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Between migration load and evolutionary
rescue: dispersal, adaptation and the
response of spatially structured
populations to environmental change
Elizabeth C. Bourne1,2,3, Greta Bocedi2, Justin M. J. Travis2, Robin J. Pakeman1,
Rob W. Brooker1 and Katja Schiffers4
Research
Cite this article: Bourne EC, Bocedi G, Travis
JMJ, Pakeman RJ, Brooker RW, Schiffers K.
2014 Between migration load and evolutionary
rescue: dispersal, adaptation and the response
of spatially structured populations to
environmental change. Proc. R. Soc. B 281:
20132795.
http://dx.doi.org/10.1098/rspb.2013.2795
Received: 26 October 2013
Accepted: 13 December 2013
Subject Areas:
evolution, ecology, genetics
Keywords:
allelic model, gene flow, linkage,
local adaptation, meta-populations
Author for correspondence:
Elizabeth C. Bourne
e-mail: [email protected]
Electronic supplementary material is available
at http://dx.doi.org/10.1098/rspb.2013.2795 or
via http://rspb.royalsocietypublishing.org.
1
The James Hutton Institute, Craigiebuckler, Aberdeen AB15 8QH, UK
Institute of Biological and Environmental Sciences, University of Aberdeen, Zoology Building, Tillydrone Avenue,
Aberdeen AB24 2TZ, UK
3
Institute für Biologie—Botanik, Freie Universität Berlin, Altensteinstrasse 6, Berlin 14195, Germany
4
Evolution, Modeling and Analyses of Biodiversity group, Laboratoire d’Ecologie Alpine, UMR CNRS 5553,
Université Joseph Fourier, Grenoble Cedex 9, France
2
The evolutionary potential of populations is mainly determined by population
size and available genetic variance. However, the adaptability of spatially
structured populations may also be affected by dispersal: positively by spreading beneficial mutations across sub-populations, but negatively by moving
locally adapted alleles between demes. We develop an individual-based,
two-patch, allelic model to investigate the balance between these opposing
effects on a population’s evolutionary response to rapid climate change.
Individual fitness is controlled by two polygenic traits coding for local adaptation either to the environment or to climate. Under conditions of selection
that favour the evolution of a generalist phenotype (i.e. weak divergent selection between patches) dispersal has an overall positive effect on the persistence
of the population. However, when selection favours locally adapted specialists, the beneficial effects of dispersal outweigh the associated increase in
maladaptation for a narrow range of parameter space only (intermediate selection strength and low linkage among loci), where the spread of beneficial
climate alleles is not strongly hampered by selection against non-specialists.
Given that local selection across heterogeneous and fragmented landscapes
is common, the complex effect of dispersal that we describe will play an important role in determining the evolutionary dynamics of many species under
rapidly changing climate.
1. Introduction
Current predictions of future climate change stand at a 0.3–4.88C rise in temperature by the end of the twenty-first century (based on the projected change in global
mean surface air temperature relative to 1986–2005) [1]. Such unprecedented rates
of change will place populations under a greater risk of extinction, particularly in
increasingly fragmented landscapes [2]. The specific response of populations
exposed to environmental change will depend upon the existence and interplay
of a suite of evolutionary and demographic processes. Foremost among these, in
situ adaptation and migration (i.e. biogeographic range shifting) will both play
key roles in determining the likelihood of population persistence during and following environmental change [3]. The capacity and speed by which a
population can respond to change will therefore be affected by evolutionary
dynamics. Specifically, a population’s level of additive genetic variance [4,5] can
directly influence evolutionary outcomes in response to environmental change
by providing the necessary genetic variation upon which selection can act [6,7].
While plasticity may facilitate changes in phenotype in response to new climatic
conditions (e.g. [8]), there is likely to be a point where plasticity alone becomes
insufficient [9]: genetic responses will then be critical for population survival.
& 2014 The Author(s) Published by the Royal Society. All rights reserved.
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changing global environmental conditions. We first establish
how, under stable climatic conditions, overall population fitness varies according to the level of divergent selection
between two sub-populations. Subsequently, we investigate
the effect of local selection, dispersal and genetic architecture
on evolutionary potential, following a directional temporal
change in the environment (i.e. an increase in the optimal
temperature at a given location).
2. Material and methods
(a) Genetic architecture
Adaptation to both the local patch (the non-climatic environment
of each sub-population) and climate was simulated using a multilocus system, reflecting the important role of polygenic traits in
determining an individual’s fitness response to its environment
[43,44]. Diploid individuals each have 20 loci, 10 of which code for
adaptation to the patch-specific environmental conditions while
the other half code for adaptation to climate. The position of the
patch-specific and climate loci relative to one another is determined
at random. The degree of linkage between loci is varied by altering
the probability that, at meiosis, a gamete’s next allele does not come
from the same chromosome copy as the previous one (i.e. a crossover
event). This probability, pC, can vary between 0.0 (i.e. full linkage)
and 0.5 (no linkage). The two alleles at each locus take continuous
values and are assumed to be co-dominant, with no epistatic or
pleiotropic effects. Heritability is assumed to be 1; thus the value
of the alleles directly determines an individual’s phenotype, each
making a small and equal contribution (as in [45,46]).
(b) Life cycle
(i) Reproduction, recombination and mutation
Offspring are generated by the mating of two individuals selected
from the same patch, with a small probability of self-fertilization
(1/local sub-population size). The number of offspring produced
by each mated pair is drawn randomly from a Poisson distribution
with mean R. An offspring’s genotype is composed of a maternal and a paternal gamete, each of which is produced following
recombination (outlined above). Mutation is applied during reproduction, where at each locus (for a haploid gamete) there is a
probability m that a mutation occurs in the allele carried. The magnitude of a mutation is drawn from a zero-mean normal
distribution with standard deviation a and is added to the initial
value of the allele. After reproduction, the parental generation dies.
Proc. R. Soc. B 281: 20132795
An allelic, individual-based simulation model was implemented to assess the effects of local adaptation and dispersal on
the adaptation potential of an annual species inhabiting two
spatially segregated patches (e.g. separate alpine meadows). The
two sub-populations, connected by dispersal, are exposed to
local differences in environmental conditions (e.g. soil heavy
metal content). Climatic conditions may change temporally, but
are assumed to be equal in both patches at any point in time. Individuals carry two sets of genes, one conferring adaptation to local
environmental conditions, and the other adaptation to climate.
An individual’s fitness is determined by its level of adaptation to
both the environmental and climatic conditions, and the strength
of penalty for maladaptation (i.e. selection strength) [33]. Each
patch supports a given number of individuals, determined by
the local carrying capacity. Generations are assumed to be discrete
and non-overlapping. Every generation undergoes the following
steps: (i) reproduction and recombination, (ii) mutation, (iii) offspring dispersal, (iv) selection based on an individual’s degree
of adaptation, and finally (v) density-dependent mortality (see
electronic supplementary material, figure S1).
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The important role of genetic adaptation in species response
to changing climate has already been demonstrated for a range
of taxa [10–14], including the rapid adaptation of both dispersal
traits and thermal tolerance [15]. The dispersal characteristics of
a species, combined with such exogenous factors as landscape
structure [16] and endogenous factors including a sub-population’s local adaptation to climate [17], immediately impact
the ability of populations to track a changing environment
by migration.
The overall effect of dispersal on rapid adaptation is not
easy to predict, in part owing to a complicated balance between
the positive and negative effects of dispersal [18,19]. Gene flow
can lead to greater evolutionary potential by promoting
the pool of genetic variation within a population [7,20]. In
addition, dispersal into new populations can both aid the purging of maladaptive alleles (if these are selected against in new
environments) and increase the rate at which any beneficial
alleles are shared between sub-populations [6,7]. However,
theoretical and empirical studies have also demonstrated negative effects of gene flow on adaptation, impairing local fitness
and slowing adaptation to alternative conditions, particularly
in cases of local adaptation (e.g. [21–23]). During centre-torange-edge migration, recipient populations swamped by
alleles that are locally less fit [24,25] experience a reduction
in performance owing to migration load (e.g. [21]). Not only
is the average fitness of individuals reduced, but also locally
adapted variants in recipient populations are diluted in
number, leading to the loss of local adaptation and niche
evolution [17,20,25], which in some cases can set the limits to
a species’s range [26,27]. In the case of spatially structured
and locally adapted populations, dispersal therefore plays an
indirect but important role in determining a population’s
evolutionary response to climatic change.
While there exists a large body of literature describing
the effect of dispersal on local adaptation in temporally
stable environments [24,26–31], fewer studies have sought to
explore the interplay of both dispersal and local adaptation in
determining the evolutionary potential of populations under
temporally changing conditions (but see [23,32]). Where temporal changes are considered, many studies have described
the dynamics of single panmictic populations [33–36]. Yet subdivided populations change the arrangement and availability of
the genetic pool [19,37] with the potential to alter the adaptive
response to environmental change [23,38,39]. The genetic
architecture of individuals also strongly modifies responses to
selection. Linkage between quantitative trait loci under antagonistic selection can slow the rate of adaptation by restricting
the fixation of beneficial mutations in a population, and
decreasing the effective population size [40–42].
Given that a genetic response to environmental pressure
may be vital for the persistence of many species, and that
empirical observations support the role of rapid adaptation
in some situations, an important question arises: what are
the conditions that favour rapid adaptation, and which exogeneous and endogeneous factors may place limits on this?
In this contribution, we explore how gene flow influences
the response of a spatially structured population to climate
change, where differential levels of local selection also operate. We use a simple, individual-based model to develop
some initial theory on how the interplay between the strength
of adaptation to the local environment, dispersal rate and the
genetic architecture of loci under selection govern the likelihood that evolution can rescue a population from rapidly
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(ii) Dispersal
(iii) Selection
with z being the overall phenotype of the individual and QP,C the
optimal phenotype with respect to local patch conditions or current climate (following [28]). As both the patch and climatic
phenotypes are polygenic, the specific phenotype of an individual for each trait (zP and zC) is determined by the mean allelic
value for all relevant trait loci. v 2 is the strength of selection
applied against departure from non-optimal allelic values, thus
determining an individual’s fitness for a given departure of the
phenotype from the optimum. The absolute effect of v 2 can be
regarded as the inverse of the value it takes (i.e. lower values
of v 2 represent stronger selection against maladapted alleles).
Thus, individual fitness is calculated as the product of the differences between the optimal and the realized phenotype
(calculated across all alleles for that trait), conditional on the
degree of divergent selection operating between patches ðv2P Þ
and the strength of selection induced by climatic conditions ðv2C Þ:
(iv) Density-dependent mortality
When the sub-population size following selection exceeds carrying capacity K, each individual has a risk of mortality that is
independent of its genotype. The probability of surviving density-dependent mortality is calculated as the quotient of the
carrying capacity K and the present sub-population size, where
the sub-population size exceeds K: 1 2 K/N. On average, this
results in the sub-population size being reduced to K.
(c) Simulations
Simulations were run to investigate the interactive effects of local
adaptation, dispersal and linkage on a sub-structured population
experiencing climate change (see the electronic supplementary
material, table S1 for model parameters and values). Each subpopulation initially comprised 100 individuals (50% of the patch
carrying capacity), all optimally adapted to both local environment and climate (with patch allele optima of 10 and 20,
respectively). The final level of local adaptation evolved from the
balance between dispersal between patches and the strength by
which the two sub-populations experienced antagonistic selection between the alleles coding for each patch. We modified
the strength of selection against deviation from the optimum
by the parameter v2P , which ranged from 1 (strong selection against
one maladapted allele) to 8192 (alleles effectively neutral). Climate
selection v2C was set to 2, and the rate of climate change v set to a
0.03758C increase per generation (for 200 generations), unless
otherwise specified. This generated a moderately high level of
selection against maladaptive climate alleles (see sensitivity analysis in electronic supplementary material, appendix S1). Individual
dispersal rates d were varied between 0 and 0.2, and the level of
linkage pC varied between 0 and 0.5. Unless otherwise stated, all
other parameters were kept constant (see electronic supplementary material, table S1). Details on sensitivity analyses varying
(i) Population response under stable climate
Twenty replicate runs were made for simulations assuming
stable climatic conditions. Initial simulations over 5000 generations indicated that 500 generations were sufficient to reach
population equilibrium.
(ii) Population response under climate change
Following 500 generations to allow the population to obtain
quasi-equilibrium, climate change was implemented as a gradual
increase from 158C over 200 generations, with rate v. For an
annual species, the rate of climate change assumed is within
the range of likely values projected by recent global climate
models (see [1]).
The resultant phenotypic distributions from the above simulations are given in the electronic supplementary material
(appendix S4 and figures S12– S15).
(iii) Population response to varied rates of climate change
The rate of climate change v was altered as the magnitude of change
per generation, with an increase ranging between 0.0225 and 0.068C
per generation, with all other parameters as before (see electronic
supplementary material, table S1). Simulations were run for 1500
generations unless the population became extinct.
Finally, in a set of diagnostic simulations to support interpretation of the simulation results, we explored the fate of single
beneficial alleles that were introduced into a population that
had experienced a recent change in climate. The probability of
the mutation surviving and establishing within each sub-population was followed under a range of conditions (see electronic
supplementary material, appendix S5).
3. Results
(a) Population response under stable climate
During a stable climate, the interplay between patch selection
strength v2P and dispersal d affected an individual’s survival
(see electronic
probability W and mean population fitness W
supplementary material, figure S2), and the point at which
specialists or generalists emerged (see below).
Under strong antagonistic patch selection ðv2P , 4Þ, individuals maladapted to the alternative environment suffered high
was unaffected by
mortality. Here, mean population fitness W
migration load as strongly maladapted alleles were quickly
purged and a high average sub-population fitness was
Proc. R. Soc. B 281: 20132795
Before density-dependence (see below), we apply hard selection,
where a juvenile’s survival probability depends upon its genotype in relation to both patch and climatic conditions. The
survival probability W of an individual is the product of its
response to both local patch conditions WP and climate WC.
Both WP and WC follow normal distributions (bounded by a
minimum of 0.0 and a maximum of 1.0) and variance v2P;C , so
that W is calculated according to
"
#
"
#
ðzP QP Þ2
ðzC QC Þ2
exp
;
WðzÞ ¼ exp 2v2P
2v2C
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Each offspring moves from its natal patch to the other patch with
probability d, simulating dispersal.
v2C and v, and mutation standard deviation a with patch selection
strength v2P , for different conditions of dispersal rate d and linkage
(as pC) are given in the electronic supplementary material (appendix S1 and table S2). Additional analyses on rates of climate change
are given in the electronic supplementary material, appendix S2.
Reported values for the strength of environmentally induced selection in the literature vary according to the system studied and the
fitness traits measured (e.g. [47–49]). Our approach allows for a
wide range of realized selection values, ranging from nil/weak
(reflecting observations of [47]) to a strong selective force (such
as in predator-driven selection of morph types [50]).
Except in a single set of diagnostic simulations (see below), we
ran between 20 and 100 replicates, recording at population level
and population size over time.
the mean population fitness W
The percentage of population extinctions (as global extinction, of
both sub-populations), and the number of extinctions in which
only one sub-population survived (i.e. only one of the patches),
was also determined across a broad range of parameter space.
Below we describe variations in parameters for each simulation.
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(b)
(a) 1.0
4
22
mean fitness
0.8
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0.9
20
0.7
0.6
18
0.5
mean of extinct runs (30%)
0.4
mean of extant runs (70%)
pC = 0.5
0.3
16
climate
22
0.8
20
0.7
0.6
18
0.5
degree celsius
mean fitness
0.9
mean of extinct runs (50%)
0.4
mean of extant runs (50%)
0.3
16
climate
pC = 0.1
1.0
22
mean fitness
0.9
w 2p = 1
0.8
20
w 2p = 2
0.7
w 2p = 4
w 2p = 8
0.6
18
w 2p = 16
w 2p = 32
0.5
mean of extinct runs (85%)
climate
0.4
mean of extant runs (15%)
pC = 0.01
0.3
0
500
1000
1500
generation
16
climate
0
500
1000
1500
generation
Figure 1. Mean fitness under climate change scenarios and moderate dispersal. (a) Mean population fitness (extant runs out of 20 replicates) for six values of patch
selection strength v2P and three values of crossover probability pC. There was no further change in results for v2P greater than 32. (b) Mean population fitness for
extant (black) and extinct (grey) runs out of 20 replicates under the scenario of strong local adaptation and low dispersal (v2P ¼ 1, d ¼ 0.05) for three values of
crossover probability pC. For all runs: d ¼ 0.05, R ¼ 2.5, K ¼ 200 and n ¼ 0.03758C generation21. Standard errors were negligible and so error bars are left out
for clarity. See electronic supplementary material, appendix S1 and figure S3 for results with d ¼ 0.
maintained, selecting strongly for well-adapted specialists (see
electronic supplementary material, figures S2 and S12). Declines
in mean fitness of the population surviving density-dependent
selection were observed only over a small range of patch selection
values ðv2P ¼ 4 16Þ: At v ¼ 4, specialists were selected for, with
dispersed poorly adapted specialists moderately purged, resulting in a small reduction in average fitness of the remaining
population. At v ¼ 8, generalists were selected for, which,
while maladapted in both patches, could still survive, causing
high genetic load (observed as the greatest dip in patch fitness;
electronic supplementary material, figure S2). From v . 8, population fitness increased because maladaptation was less strongly
punished, with population size remaining high and densitydependent selection operating to maintain sub-populations at K.
(b) Population response to climate change
Introducing climate change led to a rapid and significant
decrease in mean population fitness (figure 1). Generally, initial
levels of mean fitness were regained following a period of
steady climate. Where dispersal was permitted (and linkage
between loci strong), a persistent reduction in the post-selection
mean fitness resulted only for v2P ¼ 8 (figure 1). This result is
logical because this is the highest value of selection strength
that still allows the development of generalists, thereby leading
to mutation load (see electronic supplementary material, figure
S2) and a slowing of final fitness recovery. Under conditions of
no dispersal (see electronic supplementary material, figure S3)
fitness initially declined but subsequently improved similarly
for all levels of patch selection v2P because individuals remain
in their optimal patch, avoiding a genetic load.
Although post-selection mean fitness recovered at population level, locally adapted (specialist) populations
ðv2P 4Þ suffered declines in population size that persisted
beyond the period of climate change (figure 2a). For those
populations remaining extant, recovery was only partial;
the mean population size over both patches is almost
halved following climate change, and full recovery is only
observed when v2P is 8 or above (figure 2a).
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(a)
d=0
no. runs
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pC = 0.5
150
450
100
80
60
40
20
0
100
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degree celsius
mean population size
100
80
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pC = 0.1
pC = 0.5
16
pC = 0.1
150
22
400
w 2p = 1
w 2p = 2
w 2p = 4
w 2p = 8
w 2p = 16
w 2p = 32
climate
300
200
100
0
20
1
4
8
1
4
8
patch selection strength (w 2p )
1
4
8
18
16
pC = 0.01
500
1000
1500
generation
Figure 2. (a) Mean overall population size under climate change scenarios (extant runs out of 20 replicates) for six values of patch selection strength v2P and three
values of crossover probability pC. For all runs: d ¼ 0.05, R ¼ 2.5, K ¼ 200 and n ¼ 0.03758C generation21. (b) Histograms illustrate that the reduction in mean
population size (as observed in panel (a)) following climate change (i.e. partial rescue) is due to a proportion of simulations in which a population only successfully
adapts to climate change in one of the two patches. The percentage of simulations in which both patches go extinct (black bars), one goes extinct (grey bars) and
for which both survive (white bars) is shown for combinations of dispersal, linkage and patch selection strength. For these runs, R ¼ 2.5, K ¼ 200 and n ¼
0.03758C generation21.
Importantly, the reduction in mean population sizes in surviving systems by approximately 50% was due mainly to the
loss of a sub-population in one of the patches (figure 2b). In
these cases, there was the complete loss of phenotypes, conferring adaptation to one of the two patches during the episode of
climate change, and this local adaptation to patch conditions
was not recovered after climate change (electronic supplementary material, appendix S4 and figures S12–S15). For highly
locally adapted populations ðv2P ¼ 1Þ, at least one patch went
extinct in 80% of runs (figure 2b), and both went extinct in at
least 40% of runs. For the less strongly locally adapted populations ðv2P 4Þ, almost full recovery was possible, but only
when linkage allowed recombination of beneficial climatic
alleles and alleles coding for adaptation to one of the two habitats ( pC 0.1). Increasing dispersal from d ¼ 0 to d 0.05
marked an important transition (figure 2b). Where d ¼ 0 and
for all levels of selection, only in roughly 15–20% of the runs
did both patches survive. As soon as dispersal was permitted
the probability of each patch surviving was increased, as
long as local adaptation was not too strong ðv2P 2Þ and
only moderate linkage was permitted ( pC ¼ 0.1 or 0.5).
Increasing linkage strongly reduced the likelihood that a
population survived climate change (figures 2 and 3), and broadened the range of patch selection under which one of the patches
became extinct (figure 2b). The negative effect of linkage
was mediated by the reduction of the effective distribution of
beneficial climate alleles owing to their association with maladaptive patch alleles (see below), resulting in an increased
probability of population extinction during a shift in climate.
For example, for v2P ¼ 1 and d ¼ 0.05, the chance of global population survival decreased from 70 to only 15% as recombination
( pC) was reduced from 0.5 to 0.01 (figure 1). Under the case of
zero dispersal, survival decreases even further, from 70 to 10%,
even though migration load is not generated (see electronic
supplementary material, figure S3).
(c) Conditions favouring the spread of beneficial alleles
Having established that local adaptation can reduce population survival under climate change, we explored how
selection against maladapted patch alleles might hamper the
spread and establishment of beneficial climate alleles (see electronic supplementary material, appendix 5, and figures S16
and S17). Only strong local selection ðv2P 2Þ significantly
reduced the probability that a beneficial climate allele would
establish in the other sub-population, from a 5–10% chance
to zero. Where the penalty for maladaptation was less strong
ðv2P . 4Þ, both potentially beneficial alleles and those causing
a migration load could persist together. These results are consistent for all dispersal rates tested, indicating that only a
moderate level of dispersal is required to ensure the spread
of beneficial alleles, and that as long as local patch selection
is below a threshold ðv2P 4Þ and pC 0.01 beneficial alleles
generally have a similar probability of establishment in both
patches regardless of where they originated. Although the
absolute level of linkage on the probability of establishment
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% of extinctions
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w 2p
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60
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pC = 0.01
0
0
16
pC = 0
0.05
0.10
d
0.20
0
0.05
0.10
0.20
d
Figure 3. Percentage of global population extinctions (over both patches) following climate change, depending on the dispersal probability d and the strength of
patch selection v2P , for four different levels of crossover probability pC. All the parameter combinations were run for 100 replicates with R ¼ 2.5, K ¼ 200, v2C ¼ 2
and n ¼ 0.03758C generation21 (see electronic supplementary material, appendix S2, and figures S8 and S9 for results with alternative rates of climate change,
and appendix S3 and figure S10 for results with K ¼ 400).
is relatively weak, tighter linkage slows the speed at which
beneficial alleles establish.
(d) Rate of climate change
For the single rate of climate change implemented in the main
simulations, both population extinction and evolutionary
rescue were possible, depending upon the level of genetic
selection for patch and climate adaptation, the dispersal rate,
and the level of linkage. However, the rate of climate change
also strongly modulated the overall population response.
Faster rates of climate change exacerbated population extinction,
with extinction probability increasing rapidly over a narrow
range of climate change rates (see electronic supplementary
material, figures S7–S9), but also shifted the point at which dispersal provided a positive effect on population persistence and
adaptation, dispersal becoming more positive as rate of climate
change increased, where recombination was less restrictive
( pC . 0.01; see electronic supplementary material, appendix S2).
4. Discussion
In a recent empirical study, Bell & Gonzalez [51] demonstrated the positive effect of local dispersal on evolutionary
rescue using an experimental meta-population of yeast. In
their study, the probability of population survival depended
crucially on the spread of beneficial mutations via gene flow.
This empirical observation was consistent with earlier theoretical results predicting beneficial effects of dispersal with
source populations acting as both genetic and demographic
donors of individuals (e.g. [7]). However, as is suggested
by the recent work of North et al. [52] and Schiffers et al.
[23], the positive effect of dispersal might, under some
conditions of habitat heterogeneity, be outweighed by the
increasing maladaptation that dispersal generates. The results
of our study indicate that the potential negative effects associated with dispersal generally only dominate the opposing
positive effects of gene flow when conditions of patch selection lead to locally adapted phenotypes. In these cases, our
results described a high likelihood of patch extinction for
locally adapted sub-populations, with dispersal facilitating
population rescue only when selection for specialists was
relatively weak and recombination partially decoupled local
adaptation from adaptation to changing climate. The positive
role of dispersal increased from the point where, owing to
weaker divergent selection between patches, conditions
moved from local adaptation and the maintenance of specialists
to the favouring of generalist genotypes performing well
enough in both patches to maintain viable populations. This
transition marks a vital point in determining whether a patch
will experience partial or full extinction as opposed to rescue.
Given that local adaptation is widespread in nature (e.g.
[14,53]), our results suggest that sub-structured populations,
despite being well adapted to their current environments, may
have a higher probability of extinction at a local level than
expected from overall population size and available genetic
variation [53], as long as localized selection pressures reduce
effective dispersal and if other factors (such as demographic factors of R and K, and genetic factors, such as m) cannot provide
sufficient alternative sources of genetic variation.
The point at which dispersal switched from having positive to negative effects in our model was also affected by the
rate of climate change: dispersal was generally negative or neutral during lower rates of climate change (see electronic
supplementary material, figure S11), worsening with increased
local adaptation (where beneficial climate alleles linked with
highly maladaptive local patch alleles are purged). As the
rate of climate change increased, the effects of dispersal
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Linkage, however, is known to play an important role in
the evolutionary response of species [40,41], and our more
detailed analysis of the role of linkage illustrates clearly the
strong negative impact it can have on the survival probability
of populations. Beneficial mutations with respect to climate
that arise at certain locations across the genome cannot be
inherited independently of locally adapted alleles under full
linkage. Thus, the benefit of dispersal in providing the
necessary variation in climate alleles for adaptation
is considerably higher when relaxing the assumption of
linkage between loci. Our findings reflect recent empirical
observations on the constraining effect of linkage between
traits on the magnitude of response to various stresses
[54,55], highlighting the importance of genetic architecture
in determining the capacity of populations to respond to
environmental change (e.g. [5,14]).
An interesting outcome of the comparison of our model
results with those of Schiffers et al. [23] is the observation in
both studies of partial evolutionary rescue, despite the differences in modelling approaches. In our two-patch model,
partial rescue often occurred as an approximate halving of
the initial population size that resulted from the complete
loss of local adaptation to one of the two patches, while in
the spatially explicit model, population size was more variable and corresponded to the particular spatial constellation
of the location where mutations occurred. These independent
observations of partial rescue suggest the importance of this
result, and point towards a need for further investigations
into its causes and consequences. Decreased population size
may have the indirect effect of a further reduction in genetic
diversity through drift [56], with the potential to increase
inbreeding and with possible ecological consequences such
as changes in pollinator –plant dynamics or breeding systems
[57,58]. In our model, patch selection strongly influenced the
recovery potential of the global population, and suggested
that local adaptation is likely to seriously constrain subpopulation survival during periods of climate change.
Given the ubiquity of local adaptation, these findings have
wide implications for spatially structured populations [53].
Our results, emerging from a relatively simple modelling
exercise, reveal a complex interaction of differential selection
resulting from independent exogenous pressures, underlying
genetic architecture and the degree of dispersal across a substructured population. There are many interesting potential
extensions. For example, the degree of dispersal symmetry
between patches plays an important role in restricting evolutionary potential by constraining niche evolution [7,24,59].
Relaxing the assumption of symmetric dispersal would represent an obvious and important future study. Exploring the
consequences of some of the underlying genetic and phenotypic assumptions of our model would also be of interest. First,
the mutation variance could alter the probability of successful
adaptation to changing climate: a greater mutation variance
might reduce the probability of extinction for a given rate of
climate change and level of local adaptation; initial simulations (see electronic supplementary material, appendix S1,
and figures S5 and S6) pointed to this possibility. Second, our
assumption that the genotype fully determines the phenotype
(i.e. a heritability of 1) is relatively simplistic; a population’s
adaptability will clearly be modulated by the relative contribution of plasticity in mediating shorter-term responses (e.g.
[8,9,12]), and genetic factors such as dominance and epistasis
will reduce genetic heritability, altering the nature of genetic
rspb.royalsocietypublishing.org
became increasingly positive, providing local selection was not
extreme. Where linkage and selection were strong, beneficial
alleles could not spread to aid in climate adaptation and the
positive effect of dispersal was not realized. However, as
long as recombination was permitted, dispersal was found to
be positive, even at levels of relatively strong local selection.
These findings are in agreement with predictions of an analytical model developed by Blanquart & Gandon [32]: they
showed that when temporal environmental change is rapid,
faster rates of dispersal are favoured, as long as migration is
not costly, where instead the highest emigration rate evolves
at an intermediate rate of environmental change.
An important implication of our findings is that even
without direct genetic constraints, adaptation to a patchspecific environmental factor may affect a population’s
evolutionary response to another globally changing factor,
such as climate. This indirect link is mediated via the purging
of locally maladapted individuals that might at the same
time carry beneficial mutations with respect to the globally
changing factor. In our study, because single individuals—
constituting the units of dispersal in our simulations—carry
the genes for adaptation to both factors, the spread of a
mutation that is beneficial under changed climatic conditions
can be limited owing to their linkage to alleles coding for
local adaptation (see electronic supplementary material,
appendix S5, and figures S16 and S17).
The counteracting effects of gene flow for evolutionary
rescue were also studied in related work by Schiffers et al.
[23]. Although the same processes govern the impact of dispersal in both approaches, the balance between the positive
and negative effects was shifted considerably towards the
positive side in our study. Three factors are likely to cause
this difference. First, in this study, we investigated a much
wider range of selection strengths, resulting in a large proportion of scenarios where selection did not lead to local
adaptation and migration load consequently did not occur.
By contrast, in the work by Schiffers et al. [23], selection
strength was much stronger ðv2P ¼ 0:1Þ, probably leading to
strong local adaptation. Second, we did not consider a
single spatially continuous habitat with varying local conditions, but two discrete patches within which individuals
mix freely, representing habitats with a clearly fragmented
structure (e.g. separated meadows). Whereas in the continuous habitat model the carrying capacity of each location
was restricted to five individuals, both of our two patches
could hold up to 200 individuals (K ¼ 400 for limited runs;
electronic supplementary material, appendix S3). This refers
to an ecological setting where a coarser habitat/patch classification is suitable for the organism considered. The resulting
higher number of individuals occupying one of two patches
in our model may reduce the level of migration load compared with the smaller number experiencing greater
heterogeneity in the model of Schiffers et al. [23]. In addition,
the greater population size under the same selective conditions and in the same pool for mating in our model
would increase the probability that beneficial mutations are
spread between more individuals on a local scale, thereby
increasing the probability of establishment elsewhere. Consequently, dispersal in our two-patch model could have led to a
greater capacity for adaptation to climate. Third, for Schiffers
et al. [23], the impact of linkage between the quantitative trait
loci was considered in a much simpler way, and the interpretation of results was mainly based on full linkage scenarios.
Downloaded from http://rspb.royalsocietypublishing.org/ on May 7, 2017
Acknowledgements. We would like to thank two anonymous referees for
their thorough review of earlier versions of the manuscript and the
very constructive comments.
Funding statement. The work was supported by the Macaulay Develop-
Our model combines key features of genetic architecture
involved in adaptation, in the context of a spatially structured
population. It is also one of the first studies to address the role
of local adaptation in shaping the evolutionary potential of
species under environmental change that incorporates more
than one trait under selection.
ment Trust (PhD funding to E.C.B.) and the European Research
Council under the European Community’s Seven Framework Programme FP7/2007– 2013 (IEF Marie-Curie Fellowship 252811 and
Grant Agreement no. 281422 (TEEMBIO) to K.S.). The work of
R.J.P. and R.W.B. is funded by the Scottish Government’s Rural
and Environment Sciences and Analytical Services (RESAS) Division.
J.M.J.T. was supported by NERC.
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