about the assembly and

functioning of marine metacommunities in an era of global change.

Conceptual background: intertidal ecosystems as a model system

Intertidal ecosystems are ideal for developing and testing metacommunity theory because their

functioning has been linked to processes operating at multiple scales (Menge and Sutherland

1976, 1987, Lubchenco and Menge 1978, Menge 1978, 1992, Lubchenco 1980). Specifically,

local processes such as competition for space and predator prey dynamics work in concert with

regional processes including dispersal and environmental variability to modify community

assembly (Lubchenco and Menge 1978, Menge 1995, Bryson et al. 2014). Due to their location

at the interface of marine and terrestrial environments, intertidal ecosystems experience strong

differences in water and air temperature, desiccation stress and productivity along a well-defined

gradient of zonation. Environmental factors such as aerial and water temperature extremes have

been suggested as drivers of the upper range limits for intertidal species (Menge and Sutherland

1976, Harley and Helmuth 2003, Stickle et al. 2017), whereas ecological factors such as

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competition and predation have been associated with lower intertidal range limits (Connell 1961,

Lubchenco and Menge 1978, Sorte et al. 2017). Additionally, the rocky intertidal is composed

primarily of ectothermic invertebrates, many of which are sessile with characteristic pelagic

larval stages, during which the larvae can be transported over large distances by strong nearshore

currents (Siegel et al. 2003, Kinlan and Gaines 2003). These traits make these species

particularly sensitive to environmental perturbations such as temperature fluctuations, increased

pH and nutrient availability (Incze et al. 2010). For instance, recent work has shown that the Gulf

of Maine (GoM) is a ‘hotspot’ of change, with the sea surface temperature having risen faster

than 99.9% of the world’s oceans (Pershing et al. 2015). Although intertidal ecosystems are a

well-studied system, many questions remain regarding how the dynamics of community

composition and the processes that govern them will respond to a changing climate (Morrison et

al. 2012, Bryson et al. 2014, Sorte et al. 2017, 2018).

Significance of project

The overarching goal of this dissertation is to gain mechanistic insights about the spatiotemporal

dynamics that govern ecosystems in a changing world. In combining mathematical models,

computer simulations and statistical analyses on long-term ecological time series, this body of

work aims to disentangle the relative influence of environmental and ecological processes on the

dynamics of marine ecosystems. Incorporating empirical data from multiple long-term datasets

from intertidal systems on the East (Gulf of Maine) and the European Atlantic Coast (Canary

Current System), to parameterize and validate my models as well as conducting model

comparisons and analyzing model outputs has contributed to the identification of strengths and

limitations of some commonly used statistical frameworks. Specifically, this work addresses

prevailing scale-dependent/linear decomposition approaches commonly used to study ecological

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phenomena, which may not always capture the ubiquitous spatial heterogeneity and

nonlinearities found in nature, by making direct comparisons to cross-scale/nonlinear

frameworks.

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CHAPTER 1

The multifactorial effects of dispersal on biodiversity in environmentally forced

metacommunities

ABSTRACT

Disentangling the effects of dispersal and environmental heterogeneity on biodiversity is a

central goal in ecology. Although metacommunity structure can be partitioned into spatial and

environmental fractions, it remains unclear whether these statistical results can be used to infer

the relative importance of dispersal-limitation (spatial fraction) and environmental-forcing

(environmental fraction). Using an environmentally-forced spatially-explicit metacommunity

model, we show that the distinct effects of the mean (advection) and the standard deviation

(diffusion) of the dispersal kernel on biodiversity are not easily detectable via variation

partitioning alone. Although increasing dispersal ultimately leads to a decrease in the spatial

fraction due to reduced dispersal-limitation and greater species-sorting, the magnitude of the

spatial fraction depends on the complex interplay between the nature of dispersal and the type of

boundary conditions in the metacommunity. Indeed, metacommunities characterized by either

high or low dispersal can exhibit a small spatial fraction. A case study of a marine

metacommunity experiencing strong alongshore transport is consistent with these findings, as the

size of the spatial fraction is not associated with dispersal. Overall, our results suggest that

accounting for the nature of environmental-forcing as well as the multifactorial effects of

dispersal is critical for understanding how ecological and environmental processes give rise to

biodiversity across spatial scales.

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INTRODUCTION

Species abundance distributions are driven by a combination of abiotic and biotic processes

operating at multiple spatial and temporal scales (Leibold et al. 2004, Holyoak et al. 2005).

Although uncontroversial today, this synthetic perspective evolved from ardent and recurring

debates about the relative influence of biotic (Elton 1927, Nicholson 1933) and abiotic (Grinnell

1917, Davidson and Andrewartha 1948, Andrewartha and Birch 1954) processes on patterns of

species diversity and population dynamics (reviewed by Coulson et al. 2004). For instance,

pioneering work by Grinnell (1917) showed that species often ‘track’ the geographical

distribution of environmental conditions that characterize their habitat. In doing so, the

Grinnellian niche perspective emphasized the importance of environmental heterogeneity as a

driver of species abundance. This purely abiotic definition of the niche, which suggested a

unidirectional effect of the environment on species, was later extended by Charles Elton, who

highlighted the importance of biotic processes and the reciprocal feedbacks between species and

their environment in dictating community structure (Elton 1927). A similar but more

acrimonious argument emerged about the drivers of population dynamics, with Andrewartha and

Birch (1954) championing the role of density-independent abiotic factors such as temperature

and Nicholson (1933) arguing for the dominance of density-dependent biotic interactions such as

competition.

Although these debates initially focused on the relative importance of biotic and abiotic

processes at local scales, the role of regional factors such as dispersal began to garner greater

attention following the development of island biogeography (MacArthur and Wilson 1967). By

modeling how species diversity on islands could depend on the balance between regional

immigration from the mainland and local extinction rates, MacArthur and Wilson laid the

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foundation for metacommunity theory (Levins and Culver 1971, Hastings 1980, Tilman 1994), a

framework which depicts ecological systems as sets of discrete communities of interacting

species linked by dispersal (Leibold et al. 2004, Holyoak et al. 2005). Metacommunities are thus

ideal for understanding how biotic and abiotic processes operating at multiple scales interact to

give rise to patterns of biodiversity.

Modern theory has identified four main metacommunity ‘perspectives’ based on the relative

influence of local vs. regional (a)biotic factors on the distribution of species (Leibold et al. 2004,

Holyoak et al. 2005). The patch dynamic perspective stresses the importance of tradeoffs

between local and regional biotic processes as the drivers of community structure (Levins and

Culver 1971, Tilman 1994). For instance, an interspecific competition-colonization tradeoff can

allow an arbitrary number of species to persist on a single resource in a spatially-structured but

environmentally-homogeneous habitat (Tilman 1994). On the other hand, the species sorting

perspective focuses on the effect of spatial environmental heterogeneity in dictating the

distribution of species. Specifically, by assuming that dispersal allows species to reach patches

characterized by their preferred environmental conditions, this perspective emphasizes niche

separation due to local competitive exclusion over spatial rescue effects (Leibold et al. 2004,

Holyoak et al. 2005). The mass effects approach also considers patches to be environmentally-

heterogeneous but assumes that dispersal is sufficiently high to generate spatial dynamics that

override local competitive exclusion (Leibold et al. 2004, Holyoak et al. 2005). Indeed, when

dispersal is high, the movement of individuals from ‘source’ patches characterized by good

environmental conditions can allow species to persist in ‘sink’ patches characterized by poor

environmental conditions (Pulliam 1988, Amarasekare and Nisbet 2001, Holyoak et al. 2005).

Such source-sink dynamics can alter patterns of biodiversity in metacommunities (Mouquet and

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Loreau 2003) and erode the relationship between spatial environmental heterogeneity and the

distribution of species. Finally, the neutral perspective, which often serves as a null model,

assumes that all individuals are demographically equivalent and that community composition is

driven by the combination of limited dispersal and ecological drift (Hubbell 2001).

The metacommunity perspectives outlined above have provided the foundation for recent

theoretical developments identifying multiple dispersal-based coexistence mechanisms. These

coexistence mechanisms all rely on distinct connectivity patterns arising from interspecific

differences in spawning time, dispersal ability or dispersal direction. For instance, interspecific

differences in dispersal ability (Bode et al. 2011) or asymmetrical connectivity patterns

(Salomon et al. 2010) can promote coexistence between competing species when environmental

conditions are spatially-homogeneous. Interspecific differences in temporal variability have also

been identified as a coexistence mechanism in spatially-homogeneous environments (Berkley et

al. 2010). Here, differences in spawning time coupled with temporal variability in dispersal can

promote coexistence by creating ephemeral spatiotemporal niches that promote the long-term

coexistence of competing species (Berkley et al. 2010). Finally, Aiken and Navarrette (2014)

extended the results of Berkley et al. (2010) and Salomon et al. (2010) by showing that

differences in the dispersal properties of subordinate and dominant species could promote

coexistence in competitive metacommunities.

Although metacommunity theory has defined different perspectives based on the relative

importance of dispersal and environmental heterogeneity as drivers of biodiversity, testing this

theory will require identification of statistical signatures of these underlying mechanisms in

observational data. However, given the necessary scope and scale, it is logistically impractical to

conduct manipulative experiments in order to identify the drivers of metacommunity structure in

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the real world. One promising solution to this vexing problem is variation partitioning, a

statistical technique commonly used to decompose community variation into spatial and

environmental fractions (Borcard et al. 1992, 2004, Peres-Neto et al. 2006). Within this

framework, the environmental fraction essentially measures the degree of correlation between

local species abundances and abiotic factors such as temperature or rainfall. The spatial fraction

largely represents the ‘residual’ spatial variation in community structure not explained by the

abiotic factors. The size of the spatial fraction is most commonly interpreted as the effect of

dispersal, or more specifically, the degree of dispersal-limitation, where low dispersal rates or

geographical barriers can prevent species from reaching patches characterized by their optimal

environmental conditions (Cottenie 2005, Flinn et al. 2010, Tuomisto et al. 2012). Although this

statistical framework is powerful, there is still considerable debate about how to interpret the

‘spatial’ and ‘environment’ fractions in an ecologically meaningful way (Cottenie 2005, Gilbert

and Bennett 2010, Tuomisto et al. 2012, Legendre and Gauthier 2014). For instance, in analyses

of empirical and simulated data sets, dispersal limitation can lead to both large and small spatial

fractions (i.e., high and low ‘residual’ spatial variation in community structure respectively)

(Cottenie 2005, Gilbert and Bennett 2010). Hence, bridging the gap between metacommunity

theory and variation partitioning by identifying statistical signatures of biological and

environmental factors will promote our ability to predict and manage the dynamics of complex

and interconnected ecosystems.

Here, we use spatially-explicit models to explore the ability of variation partitioning to detect

a dispersal signal in environmentally-forced metacommunities. Specifically, we found that

although increasing advection (i.e., the mean of the dispersal kernel) or diffusion (i.e., the

standard deviation of the dispersal kernel) ultimately leads to a decrease in the spatial fraction,

23

the magnitude of the spatial fraction does not map to the dispersal rate directly. Indeed, large

spatial fractions can be associated with both high and low dispersal rates and the strength of the

environmental gradient amplifies this inconsistency. These results hold in the presence of

environmental noise as well as across a range of environmental gradients and are consistent with

observational data from an intertidal metacommunity along the West Coast of the United States.

Overall, our findings suggest that the interpretation of the spatial fraction does not map onto a

particular process, but rather depends on the complex interaction between dispersal, boundary

conditions and strength of environmental forcing.

MATERIALS AND METHODS

The model

To determine how environmental heterogeneity and different aspects of dispersal affect patterns

of species diversity and abundance, we developed a spatially-explicit metacommunity model

with lottery competition by extending Levins’ classical spatially-implicit framework (see

Appendix S1, Fig. S1; Levins 1969, Levins and Culver 1971). This type of model is well suited

for describing competition between sessile species with mobile dispersal stages in both terrestrial

(e.g., plants; Tilman 1994, Mouquet and Loreau 2003) and aquatic ecosystems (e.g.,

invertebrates; Gouhier et al. 2010b, 2011). Each metacommunity consists of L distinct sites

linked by propagule dispersal, a process that determines each of the S species’ potential

recruitment according to a Gaussian kernel whose advection and diffusion rates can be specified

(Appendix 1.1, Fig. S1.1c,d). Although all species share the same dispersal kernel, their realized

recruitment patterns depend on the match between a site’s environment and each species’

physiological requirements, depicted by a Gaussian distribution around an optimal

environmental value (Appendix 1.1, Fig. 1.1b). Environmental heterogeneity was implemented

24

as a simple linear gradient (Appendix 1.1, Fig. 1.1a). These processes were modeled using the

following set of coupled ordinary differential equations, which track the abundance 𝑁" of each

species i at site x along a one-dimensional array of size L:

d#$(&)d(

= 𝑟"(𝑥)𝐹(𝑒(𝑥), 𝑜")01 − ∑ 𝑁4(𝑥)5467 8 − 𝑚"𝑁"(𝑥) (Eq. 1)

Here, the first term on the right hand side represents the realized recruitment rate of species i at

site x, the second term in parentheses represents lottery competition for space, and the third term

represents species-specific background mortality. The realized recruitment rate is the product of

each species’ potential recruitment rate 𝑟"(𝑥) and survivorship F in that environment 𝑒(𝑥). The

potential recruitment rate 𝑟"(𝑥) is the convolution of the product of propagule production 𝑝"(𝑦)

and density 𝑁"(𝑦) at each source site y with the dispersal kernel k(x) at destination site x:

𝑟"(𝑥) = ∫ 𝑝"(𝑦)𝑁"(𝑦)𝑘(𝑥 − 𝑦)d𝑦?/AB?/A (Eq. 2)

Thus, the term 𝑟"(𝑥) denotes the total number of recruits arriving at each destination site x from

all other source sites y via dispersal. The dispersal kernel itself is a normalized Gaussian

distribution (i.e., sums to 1) with mean μ and standard deviation σ (Siegel et al. 2003):

𝑘(𝑥) = 7C√AE

𝑒B(FGH)I

IJI (Eq. 3)

Where μ represents alongshore advection and σ represents diffusion. We manipulated both μ and

σ independently for each simulation, allowing us to control the extent (advection) and scale

(diffusion) of dispersal. Each species’ propagule survivorship is represented by a Gaussian curve

centered around a species-specific environmental optimum 𝑜" (Appendix 1.1, Fig. 1.1b) such that

survivorship F of species i at site x is:

𝐹(𝑒(𝑥), 𝑜") = 𝑒B0K(F)GL$8

I

I

(Eq. 4)

25

Hence, the smaller the difference between a species optimum and the environment, the greater its

propagule survivorship and realized recruitment rate.

Spatial environmental variation was modeled using a simple linear gradient:

𝑒(𝑥) = M 𝑢𝑥 if𝑥 ≤ 𝐿/2−𝑢𝑥 if𝑥 > 𝐿/2 (Eq. 5)

Here, 𝑢 represents the slope of the linear environmental gradient. We simulated 10 different

levels of 𝑢 ranging from 0.02 to 0.16 in order to determine the robustness of our results to the

strength of the environmental gradient. We also ran additional simulations that included random

noise affecting local environmental conditions 𝑒(𝑥) within each site x using a white noise

(spatially-uncorrelated) process to determine the robustness of our results to different levels of

environmental stochasticity (See Appendix 1.2):

𝑒(𝑥) = 𝑢𝑥 + 𝑣(𝑥) (Eq. 6)

Here, 𝑣(𝑥) represents environmental stochasticity via a random deviate drawn from a normal

distribution with a mean of zero and a standard deviation ranging from 0 (no noise) to 1 (high

noise). Running simulations for 10 uniformly-spaced standard deviations between 0 and 1

allowed us to determine the robustness of our model results to variation in the linearity and

stochasticity of the environmental gradient (Appendix 1.2).

Model simulations

The model equations were solved numerically using an explicit Runge-Kutta (4, 5) formula in

MATLAB (function ode45) for 2,000 time steps. The metacommunity consisted of S = 20

species competing across L = 140 sites (absorbing boundary conditions) or L = 100 sites

(periodic boundary conditions). We varied the dispersal advection and diffusion rates

independently to simulate the dynamics of species ranging from direct developers, whose

propagules remain in their natal site (i.e., zero advection and diffusion), to long-distance

26

dispersers (i.e., high advection or diffusion). For simulations manipulating the advection rate 𝜇,

the diffusion rate was fixed at 𝜎 = √10. For simulations manipulating the diffusion rate 𝜎, the

advection rate was fixed at 𝜇 = 0. We followed existing approaches (e.g., Mouquet and Loreau

2003) and used our model to simulate the simplest and most generic metacommunity scenarios.

Specifically, initial abundances for all species were random across all sites, the same dispersal

kernel was used for each species and the propagule production rates 𝑝" were randomly selected

from a uniform distribution with a minimum value of 5 and a maximum value of 10. The

mortality rates 𝑚" were selected so that each species had the same production-to-mortality ratio

𝑝"/𝑚" in order to ensure coexistence in the absence of environmental heterogeneity and

dispersal. Additionally, each species’ environmental optimum 𝑜" was selected randomly from a

uniformly-spaced vector of 20 values ranging from the minimum to the maximum environmental

condition 𝑒(𝑥). Overall, adopting this approach allowed us to generate baseline and system-

agnostic results. Simulations were run under one of two scenarios to explore the effects of

boundary conditions. First, we used absorbing boundary conditions to simulate a finite-size

linear environment where propagules are able to leave the system. Second, we used periodic

boundary conditions to simulate an infinite-size environment without edge effects (e.g., Gouhier

et al. 2010a, 2010b, 2013). Here, the linear environmental gradient was thus altered in order to

avoid sudden spatial discontinuities at the ends of the spatial domain. Specifically, the

environmental gradient in our simulations increases linearly with slope u from the beginning of

the spatial domain (i.e., site 1) to the middle (i.e., site 50) and then decreases linearly from the

middle to the opposing end of the spatial domain (i.e., site 100) with slope -u. This ensures the

two ends of the spatial domain (sites 1 and 100), which are in fact nearest neighbors under

periodic boundary conditions, experience similar environmental conditions. To test the

27

robustness of the model results to covariation in advection and diffusion, we also ran additional

simulations where both aspects of dispersal (advection, diffusion) covaried as predicted under

climate change (e.g., Gerber et al. 2014; see Appendix 1.3). All analyses were performed on final

species abundances. Species whose final local abundances were lower than 10-8 were considered

to have gone extinct.

Model analysis

The model results were analyzed using two complementary approaches. First, we used species’

presence/absence information to partition biodiversity into local (α), between-community (β),

and regional (γ) diversity using standard methods (Whittaker 1972, Mouquet and Loreau 2003).

Here, regional diversity γ was measured as the total species richness across the entire

metacommunity, local diversity α was measured as the average species richness within each site,

and between-community diversity β was measured as the difference between regional and local

diversity. Second, we used partial redundancy analysis (RDA) to partition species abundances

across the metacommunity into their spatial (S|E), environmental (E|S), and shared (EÇS)

fractions (Borcard et al. 1992, 2004, Peres-Neto et al. 2006). This was achieved by relating the

matrix of species abundances Y to (i) the environmental matrix X1, which consisted of the

variables that characterized the environmental gradient, and (ii) the spatial matrix X2, which was

created via a spectral decomposition of the spatial structure of the metacommunity using the

principle coordinates of neighboring matrices (PCNM) method (Borcard et al. 2004). The

environmental fraction E|S thus represents the spatial variation in community structure that is

strictly due to the environment whereas the spatial fraction S|E represents the ‘residual’ spatial

variation in community structure that cannot be explained by the environment. This method is

particularly powerful because it can partition the spatial and environmental fractions of

28

metacommunity structure even when the shared fraction EÇS is large because the environment is

spatially-structured (Borcard et al. 1992, 2004, Peres-Neto et al. 2006). This is important given

that the environment is strongly spatially-structured in both our simulations and our test system,

the intertidal metacommunity along the West Coast of the US (Gouhier et al. 2010).

Empirical case study

We used community data from the rocky intertidal along the West Coast of the United States

(Schoch et al. 2006, Russell et al. 2006, Gouhier et al. 2010) to determine the empirical

relationship between the spatial fraction and dispersal. This is an ideal test system because it is

characterized by (i) strong latitudinal environmental gradients in sea surface temperature,

primary production and upwelling (Menge et al. 2004, Gouhier et al. 2010b, Menge and Menge

2013), and (ii) the relatively rapid southward advective California Current (Hickey 1979, Huyer

1983, Largier et al. 1993). Data were collected annually from 2000 to 2003 at 48 sites ranging

from southern California to northern Washington (32.7°N to 48.4°N). Community structure was

determined by averaging the abundance of each species across 10 randomly-placed 0.25m2

quadrats along 3-4 random transects at each site for the low, mid and high zone (see details in

Gouhier et al. 2010). Environmental variables included chlorophyll-a concentration (chl-a, in

mg/m3), upwelling index (m3/s/100 m of coastline) and mean annual sea surface temperature

(SST, in °C). Data were obtained from the sea-viewing wide field of view sensor (SeaWiFS;

NASA), sea level pressure maps (Pacific Fisheries Environmental Laboratory) and from a high-

resolution radiometer (NOAA), respectively (see Gouhier et al. 2010). Pelagic larval duration

(PLD) is commonly used as a proxy for dispersal ability for sessile marine organisms, as directly

assessing larval movement remains a challenge (Shanks et al. 2003, Siegel et al. 2003, Shanks

2009, Selkoe and Toonen 2011). For our empirical test, we used this approach to split the species

29

found in our surveys into four distinct groups based on their dispersal potential: direct developers

(0 days), low PLD (~8 days), intermediate PLD (~ 21 days) and high PLD (~ 70 days). We

conducted variation partitioning for each group of species across all zones in this empirical

dataset to determine the size of the spatial and environmental fractions. The approach we used

was identical to the one used for the model simulations, where species abundances across the

metacommunity were partitioned into their spatial (S|E), environmental (E|S), and shared (EÇS)

fractions (Borcard et al. 1992, 2004, Peres-Neto et al. 2006).

RESULTS

Patterns of biodiversity

We begin by analyzing the closed version of the metacommunity model (i.e., self-recruitment

only). Under this scenario, the following relationship between all pairs of species {𝑖, 𝑗} must hold

for coexistence to occur at equilibrium:

\$(&)]$(&)^(_(&),`$)

= \a(&)

]a(&)^(_(&),`a) (Eq. 7)

The ratio of mortality to realized recruitment must thus be identical across all species in order

for coexistence to occur within each site x. Hence, in the absence of dispersal, an arbitrary

number of species can coexist via a fitness equalizing tradeoff between mortality and realized

recruitment (sensu Chesson 2000). Because any species with a higher ratio is expected to

competitively exclude all other species locally, environmental heterogeneity promotes species-

sorting by generating low within-site diversity α, high between-site diversity β, and maximizing

regional diversity γ (Fig. 1a, b, dispersal advection and diffusion rates = 0). This is because each

species essentially monopolizes the site whose environmental conditions are closest to its

optimum.

30

In general, the introduction of dispersal between sites generates the species diversity patterns

commonly described in the literature (Mouquet and Loreau 2002, 2003, Shanafelt et al. 2015,

Thompson and Gonzalez 2016). Here, the type of dispersal (advection vs. diffusion) and the

nature of the boundary conditions (absorbing simulating a finite-size linear environment vs.

periodic simulating an infinite-size environment) determine the structure of biodiversity in the

metacommunity. As species are subject to the same linear gradient under each scenario

(absorbing or periodic), differences only occur at high dispersal rates, which lead to lower

recruitment rates (due to greater propagule loss) with absorbing boundary conditions and higher

recruitment rates with periodic conditions, as species are able to reach parts of the spatial domain

that are similar to their optimal environmental condition. Overall, the shapes of the species

diversity curves are largely driven by the nature of dispersal whereas the heights of the curves

are mediated by the boundary conditions (Fig. 1). In the absence of dispersal, our simulations

confirm our analytical results: self-recruitment generates a strong positive local feedback

between adult abundance and propagule production that promotes species abundance in sites

characterized by their optimal environmental conditions (Fig. 1). This promotes competitive

exclusion and species sorting, which lead to low local diversity (α), high between-community

diversity (β) and high regional diversity (γ). Increasing dispersal (0 <μ < 3, 0 < σ < 5) reduces the

degree of self-recruitment and species sorting by generating a positive regional feedback

between sites via spatial rescue effects (Brown and Kodric-Brown 1977). This leads to an

increase in local diversity, a sharp reduction in between-community diversity, and a moderate

decline in regional diversity (Fig. 1a-d). Further increasing dispersal (μ, σ ≈ 5, 30) spatially-

homogenizes the metacommunity, destroys all spatial rescue effects, and reduces diversity at all

31

scales as regionally dominant species are able to competitively exclude most species across the

metacommunity (Fig. 1a-d).

For advective dispersal, local diversity is thus maximized at intermediate rates when

advection is high enough to promote spatial rescue effects but not so high as to prevent self-

recruitment. Indeed, high advective dispersal rates will spatially couple distant sites experiencing

different parts of the environmental gradient, so a species growing in a site characterized by good

environmental conditions will receive relatively few recruits from unproductive sites

experiencing poor environmental conditions. Hence, even if the vast majority of these arriving

recruits survive, abundance at the site experiencing good environmental conditions will be

relatively low since the supply rate will be limited. Conversely, a site characterized by poor

environmental conditions might receive a large supply of recruits from sites experiencing good

environmental conditions, but because most of those recruits will not survive, local species

abundance will also be low.

Diffusive dispersal promotes higher overall levels of species diversity by maintaining the

local positive feedback between abundance and recruitment as the dispersal kernel remains

centered on the natal site. Hence, self-recruitment can allow species in sites experiencing good

environmental conditions to establish larger populations and subsequently subsidize populations

at sites experiencing poor environmental conditions via source-sink dynamics (Pulliam 1988). At

higher dispersal rates, these mass effects allow for increased abundances for species in non-

optimal environments. While these patterns hold regardless of the strength of the environmental

gradient (Fig. 1a-d), differences in the diversity-dispersal relationship emerge in

metacommunities with absorbing vs. periodic boundary conditions (Fig.1 a,b vs. c,d).

32

Diversity levels are generally higher under periodic than absorbing boundary conditions

because under the latter, all species experience an effective reduction in their recruitment rates as

propagules are lost from the metacommunity (Fig. 1). This is particularly true when increasing

advective versus diffusive dispersal, which increases the rate at which propagules are whisked

away from the metacommunity (Fig. 1a,c vs. Fig. 1b,d). Regional diversity is driven by between-

community diversity (β) at low dispersal in metacommunities with absorbing boundary

conditions, as spatial rescue effects allow most species in the metacommunity to persist.

Intermediate rates of advection (Fig. 1a,b: μ, σ = 6, 10) reduce regional species diversity by

replacing the local positive feedback between abundance and self-recruitment in closed

communities with a regional negative feedback that allows the same set of regionally-dominant

species (species with higher regional- scale realized recruitment rate F) to monopolize the

metacommunity regardless of local environmental conditions. In doing so, advection shifts

control of regional diversity (γ) from between-community (β) to local (α) diversity. Additionally,

the negative regional feedback generates relatively uniform abundances for the few regionally-

dominant species across the entire range of dispersal advection (Fig. 2a; μ > 5).

Initially, similar trends appear in metacommunities characterized by periodic boundary

conditions (Fig. 2c,d). Low levels of diffusive dispersal promote spatial rescue effects and

spatially homogenize the metacommunity, thus allowing local diversity (α) rather than between-

community diversity (β) to dictate regional diversity (γ). Intermediate rates of diffusive dispersal

fully spatially homogenize the metacommunity, thus promoting competitive exclusion.

Interestingly, further increasing diffusion leads to an additional peak in both local and regional

diversity (σ ~ 10 – 30, depending on environmental gradient). Here, species are able to persist in

more locations throughout the metacommunity due to an environmental rescue effect whereby a

33

portion of the propagules produced in optimal natal sites arrive in equivalently optimal sites far

from their origin. This secondary match between a species’ physiological optima and the local

environment creates a boost in fitness resulting in the resurgence of rare species (Fig. 2d). Hence,

the primary peak in species diversity due to spatial rescue and the secondary peak in species

diversity due to environmental rescue yield fundamentally different patterns of community

structure, with the former being characterized by a more uniform species abundance distribution

(many abundant species) and the latter a skewed species abundance distribution (many rare

species; Fig. 2d).

This environmental rescue occurs at diffusion rates where dispersal is strong enough to

dampen spatial rescue effects, but not strong enough to homogenize the whole system, thus a

secondary peak in diversity exists for all environmental gradients. For weaker gradients (slopes

of 0.02 to 0.05), the secondary peaks in local and regional diversity emerge at lower levels of

diffusion because it is easier for dispersal to spatially homogenize a system that is less

environmentally heterogeneous (Fig. 1d). Hence, we expect that the second peak should shift to

the left (to lower diffusion rates) with decreasing environmental variation slopes (i.e., weaker

environmental gradients). Conversely, increasing the slope of the environment leads to the

occurrence of an increasingly distinct secondary peak at higher diffusion rates.

Patterns of metacommunity structure

We applied variation partitioning to the model output in order to determine how different levels

of dispersal advection and diffusion affect the ecological interpretation of the spatial and

environmental fractions in metacommunities with either absorbing or periodic boundary

conditions. In environments characterized by either absorbing and periodic boundary conditions,

increasing the advection (μ) or the diffusion (σ) rate ultimately decreases the spatial fraction by

34

allowing species to increasingly find and monopolize the sites characterized by their optimal

environmental conditions (Fig. 3). Regardless of the nature of dispersal or the boundary

conditions, the introduction of dispersal promotes spatial rescue effects that erode the

relationship between the environment and community structure, resulting in a spatial fraction

explaining as much as 90% of the total variation in community structure. Despite these general

similarities, there are key differences in the effect of increased dispersal on the spatial fraction

that depend on the boundary conditions and the nature of dispersal.

For absorbing boundary conditions, increasing either aspect of dispersal (advection or

diffusion) beyond the levels required for spatial rescue generally promotes species sorting which,

in effect, reduces the spatial fraction. However, as previously stated, a few regionally dominant

species dominate regardless of environmental conditions, so the spatial fraction never explains

less than 40% of the total variation in community structure regardless of the extent of dispersal

(Fig. 3c,f).

Conversely, under periodic boundary conditions, increasing advection versus diffusion has

different effects on the sign and the magnitude of the change in the spatial fraction. The most

discernible difference between the advection and diffusion appears at low levels of dispersal

(Fig. 3; i vs. l: 0 < μ, σ < 8). Initially, increasing the dispersal advection rate increases the spatial

fraction, with space explaining anywhere from 40 to 100% of the variation in community

structure, whereas increasing the diffusion rate causes a reduction in the variation explained by

the spatial fraction from 80 to less than 10% depending on strength of the gradient. Increasing

the dispersal advection rate creates a spatial lag between local environmental conditions and their

effects on recruitment and community structure. This spatial lag disrupts the local positive

feedback between abundance and self-recruitment, replacing it with a regional negative feedback

35

that erodes the correlation between environmental conditions and community structure and thus

increases the spatial fraction (Fig. 3i). Apart from the initial increase under advective dispersal,

the predominant trend is a reduction in the spatial fraction. This decrease begins at intermediate

dispersal rates (μ > 8), which lead to spatial homogenization and the loss of spatial rescue

effects. The spatial fraction remains high relative to the spatial fraction observed under diffusive

dispersal because species are less able to exploit the periodicity of the environment and do not

experience environmental rescue, resulting in the presence of a few regionally dominant species,

as in absorbing conditions.

Under diffusive dispersal, the initial decrease in the spatial fraction is a consequence of high

species sorting, where species are able to reach their environmental niche and exclude their

inferior competitors locally (Fig. 3l). As the diffusion rate increases, environmental rescue

increases the degree to which species are able to persist at (multiple) optimal locations,

effectively increasing the variation explained by the environment and further reducing the spatial

fraction. Overall, these results demonstrate that altering the rates of advective vs. diffusive

dispersal can lead to very different patterns of spatial variation in community structure under

periodic boundary conditions.

Empirical case study

To test our model predictions, we applied variation partitioning to a dataset containing

abundances of rocky intertidal species in the high, mid and low zone along the West Coast of the

United States. Species were grouped based on their pelagic larval duration (PLD), which served

as a proxy for dispersal ability (Shanks et al. 2003, Shanks 2009, Selkoe and Toonen 2011). This

case study shows that the spatial fraction can map to different PLD values (Fig. 4). Indeed, we

found no relationship between the spatial fraction and the community’s mean group PLD

36

(ANOVA; df = 3, F = 2.498, p-value = 0.07518; Table 1, Fig. 4) and a significant interaction

between PLD and zone (ANOVA; df = 6, F = 4.408, p-value = 0.00194; Table 1). Hence, the

relationship between PLD and the spatial fraction depends on zone. For instance, large spatial

fractions were associated with high PLD in the low zone but low PLD in the high zone (Fig. 4).

This means that the size of the spatial fraction alone is not a reliable predictor of the extent of

dispersal. Additionally, there was a significant relationship between the spatial fraction and zone

(ANOVA; df = 2, F = 14.933, P-value < 0.0001; Table 1). Furthermore, PLD explained a smaller

proportion of the variance in the spatial fraction than zone (𝜂A = 0.075 vs. 𝜂A = 0.299, Table

1). This suggests that there are other factors affecting the size of the spatial fraction beyond

dispersal (e.g., differences in desiccation stress across zones). Overall, these empirical results are

consistent with the effects of dispersal predicted by our model: the spatial fraction is not a

measure of dispersal alone and should thus not be used as a direct proxy. Instead, one needs to

account for the strength and nature of environmental forcing as well as the type of dispersal in

order to correctly interpret the size of the spatial fraction.

DISCUSSION

Our empirical and theoretical results indicate that the effects of dispersal on patterns of species

diversity and abundance cannot easily be determined by applying statistical variation partitioning

to observational data collected across multiple scales. Indeed, although increasing dispersal

consistently leads to a reduction in the spatial fraction, as predicted by theory, this signature

trend is unlikely to be detected from statistical snapshots of observational data because the size

of the spatial fraction depends on the complex interaction between environmental heterogeneity,

boundary conditions and dispersal. Our results have important implications for managing

complex and interconnected ecosystems experiencing environmental variability.

37

The effects of dispersal on biodiversity across scales

The effects of dispersal on community stability (Holland and Hastings 2008, Gouhier et al.

2010), persistence (Huffaker 1958, Blasius et al. 1999) and biodiversity (Brown and Kodric-

Brown 1977, Tilman 1994) have been well established in theory and practice (reviewed by

Briggs and Hoopes 2004, Holyoak et al. 2005). When dispersal is too low, environmentally

heterogeneous communities become dominated by the strongest local competitors, thus

generating low local (α) diversity and high between-community (β) diversity. This type of

species-sorting is typically associated with low community stability and persistence because each

species is rare at the regional scale and thus vulnerable to the loss of the few locations where

they are found. Intermediate levels of dispersal promote both species coexistence and community

stability by allowing source-sink dynamics to emerge across the metacommunity (Mouquet and

Loreau 2003, Gouhier et al. 2010). Under this scenario, the increased movement of organisms

leads to high local diversity and low between-community diversity. Overall, these types of

spatial rescue effects will arise as long as dispersal is not high enough to fully synchronize the

dynamics of all communities. If dispersal is too high, the entire metacommunity behaves like a

single, well-mixed community with low local diversity due to competitive exclusion by the

regionally dominant species, zero between-community diversity and low stability (Mouquet and

Loreau 2003, Gouhier et al. 2010).

Our results based on manipulating dispersal diffusion rates are largely consistent with these

predictions. Increasing diffusion initially leads to high local diversity and lower between-

community diversity due to source-sink dynamics (Fig. 1b,d). Further increasing diffusion leads

to spatial-homogenization and species-sorting, with low local, between-community and regional

diversity (Fig. 1b,d). However, when environmental conditions are periodic in nature, increasing

38

diffusion even further leads to an unexpected spike of local and regional diversity by (Fig. 1d)

due to environmental rescue effects. High levels of dispersal open up the opportunity for species

to reach a secondary optimal location, promoting the persistence and subsequent resurgence of

rare species, thereby promoting both local and regional diversity. Ultimately, very high diffusion

leads to spatial homogenization and low local, between-community and regional diversity (Fig.

1d).

This dispersal-induced bimodal diversity pattern in periodic environments, which is robust to

(i) the strength of the environmental gradient (Fig. 1d) and (ii) the addition of environmental

stochasticity (Appendix 1.2), differs from the unimodal predictions based on classical theory

(Mouquet and Loreau 2003). The difference is likely due to the use of a spatially-implicit

approach by Mouquet and Loreau (2003) whereby dispersing propagules were redistributed

uniformly across the metacommunity. Hence, although they were able to manipulate the degree

of mixing by altering the dispersal rate, the scale of mixing remained constant and global. In our

spatially-explicit framework, however, varying the diffusion rate and boundary conditions alters

the degree and the scale of mixing by changing the breadth of the dispersal kernel and the

linearity of the environmental gradient. We suggest that our results stem from the simultaneous

effect of the diffusion rate on the degree of self-recruitment, the scale of dispersal and the size of

the metacommunity. Our advection results further reinforce the notion that some degree of self-

recruitment is necessary to generate the spatial rescue effects described by classical theory. We

showed a uniform reduction in local, between-community and regional diversity when dispersal

advection was sufficiently large to disrupt self-recruitment (Fig. 1a). Here, by replacing the local

positive feedback between abundance and self-recruitment with a regional negative feedback,

advection essentially reduces the fitness of all species thus resulting in all communities

39

becoming populated by the same few regional dominants. These patterns are expected to hold as

long as the advection-to-diffusion ratio is sufficiently high so as to prevent self-recruitment (see

Appendix 1.3). Overall, our results suggest that species diversity across scales and the relative

influence of local vs. regional processes depend on the complex interplay between the size of the

metacommunity, the degree of self-recruitment and spatial extent of dispersal in

environmentally-forced metacommunities.

Detecting the effects of dispersal in the real world

The impracticality of conducting manipulative experiments at the scales needed to document the

effects of dispersal on biodiversity has prompted much interest in the development of statistical

variation partitioning methods to decompose metacommunity structure into its spatial and

environmental fractions (Borcard et al. 1992, 2004, Dray et al. 2006, Peres-Neto et al. 2006).

According to these variation partition frameworks, the environmental fraction will be large if

dispersal is high enough to allow species to reach their environmental niche and exclude their

competitors at local scales (species sorting), whereas the spatial fraction will be large if dispersal

is low enough to allow spatial rescue effects without promoting local competitive exclusion

(mass effect). Hence the spatial fraction should be proportional to the degree of dispersal

limitation in the metacommunity. Although such variation partitioning methods are increasingly

being applied to empirical datasets in order to determine the relative influence of environmental

heterogeneity and dispersal on (meta)community structure in nature, the interpretation of the

spatial fraction remains controversial (Gilbert and Bennett 2010, Tuomisto et al. 2012). For

example, using simulated data, Gilbert and Bennett (2010) showed that variation partitioning

methods were unable to correctly identify the relative importance of dispersal and environmental

heterogeneity. However, their tests of variation partitioning methods were based on ‘model-free’

40

simulated data that did not incorporate the dynamical feedbacks between local competition and

regional dispersal over multiple generations.

Here, using a dynamic metacommunity model, we were able to show that dispersal advection

and diffusion leave similar yet distinct signatures that can be detected via variation partitioning

under certain scenarios. Our results extend and support the classical ecological interpretation of

the spatial fraction by showing that increasing advective or diffusive dispersal ultimately reduces

the size of the spatial fraction under both absorbing and periodic boundary conditions. Although

this trend (i.e., the negative correlation between the spatial fraction and dispersal) is clear and

consistent across all simulated scenarios, the size of the spatial fraction alone cannot be used to

infer the relative importance of dispersal because the former depends on a multitude of factors

including the strength of the environmental gradient, the nature of dispersal and the type of

boundary conditions. Our empirical results are consistent with our simulations in that the spatial

fraction varies significantly across zones, a proxy for environmental stress, but not across PLD, a

proxy for dispersal. Furthermore, the significant interaction between PLD and zone suggests that

PLD is not a consistent predictor of the spatial fraction.

Taken together, these results resolve an important discrepancy between theoretical

expectations and empirical observations: although increased dispersal will ultimately reduce the

spatial fraction (negative trend) under all scenarios, as predicted by theory, detecting this elusive

signal in nature is likely to be fraught with difficulties due to the fact that observational studies

provide snapshots of the spatial fraction rather than trends and the former are influenced not only

by dispersal, but by the strength of the environmental gradient and the nature of the boundary

conditions.

41

That being said, the more information available about the nature of dispersal and the size of

the metacommunity, the more insights can be gleaned about the mechanisms driving the patterns

in community structure. In finite-size metacommunities (simulated via absorbing boundaries and

a linear environment), the spatial fraction explains more than 40% of the variation in community

structure, suggesting that spatial rescue effects are driving coexistence patterns and diversity

levels. The added mortality associated with finite boundaries (propagules are leaving the system)

mitigates the differential impact of advective vs. diffusive dispersal on spatial community

structure. Conversely, in infinite-size metacommunities (simulated via periodic boundaries and a

periodic environment), species do not have to contend with added propagule loss, so the nature

of dispersal plays a much larger role. Here, a higher degree of self-recruitment can bolster the

ability of species to thrive locally and persist at the regional level. Thus, the mechanisms driving

the magnitude of the spatial fraction in periodic environments are the increased availability of

suitable environmental conditions and the high degree of self-recruitment due to diffusive

dispersal which, when combined, enable rare species to persist across the metacommunity via

both spatial and environmental rescue. Overall, our results suggest that although variation

partitioning methods could, in theory, be used to tease apart the relative importance of

environmental heterogeneity and dispersal on community structure, their direct applicability in

the real world is likely to be limited. Hence, while a negative relationship between dispersal and

the spatial fraction may be an indicator of increased connectivity in metacommunities, the size of

the spatial fraction alone is not sufficient to determine the extent of connectivity in natural

systems. Consequently, our results highlight the mistakes likely to be made when attempting to

infer ecological mechanisms from statistical snapshots of natural metacommunities via variation

partitioning.

42

Managing environmentally-forced and interconnected ecosystems

Metapopulation theory has long been used to inform conservation and management decisions

because of its ability to account for the effects of local and regional processes on the persistence

of species across scales (reviewed by Hanski 1998). Indeed, metapopulation theory is largely

responsible for identifying the role of connectivity in maintaining local populations. Although

promoting connectivity has become a key objective in the spatial management of interconnected

ecosystems (Botsford et al. 2001, 2003), too much connectivity can be detrimental to persistence

by synchronizing and destabilizing the dynamics of metacommunities (Gouhier et al. 2010a,

2013). Hence, determining when connectivity will promote or reduce persistence is critical in

order to effectively manage and conserve natural ecosystems (Earn et al. 2000).

Our results suggest exercising caution when attempting to evaluate the extent of connectivity

in a metacommunity via variation partitioning. Indeed, a small spatial fraction can emerge for

either low or high rates of advective or diffusive dispersal under both absorbing and periodic

boundary conditions. Hence, the size of the spatial fraction alone is not sufficient to infer the

extent of dispersal or connectivity in metacommunities. We suggest that applying variation

partitioning to system-specific dynamical models parameterized with real data can help improve

our ability to understand and manage natural systems by mapping statistical patterns in

metacommunity structure to their underlying ecological processes.

43

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Table 1.1 Summary of ANOVA model testing the effects of mean group pelagic larval duration (PLD) and zone on the spatial fraction obtained via variation partitioning. Source df MS F P-value Effect size ("#)

Mean PLD 3 0.2167 2.498 0.07518 0.075

Zone 2 1.2954 14.933 1.89e-05 0.299

Mean PLD x Zone 6 0.3824 4.408 0.00194 0.265

Residuals 36 0.0868 0.361

Note: Analysis was conducted on log10-transformed spatial fractions.

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FIGURES

Figure 1.1 Metacommunity species richness at multiple spatial scales as a function of dispersal advection (a) and diffusion (b) for different environmental gradients. Red, blue and black lines depict local (α), between community (β) and regional diversity (γ), respectively. In addition to the color (red, blue, black) the translucence of each line represents the strength (slope) of the environmental gradient, which ranges from low (lighter hues) to high (darker hues). Results represent means from 10 replicate simulations. The vertical dashed line in panel (a) depicts when advection rates are high enough to prevent self-recruitment (μ > 2σ » 5).

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51

Figure 1.2. Species rank abundance as a function of dispersal advection rate (a) and diffusion rate (b). The regional mean abundance of each species is plotted on a log scale as a function of species rank abundance. Color represents log abundance, which ranges from low (cool colors) to high (warm colors). Results represent means from 10 replicate simulations.

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52

Figure 1.3. Variation partitioning of community structure as a function of dispersal advection rate (a-c) and diffusion rate (d-f). Community structure was partitioned into three fractions: the environment ⟨𝐸|𝑆⟩, space⟨𝑆|𝐸⟩, and their joint influence or intersection ⟨𝐸 ∩𝑆⟩ (i.e., the fraction of the variation in community structure jointly influenced by space and the environment). Line color and translucence represent the strength (slope) of the environmental gradient, which ranges from low (lighter hues) to high (darker hues). Results represent means from 10 replicate simulations.

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∩

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53

Figure 1.4. Variation partitioning results for an intertidal metacommunity. Community structure was partitioned into three fractions: the environment ⟨𝐸|𝑆⟩, space⟨𝑆|𝐸⟩, and their joint influence or intersection ⟨𝐸 ∩𝑆⟩. The spatial fraction was plotted as a function of intertidal zone (low, mid, high). The color of the bar (white, light grey, dark grey, black) indicates mean group pelagic larval durations (PLD), a measure of dispersal ability (direct dispersers, low, medium, high). Overlapping horizontal lines indicate bars that are not statistically different at the alpha = 0.05 significance level. Analysis was conducted on log10-transformed spatial fractions.

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54

CHAPTER 2

Coexistence mechanisms collide across scales

ABSTRACT

Understanding how coexistence mechanisms operating at different scales give rise to

biodiversity is critical for both predicting and managing the dynamics of natural ecosystems in a

variable world. For instance, species interactions such as facilitation have been shown to

promote coexistence at local scales. At regional scales, dispersal across environmentally

heterogeneous landscapes can promote coexistence via spatial rescue effects that prevent species

from monopolizing their preferred habitat. Although a number of coexistence mechanisms have

been identified, relatively little is known about how they interact across scales to control local

and regional biodiversity. To address this issue, we developed a spatially-explicit

metacommunity model that included local (recruitment facilitation), regional (spatial

environmental heterogeneity) and tradeoff-based (competition-colonization) coexistence

mechanisms in order to determine their joint influence on patterns of diversity and extinction

risk. We found that recruitment facilitation, competition-colonization tradeoffs and

environmental heterogeneity interacted antagonistically to reduce biodiversity and promote

extinction risk at both local and regional scales. Our results suggest that classical approaches

focusing on a single spatial scale or a single coexistence mechanism may not yield fundamental

insights about the processes that structure natural ecosystems. Instead, our results call for a shift

from single- to multi-scale frameworks that account for interactions between coexistence

mechanisms in order to better understand the dynamics of complex and interconnected

ecosystems.

55

INTRODUCTION

Ecologists have long sought to explain Hutchinson’s “paradox of the plankton”, or how multiple

species can persist in natural systems despite competing for the same set of limiting resources

(Hutchinson 1961). Initial efforts to understand this phenomenon were primarily focused on

local scales, with studies investigating how species interacted in their local environments. For

instance, Connell (1961) showed how environmental differences between tidal zones influenced

interactions and community structure, with high (low) desiccation stress in the high (low) zone

leading to weak (strong) species interactions and dominance between by inferior (superior)

competitors. Following this work, Menge and Sutherland (1987) examined the roles of predation

and competition along a gradient of environmental stress in intertidal communities by developing

Environmental Stress Models (ESM). ESM suggested that community regulation depended on

the interaction between abiotic and biotic factors, with disturbance rather than species

interactions driving community structure under stressful environmental conditions. With

competition as the dominant driver under intermediate environmental conditions, and trophic

interactions playing a more prominent role under favorable environmental conditions. ESM set

the stage for studies investigating the relative influence of both abiotic and biotic factors in

understanding local species assemblages and coexistence. By incorporating facilitation, Bruno et

al. (2003) extended classic ESM by including the influence of intraspecific facilitative

interactions such as associative defenses on community structure under favorable environmental

conditions and the effects of interspecific facilitation under stressful environmental conditions.

That study highlighted the importance of positive interactions in structuring ecological

communities and introduced a reexamination of well-established paradigms about species

assemblages based solely on negative species interactions (e.g., competition, predation).

56

Together, this early work demonstrated the importance of incorporating information about both

environment and species interactions to understand coexistence at local scales.

Motivated by the fact that habitat patches do not exist in isolation, studies examining the

drivers of species coexistence expanded beyond local scales, focusing on the role of regional

scale processes. The theory of island biogeography began much of this work, investigating

regional processes such as colonization and patch size as drivers of biodiversity (MacArthur and

Wilson 1967). This theoretical framework showed that an island’s size and distance to the

mainland were critical determinants of species richness because they controlled, respectively, the

regional colonization rate and the local extinction rate. However, this framework focused

exclusively on the unidirectional effects of the mainland on islands and thus ignored both island-

to-island and island-to-mainland spatial feedbacks. Patch-dynamic models emerged as a way to

account for such feedbacks by examining the reciprocal effects of dispersal between local

patches on diversity at regional scales (Levins and Culver 1971, Hastings 1980, Tilman 1994).

For example, Levins and Culver (1971) showed that when environmental conditions were

homogeneous throughout the landscape, an interspecific competition-colonization tradeoff could

allow coexistence between species that were competitively superior but relatively sessile and

those that were competitively inferior but sufficiently mobile. By including spatial feedbacks

between patches, this framework highlighted the ability of tradeoffs across scales to promote

coexistence even when species competed for the same set of limiting resources (e.g., space). The

finding that two species could exhibit stable coexistence on a single resource via a competition-

colonization tradeoff was later extended to an indefinitely large number of species (Hastings

1980, Tilman 1994) despite the suggestion that doing so would be “formidable mathematically”

(Levins and Culver 1971). These and similar studies led to the development of metacommunity

57

theory, which sought to understand how local species interactions and regional dispersal interact

to govern the distribution of species across scales (Leibold et al. 2004, Holyoak et al. 2005).

Just as the inclusion of positive interactions in ESM affected predictions about

communities assembled, the integration of facilitation into metacommunity theory led to the

emergence of new and often less restrictive coexistence conditions (Guichard 2005, Gouhier et

al. 2011). For instance, Gouhier et al. (2011) found that recruitment facilitation could give rise to

coexistence even in the absence of a competition-colonization tradeoff. Specifically, the ability

of a subordinate species to facilitate the recruitment of a dominant species was found to promote

stable coexistence (and thus diversity) and buffer population growth by shifting patterns of

abundance from regional to local competitive processes. In addition to elucidating the effects of

positive species interactions, modern metacommunity theory has also shown how environmental

heterogeneity and dispersal can jointly influence biodiversity across scales (Loreau et al. 2003,

Mouquet and Loreau 2003, Bode et al. 2011, Salois et al. 2018). For instance, under spatially

variable but temporally constant environmental conditions, limited dispersal between discrete

populations due to either low rates (Mouquet and Loreau 2003) or small scales (Salois et al.

2018) tends to reduce local (α) diversity and increase between-community (β) diversity due to

species sorting, whereas intermediate dispersal tends to increase local diversity and reduce

between-community diversity by allowing the emergence of spatial rescue effects. Recent

theoretical advances have also demonstrated that spatiotemporal variation in dispersal can

promote coexistence when species experience sufficiently different connectivity patterns due to

asynchronous spawning times (Berkley et al. 2010, Aiken and Navarrete 2014).

Despite the large body of work identifying a variety of local and regional coexistence

mechanisms, little is known about how these processes interact. For this study, we created a

58

synthetic metacommunity which included both local (competition, recruitment facilitation) and

regional processes (dispersal, spatial heterogeneity) known to promote coexistence to determine

the consequence of their interaction on patterns of species diversity and abundance. Specifically,

we extended the patch-dynamic metacommunity framework by simulating species whose

competitive abilities were negatively correlated with their colonization rates in order to ensure

coexistence within a site. We then added recruitment facilitation, which controlled the degree to

which dominant species could colonize free space. Finally, we implemented spatial

environmental heterogeneity in the form of a linear gradient controlling recruitment success,

which each species having a different optimum.


The metacommunity model

To determine how local and regional processes known to promote coexistence interact to affect

species diversity and abundance, we constructed a hierarchical metacommunity model whereby

local (within-site) dynamics are spatially-implicit and regional (among-site) dynamics are

spatially-explicit (Fig.1). Sites in the model are (i) arranged along a 1-dimensional array with

absorbing boundary conditions (e.g., a coastline; Fig.1a), (ii) characterized by different

environmental conditions (Fig. 1b) and (iii) interconnected by regional dispersal (Fig.1a,c).

Coexistence in the metacommunity can arise via three distinct mechanisms: a competition-

colonization tradeoff between species (Levins and Culver 1971, Hastings 1980, Tilman 1994),

recruitment facilitation (Menge et al. 2011, Gouhier et al. 2011) and regional environmental

heterogeneity (Mouquet and Loreau 2003). Competition between species is hierarchical so that

dominant species deterministically displace subordinate species (Levins and Culver 1971,

Hastings 1980, Tilman 1994). Recruitment facilitation in the model describes the dependency of

59

the dominant species on the subordinates, with obligate facilitation depicting full dependency

whereby dominant species can only colonize patches already occupied by their subordinates (see

Fig. 1a, Guichard 2005, Gouhier et al. 2011). This type of positive interaction is common in

intertidal systems where subordinate species often facilitate the recruitment of dominant species

by providing them with a rugose surface to settle onto and avoid disturbance (Connell and

Slatyer 1977; Berlow 1997; Halpern et al. 2007; Menge et al. 2011). More generally, this

formulation of facilitation corresponds to Connell & Slatyer’s (1977) classical facilitative model

of succession, whereby early succession species (i.e., subordinates) modify the substrate and

promote the subsequent colonization of late succession species (i.e., dominants). Overall, these

processes are modeled with the following set of ordinary differential equations that describe the

dynamics of S species ranked from dominant (species 1) to subordinate (species S) interacting at

each site, x, along a one-dimensional array consisting of L distinct sites:

d𝑁"(𝑥)d𝑡 = 𝑐"(𝑥)p q 𝑁4(𝑥) + (1 − 𝑓)

5

46"s7

t1 −q𝑁"(𝑥)5

"67

uv −𝑚"𝑁"(𝑥) − 𝑁"(𝑥)q𝑐4(𝑥)"B7

467

d𝑁5(𝑥)d𝑡 = 𝑐5(𝑥) t1 −q𝑁"(𝑥)

5

"67

u − 𝑚5𝑁5(𝑥) − 𝑁5(𝑥)q𝑐4(𝑥)5B7

467

Where the density 𝑁" of each species 𝑖 is mediated by the interplay between its realized

colonization rate (𝑐"), the amount of space available 01 − ∑ 𝑁"(𝑥)5"67 8, the degree of recruitment

facilitation (𝑓), natural mortality (𝑚"), and competitive displacement by dominant species

0−𝑁"(𝑥)∑ 𝑐4(𝑥)"B7467 8. Here, 𝑐"(𝑥) represents the realized colonization rate of species 𝑖 at site 𝑥.

This realized colonization rate is the product of each species’ potential recruitment rate 𝑟"(𝑥),

and fitness 𝐹 in that environment𝐸(𝑥) according to the following relationship:

𝑐"(𝑥) = 𝑟"(𝑥)𝐹(𝐸(𝑥), 𝑜")

60

Where the potential recruitment rate 𝑟"(𝑥) is the convolution of the product of propagule

production 𝑝" and density 𝑁" at site 𝑥 with the dispersal kernel 𝑘(𝑥):

𝑟"(𝑥) = w 𝑝"𝑁"(𝑦)𝑘(𝑥 − 𝑦)d𝑦?/A

B?/A

The term 𝑟"(𝑥) thus denotes the total number of recruits from species 𝑖 arriving at each site

from all other sites 𝑦 via dispersal. The dispersal kernel itself is a normalized (i.e., sums to 1)

Gaussian distribution with mean 𝜇 = 0 and variance 𝜎:

𝑘(𝑥) =1

𝜎√2𝜋𝑒B

(&By)IACI

Finally, each species’ fitness 𝐹 is represented by a bell-shaped curve around a species-specific

optimum 𝑜" such that the fitness of species 𝑖 at site 𝑥 is:

𝐹(𝐸(𝑥), 𝑜") = 𝑒B(z(&)B`$)I

A

Hence, the smaller the difference between a species optimum and the environment, the greater its

propagule survivorship and realized recruitment rate. Spatial environmental heterogeneity was

implemented via a simple linear gradient as follows:

𝐸(𝑥) = 𝑚𝑥 + 𝑣

Model simulations We simulated a range of recruitment facilitation scenarios via a uniformly-spaced vector of 50

values ranging from 0 (no facilitation) to 1 (full facilitation). We included a competitive

hierarchy and facultative dependency between species to model interactions commonly found in

marine systems between sessile species with larval dispersal (Connell 1961, Paine 1992, Menge

et al. 2011, Gouhier et al. 2011). Species within our metacommunity interacted in continuous

time over a spatially-heterogenous landscape of 140 sites that comprised a linear gradient of

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61

environmental conditions (i.e., a uniformly spaced vector of 140 values ranging from 0 to 1). We

varied the diffusion rate (𝜎) of the dispersal kernel across simulations to simulate an array of life

history strategies for propagules ranging from direct developers (𝜎 = 1 ×10B|) to long

distance dispersers (𝜎 = 30). For each simulation, the facilitation level and dispersal rate were

fixed and abiotic conditions were constant in time (slope 𝑚 = 0.05) but species-specific

environmental optima 𝑜" were selected randomly from a uniformly-spaced vector of 20 values

ranging from the minimum to the maximum environmental condition 𝐸(𝑥). Initial conditions for

all species paired random mortality rates with negatively correlated competitive abilities and

colonization rates in order to ensure coexistence under the competition-colonization tradeoff

(following the scheme described in Tilman 1994). Specifically, we set the equilibrium abundance

�̂�" of species 𝑖 to a value based on a geometric series such that �̂�" = 𝑧(1 − 𝑧)"B7 with 𝑧 = 0.15.

We then set each species’ mortality rate 𝑚" to a random value from the uniform distribution

𝑈(0,1) and computed the necessary colonization rate needed for coexistence 𝑐" =

∑ ]�a\as�7B∑ ]�a$G�a�� \$

$G�a��

�7B∑ ]�a$G�a�� 7B∑ ]�a$

a�� . The model equations were solved numerically using an explicit Runge-

Kutta (4,5) formula in MATLAB (function ode45) for 2,000 time steps.

Model analyses

The model results were analyzed using two complementary approaches. First, we used species’

presence/absence information to partition biodiversity into local (α), between-community (β),

and regional (γ) diversity using standard methods (Whittaker 1972, Mouquet and Loreau 2003).

Regional diversity γ was measured as the total species richness across the entire metacommunity

and local diversity α was measured as the average species richness within each site. Between-

community diversity β was measured as the difference between regional and local diversity.

62

Next, extinction risk was calculated for each species across all dispersal-diffusion rates (s) and

facilitation levels (f). Specifically, for each combination of dispersal diffusion rate and

facilitation level, each species’ extinction risk was computed as the proportion of replicate

simulations where abundance fell below a minimum threshold of 10-6.

RESULTS

Diversity across scales

In the absence of dispersal (𝜎 ≈ 0), regional diversity (𝛾) across the metacommunity is largely

driven by high between-community diversity (𝛽) because local diversity (𝛼) is low, with each

site being dominated by the species whose physiological optimum most closely matches the local

environment (Fig. 2). The introduction of dispersal (𝜎 > 0) shifts the driver of regional diversity

from 𝛽 to 𝛼 diversity due to spatial rescue effects, which promote local species richness.

Eventually, at high levels of dispersal (𝜎 > 5), spatial rescue effects are lost resulting in a decay

of species richness as the system becomes homogenized due to increased mixing. Facilitation

works to amplify these trends as evidenced by a general decrease in species diversity across all

levels of facilitation and a sharp reduction at higher facilitation levels (Fig. 2a-c). In this case,

facilitation has a negative impact on species diversity, as it reduces species richness at all scales.

Hence, spatial environmental heterogeneity and recruitment facilitation, two mechanisms that are

often associated with coexistence, actually interact antagonistically when combined (Fig. 2). This

pattern emerges due to the fact that dominant and subordinate species do not have the same

optimum environment, yet under full facilitation the dominant species can only colonize sites

where the subordinate species is present. The dominant is thus co-dependent on both the

subordinate species and site-specific environmental conditions for recruitment. Because both

requirements can never be met in a single location (i.e., no location will be characterized by

63

optimal environmental conditions for both the dominant species and the subordinate species it

depends on), the dominant species must recruit in locations that are environmentally suboptimal,

which decreases its overall fitness.

Extinction risk Extinction risk provides a useful metric that complements patterns of diversity by highlighting

winning vs. losing species across the metacommunity in the presence of multiple coexistence

mechanisms. Overall, there is a U-shaped relationship between dispersal and extinction risk (Fig.

3). This general pattern of extinction risk occurs across all levels of facilitation, with the strength

of the signal dependent on each species’ competitive ranking. Dominant species experience a

shallower dip and faster recovery than subordinate species. This distinction is dampened as

facilitation increases (Fig. 3a vs. 3c). Regardless of species identity and facilitation, species

persistence is highest at intermediate dispersal values (0 < s < 10) due to spatial rescue effects,

resulting in high local diversity (α) driving high regional diversity (γ; Fig. 2) and low extinction

risk (Fig. 3).

In a purely competitive system (recruitment facilitation f = 0), the average local

extinction risk for the dominant species is high at all but intermediate levels of dispersal (Fig.

3a,b). At low dispersal rates (𝜎 ≈ 0), while the dominant species does not experience

competition for space, their low recruitment potential necessitates a reliance on spatial rescue

effects, which only occur at intermediate diffusion rates. At high rates of dispersal (𝜎 > 10), the

propagules produced by the dominant species become spread too thin across the spatial domain,

resulting in fewer of them landing in source sites, and thus eroding the spatial rescue of sink

populations and promoting extinction risk. The introduction of facilitation only serves to amplify

this effect of dispersal, with the dominant species losing the benefits of low-to-intermediate rates

64

of dispersal and suffering high extinction risk across the metacommunity (Fig. 3b,c). The

subordinate species performs much better across the whole range of dispersal because they have

much higher colonization potential due to the nature of the competition-colonization tradeoff.

Additionally, the introduction of recruitment facilitation competitively releases subordinate

species, thus decreasing extinction risk regardless of dispersal ability (Fig 3a vs. b,c).

The shifting burden of coexistence In classical competition-colonization tradeoff models (Levins and Culver 1971, Hastings 1980,

Tilman 1994), the burden of coexistence is always on the subordinate species, whose

colonization rates must be sufficiently larger than those of dominant species in order to persist.

However, our results show a shift in the burden of coexistence from the subordinate species to

the dominant. This shift emerges regionally via dispersal and locally via facilitation and becomes

amplified as the two processes interact. At regional scales, because the competition-colonization

tradeoff necessitates that dominant species produce fewer propagules than subordinates,

increased dispersal causes dominant species to spread their limited number of propagules across

more sites characterized by unfavorable environmental conditions, resulting in higher extinction

rates across the metacommunity (Fig. 3a). By increasing the dominant species’ extinction risk,

dispersal shifts the burden of coexistence away from the more productive and less extinction-

prone subordinate species. This is exacerbated by facilitation due to the dominant’s

irreconcilable co-dependency on the environment and subordinate species (Fig. 3b,c). At local

scales, facilitation drives this shift by reducing the available habitat for the dominant species. As

facilitation increases, the dominant species suffers even greater extinction risk with the added

dependency on the subordinate. This dependency generates a reduction in the recruitment of the

dominant species as they are increasingly confined to sites characterized by suboptimal

65

environmental conditions where the subordinate species are abundant. At intermediate to high

levels of dispersal and facilitation, these patterns become more pronounced as dispersal,

facilitation and environmental heterogeneity interact to promote the persistence of subordinate

species and the extinction of the dominant species. Indeed, when recruitment facilitation is

obligate (facilitation f = 1), only the most subordinate species is able to persist across the

metacommunity (Fig. 3a vs. c).

DISCUSSION

Diversity can be maintained via many types of coexistence mechanisms operating at different

scales (Levins and Culver 1971, Hastings 1980, Tilman 1994, Chesson 2000, Amarasekare et al.

2004, Aiken and Navarrete 2014). Although it is widely accepted that many of these coexistence

mechanisms likely operate simultaneously in nature (Levine et al. 2017, Letten et al. 2018), the

logistical constraints associated with documenting them across different spatial and temporal

scales have left their interactions relatively under-explored. Here, we have shown that in a virtual

metacommunity, coexistence mechanisms operating at different scales can interact

antagonistically to erode biodiversity and shift the burden of coexistence from competitively

subordinate to dominant species. These results have important implications for linking patterns

to their underlying processes across scales and for understanding how ecological communities

may disassemble and reassemble in response to environmental change.

Linking patterns to processes across scales Competition-colonization tradeoffs (Levins and Culver 1971, Tilman 1994), spatial

environmental heterogeneity (Mouquet and Loreau 2003), and recruitment facilitation (Gouhier

et al. 2011) can promote coexistence in metacommunities. However, instead of operating

additively to promote biodiversity, we found that these coexistence mechanisms actually reduced

66

biodiversity due to their antagonistic interaction across scales. Specifically, when facilitation was

combined with regional environmental heterogeneity and a competition-colonization tradeoff, a

shift occurred in individual species’ response to increased dispersal and species interaction

strength. Interspecific differences in environmental optima, when combined with spatial

environmental heterogeneity, led to spatial variation in fitness across species. Biodiversity was

maintained either regionally via high between-community but low within-community diversity

when dispersal was low due to species sorting, or locally via low between-community but high

within-community diversity due to spatial rescue effects when dispersal was high. The addition

of recruitment facilitation reduced the fitness of dominant species by inducing a co-dependency

on the environment and subordinate species that was unattainable due to interspecific differences

in environmental optima (“collision of coexistence mechanisms”).

The effects of this antagonistic interaction between coexistence mechanisms have

parallels to how habitat destruction competitively releases inferior species in metacommunities

(Nee and May 1992). Both mechanisms (habitat destruction, collision of coexistence

mechanisms) increase the regional abundance of the subordinate species and reduce that of the

dominant species. Similar to habitat destruction, recruitment facilitation is able to promote the

persistence of the inferior competitor by decreasing the number of patches that can be occupied

by the superior species. Unlike habitat destruction, this reduction in available patches occurs

both directly by effectively removing free space for dominant species and indirectly by making

dominants depend on subordinate species who do not share the same optimal environmental

conditions. This shift in the way in which species are interacting in space explains how

mechanisms found to promote coexistence when studied in isolation, can lead to extinction and

lower diversity at both local and regional scales when combined. Overall, our results suggest that

67

understanding the drivers of community structure in nature requires the integration of

coexistence mechanisms and their interactions across scales.

Accounting for interacting coexistence mechanisms to prioritize conservation efforts Landscapes are changing across all scales due to the direct and indirect effects of anthropogenic

pressures. While some ecosystems are becoming more heterogeneous in space via fragmentation

or changes in nutrient availability due to eutrophication (Hanski 2011, Hautier et al. 2014,

Gerber et al. 2014), others are becoming more homogenous due to large scale changes in climate

(Bertness et al. 2002, Pershing et al. 2015, Wang et al. 2015). Developing an understanding of

why and how communities shift across scales will be of particular importance in areas where

land use changes alter spatial heterogeneity and thus the competitive environment. Recent work

has identified the colonization ability of dominant species as a principal factor driving

community composition and species richness in marine intertidal systems (Bryson et al. 2014,

Morello and Etter 2018). Furthermore, Sorte et al. (2017) documented large declines in Mytilus

edulis populations (> 60%) along the Gulf of Maine, an area known for its rapid warming

(Pershing et al. 2015, Sorte et al. 2017). Unfortunately, increased extinction risk for dominant

species is not unique to intertidal systems in the Anthropocene (Bertness et al. 2002, Ellison et

al. 2005).

Our results demonstrate that such outcomes are to be expected when coexistence is

mediated by a competition-colonization tradeoff and recruitment facilitation, as dominant species

tend to be more susceptible to extinction (depending on dispersal ability), whereas subordinate

species are less prone to extinction (regardless of dispersal ability). It is thus crucial to include

coexistence mechanisms such as positive species interactions when attempting to both predict the

community-level effects of climate change and prioritize conservation efforts (Davis et al. 1998,

68

Suttle et al. 2007, Harley 2011). Determining how coexistence mechanisms interact in nature and

understanding the resulting effects on species extinction risk will require the quantification of

interspecific differences in recruitment and production at both local and regional scales. An

important next step will be to determine how the relative importance of different coexistence

mechanisms varies in space and time as communities become reorganized due to species

extinctions following environmental perturbations (Levine et al. 2017). Information of this kind

will be critical for prioritizing conservation efforts going forward. If for instance, the dominant

species is also a foundational species (e.g.: Spartina alternaflora, Mytilus edulis, Crassostrea

virginica, Zostera marina, etc.), changes in the dynamics, abundance or relative fitness of that

species could have wide ranging repercussions. As foundational species fundamentally shape and

modify species assemblages and habitats, increased extinction risk among these species can

cascade across scales by affecting species composition and modulating ecosystem processes

across whole landscapes. Additionally, because many foundational species provide key

ecosystem services, the ability to better understand shifts in the persistence of dominant species

would likely aide mitigation strategies in economically and ecologically important ecosystems.

Hence, incorporating multiple local and regional coexistence mechanisms is critical for

predicting their interactive effects on spatial patterns of biodiversity and prioritizing conservation

efforts in a rapidly changing world.

69

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FIGURES

Figure 2.1 Schematic diagram of the spatially-explicit metacommunity model. Panel (a) describes competition for space between a dominant (N1) and subordinate (N20) species along an environmental gradient. Each site x along the one-dimensional array is characterized by a particular environmental condition 0𝑒(𝑥)8, based its location, (𝑥"), along the linear gradient ranging from high (black: E+) to low (grey: E-). Sites exchange propagules via dispersal. In the absence of facilitation (𝑓 = 0), competition for space is based on classic competition-colonization tradeoffs where the dominant species can colonize both free space and any patch occupied by a subordinate species. Conversely, when facilitation is obligate (𝑓 = 1), the dominant species can only colonize sites occupied by a subordinate. Panel (b) describes how recruitment is modified by the environment, where propagule survivorship in a given site is determined by the match or mis-match between each species’ optimum (𝑜") and local environmental conditions 0𝑒(𝑥)8. Panel (c) depicts dispersal which was implemented via a Gaussian kernel whose standard deviation (𝜎) controls the degree of diffusion.

0.0

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Environment at each site & '

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74

Figure 2.2 Metacommunity species richness at multiple spatial scales as a function of dispersal diffusion and recruitment facilitation. Panels depict (a) local (α), (b) between-community (β) and (c) regional (γ) diversity. Color represents species richness, with cool colors representing low species richness and warm colors representing high species richness. Results represent means from 10 replicate simulations across 30 levels of dispersal and 50 levels of facilitation.

Species richness

Dispersal rate

Facilitation

Species richnessDispersal rate

Facilitation

Species richness

Dispersal rate

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Dispersal rate

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Spp. richness

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75

Figure 2.3 Species extinction risk as function of dispersal rate (a) without recruitment facilitation, (b) with intermediate recruitment facilitation, and (c) with full facilitation. Color represents species identity based on competitive ranking, with cool colors representing subordinate species and warm colors representing dominant species. Results represent means from 50 replicate simulations across 30 levels of dispersal and 3 levels of facilitation.

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76

CHAPTER 3

Coastal upwelling generates cryptic temperature refugia

ABSTRACT

Natural systems are undergoing tremendous modification due to the rapidly changing

climatic conditions of the 21st century. Anticipated changes in the intensity, frequency and

duration of extreme events are expected to impact the biogeographical patterns of organisms

across the globe; therefore, ecological studies are increasingly focused on forecasting shifts in

the distribution and persistence of species. However, a consensus on which scales are needed to

accurately predict patterns of change and their underlying mechanisms has not yet been reached.

Here, we used wavelet analysis to document variation in daily water temperature at biologically-

relevant scales over 7 years and across 16 intertidal sites spanning 2,000 km of the Canary

Current System. We found that coastal upwelling promotes the emergence of both temporal and

spatial refugia during summer months when temperature stress is at its highest. In doing so, this

study highlights the importance of accounting for small-scale variation in water temperature to

accurately quantify temporal trends and identify spatiotemporal ecological refugia that could

promote persistence in a rapidly warming world.

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INTRODUCTION

Ascribing ecological patterns to their underlying processes is fraught with difficulties because

the dynamics of natural systems are linked across time and space via the interplay of ecological

and environmental factors operating at multiple scales (Levin 1992). This inherent complexity

(May 1972, Menge and Sutherland 1987) has led to fundamental debates about the most

appropriate scale for studying ecological systems (Lawton 1999, Simberloff 2004, Ricklefs

2008). Some ecologists favor macroecology, where the focus is on large scales, claiming that

small-scale idiosyncrasies disappear at large scales making statistically consistent patterns more

likely (Lawton 1999). While macroecological studies may be useful for documenting patterns

that hold across large swaths of taxa and systems, these approaches are often unable to link these

general patterns to their causal mechanisms. For instance, a review by McGill et al. (2007)

highlighted dozens of mechanisms ranging from niche to neutral assembly processes that could

explain the “hollow curve”, the quasi-universal distribution of abundance observed across

communities dominated by a few abundant species and a multitude of rare ones. Because such

patterns often emerge in response to a myriad of processes based on fundamentally different

assumptions about the natural world, ascribing them to a specific mechanism is often difficult.

Hence, the search for universality can be characterized as a double-edged sword because

predictability often comes at the cost of understanding. Conversely, community ecology is

focused on local processes and patterns. This approach is amenable to experimental work which

has proven to be a valuable way to determine the mechanistic underpinnings of many ecological

patterns (Simberloff 2004). While the local scales of community ecology more readily lend

themselves to empirical work (as compared to the regional scales of macroecology), including

exhaustive communities via manipulative studies is not feasible, so a majority of work has

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focused on pairwise interactions between species which are then built into n-species models to in

effort to gain insights about population dynamics (McGill et al. 2006). This combined with the

fact that there are an intractably large number and types of species interactions simultaneously

occurring at the community level, make it hard to ‘scale up’ to whole communities from simple

community modules (Brose et al. 2005). Hence, while community ecology can often reveal the

mechanisms that underpin local patterns, these relationships often do not hold across systems and

scales (Ricklefs 2008). Metacommunity ecology attempts to bridge the gap between community

ecology and macroecology by integrating both local and regional processes in order to

understand ecosystem structure across scales (Leibold et al. 2004, Holyoak et al. 2005). This

framework evolved in response to findings that scale-dependent approaches of both

macroecology and community ecology were fundamentally limited by the shared assumption

that processes give rise to patterns at corresponding scales. More specifically, this approach

addressed the limitations of macroecology, which necessitates the exclusion of biotic interactions

(Pearson and Dawson 2003), environmental variables and spatial heterogeneity, common in

community ecology (Gilman et al. 2010). This cross-scale approach demonstrated that even in

the presence of strong regional processes, species interactions can have significant impacts on

the demographic properties of local populations, generating dynamical signals which can

propagate across scales via dispersal to control the spatial structure of metacommunities (Gotelli

2010, Gouhier et al. 2010b, Salois et al. 2018). While this framework has revealed great insights

about interconnected natural systems, it has done so largely via modeling and multi-scale surveys

as empirical tests and experimental data are hard to obtain.

Addressing the problem of scale is particularly important for understanding and

predicting the effects of climate change on the distribution of species, yet accurate and reliable

79

forecasts of the ecosystem-level effects of climate change remain one of the greatest

contemporary challenges (Helmuth et al. 2014, Pacifici et al. 2015, Gunderson et al. 2016).

Bioclimate envelopes, a type of species distribution model (SDMs), uses contemporary

relationships between environmental variables and abundances to make spatial predictions of

distributions of species in response to future climatic conditions (Pearson and Dawson 2003,

Gilman et al. 2010). Despite their power and simplicity, bioclimate envelope approaches make

assumptions that may fundamentally limit their forecasting ability in most systems (Davis et al.

1998, Araújo and Peterson 2012, Pacifici et al. 2015). Specifically, assuming that fine-scale

variation in climatic and environmental variables does not affect ecological patterns at larger

scales largely ignores evidence that cross-scale interactions between regional dispersal and local

processes can give rise to large-scale patterns (Gotelli 2010, Gouhier et al. 2010). Additionally,

even in the absence of such cross-scale interactions, measuring environmental variables at coarse

spatial and temporal scales can mask important variation that could influence organisms

(Helmuth et al. 2006, 2014, Vasseur et al. 2014, Dillon et al. 2016). For instance, using mean

trends of climatic variables often oversimplifies the complexity of environmental stressors by

averaging out meaningful variability (e.g., maximum and minimums) that can dictate organismal

performance and survival (Dillon et al. 2016). Disregarding important metrics (complexity) in

the spatial or temporal characteristics of climatic variables can result in range shift predictions

that are not reflective of either contemporary or projected directions of species distributions

(Seabra et al. 2015).

Similar mistakes can be made when attempting to characterize ecological refugia without

considering fine-scale variation and lead to errors when attempting to predict the effects of

environmental change. Helmuth et al. (2006) showed this empirically when they revealed the

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complex and counterintuitive way fine-scaled temperature varied in space and time along a

previously well described broad-scale temperature gradient. Specifically, they found that the

fine-scale variation of organismal body temperature differed greatly from that predicted by

broad-scale climatic patterns (Helmuth et al. 2006). Thus, ignoring ecologically relevant scales

by averaging out environmental variables (e.g. temperature) can mask refugia in space and time.

This is problematic because spatial and temporal refugia can promote persistence at local and

regional scales (Levins 1969, Brown and Kodric-Brown 1977, Chesson 2000). Temporal refugia

associated with temporal environmental variation can lead to variation in recruitment, buffered

population growth and other mechanisms (promoting temporal storage effects) enabling species

persistence and coexistence (Warner and Chesson 1985, Cáceres 1997, Chesson 2000). Spatial

refugia can arise from species-specific responses to spatially varying environmental variables.

For example, source-sink dynamics can arise due to spatial variation in environmental conditions

and promote regional species persistence as populations in locations characterized by favorable

environmental conditions (sources) can maintain populations in locations characterized by poor

environmental conditions (sinks) (Pulliam 1988, Gotelli 1991, Chesson 2000).

In order to identify fine-scale spatiotemporal temperature variation and its impact on the

frequency of temporal and spatial refugia in an upwelling system, we examined daily

microhabitat water temperature data spanning over 7 years from biomimetic limpets along

approximately 20 degrees of latitude within the Canary Current System (CanCs). We focused on

water temperatures in the intertidal, because these ecosystems experience some of the most

severe marine environmental conditions via large temperature fluctuations. These conditions

have resulted in strong (and well documented) relationships between thermal stress, fitness and

survival for the organisms who live there (Helmuth and Hofmann 2001, Helmuth et al. 2002,

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2006b, Lima and Wethey 2009), providing an excellent study system from which we can gain

greater understanding species response to external environmental forcing. Additionally, the

oceanographic variability associated with upwelling systems makes them model regions to

examine how coastal currents can govern temperature experienced at organismal scales now and

in the future as their duration and intensity is expected to increase under climate change (Wang

et al. 2015).

Here, we used wavelet analysis to evaluate intertidal microhabitat water temperature at

different spatiotemporal scales along the European Atlantic Coast. The goal of this study was to

compare how the same time series resolved in time and frequency can influence the

interpretation of water temperature trends and subsequent identification of ecological refugia in

space and time. Specifically, we used hierarchical clustering, pairwise correlations and wavelet

coherence of water temperature data across 16 sites to examine how temperature varied across

region characterized by differential (strong, weak, none) upwelling intensities. We found that

using simple raw time series alone masked underlying relationships between water temperature

and upwelling strength, whereas upwelling dependent spatiotemporal refugia emerged when the

same data was resolved in both time and frequency. These results highlight the importance of

considering both resolution and scale when projecting the ecological implications of trends

derived from climatic data.


Microhabitat water temperature dataset

Data were acquired from a dataset comprised of daily intertidal microhabitat water temperatures

recorded via biomimetic temperature loggers (robolimpets; see Lima and Wethey 2009) along

the European Atlantic coast (as in Seabra et al. 2016 and Lima et al. 2016). Robolimpets are

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autonomous temperature sensing devices which are comprised of a lithium battery connected to a

circuit board encased within an empty limpet shell and designed to mimic the temperatures

experienced by actual limpets (Lima and Wethey 2009). These loggers were deployed to cover a

spectrum of microhabitats occupied by real limpets as in Seabra et al. (2011). Daily water

temperature data were recorded during high tide for loggers located in mid and low zones and

averaged per microhabitat when there was replicate data as described in Seabra et al. 2016. The

resulting timeseries from each of the 16 wave-exposed shores spanning from Southwest Scotland

to Southern Portugal (latitudes ranging from 37° - 55° N) were truncated to a common seven-

year period ranging from July 2010 to August 2017. These sites are located in the Canary

Current System (CanCS), one of the four coastal upwelling regions classified within the Eastern

Boundary Upwelling System (EBUS). Robolimpets were deployed throughout the CanCs, at

sites characterized by an upwelling gradient, experiencing a range of upwelling conditions from

strong to no upwelling. Robolimpets are a specific type of autonomous temperature logging

device, termed biomimetic logger, devised by Lima and Wethey (2009) to mimic the thermal

characteristics of the common intertidal limpet, Patella vulgata. Robolimpet temperature

measurements, like other biomimetic temperature loggers, have been shown to match

temperature trajectories of live organisms (here, limpets), thus providing temperature

measurements at an ecologically relevant scales (Helmuth 2002, Fitzhenry et al. 2004, Lima and

Wethey 2009).

Detecting spatiotemporal trends in microhabitat water temperature

In order to fully document the spatiotemporal trends in microhabitat water temperature, we

analyzed the raw water temperature time series using classical methods resolved in time as well

as methods capable of analyzing the time series in both the time and frequency domains.

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Raw Time Series

We computed a dissimilarity matrix of the raw temperature time series for each of the 16 sites

along the European Atlantic coast. Then we performed a hierarchical cluster analysis on the

dissimilarity matrix to identify how sites cluster based on Euclidean dissimilarity (distance) in

intertidal microhabitat water temperature.

Wavelet Analysis

We examined the 16 time series via wavelet analysis to determine if clusters based on the

variability of water temperature exhibited similar trends to those derived from clusters based on

the raw water temperature. Using wavelet analysis allowed us to examine the relative

contribution of each frequency (period) in the signal (time series) to the overall variance of

microhabitat water temperature over time (Torrence and Compo 1998, Cazelles et al. 2008). As

compared to traditional spectral analysis which is not resolved in time and more appropriate for

stationary (statistical properties of signal do not vary over time) time series, the wavelet

transform, resolved in both time and frequency was the analysis of choice for this study (Cazelles

et al. 2008). Additionally, the ability to relate scales to periodic components of a signal, is

particularly useful for analyzing ecological time series which are often nonlinear and non-

stationary(Recknagel et al. 2013, Vasseur et al. 2014). Here, we outline a brief summary of the

wavelet analysis used in this study and include more detailed description of the analyses in

Appendix 3.1.

We computed a continuous wavelet transform for each time series, using the Mortlet

wavelet as a base. This method decomposed the variance of water temperature ineach time

series over both the time and frequency domains and resulted in a wavelet power spectrum for

each of the 16 time series of microhabitats along the Eastern Atlantic Coast. In order to draw

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comparisons between and within regions of differential upwelling intensity in an upwelling

system, the resulting wavelet power spectra were grouped by upwelling regime (strong, weak, no

upwelling). From each wavelet transform, we extracted the resulting bias-corrected power, and

created a dissimilarity array on which we computed hierarchical cluster analysis to identify how

sites cluster based on Euclidean dissimilarity (distance) in the variability of intertidal

microhabitat water temperature (Appendix S1).

Identifying mechanisms driving patterns in time

Raw Time Series

As a baseline, all time series were truncated to a common time frame (07-18-2010 to 08-34-

2017) and grouped based on the upwelling regime each site was characterized by (e.g., strong,

weak or no upwelling) (Lemos and Pires 2004, Seabra et al. 2011, 2016). Daily water

temperature values were plotted as a function of time for each individual site as well as averaged

across sites for each upwelling region (Fig. 3, row 1). We calculated Kendall’s coefficient of

concordance (W) to measure the degree of synchrony between sites within each upwelling

region. Kendall's W is a non-parametric statistic that ranges from 0 to 1 and measures the level of

agreement between multiple ranked variables (Legendre 2005, Gouhier et al. 2010). Here, we

calculated Kendall’s W between time series for each site within a particular upwelling regime

(strong, weak, no upwelling) and we determined its significance using Monte Carlo

randomizations which shuffled the sites (columns) of the community matrix randomly (Legendre

2005, Gouhier and Guichard 2014). The Kendall’s W coefficient values reported are corrected

for tied ranks and the p-values are based on the randomization test (Table 1).

Waveletanalysis

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To investigate which scales or periods (1/frequency) dominated the patterns we detected in the

hierarchical clustering analysis, we calculated the scale-averaged wavelet power across all sites.

Specifically, wavelet transformations were truncated to a common time frame (07-18-2010 to

08-34-2017) and then subset into a series of standard arrays of scales into examine different

periodicities (annual [300-400 days], monthly [15-45 days], weekly [2-10 days]). To compute

the scale-averaged power, the wavelet power spectrum of water temperature was averaged across

each group of periods (annual, monthly, weekly). This metric represents the average variation of

the signal for each group of periods at each time point, allowing us to examine the variability of

water temperature at different temporal scales for each site. As with the raw time series data, we

then calculated Kendall’s Coefficient of Concordance (W) to measure the degree of synchrony

between sites within each upwelling regime (strong, weak, no upwelling) for each temporal scale

(annual, monthly, weekly). The Kendall’s W coefficient values reported are corrected for tied

ranks and the p-values are based on the randomization test (Table 1).

Identifying mechanisms driving patterns in space

In order to quantify the potential for spatial refugia in addition to temporal refugia, we calculated

the correlation and coherence in water temperature as a function of distance both within and

across upwelling regimes.

Raw time series

We used Pearson’s Correlation Coefficient (PCC) to measure the strength of the association of

microhabitat water temperature between each pairwise combination of sites (n = 16, 120 pairwise

combinations). Pearson’s correlation (r) is a parametric statistic that measures the strength of the

linear relationship between paired data, and ranges from -1 to 1. We performed a permutation-

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based ANCOVA to determine if correlation in microhabitat water temperature was driven by

upwelling regime, geographical distance or their interaction (Fig. 4, see tables in Appendix 3.2).

Wavelet analysis

Due to the nonlinearity and non-stationarity of ecological time series, we decided to use a more

detailed metric to evaluate the associations of water temperature between sites across the CanCs.

Here, we used a bivariate extension of wavelet analysis (wavelet coherence) to assess the

temporal variability in the relationship between microhabitat water temperature and space.

Wavelet coherence is the cross-correlation of two time series in the time-frequency domain

(Grinsted et al. 2004, Cazelles et al. 2008), which allowed us to examine patterns of correlation

between pairs of sites. Specifically, we calculated the wavelet coherence for all pairwise

combinations of sites within and across upwelling regions (n = 120 pairwise combinations).

Next, we computed the average coherence between the two sites of interest across the entire time

series for each pairwise combination. These values were plotted as a function of geographical

distance (Fig. 5, column 1). Similarly, we calculated the mean and standard deviation of the

phase difference of coherence across the entire time series of each pairwise combination of sites

and plot those values against geographical distance (Fig. 5, columns 2,3, respectively). In

addition to calculating how correlations in fluctuations of water temperature between sites varies

over time at periods ranging from 2 to 890 days, we also made comparisons across different

periodicities (annual [300-400 days], monthly [15-45 days], weekly [2-10 days]) to examine

trends at biologically relevant scales. Mean coherence, mean phase difference and standard

deviation of phase difference were calculated for each subset of periodicities as described above.

We performed a permutation-based ANCOVA to determine if coherence in microhabitat water

87

temperature was driven by upwelling regime, geographical distance or their interaction (Fig. 5,

see tables in Appendix 3.2).

RESULTS

Detecting spatiotemporal patterns across a current system

The hierarchical clustering analysis on the raw time series was resolved only in time and resulted

in clusters which were very weakly associated with latitude and upwelling intensity (strong,

medium, weak, or none). However, including both time and frequency information in our

analysis revealed an improved ability to interpret these clusters. Including the added information

about the frequency of the signal allowed us to identify hidden similarities in the water

temperature time series that map onto upwelling conditions. This strong association suggests that

upwelling is a major driver of (dis)similarity in water temperature.

Identifying mechanisms driving patterns in time

Raw time series

As the previous analysis revealed that correlations in the wavelet power of intertidal microhabitat

water temperature are stronger than that of correlations in average daily water temperature, the

next step was to investigate which scales or periods (1/frequency) dominated these patterns. As a

baseline, time series were plotted individually and averaged according to groupings based on the

upwelling regime each site was characterized by (e.g.: strong, weak or no upwelling) (Fig. 3, row

1 *note need to fix edges). The main signal detected via the raw temperature timeseries is full

synchrony in water temperature across upwelling regimes (Table 1. W = 0.83, 0.89, 0.92 for

strong, weak or no upwelling sites, respectively), that is likely driven by seasonality. While there

is strong synchrony of temperature in the raw data regardless of upwelling intensity, seasonality

is least pronounced in sites categorized by strong upwelling. Here, upwelling disrupts this signal,

88

as sites in regions without upwelling reveal strong, predictable peaks in temperature in spring

and summer months as well as strong, predictable troughs in fall and winter months. These peaks

and troughs are less pronounced in regions that experience weak upwelling, as the difference in

temperature decreases slightly between the warm and cool seasons.

Wavelet analysis

In computing scale averaged power, the wavelet transform was decomposed into different

periodicities of interest (annual [300-400 days], monthly [15-45 days], weekly [2-10 days]) to

examine the variability of water temperature at different temporal scales. This analysis revealed

that the synchrony of variability of temperature is negatively correlated with the synchrony of

temperature at ecologically relevant scales. For instance, sites characterized by weak and no

upwelling displayed strong correlations in temperature (W = 0.89, 0.92, respectively) but weak

correlations in variability in temperature at monthly (W = 0.46, 0.39, respectively) and weekly

scales (0.46, 0.34, respectively). However, sites characterized by strong upwelling showed

weaker correlations in temperature (W = 0.83), yet strong synchrony in the variability of

temperature at monthly (W = 0.74) and weekly scales (W = 0.72). The systematic variation

across periodicities in strong upwelling sites suggests that upwelling brings consistent levels of

temperature variability to a system at scales relevant to organisms (Fig. 3,d:l), as variability in

temperature is occurring at the same temporal (subannual) scales, resulting in strong

synchronization between sites (Table 1, strong monthly, weekly > 0.7).

Conversely, in regions classified by weak or no upwelling, there is very little temporal variation

in water temperature that is consistent. Here, while sites are experiencing strong fluctuations,

they are out of phase (Table 1, weak/no monthly, weekly < 0.4), thus the magnitude of the

fluctuations are lost when the power is averaged across sites (Fig. 3h,i,k,l). The scale-dependent

89

synchronization of the variability of intertidal microhabitat water temperature may have

important implications for spatial rescue effects. Knowledge about whether or not the variation

in temperature is systematic across a region classified by an upwelling regime may improve our

ability to forecast ecological impacts in the context of climate change. For instance, in upwelling

regimes where variation in temperature is systematic across the region at biologically relevant

temporal scales, we might predict that organisms will primarily rely on temporal refugia during

temperature extremes, since the variation in temperature will be highly synchronous across sites.

In our example, in strong upwelling regions, where sites are experiencing a high degree of

synchrony in the variability of water temperature (Fig. 3 g,j), organisms are most likely to benefit

from local (within-site) temporal rescue effects as temporal refugia will emerge simultaneously

during the summer when temperature extremes are most lethal. In contrast, in regions with weak

to no upwelling (Fig. 3 h,i,k,l), where variation in temperature is non-synchronous at relevant

time scales (monthly, weekly), organisms are less likely to experience this temporal refugia

during temperature extremes due to the anti-phase dynamics of temperature variability.

Identifying mechanisms driving patterns in space

Raw time series

Pairwise correlations on the raw water temperature timeseries revealed seasonality as the main

driver of correlation between sites. Generally speaking, there is high correlation between sites

within and between different upwelling regimes, with fairly weak decays in correlation with

distance (Fig. 4). Specifically, in sites that do not experience upwelling, no spatial pattern

emerges (N-N, r > 0.8 correlation over distances spanning >1300 km). Similarly, correlations in

temperature for sites experiencing no to weak upwelling (N-W and W-W) remain high withlittle

to no decay with distance (r = 0.9 - 0.7 over distances ranging from 250 km to 2000 km), a trend

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again likely dictated by seasonality which is common to all sites within these regions. While sites

belonging to regions characterized by opposite upwelling regimes show lower correlations in

temperature (S-N, r < 0.6), again there is relatively no decay with distance as some sites are

dominated by season fluctuations and others by upwelling. These findings on correlations in raw

temperature time series combined with the previous analysis about variability of temperature

(above) suggests that sites experiencing little to no upwelling do not benefit from temporal

refugia (low synchrony of variability at weekly/monthly scales) nor spatial refugia (high spatial

synchrony of water temperature across 1000s of km). Conversely, the strong decay in correlation

with distance for sites in strong upwelling regimes (N-N, r = 0.85 – 0.5 over 500 km), would

suggest sites characterized by strong upwelling may benefit from spatial refugia (as temperatures

are not correlated at large distances) in addition to temporal refugia (high synchrony of

variability of temperature).

Wavelet analysis

Overall, regardless of upwelling regime, there is a general reduction in mean water temperature

coherence between sites when the analysis is restricted to monthly and weekly periods. When

mean coherence is calculated across all periods, the signal of upwelling is lost as upwelling

affects a very narrow band of frequencies (Fig. 5a) however, unlike in the correlations in time

series, we begin to see a slight decay in coherence with distance. Annual periods are dominated

by seasonality as we saw in the raw time series data (Fig. 5b). Coherence decreases significantly

as scale decreases, because the driving force (seasonality) is lost at monthly and weekly scales

(Fig. 5c,d). Both the mean and standard deviation of phase difference were calculated to parse

out the type of synchrony of coherence between sites. Examining the mean phase difference in

coherence is useful in clarifying the point at which the peaks and troughs in water temperature

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are aligned in time. Likewise, the standard deviation of phase difference will reveal the degree of

phase locking over time. For reference, sites that experience full synchrony of water temperature

would have a value of zero for both the mean and standard deviation of phase difference. Here,

regardless of upwelling condition the mean phase difference is clustered around zero for all

periodicities (Fig. 5e:h) and does not decay with distance. Interestingly, there is a negative

correlation between the mean coherence and the spread of phase differences across scales (Fig.5

a:d vs. i:l). This trend is most pronounced at annual and weekly scales. For instance, at annual

scales, sites in regions without upwelling are highly correlated (Fig.5 b, R2 > 0.9) and in phase

(zero mean phase difference, Fig. 5 f) yet show a high degree of phase locking (low spread; Fig.

5 j, 0 < sd < 0.05). Similarly, at weekly scales, the mean coherence and spread of phase

difference are negatively correlated as well. Here, the mean coherence is low across all sites (Fig.

5 d, R2 < = 0.4) and declines slightly with distance, however the standard deviation of phase

difference is high across sites (Fig. 5 l, sd > 1.5) and increases with distance. This result suggests

that at there is less synchrony between sites than would be expected by looking at coherence

alone. Specifically, there is little to no phase locking at biologically relevant scales (monthly and

weekly), evidenced by the fluctuations becoming increasingly out of phase over larger distances,

indicating strong spatial heterogeneity in water temperature regardless of upwelling condition.

Together, the relatively low coherence in water temperature and low degree of phase locking

across 1000s of km indicates a high potential for spatial rescue across all sites, irrespective of

upwelling regime at biologically relevant temporal scales (monthly and weekly). These results

highlight the power of including information about the frequencies and scales at which we are

investigating trends. While we see a general negative correlation between mean coherence and

the spread of phase differences across periodicities, it is important to note how the temporal scale

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of this information effects our interpretation. In considering only annual scales, one might

predict a low potential for spatial rescue effects as water temperature appears to be spatially

homogenous with sites both in phase and nearly phase locked. However, organisms are not

experiencing water temperature trends observed at annual scales and thus analyzing microhabitat

water temperature resolved in both time and frequency at biologically relevant scales revealed

hidden spatial rescue effects for non to weak upwelling sites that were masked when the analysis

was focused in the temporal domain alone (Fig. 4 vs 5). This analysis illuminated high potential

for spatial rescue effects across all upwelling regimes, with sites characterized by strong

upwelling also benefiting from temporal refugia.

DISCUSSION

Our results indicate that the resolution and scale at which environmental data is analyzed can

have profound effects on the ecological interpretation of the resulting spatiotemporal trends.

Many existing predictions about the ecological impacts of increased temperatures are based on

spatial or temporal averaging (Keppel et al. 2015, Molinos et al. 2015, Barceló et al. 2018).

While means can be informative, averaging over space and time can mask important signals

(e.g., variability, memory) occurring around the mean (Helmuth et al. 2014, Vasseur et al. 2014b,

Dillon et al. 2016). Indeed, our results highlight the importance of investigating trends in data

resolved in both frequency and time, as wavelet analysis revealed details about locations in the

Canary Current Upwelling System that went undetected when analyzing the raw time series. For

instance, including both time and frequency information in our analysis improved our ability to

interpret how sites clustered based on intertidal microhabitat water temperature. Specifically, we

identified upwelling as a major driver of (dis)similarity in water temperature, suggesting that

upwelling is a modulator of water temperature variation. The identification of a strong

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correlation between upwelling and temperature (as compared to latitude) is just one example of

how important information can be missed via frequency and temporally unresolved analysis.

Additionally, analyzing water temperatures in both frequency and time revealed information

about the synchronization of variability of temperature within (and across) upwelling regime

illuminating the potential for spatial and temporal rescue effects. Specifically, we found that

synchronization of the variability of temperature is dependent on upwelling intensity, with strong

upwelling sites showing systematic variation in temperature. Ecologically, areas with a high

degree of synchrony in the variability of microhabitat water temperature are also areas with high

potential for temporal refugia. In addition to resolution, the spatial and temporal scales at which

data is analyzed can lead to dramatic differences in forecasts of ecological responses to climate

change.

The problem of scale in a changing world

Forecasting shifts in the biogeographical patterns of species in response to global change is often

done at spatial and temporal scales unreflective of scales relevant to species. For instance,

species range shifts are often classified at macroscales correlating species habitat or thermal

preferences to contemporary or projected climatic variables over large spatial scales (Pearson

and Dawson 2003, Araújo and Luoto 2007, Sandel et al. 2011, Pinsky et al. 2013, Molinos et al.

2015). While these macroscale models result in generalizations and forecasts which can account

for large swaths of taxa over large ranges of space (Keppel et al. 2012, Morelli et al. 2016), the

resulting coarse-scale species distribution predictions are likely be over (or under) estimates of

species response to a changing climate as body temperatures and thermal tolerances oforganisms

do not always correspond to those predicted by large-scale climate data (Helmuth and Hofmann

2001, Potter et al. 2013, Seabra et al. 2015).

94

Microclimates are increasingly being recognized for their importance for ecosystem

dynamics and processes (Potter et al. 2013, Morelli et al. 2016, Zellweger et al. 2019) as species

distributions obtained from macroclimate data is unrepresentative of the range of microclimates

most organisms experience (Helmuth et al. 2006b, Zellweger et al. 2019). Therefore,

microclimates have proven a more ecologically relevant scale at which to measure environmental

variables and examine climate-species interactions (Helmuth and Hofmann 2001, Seabra et al.

2011, 2015, Helmuth et al. 2016, Zellweger et al. 2019). Our results are consistent with these

findings. For instance, at coarse temporal scales (annual) microhabitat water temperature

appeared spatially homogenous with low variability, regardless of upwelling intensity.

Conversely, we found increased variability at ecologically relevant temporal scales (monthly and

weekly), that was dependent on upwelling intensity. The added information we gained with

increased resolution of our data indicates that examining environmental variables at finer

temporal and spatial scales will aid in our ability to forecast species persistence and survival

during extreme events.

Environmental refugia and persistence of ecological systems

Identifying ecological refugia is a common strategy used to predict species’ capacity to cope

with climactic change (Ashcroft 2010, Morelli et al. 2016). In natural systems, which are

environmentally variable, species that cannot acclimate will rely on spatial or temporal refugia to

persist. Historically, glacial and interglacial periods have provided a useful record from which to

gain insights on range contractions and expansions and define refuges for flora and fauna (Maggs

et al. 2008, Bennett and Provan 2008). From this work, ecological refugia came to be defined as

areas which facilitate the persistence of organisms in the face of climatic change. To this end,

recent studies have largely classified refugia by habitat (Keppel et al. 2012, Lima et al. 2016) or

95

climactic stability (Ashcroft et al. 2009, Barceló et al. 2018). A common hypothesis is that as

temperatures increase, species distributions should shift poleward. While intuitive, the data has

not supported this hypothesis for a wide variety of species (Molinos et al. 2015). This is likely

due to the fact that many of these projections of range shifts refer exclusively to those expected

in response to change in the mean climatic variable. Results from our study suggest that

identifying areas with potential for spatiotemporal rescue (via understanding how climatic

variables will vary in space and time) can provide insights as to where populations are more

likely to persist even when they seemingly cannot ‘keep pace’ with the climate.

To date, most approaches to defining ecological refugia have involved linking habitat

characteristics to climatic conditions (Keppel et al. 2015, Molinos et al. 2015, Barceló et al.

2018). This can be useful for mapping and forecasting climatic change, but not adequate for

defining the mechanisms behind ecological refugia important for predicting species persistence.

In particular, simply equating topological characteristics of a habitat to stability of climate may

result in liberal definitions of refugia that are not relevant to many species. Upwelling systems

have a high degree of spatial heterogeneity in temperature as sites throughout each region

experience a gradient of upwelling intensities, which has prompted generalizations about

upwelling regions as ‘climate refugia’ (Barceló et al. 2018). However, since upwelling systems

are both ecologically and economically important systems that are projected to change under a

changing climate, it is important to understanding the mechanisms driving potential for refugia to

better inform management and conservation objectives. By examining how the variability of

microhabitat water temperature changed across space within an upwelling system, we found that,

the strong spatial heterogeneity in water temperature led to out of phase dynamics (low degree of

phase locking), indicating a high potential for spatial refugia (via rescue effects) across the

96

upwelling system (regardless of upwelling intensity). Furthermore, locations characterized by

strong upwelling also had a high potential for temporal refugia. The ability to reveal cryptic

spatiotemporal refugia highlights the power of this approach in an era of global change where

climatic uncertainty will be the new normal. Understanding the variability of climatic variables

will be better tool for tackling environmental uncertainty and documenting areas of refuge than

current static approaches.

Changes in mean temperature and other environmental variables for the remainder of the

21st century are well documented and understood, yet less is known about how the variability of

environmental variables will change in time. For instance, while Seabra et al. found that the

mean sea surface temperature in Eastern Boundary Upwelling Systems has not increased at the

same rate as SST outside these regions (Seabra et al. 2019), we found that the variability of

temperature can be informative for elucidating ecologically relevant refugia potential, thus it

would be relevant to determine how the variability of temperature differs between upwelling

systems and neighboring regions. In fact, knowing more about the variability of temperature in

areas outside of Eastern Boundary Upwelling Systems, which are warming faster, would enable

the identification of areas with high or low potential for spatial or temporal refugia (due to high

synchronization of variability). It is also important to note that all upwelling systems are not

changing equivalently (Iles 2014, Wang et al. 2015), it will be important to quantify region-

specific variation in environmental variables of interest (e.g., temperature) and avoid

generalizing across locations that experience ‘similar’ upwelling intensities (e.g., strong

upwelling sites in Canary Current System vs California Current System). While understanding

general climatic trends (via computing global averages and climate velocity trajectories) has

resulted in important baseline understandings of how species ranges are likely to shift in space

97

and time, a better understanding of the mechanisms driving the patterns will improve our ability

to forecast changes in community composition and species assemblages. Since temperature

extremes are some of the most important drivers of population dynamics (Harris et al. 2018,

Salinas et al. 2019) and are becoming increasingly more common in an era of global change

(Fischer and Knutti 2015, Buckley and Huey 2016), it is imperative to adopt statistical

approaches that are able to decompose temperature variability at ecologically relevant scales to

accurately quantify the potential for temporal and spatial refugia in complex ecological systems.

98

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risk to species than climate warming. Proceedings of the Royal Society of London B:

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Vasseur, D., J. Fox, A. Gonzalez, R. Adrian, B. Beisner, M. Helmus, C. Johnson, P. Kratina, c

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homogenization of coastal upwelling under climate change. Nature 518:390–394.

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105

TABLES

Table 1. Kendall’s coefficient of concordance (W) measuring degree of synchrony between sites

within a specified upwelling region ranging from regions characterized by strong upwelling to

those without upwelling. This statistic was measured across sites for the raw time series as well

as for scale-averaged wavelet power at annual, monthly and weekly scales. Values represent

Kendall’s W corrected for tied ranks. Rows correspond to upwelling regime (strong, weak or no

upwelling). Columns correspond to values computed for the raw time series and resulting p-

value, and scale averaged power at annual (300-400 days), monthly (15-45 days) and weekly (2-

10 days) periodicities, respectively.

Raw TS P-value Annual P-value Monthly P-value Weekly P-value

Strong 0.8332525 0.001 0.9178599 0.001 0.7379248 0.001 0.7219196 0.001

Weak 0.8867467 0.001 0.9425014 0.001 0.4625272 0.001 0.4616176 0.001

No 0.9219468 0.001 0.8604674 0.001 0.3895519 0.001 0.3394520 0.001

106

FIGURES

Figure 1. Hierarchical clustering of correlations of water temperature from time series across 16 sites

54.9

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107

Figure 2. Hierarchical clustering of correlations of wavelet power extracted from wavelet analysis across 16 sites.

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108

Figure 3. Time series and scale averaged wavelet power for daily microhabitat water temperature for all sites. Columns represent upwelling regime (strong, weak or no upwelling). The first row is the raw time series, and subsequent rows represent scale averaged power at annual (300-400 days), monthly (15-45 days) and weekly (2-10 days) periods. Bold black lines represent means across all sites, grey lines each individual site. Orange background refers to spring/summer seasons and fall/winter are represented by a blue background.

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109

Figure 4. Correlation as a function of distance. Pairwise comparisons between sites within the Canary Current System. P-value reported from ANCOVA results for interaction between upwelling intensity and distance.

p = 0.003 **

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110

Figure 5. Coherence and phase difference as a function of distance. Pairwise comparisons between sites within CanCs on wavelet coherence data. Columns represent mean coherence, mean phase difference and standard deviation of phase difference (from left to right). Rows represent all periods (2-889), annual (300-400 days), monthly (15-45 days) and weekly (2-10 day) periods. P-values reported from ANCOVA results for interaction between upwelling intensity and distance.

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111

CONCLUSIONS AND RECOMMENDATIONS

By using mathematical and statistical theory to address classical issues of scale, the models and

analyses described in this thesis have revealed the relative importance of ecological (dispersal,

species interactions) and environmental (heterogeneity and fine-scale abiotic fluctuations)

variables while highlighting the vulnerability of ecosystems to a changing and variable climate.

Implementing a metacommunity framework enabled me to address the mechanistic goals of

community ecology while still recognizing the large-scale patterns and processes important in

macroecology. Specifically, this work has examined the complex and variable interactions

between patterns and process across scales by investigating the roles of heterogeneity in

dispersal, species interactions and environmental forcing on metacommunity composition,

persistence and biodiversity across scales.

Chapter one emphasized the role of dispersal in structuring communities and indicated

how signatures of dispersal in real communities can be empirically detect by integrating

metacommunity models and empirical data. System-specific models which include information

about the size of metacommunity, spatial extent of dispersal and degree of self-recruitment of

species of interest combined with survey data can clarify the mechanistic underpinnings of

spatial variation in a metacommunity.

Chapter two highlighted the importance of considering the interaction of ecological

processes. This work addressed the fact that multiple coexistence mechanisms are operating

simultaneously and at different scales in natural systems. Quantifying interspecific differences in

recruitment and production at both local and regional scales can help to define the ‘winners’ and

‘losers’ when coexistence mechanisms act antagonistically in a metacommunity.

112

Chapter three quantified the uncertainty surrounding the effects of climate variability on

marine species in an upwelling system. Analyzing temporally- and frequency- resolved data of

water temperatures revealed how coastal upwelling promotes spatial and temporal temperature

refugia for intertidal species.

Together, this work has highlighted the importance of considering the scale and

resolution at which ecological systems are studied. Natural extensions of this work would

include how the relative importance of some of the mechanisms investigated in this study (e.g.,

interspecific differences in recruitment and production, variability of climatic stressors, spatial

extent of dispersal) might vary in space and time as ecological communities become reorganized

due to species invasions and extinctions following environmental and anthropogenic

perturbations. Specifically, one could explore the impacts of variability, memory and extremes

for multiple climatic variables by extracting trends from climate models and incorporating these

different projected carbon emission scenarios in metacommunity and metaecosystem models.

Insights about the roles of connectivity in natural systems gleaned from this work will

likely be critical for understanding the links between humans and ecological systems in an era

where human activity is increasingly altering the natural flow of organisms and matter within

and across ecosystems. Extending the models and frameworks used for this project could be

useful in understanding the relative importance of direct and indirect drivers of abundance and

distributions of species as well as highlighting the potential vulnerability or persistence of

geographical ‘hot spots’ to climate change. This type of information could be valuable in an

applied setting, and aid in the understanding of the spatiotemporal distribution of fishing activity

or key harvested and protected species in marine ecosystems. For instance, statistical approaches

from this dissertation are applicable to many types of survey data (e.g., biomass, abundance,

113

acoustic survey data) and could aid in determining statistical relationships between economically

important species and environmental variables at ecologically relevant scales. Furthermore,

developing a metacommunity (or metaecosystem) model with environmentally dependent

parameters (e.g., thermal breadths) could reveal underlying mechanisms driving the statistical

relationships derived from actual data. These types of approaches could also be useful in

determining to what extent species distributions are driven by direct (environmental) or indirect

(fishing pressure) factors. Combining both statistical and dynamical models is an ideal way to

push this work forward and could prove a useful tool in understanding important ecological

shifts in many applied subsets of ecology (e.g., conservation, fisheries). This dissertation is

further evidence that the complex, variable nature of ecosystems necessitates the use of

frameworks that are dynamic in space and time, as these approaches will be invaluable for

improving our ability to generate accurate forecasts and devise successful large-scale

conservation, mitigation, and management strategies (Gouhier et al. 2013, Holsman et al. 2016,

Young et al. 2019).

114

LITERATURE CITED

Gouhier, T. C., F. Guichard, and B. A. Menge. 2013. Designing effective reserve networks for

nonequilibrium metacommunities. Ecological Applications 23:1488–1503.

Holsman, K. K., J. Ianelli, K. Aydin, A. E. Punt, and E. A. Moffitt. 2016. A comparison of

fisheries biological reference points estimated from temperature-specific multi-species

and single-species climate-enhanced stock assessment models. Deep Sea Research Part

II: Topical Studies in Oceanography 134:360–378.

Young, T., E. C. Fuller, M. M. Provost, K. E. Coleman, K. St. Martin, B. J. McCay, M. L.

Pinsky, and Handling editor: Mitsutaku Makino. 2019. Adaptation strategies of coastal

fishing communities as species shift poleward. ICES Journal of Marine Science 76:93–

103.

115

APPENDICES

Appendix 1.1: Mechanistic schematics

Figure 1.1i: The spatially-explicit metacommunity model. (a) Each site x along the one dimensional array is characterized by a particular environmental condition e(x), based its location along the linear gradient which ranges from high (E+) to low (E-). Simple lottery competition determines which species (N) occupy each patch within a site. Sites exchange propagules via dispersal. (b) The environment modifies realized recruitment, with propagule survivorship in a given patch depending on the similarity between each species’ optimum oi and local environmental conditions e(x). (c, d) Dispersal is implemented via a Gaussian kernel whose mean, μ, and standard deviation, σ, control advection and diffusion, respectively.

(a) Species 1Species 2Species 3

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y of

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urvi

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116

Appendix 1.2: Robustness of the metacommunity model results to environmental stochasticity

Robustness of metacommunity model results

To determine the robustness of model results to variation in the linearity of the

environmental gradient, stochastic noise was added to our simple linear gradient. Below, we

present model results from simulations from one environmental gradient (u = 0.1), identical to

those described in the main text and Appendix 1.3 in every respect except for the addition of

environmental stochasticity. The recovery of our results under different levels of environmental

noise demonstrates that these findings are robust and do not require strictly linear environmental

gradients (Fig 1.2i -1.2ii).

Patterns of biodiversity

We found that the effects of increasing dispersal advection on biodiversity and

metacommunity structure described in the main text held under different levels of environmental

stochasticity for both absorbing and periodic conditions (Fig. 1.2i a-f, g-l). Briefly, increasing the

dispersal advection rate replaces the local positive feedback between abundance and self-

recruitment with a regional negative feedback that allows regionally dominant species to

monopolize the metacommunity, shifting control of regional diversity (γ) patterns from between-

community (β) to local (α) diversity (Fig. 1.2i a-c, g-i). Again, the negative regional feedback

generated relatively uniform abundances for the few regionally-dominant species across the

entire range of dispersal advection rates. Additionally, dispersal advection reduces local,

between-community and regional diversity by increasing the rate at which propagules are lost

from the finite-size metacommunity. These results hold across all levels of environmental noise.

The effects of increasing dispersal diffusion on biodiversity and metacommunity structure

described in the main text also hold under different levels of environmental stochasticity for both

117

periodic and absorbing conditions (Fig. 1.2i d-f, j-l). Indeed, increasing dispersal diffusion

initially leads to high local diversity and lower between-community diversity due to spatial

rescue effects, while higher rates of dispersal diffusion leads to increased spatial homogenization

and species-sorting resulting in low local, between-community and regional diversity. Again, as

in the main text, we see a bimodal effect of dispersal diffusion under periodic boundary

conditions, with low rates of diffusion (0 < σ < 5) leading to peaks in local and regional diversity

due to spatial rescue effects and intermediate rates of diffusion (10 < σ < 18) leading to a

prominent secondary peak in local and regional diversity as an effect of environmental rescue

(Fig. 1.2i j-l). Here again, species are able to exploit a secondary match between their

physiological optima and the local environment, resulting in a fitness boost and the subsequent

resurgence of rare species.

Patterns of (meta)community structure

Applying variation partitioning to simulations where dispersal rates varied yielded results

that were qualitatively identical to those described in the main text (Fig. 1.2ii a-f, g-l).

Specifically, increasing either the dispersal advection or diffusion rate ultimately resulted in

decreases in the spatial fractions for both absorbing and periodic boundaries conditions, as in the

main text. The initial introduction of dispersal (whether it be advection or diffusion) works to

erode the correlation between environmental conditions and community structure via spatial

rescue effects leading to a larger spatial fraction. However, as dispersal rate increases (for both

advection and diffusion), the spatial fraction decreases in communities with absorbing and

periodic boundary conditions. The mechanisms behind the decrease mirror those from the main

text; high rates of dispersal lead to spatial homogenization and the loss of spatial rescue effects,

or environmental rescue increases the correlation between the environment and community

118

structure. These results are robust to intermediate levels of environmental noise but begin to

erode at higher levels of noise (Fig. 1.2ii a-f, g-l).

Similarly, applying variation partitioning to simulations where dispersal diffusion rates

varied yielded results that were qualitatively identical to those described in the main text (Fig.

1.2ii c, f, i, l). Specifically, increasing the dispersal diffusion rate resulted in smaller spatial

fractions by spatially homogenizing the metacommunity and promoting species-sorting. In doing

so, dispersal diffusion generates a strong correlation between environmental conditions and

community structure leading to small spatial fraction. These results are fairly robust to across all

levels of environmental noise (Fig. 1.2ii a, d, g, j vs. c, f, i, l).

119

Figure 1.2i. Metacommunity species richness at multiple spatial scales as a function of dispersal advection (a-c) and diffusion (d-f) for different noise levels and boundary conditions. Red, blue and black lines respectively depict local (α), between community (β) and regional diversity (γ). Results represent means from 10 replicate simulations.



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Figure 1.2ii Variation partitioning of community structure as a function of dispersal advection rate (a-c, g-i) and diffusion rate (d-f, j-l) for different noise levels and boundary conditions. Community structure was partitioned into three fractions: the environment ⟨𝐸|𝑆⟩, space⟨𝑆|𝐸⟩, and their joint influence or intersection ⟨𝐸 ∩𝑆⟩ (i.e., the fraction of the variation in community structure jointly influenced by space and the environment). Line color represents the level of environmental noise, which ranges from low (cool colors) to high (warm colors). Results represent means from 10 replicate simulations.

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Appendix 1.3: Robustness of the metacommunity model results to covariation in advection and diffusions rates

Robustness of metacommunity model results

To determine the robustness of our model results to covariation in advection and

diffusion rates, we ran additional simulations where both aspects of dispersal (advection and

diffusion) were positively correlated as predicted under climate change (e.g., Gerber et al. 2014).

We found that the effects of increasing dispersal advection on biodiversity and metacommunity

structure described in the main text held when dispersal diffusion also increased under both

boundary conditions (Fig. 1.3i- 1.3ii). Briefly, increasing the dispersal advection rate replaced

the local positive feedback between abundance and self-recruitment with a regional negative

feedback that allowed regionally dominant species to monopolize the metacommunity, shifting

control of regional diversity (γ) patterns from between-community (β) to local (α) diversity (Fig.

S1). Again, the negative regional feedback generated relatively uniform abundances for the few

regionally-dominant species across the entire range of dispersal advection rates. These results

held across all levels of environmental gradient (1.3ia,b).

Similarly, applying variation partitioning to simulations where dispersal advection and

diffusion rates covaried yielded results that were qualitatively identical to those described in the

main text (Fig. 1.3ii). Specifically, increasing the dispersal advection rate resulted in smaller

spatial fractions due to the same mechanism whereby the loss of spatial rescue effects (absorbing

boundaries) or the emergence of environmental rescue effects (periodic boundaries) decreased

the correlation between community structure and spatial structure. Overall, these results suggest

that the effect of dispersal advection on biodiversity and metacommunity structure will hold as

long as the advection rate is sufficiently larger than the diffusion rate so as to significantly limit

self-recruitment.

122

LITERATURE CITED



5:art33.

123

Figure 1.3i: Metacommunity species richness at multiple spatial scales as a function of dispersal (advection and diffusion covaried) (a,b) for different noise levels. The first panel (a) contains results from simulations with absorbing boundary conditions and the second column refers to simulations with periodic boundary conditions (b). Red, blue and black lines depict local (α), between community (β) and regional diversity (γ), respectively. In addition to the color (red, blue, black) the translucence of each line represents the strength (slope) of the environmental gradient, which ranges from low (lighter hues) to high (darker hues). Results represent means from 10 replicate simulations.

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Figure 1.3ii: Variation partitioning of community structure as a function of dispersal (advection and diffusion covaried). The first column contains results from simulations with absorbing boundary conditions (panels a-c) and the second column refers to simulations with periodic boundary conditions (panels d-f). Community structure was partitioned into three fractions: the environment ⟨𝐸|𝑆⟩, space ⟨𝑆|𝐸⟩, and their joint influence or intersection ⟨𝐸 ∩𝑆⟩ (i.e., the fraction of the variation in community structure jointly influenced by space and the environment). Line color and translucence represent the strength (slope) of the environmental gradient, which ranges from low (lighter hues) to high (darker hues). Results represent means from 10 replicate simulations.

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Appendix 3.1: Wavelet analysis

Background

Ecological time series have proved a valuable tool for understanding the dynamics of ecosystems

(Benincà et al. 2009, Wootton and Forester 2013) and have traditionally been analyzed via

spectral analysis. Spectral analysis reveals what frequencies (i.e., spectral components) exist in a

signal (i.e., the times series) via a decomposition of the variance (power) of the signal into its

different frequencies (periods) obtained by a transform (e.g., Fourier Transform, Hilbert

transform, etc.) (Cazelles et al. 2008). While spectral analysis has been a fundamental tool in

understanding the variability of time series by giving information about how much of each

frequency exists in a signal, it does not tell us when in time these frequency components exist.

Thus, spectral analysis assumes that the statistical properties of a time series are stationary (do

not change in time) which becomes particularly important when analyzing ecological time series,

which are largely found to be non-stationary (Benincà et al. 2008, Cazelles et al. 2008, Rouyer et

al. 2008a, Gouhier et al. 2010). Wavelet analysis provides a solution, as it is a more sophisticated

time-resolved method. Thus, we used wavelet analysis to determine how fluctuations in

microhabitat water temperature varied within and across sites at 16 locations along the European

Atlantic Coast. Here, we provide a summary of the wavelet methods we used in the main text

and provide reference to many published guides for further details (e.g., Torrence and Compo

1998, Grinsted et al. 2004, Cazelles et al. 2008, Iles et al. 2012). All of our analyses were

conducted with the Biwavelet-package for R written by T. Gouhier.

Wavelet analysis

Wavelet analysis is able to resolve both the time and frequency domains of a signal, via the

wavelet transform. Specifically, a transforming function (mother wavelet) is passed through a

126

signal via windows 𝜏 across a series of scales 𝑠. For this study we chose to the Morlet wavelet,

which represents a sine wave modulated by a Gaussian function (Fig. S1-2; (Torrence and

Compo 1998):

𝜓�(𝑡) = 𝜋B7/�𝑒"��𝑒B�I/A

Where 𝑖 is the imaginary unit, 𝑡 represents nondimensional time, and 𝜔� = 6 is the

nondimensional frequency (Torrence and Compo 1998). The continuous wavelet transform of a

discrete time series 𝑥(𝑡) with equal spacing 𝛿𝑡 and length 𝑇 is defined as the convolution of 𝑥(𝑡)

with a normalized Morlet wavelet (Torrence and Compo 1998a, Grinsted et al. 2004b):

𝑊&(𝑠, τ) = �𝛿𝑡𝑠 q𝑥(𝑡)𝜓�

�B7

(6�

∗ �(𝑡 − τ)𝛿𝑡

𝑠 �

where * indicates the complex conjugate. By varying the wavelet scale 𝑠 (i.e., dilating and

contracting the wavelet) and translating along localized time position τ, one can calculate the

wavelet coefficients 𝑊&(𝑠, τ) across the different scales 𝑠 and positions τ. These wavelet

coefficients can be used to compute the bias-corrected local wavelet power, which describes how

the contribution of each frequency or period in the time series varies in time (Torrence and

Compo 1998a, Liu et al. 2007, Cazelles et al. 2008):

𝑊&A(𝑠, τ) = 2�|𝑊&(𝑠, τ)|A

Where 2� is the bias correction factor (Liu et al. 2007). The local wavelet power spectrum can

then be visualized via contour plots (Grinsted et al. 2004b, Cazelles et al. 2008).

The scale 𝑠 of the Morlet wavelet is related to the Fourier frequency 𝑓 (Maraun and Kurths

2004, Cazelles et al. 2008):

127

1𝑓 =

4𝜋𝑠𝜔� + 2 + 𝜔�A

When 𝜔� = 6, the scale 𝑠 is approximately equal to the reciprocal of the Fourier frequency 𝑓:

𝑠 ≈1𝑓

Hence, in all equations the scale can be converted to the Fourier frequency

𝑓 ≈1𝑠

or period

𝑝 =1𝑓 ≈ 𝑠

Zero-padding and the cone of influence

While the continuous wavelet transform can be approximated by using discrete Fourier

transforms to compute T convolutions for each scale 𝑠, it is more efficient to use discrete Fourier

transforms to calculate all T convolutions simultaneously (Torrence and Compo 1998). However,

method will introduce errors in the estimation of the local wavelet power spectrum at both the

beginning and end of a finite time series (Torrence and Compo 1998, Cazelles et al. 2008). This

occurs because the Fourier transform assumes that the data is periodic, thus the end of a time

series is padded with zeros before the wavelet transform is computed and then they are removed.

In effort to sufficiently deal with these edge effects, generally enough zeros are added in order

for the total length T of the time series to reach the next-higher power of two (Torrence and

Compo 1998, Cazelles et al. 2008). This procedure does reduce reliability in the estimation of the

local wavelet spectrum (by a factor of 𝑒BA in the region where the zero padding (via artificial

discontinuities at endpoints of data), thus this region is termed the ‘cone of influence (COI),

128

demarcating the area below as susceptible to edge effects (Torrence and Compo 1998a, Cazelles

et al. 2008).

Statistical significance testing

In order to determine the statistical significance of the wavelet spectrum obtained from a time

series, one must first formulate an appropriate null hypothesis. Here, the null hypothesis is that

the observed time series is generated by a stationary process with a given background power

spectrum 𝑝(𝑘) (Torrence and Compo 1998b, Grinsted et al. 2004a). Since many ecological and

environmental time series exhibit strong temporal autocorrelation (i.e. high power associated

with low frequencies; e.g. Beninca et al. 2009, see Ruokolainen et al. 2009 for review), we used

a first order autoregressive model [AR(1)] to generate a temporally autocorrelated time series or

red noise, which served as our null hypothesis. Specifically, the power spectrum 𝑝(𝑘) of our red

noise process was calculated with (Gilman et al. 1963):

𝑝(𝑘) =1 − 𝛼A

1 + 𝛼A − 2𝛼 cos(2𝜋𝑘 /𝑁)

where the autocorrelation coefficient 𝛼 at time lag 1 is estimated from the observed time series

and 𝑘 = 0,… , #A represents the frequency index. The observed wavelet spectrum can be

compared to the wavelet spectrum of the red noise process by means of a chi-square test. The

distribution of the local wavelet power spectrum of a red noise process is ¥¦F(�,§)I¥

CI, which is

distributed according to 7A𝑝(𝑘)𝒳A

A, with 𝑘 representing the frequency index,𝜎A representing the

variance of the time series and 𝒳AA representing the chi-square distribution with 2 degrees of

freedom (Torrence and Compo 1998). The value of𝑝(𝑘) is the mean wavelet power spectrum

at frequency 𝑘 that corresponds to the wavelet scale 𝑠 (Torrence and Compo 1998b). Using this

129

equation, one can construct 95% confidence contour lines at each scale using the 95th percentile

of the chi-square distribution 𝒳AA (Torrence and Compo 1998b).

Hierarchical cluster analysis

In order to determine how sites cluster based on Euclidean dissimilarity (distance) in intertidal

microhabitat water temperature we computed the wavelet spectra 𝑊&(𝑠, 𝜏) for each time series

𝑥(𝑡) and extracted a matrix containing the bias-corrected power obtained via the method

described by Liu et al. (2007). We then computed the dissimilarity between all time series via an

𝑁 ∗ 𝑝 ∗ 𝑡 array of wavelet spectra, where 𝑁 is the number of wavelet spectra to be compared

(𝑁 = 16), 𝑝 is the number of periods in each wavelet (𝑝 = 106), and 𝑡 is the number of time

steps in each wavelet spectrum (𝑡 = 2595). We then performed a hierarchical cluster analysis on

the set of dissimilarities for all sites being clustered. This clustering analysis works by assigning

each site to its own cluster and then iteratively joining the two most similar clusters, until there is

just a single cluster. Here, at each stage distances between clusters were recomputed according to

the version of the Ward clustering algorithm that necessitates the dissimilarities to be squared

before cluster updating (Murtagh and Legendre 2014).

Wavelet coherence

Wavelet coherence quantifies the coherence of fluctuations (strength of the covariation) between

two signals (Torrence and Compo 1998a, Grinsted et al. 2004b), thus is essentially the time-

resolved correlation between two time series (Cazelles et al. 2008, Rouyer et al. 2008b, 2008a).

Specifically, this method requires taking the wavelet transforms 𝑊&(𝑠, 𝜏) and 𝑊©(𝑠, 𝜏) of each

time series 𝑥(𝑡) and 𝑦(𝑡) and then calculating the cross-wavelet via (Torrence and Compo

1998a, Grinsted et al. 2004b):

𝑊&,©(𝑠, 𝜏) = 𝑊&(𝑠, 𝜏)𝑊©∗(𝑠, 𝜏)

130

where * indicates complex conjugation. The wavelet coherence is then defined as:

𝑅&,©A (𝑠, 𝜏) =¥⟨𝑠B7𝑊&,©(𝑠, 𝜏)⟩¥

A

⟨𝑠B7|𝑊&(𝑠, 𝜏)|A⟩ ⟨𝑠B7¥𝑊©(𝑠, 𝜏)¥A⟩

Where ⟨∙⟩ denotes smoothing in both time 𝜏 and scale 𝑠 and 0 ≤ 𝑅&,©A (𝑠, 𝜏) ≤ 1. Here, the time

smoothing is done via a filter derived from the absolute value of the wavelet function at each

scale, normalized to have a total weight of unity, which is a Gaussian function 𝑒G�I

I®I for the

Mortlet wavelet. The scale smoothing is done with a boxcar function of width 0.6, which

corresponds to the decorrelation scale of the Morlet wavelet (Torrence and Webster 1998,

Torrence and Compo 1998, Grinsted et al. 2004).

Statistical significance testing

The statistical significance of wavelet coherence can be tested by using Monte Carlo

randomization techniques (Torrence and Compo 1998a). Following the approach detailed by Iles

et al. (2012), 1,000 pairs of surrogate time series were generated using the same first order

autoregressive coefficients as our observed time series. Wavelet coherence was computed for

each pair of surrogate time series, in effort to generate a distribution of wavelet coherence. From

this distribution, we obtained the 95% significance level for each scale by computing the 95th

percentile of the wavelet coherence distribution.

131

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Gilman, D. L., F. J. Fuglister, and J. M. Mitchell. 1963. On the Power Spectrum of “Red Noise.”

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Grinsted, A., J. C. Moore, and S. Jevrejeva. 2004a. Application of the cross wavelet transform

and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics

11:561–566.

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and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics

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Iles, A. C., T. C. Gouhier, B. A. Menge, J. S. Stewart, A. J. Haupt, and M. C. Lynch. 2012.

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California Current System. Global Change Biology 18:783–796.

Liu, Y., X. San Liang, and R. H. Weisberg. 2007. Rectification of the Bias in the Wavelet Power

Spectrum. Journal of Atmospheric and Oceanic Technology 24:2093–2102.

Maraun, D., and J. Kurths. 2004. Cross wavelet analysis: significance testing and pitfalls.

Nonlinear Processes in Geophysics 11:505–514.

Murtagh, F., and P. Legendre. 2014. Ward’s Hierarchical Agglomerative Clustering Method:

Which Algorithms Implement Ward’s Criterion? Journal of Classification 31:274–295.

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133

Appendix 3.2: Permutation based ANCOVA tables

Raw Time Series: Correlation Table 3.2i. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the pairwise correlation of variably of temperature for 16 along the Canary Current System. Upwelling intensity ranged from strong to no upwelling. P-values from permutation test (Pperm) are reported for each factor in our analysis. Effect DF F P Pperm Upwelling 5 108.99 < 0.0001 0.001

Distance 1 8.69 0.0039 0.001

Upw x Dist 5 8.32 < 0.0001 0.003

134

Wavelet Coherence: Mean coherence Table 3.2ii. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean coherence across all periodicities. Upwelling intensity ranged from strong to no upwelling. P-values from permutation test (Pperm) are reported for each factor in our analysis. Effect DF F P Pperm Upwelling 5 46.46 < 0.0001 0.001

Distance 1 94.68 < 0.0001 0.001

Upw x Dist 5 7.29 < 0.0001 0.001

Table 3.2iii. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean coherence at annual periods. Effect DF F P Pperm Upwelling 5 71.17 < 0.0001 0.001

Distance 1 3.08 0.0823 0.088

Upw x Dist 5 4.42 0.0011 0.002

Table 3.2iv. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean coherence at monthly periods. Effect DF F P Pperm Upwelling 5 18.30 < 0.0001 0.001

Distance 1 145.14 0.0039 0.001

Upw x Dist 5 4.54 0.0009 0.004

Table 3.2v. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean coherence at weekly periods. Effect DF F P Pperm Upwelling 5 11.07 < 0.0001 0.001

Distance 1 57.91 < 0.0001 0.001

Upw x Dist 5 4.82 0.0005 0.003

135

Wavelet Coherence: Mean phase difference Table 3.2vi. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean phase difference of coherence across all periodicities. Upwelling intensity ranged from strong to no upwelling. P-values from permutation test (Pperm) are reported for each factor in our analysis. Effect DF F P Pperm Upwelling 5 8.08 < 0.0001 0.001

Distance 1 0.12 0.7342 0.72

Upw x Dist 5 2.24 0.0554 0.048

Table 3.2vii. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean phase difference of coherence at annual periods. Effect DF F P Pperm Upwelling 5 10.27 < 0.0001 0.001

Distance 1 2.15 0.1450 0.148

Upw x Dist 5 0.77 0.5729 0.595

Table 3.2viii. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on mean phase difference of coherence at monthly periods. Effect DF F P Pperm Upwelling 5 11.32 < 0.0001 0.001

Distance 1 14.46 0.0002 0.002

Upw x Dist 5 2.48 0.0363 0.041

Table 3.2ix. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean phase difference of coherence at weekly periods. Effect DF F P Pperm Upwelling 5 6.04 < 0.0001 0.001

Distance 1 16.35 < 0.0001 0.001

Upw x Dist 5 3.62 0.0046 0.007

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Wavelet Coherence: Standard deviation of phase difference Table 3.2x. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the standard deviation of phase difference of coherence across all periodicities. Upwelling intensity ranged from strong to no upwelling. P-values from permutation test (Pperm) are reported for each factor in our analysis. Effect DF F P Pperm Upwelling 5 42.36 < 0.0001 0.001

Distance 1 115.63 < 0.0001 0.001

Upw x Dist 5 5.30 0.0002 0.001

Table 3.2xi. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the standard deviation of phase difference of coherence at annual periods. Effect DF F P Pperm Upwelling 5 27.86 < 0.0001 0.001

Distance 1 9.03 0.0033 0.002

Upw x Dist 5 3.77 0.0035 0.005

Table 3.2xii. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the standard deviation of phase difference of coherence at monthly periods. Effect DF F P Pperm Upwelling 5 21.65 < 0.0001 0.001

Distance 1 121.79 < 0.0001 0.001

Upw x Dist 5 4.81 0.0005 0.002

Table 3.2xiii. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the standard deviation of phase difference of coherence at weekly periods. Effect DF F P Pperm Upwelling 5 14.26 < 0.0001 0.001

Distance 1 87.50 < 0.0001 0.001

Upw x Dist 5 3.14 0.0110 0.022

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