1 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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1
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
2
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.
3
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.
4
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.
5
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
Materials and Methods 58
Results 62
6
Table of Contents (continued)
Discussion 65
Literature Cited 69
Figures 73
Chapter 3: Coastal upwelling generates cryptic temperature refugia 76
Abstract 76
Introduction 77
Materials and Methods 81
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
7
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
Huyer, A. 1983. Coastal upwelling in the California Current system. Progress in Oceanography
12:259–284.
Largier, J. L., B. A. Magnell, and C. D. Winant. 1993. Subtidal circulation over the northern
California shelf. Journal of Geophysical Research: Oceans 98:18147–18179.
Legendre, P., and O. Gauthier. 2014. Statistical methods for temporal and space–time analysis of
community composition data. Proceedings of the Royal Society B: Biological Sciences
281:20132728.
46
Leibold, M. A., M. Holyoak, N. Mouquet, P. Amarasekare, J. M. Chase, M. F. Hoopes, R. D.
Holt, J. B. Shurin, R. Law, D. Tilman, M. Loreau, and A. Gonzalez. 2004. The
metacommunity concept: a framework for multi-scale community ecology. Ecology
Letters 7:601–613.
Levins, R. 1969. Some demographic and genetic consequences of environmental heterogeneity
for biological control. Bulletin of the Entomological Society of America 15:237–240.
Levins, R., and D. Culver. 1971. Regional coexistence of species and competition between rare
species. Proceedings of the National Academy of Sciences 68:1246–1248.
MacArthur, R. H., and E. O. Wilson. 1967. The Theory of Island Biogeography. Princeton
University Press, Princeton, New Jersey, USA.
Menge, B. A., C. Blanchette, P. Raimondi, T. Freidenburg, S. Gaines, J. Lubchenco, D. Lohse,
G. Hudson, M. Foley, and J. Pamplin. 2004. Species interaction strength: testing model
predictions along an upwelling gradient. Ecological Monographs 74:663.
Menge, B. A., and D. N. Menge. 2013. Dynamics of coastal meta-ecosystems: the intermittent
upwelling hypothesis and a test in rocky intertidal regions. Ecological Monographs
83:283–310.
Mouquet, N., and M. Loreau. 2002. Coexistence in metacommunities: the regional similarity
hypothesis. The American Naturalist 159:420–426.
Mouquet, N., and M. Loreau. 2003. Community patterns in source‐sink metacommunities. The
American Naturalist 162:544–557.
Nicholson, A. J. 1933. The balance of animal populations. Journal of Animal Ecology 2:131–
178.
Peres-Neto, P. R., P. Legendre, S. Dray, and D. Borcard. 2006a. Variation partitioning of species
data matrices: Estimation and comparison of fractions. Ecology 87:2614–2625.
Peres-Neto, P. R., P. Legendre, S. Dray, and D. Borcard. 2006b. Variation Partitioning of
Species Data Matrices: Estimation and Comparison of Fractions. Ecology 87:2614–2625.
Pulliam, H. R. 1988. Sources, Sinks, and Population Regulation. The American Naturalist
132:652–661.
47
Russell, R., S. A. Wood, G. Allison, and B. A. Menge. 2006. Scale, environment, and trophic
status: the context dependency of community saturation in rocky intertidal communities.
The American Naturalist 167:E158–E170.
Salomon, Y., S. R. Connolly, and L. Bode. 2010. Effects of asymmetric dispersal on the
coexistence of competing species. Ecology Letters 13:432–441.
Schoch, G. C., B. A. Menge, G. Allison, M. Kavanaugh, S. A. Thompson, and S. A. Wood.
2006. Fifteen degrees of separation: latitudinal gradients of rocky intertidal biota along
the California Current. Limnology and Oceanography 51:2564–2585.
Selkoe, K. A., and R. J. Toonen. 2011a. Marine connectivity: a new look at pelagic larval
duration and genetic metrics of dispersal. Marine Ecology Progress Series 436:291–305.
Selkoe, K. A., and R. J. Toonen. 2011b. Marine connectivity: a new look at pelagic larval
duration and genetic metrics of dispersal. Marine Ecology Progress Series 436:291–305.
Shanafelt, D. W., U. Dieckmann, M. Jonas, O. Franklin, M. Loreau, and C. Perrings. 2015.
Biodiversity, productivity, and the spatial insurance hypothesis revisited. Journal of
theoretical biology 380:426–435.
Shanks, A. L. 2009a. Pelagic larval duration and dispersal distance revisited. The Biological
Bulletin 216:373–385.
Shanks, A. L. 2009b. Pelagic Larval Duration and Dispersal Distance Revisited. Biol Bull
216:373–385.
Shanks, A. L., B. A. Grantham, and M. H. Carr. 2003a. Propagule dispersal distance and the size
and spacing of marine reserves. Ecological Applications 13:S159–S169.
Shanks, A. L., B. A. Grantham, and M. H. Carr. 2003b. Propagule dispersal distance and the size
and spacing of marine reserves. Ecological applications 13:159–169.
Siegel, D. A., B. P. Kinlan, B. Gaylord, and S. D. Gaines. 2003. Lagrangian descriptions of
marine larval dispersion. Marine Ecology Progress Series 260:83–96.
Thompson, P. L., and A. Gonzalez. 2016. Ecosystem multifunctionality in metacommunities.
Ecology 97:2867–2879.
Tilman, D. 1994. Competition and biodiversity in spatially structured habitats. Ecology 75:2–16.
48
Tuomisto, H., L. Ruokolainen, and K. Ruokolainen. 2012a. Modelling niche and neutral
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49
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.
50
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).
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.
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.
(d) Environment (E | S) (g) Environment (E | S) (j) Environment (E | S)
(c) Space (S | E) (f) Space (S | E) (l) Space (S | E) (i) Space (S | E)
∩
(b) Intersection (E S) ∩ (e) Intersection (E S) ∩ (h) Intersection (E S) ∩ (k) Intersection (E S) ∩
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.
Lowzone
Midzone
Highzone
0.0
0.2
0.4
0.6
0.8
1.0
bc abcac
ba a
abcabc
a
aabc
a
Com
mun
ity v
aria
nce
expl
aine
d (R
adj
2)
Direct DevelopersLow PLDIntermediate PLDHigh PLD
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.
MATERIALS AND METHODS
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
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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73
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
0.2
0.4
0.6
0.8
1.0
o1 o20
−40 −20 0 20 400.00
0.01
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0.03
0.04
S
!"
!#
Dispersal $!
N1
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N1 N20
N20
!%: Facilitation = 0
N1
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!%: Facilitation = 1
N1
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N20
N20
Dominant (N1)Subordinate (N20)
Low diffusionIntermediate diffusionHigh diffusion
Environment at each site & '
Site location '
Pote
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l rec
ruitm
ent ( %!
Prob
abili
ty o
f pro
pagu
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rviva
l )*!,,%
(a) (b)
(c)
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
Facilitation
Species Richness
Dispersal rate
Facilitation
Spp. richness
Alpha
3 4 5 6 7 8
Dispersal rate
Facilitation
Spp. richness
Beta
4 6 8 10 12 14
Dispersal rate
Facilitation
Spp. richness
Gam
ma
6 8 10 12 14 16 18 20
0 2010
(a) Local - ! (b) Between - " (c) Regional - #
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.
0.40.50.60.70.80.91.0
Extin
ctio
n R
isk
(a) No Facilitation
0.40.50.60.70.80.91.0
Extin
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(b) Intermediate Facilitation
0 5 11 17 23 300.40.50.60.70.80.91.0
Dispersal diffusion rate (σ)
Extin
ctio
n R
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(c) Full Facilitation
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.
77
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
78
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
80
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
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
7
53.7
5
48.5
4
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Cluster Dendrogram
hclust (*, "ward.D2")
Latitude (°N )
Dis
sim
ilarit
y
0
100
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500Strong
Medium
Weak
None
Upwelling Strength
107
Figure 2. Hierarchical clustering of correlations of wavelet power extracted from wavelet analysis across 16 sites.
37.0
7
37.5
2
43.5
7
47.2
9
43.4
1
52.1
3
53.3
2
43.4
8
50.3
1
53.7
5
48.5
4
45.6
1
54.9
7
43.0
4
39.0
1
41.8
4
050
015
0025
00
Latitude (CanCs)
Dis
sim
ilarit
y
54.9
7
53.7
5
48.5
4
52.1
3
50.3
1
53.3
2
45.6
1
47.2
9
43.4
8
43.5
7
43.4
1
37.0
7
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4
43.0
4
37.5
2
39.0
1
hclust (*, "ward.D2")
Latitude (°N )
Dis
sim
ilarit
y
0
500
1000
1500
2000
2500
54.9
7
53.7
5
48.5
4
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1
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2
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1
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9
43.4
8
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7
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1
37.0
7
41.8
4
43.0
4
37.5
2
39.0
1
hclust (*, "ward.D2")
Latitude (°N )
Dis
sim
ilarit
y
0
500
1000
1500
2000
2500 Strong
Medium
Weak
None
Upwelling Strength
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.
2011 2013 2015 2017
(a)
Wat
er te
mpe
ratu
re
°C( )
Strong Upwelling
05
10152025
2011 2013 2015 2017
(b)
Scal
ed A
vera
ged
Powe
r (lo
g 2)
02468
10
2011 2013 2015 2017
(c)
Scal
ed A
vera
ged
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r (lo
g 2)
02468
10
2011 2013 2015 2017
(d)
Year
Scal
ed A
vera
ged
Powe
r (lo
g 2)
02468
10
2011 2013 2015 2017
(e)
Weak Upwelling
05
10152025
2011 2013 2015 2017
(f)
02468
10
2011 2013 2015 2017
(g)
02468
10
2011 2013 2015 2017
(h)
Year
02468
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2011 2013 2015 2017
(i)
No Upwelling
Raw
Tim
e Se
ries
05
10152025
2011 2013 2015 2017
(j)
Annu
al
02468
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2011 2013 2015 2017
(k)
Mon
thly
02468
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2011 2013 2015 2017
(l)
YearW
eekl
y
02468
10
Spring/Summer Fall/Winter
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 **
Distance Between Sites (km)
Cor
rela
tion
0 500 1000 1500 2000
0.0
0.2
0.4
0.6
0.8
1.0
● ● ● ● ● ●S−S S−W W−W W−N N−N S−N
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.
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
0.0
0.2
0.4
0.6
0.8
1.0
o1 o2 o3Environment at each site (e(x))
Prob
abilit
y of
pro
pagu
le s
urvi
val (
F (e
(x) ,
oi))
(b)
Low advectionMedium advectionHigh advection
Site location (x)
Pote
ntia
l rec
ruitm
ent (
r i(x)
)
0.01
0.02
0.03
0 20 40 60 80 100
(c)
−40 −20 0 20 40
Low diffusionMedium diffusionHigh diffusion
Site location (x)
(d)
Dis
pers
al (k
) N2
x1
xn
E +
E -
N2
N1 N1
N1
N1
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
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.
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.
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
Gerber, L. R., M. D. M. Mancha-Cisneros, M. I. O’Connor, and E. R. Selig. 2014. Climate
change impacts on connectivity in the ocean: Implications for conservation. Ecosphere
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.
0 2 4 6 8 100
5
10
15
20Sp
ecie
s ric
hnes
s
Dispersal rate
DiversityRegional (γ)Between (β)Local (α)
(a)
0 2 4 6 80
5
10
15
20
Spec
ies
richn
ess
Dispersal rate
(b)
124
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.
0.0
0.2
0.4
0.6
0.8
1.0
Com
mun
ity v
aria
nce
expl
aine
d (R
adj
2)
(a) Environment (E | S)
0.0
0.2
0.4
0.6
0.8
1.0
Com
mun
ity v
aria
nce
expl
aine
d (R
adj
2)
(b) Intersection (E ∩ S)
0 2 4 6 80.0
0.2
0.4
0.6
0.8
1.0
Com
mun
ity v
aria
nce
expl
aine
d (R
adj
2)
(c) Space (S | E)
Dispersal rate
(d) Environment (E | S)
(e) Intersection (E ∩ S)
0 5 10 15 20 25 30 350 10 20 30
(f) Space (S | E)
Dispersal rate
125
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).
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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Benincà, E., J. Huisman, R. Heerkloss, K. D. Jöhnk, P. Branco, E. H. Van Nes, M. Scheffer, and
S. P. Ellner. 2008. Chaos in a long-term experiment with a plankton community. Nature
451:822–825.
Benincà, E., K. D. Jöhnk, R. Heerkloss, and J. Huisman. 2009. Coupled predator–prey
oscillations in a chaotic food web. Ecology letters 12:1367–1378.
Cazelles, B., M. Chavez, D. Berteaux, F. Ménard, J. O. Vik, S. Jenouvrier, and N. C. Stenseth.
2008. Wavelet Analysis of Ecological Time Series. Oecologia 156:287–304.
Gilman, D. L., F. J. Fuglister, and J. M. Mitchell. 1963. On the Power Spectrum of “Red Noise.”
Journal of the Atmospheric Sciences 20:182–184.
Gouhier, T. C., F. Guichard, and B. A. Menge. 2010. Ecological processes can synchronize
marine population dynamics over continental scales. Proceedings of the National
Academy of Sciences 107:8281–8286.
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.
Grinsted, A., J. C. Moore, and S. Jevrejeva. 2004b. Application of the cross wavelet transform
and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics
11:561–566.
Iles, A. C., T. C. Gouhier, B. A. Menge, J. S. Stewart, A. J. Haupt, and M. C. Lynch. 2012.
Climate-driven trends and ecological implications of event-scale upwelling in the
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.
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Rouyer, T., J.-M. Fromentin, F. Ménard, B. Cazelles, K. Briand, R. Pianet, B. Planque, and N. C.
Stenseth. 2008a. Complex interplays among population dynamics, environmental forcing,
and exploitation in fisheries. Proceedings of the National Academy of Sciences
105:5420–5425.
Rouyer, T., J.-M. Fromentin, N. Chr. Stenseth, and B. Cazelles. 2008b. Analysing multiple time
series and extending significance testing in wavelet analysis. Marine Ecology Progress
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Ruokolainen, L., A. Linden, V. Kaitala, and M. S. Fowler. 2009. Ecological and evolutionary
dynamics under coloured environmental variation. Trends in Ecology & Evolution
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Torrence, C., and G. P. Compo. 1998a. A Practical Guide to Wavelet Analysis. Bulletin of the
American Meteorological Society 79:61–78.
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Density-Linked Stochasticity. PloS one 8:e75700.
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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
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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
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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