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Limited evolutionary rescue of locally adapted populations facing climate change

Limited evolutionary rescue of locally adapted populations facing climate change Limited evolutionary rescue of locally adapted populations facing climate change 1 2,3,4 1 Katja Schiffers , Elizabeth C. Bourne ,Sebastien Lavergne , 1 2 rstb.royalsocietypublishing.org Wilfried Thuiller and Justin M. J. Travis Laboratoire d’Ecologie Alpine, Universite´ Joseph Fourier, Grenoble 1, UMR-CNRS 5553, BP 53, 38041 Grenoble Cedex 9, France Institute of Biological and Environmental Sciences, University of Aberdeen, Zoology Building, Tillydrone Avenue, Aberdeen AB24 2TZ, UK Research The James Hutton Institute, Craigiebuckler, Aberdeen AB15 8QH, UK Institut fu¨r Biologie—Botanik, Freie Universita¨t Berlin, Altensteinstrasse 6, 14195 Berlin, Germany Cite this article: Schiffers K, Bourne EC, Dispersal is a key determinant of a population’s evolutionary potential. It Lavergne S, Thuiller W, Travis JMJ. 2012 facilitates the propagation of beneficial alleles throughout the distributional Limited evolutionary rescue of locally adapted range of spatially outspread populations and increases the speed of adap- populations facing climate change. Phil tation. However, when habitat is heterogeneous and individuals are locally Trans R Soc B 368: 20120083. adapted, dispersal may, at the same time, reduce fitness through increasing http://dx.doi.org/10.1098/rstb.2012.0083 maladaptation. Here, we use a spatially explicit, allelic simulation model to quantify how these equivocal effects of dispersal affect a population’s evo- lutionary response to changing climate. Individuals carry a diploid set of One contribution of 15 to a Theme Issue chromosomes, with alleles coding for adaptation to non-climatic environ- ‘Evolutionary rescue in changing mental conditions and climatic conditions, respectively. Our model results environments’. demonstrate that the interplay between gene flow and habitat heterogeneity may decrease effective dispersal and population size to such an extent that substantially reduces the likelihood of evolutionary rescue. Importantly, Subject Areas: even when evolutionary rescue saves a population from extinction, its spatial evolution range following climate change may be strongly narrowed, that is, the rescue is only partial. These findings emphasize that neglecting the impact of non- Keywords: climatic, local adaptation might lead to a considerable overestimation of a allelic model, dispersal, gene flow, habitat population’s evolvability under rapid environmental change. heterogeneity, migration load, rapid adaptation Author for correspondence: 1. Introduction Katja Schiffers e-mail: [email protected] Facing one of the most drastic global changes in the Earth’s history, a funda- mental objective of current ecological and evolutionary research is to understand and predict species’ responses to changing environmental con- ditions [1]. Three key types of response may ameliorate the threat of extinction: buffering against negative effects of deteriorating habitat by pheno- typic plasticity [2–5], tracking suitable climate through range shifting [6,7] and adapting to changing conditions by rapid evolution [8,9]. Some authors suggest that most species will more likely shift their distributional ranges or respond by phenotypic plasticity rather than adapt in situ to new conditions [6,10]. This is mainly because plasticity and range shifting may be substantially faster in matching phenotypic preferences with environmental conditions than evo- lutionary processes. Nonetheless, a number of species have been shown to adapt with remarkable rapidity in response to environmental change [11,12], and numerous studies have identified heritable population differentiation in ecologically relevant traits, providing indirect evidence for the potential of adaptive evolution over ecological time-scales [8,13,14]. It thus seems impera- Electronic supplementary material is available tive to consider the role of evolutionary rescue—the phenomenon of once at http://dx.doi.org/10.1098/rstb.2012.0083 or declining populations evolving back to positive growth by evolutionary via http://rstb.royalsocietypublishing.org. & 2012 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0/, which permits unrestricted use, provided the original author and source are credited. rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 adaptation—in assessments of the likely impacts of global from those that undergo temporal changes. A simple example change on species abundance, distribution and persistence. can illustrate this statement. Many plant populations are locally The theoretical foundations of adaptive dynamics have adapted to varying abiotic conditions (e.g. edaphic factors) or been established over the past decades by a growing biotic context (e.g. presence/absence of herbivores), but the number of studies in the fields of population and quantitative mosaic of this local adaptation will mostly be decoupled genetics. A key theorem states that the rate of adaptation is from currently changing climatic gradients. Under these cir- predominantly driven by the amount of available additive cumstances, the central question is: how do the contradictory genetic variance and the strength of environmental selec- effects of dispersal influence the evolutionary response of tion [15,16]. In principle, given sufficient genetic variance, populations to environmental change? populations should adapt to virtually any environmental In this study, we address the above question by integrat- condition [17]. However, under natural conditions, an ing the key processes that have until now typically been often-complex interaction between demographic processes studied separately: the role of dispersal as the mechanism dis- and evolutionary dynamics may result in failure of adap- tributing adapted alleles across populations and the tation and ultimate extinction of the population [18–20]. To feedbacks between dispersal and local adaptation. We do gain initial insights into such interactive processes, synthetic this within the context of an allelic model, where population approaches linking genetics with population demography genetics are coupled with population ecology by condition- are being applied increasingly frequently, addressing ques- ing demographic rates on the match of genetically variable tions on, e.g. the formation of species range edges [21–23] traits to environmental characteristics. We use our model to and invasion dynamics [24,25], including invasion dynamics examine how the interplay between dispersal and local in heterogeneous landscapes [26,27]. adaptation across spatially heterogeneous habitats influences In the context of eco-evolutionary processes, dispersal is a the probability of evolutionary rescue of populations facing key determinant of population dynamics, owing to its impact changing climatic conditions. We also examine how the on both spatial demography [28,29] and the speed of local genetic architecture of adaptive traits modulates this interplay. adaptation [29–31]. As a consequence, dispersal is likely to be crucial for evolutionary rescue. The main responsible mechanism is the spreading of newly arising, beneficial alleles 2. The model throughout a population’s distributional range [32–35]. In a recent study, Bell & Gonzalez [35] empirically tested these We developed an allelic, spatially explicit and individual- theoretical predictions with an experiment on bakers yeast: based simulation model to investigate the interactive effects they demonstrated that spatially structured populations had of gene flow and local adaptation on the evolutionary a significantly higher chance of surviving a period of deterior- response of populations to environmental change. The full ating growth conditions and adapting to the new state, when source code and an accompanying readme file are available dispersal allowed for gene flow across subpopulations. as electronic supplementary material, and a maintained ver- In contrast to its beneficial effect for rapid adaptation sion of the model is downloadable from http://www.katja- under temporally changing conditions, dispersal is known schiffers.eu/docs/allele_model.zip. to have an overall negative influence on population fitness The model organism we had in mind during implementa- under most scenarios of local adaptation [36,37]. In a spatially tion was a bisexual, annual plant species with xenogamous heterogeneous environment, mismatches between immi- breeding system. Population dynamics take place within a grants’ genotypes and the environmental conditions at their continuous region of 32  32 grid cells. To avoid arbitrary destination locations result in a reduction in overall fitness, edge effects, the area is simulated as a torus, i.e. the edges termed migration load. With analytical predictions and indi- of both axes are joined. Grid cells are characterized by two vidual-based simulations, Lopez et al. [37] have illustrated environmental conditions: (i) local environmental conditions how, under gene flow through both pollen and seed move- such as edaphic parameters or particular biotic settings, ment, migration load increases with the degree of habitat which follow a fractal distribution and are stable over time; heterogeneity. In a further theoretical study, Alleaume- and (ii) climatic conditions, e.g. maximal annual temperature, Benharira et al. [38] demonstrated that in a patchy population, which change during the simulated period. For simplicity, we distributed across an environmental gradient, intermediate assume climate to be homogeneous across space. Each grid rates of dispersal optimized fitness. This was the result of a cell can support a number of individuals, the maximal trade-off between some dispersal having benefits in terms number given by the local carrying capacity, which is con- of purging deleterious alleles, especially from smaller mar- stant across the region. Individuals are diploid, carrying ginal populations, and increasing dispersal resulting in two copies of either one or several chromosomes coding for higher migration load owing to gene flow between patches an individual’s level of adaptation to climatic and local of differing local conditions. environmental conditions. Individuals are located in continu- Clearly, adaptation to heterogeneous habitat and tem- ous space and are assigned to the grid cell within which their poral changes in environmental conditions often occur x- and y-coordinates fall. hand in hand [39], confronting populations with multiple Within each generation, the following processes are simu- sources of potential maladaptation. However, the few exist- lated: (i) reproduction with mutation, recombination, gamete ing studies investigating population responses to a spatially dispersal and subsequent death of the parental generation, and temporally changing optimum focus predominantly on (ii) dispersal of the offspring, (iii) selection acting on the survi- a single environmental variable [40–42]. Such an approach val probabilities of the juveniles, and (iv) density-dependent neglects a situation that is likely to be very common in nat- mortality. Selection takes the form of density-independent, ural conditions, that is where the spatially heterogeneous hard selection for an individual’s adaptation to both climatic conditions driving local adaptation of populations differ and local environmental conditions. rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 To gain sufficient computational efficiency, we do not (a) Genetic architecture explicitly simulate the dispersal of pollen. Instead, we use A number of previous studies have shown that traits affecting the following algorithm. As for offspring dispersal, species’ adaptation, particularly to climatic conditions, are x/y-coordinates are chosen randomly in the neighbourhood usually polygenic. For example, 12 quantitative trait loci of the focal individual. The mating partner is then randomly have been identified for climatic adaptation in Arabidopsis drawn from all individuals inhabiting the grid cell within thaliana [43], 33 for bud-flush, nine for autumn cold hardiness which the random position is located. In case the selected and nine for spring cold hardiness in Pseudotsuga menziesii grid cell is empty, the procedure is repeated up to 99 times. [44] (see also Falconer & Mackay [45] for a general overview). If all trials are unsuccessful, we assume the ovule not to On the basis of this information, we simulated genomes com- be fertilized. posed of n ¼ 15 loci for each of the two considered traits. To To test for potential undesirable effects of this simplifica- represent two contrasting scenarios of linkage, we considered tion, we also developed implementation of gamete dispersal the genome to be composed either of one or several pairs of that is more precise in the sense of linking fertilization prob- chromosomes. In the first case, all loci are situated on a single ability to the exact distance between individuals. For each chromosome and, as we do not allow for crossovers during individual of the population, the probability of fertilizing a recombination, the loci are fully linked. Effectively, this could specific ovule is calculated based on the inter-individual dis- also be considered a single locus with multiple alleles and tances and the shape of the dispersal kernel. Following that, pleiotropic effects. In the second case, we assume the opposite the probability of no fertilization can be determined. Rescal- possible extreme case of no linkage. This may correspond to a ing all resulting probabilities so that they add up to unity situation where a genome is made of 30 chromosome pairs then allows sampling of the pollen donor by a draw of a uni- each carrying a single locus, implying completely independent form random number between zero and unity. Comparisons inheritance of alleles. Or, this might mimic a situation where all between the two approaches showed that there are no obvious the loci are on a single (or multiple) chromosome, but with suf- differences at the level of evolutionary or demographic ficient distance between the loci and sufficient frequency of dynamics. We thus chose the former, computationally much crossover events that they are effectively unlinked. Alleles are less intensive method. described by continuous values and are additive within and between loci, i.e. neither epistatic nor pleiotropic effects are considered. Individuals’ phenotypes are directly determined (iii) Selection by their genotypes, that is, environmental effects on pheno- Selection acts on population demography by modulating types are neglected, and heritability is thus assumed to be juvenile survival probability. Each individual’s survival prob- unity [21–23,46]. ability W is calculated as the product of its condition related to climate W and its condition related to the local environ- ment W . Both of these values, W , are functions of the E C,E (b) Simulated processes difference between the individual’s phenotype z , and C,E the optimal phenotype under the current climatic or local (i) Reproduction environmental conditions Q . They follow a normal C,E All individuals can potentially bear offspring. The number of distribution with maximum unity and variance v : C,E ovules produced by each individual is drawn from a Poisson "# distribution with average R ¼ 100. Whether, and by which ðz  Q Þ C;E C;E W ðzÞ¼ exp  ; C;E mating partner, single ovules are fertilized is modelled stochas- 2v C;E tically with the probabilities of fertilization derived from the individuals’ distances and the shape of the pollen dispersal where v is traditionally referred to as selection strength, but kernel (see §2b(ii)). Gametes are composed by duplicating par- can also be interpreted as a measure of the species’ tolerance ental chromosomes, one of each homologous pair being chosen to suboptimal conditions, i.e. its niche breadth [40]. Here, for randomly. Alleles mutate with a probability ofm ¼ 10 , which the default parameter settings, this value was fixed at 0.1, represents the average rate found for the annual plant species resulting in W , 0.01 and thus in a negative population Arabidopsis thaliana [47–49]. The mutational effect, i.e. the growth rate (given the average number of offspring per amount by which the allelic value is changed, is drawn from individual is 100) when temperature has changed by approxi- a zero-mean normal distribution with variance a ¼ 0.2, mately 18C, assuming the phenotype is fixed. In a number of approximately fitting empirical observations [47]. additional runs, selection strength was reduced by increasing v to 0.2. (ii) Dispersal (iv) Density-dependent mortality There are two phases of dispersal in each generation cycle: We assume a simple ceiling form of density dependence pollen dispersal and offspring dispersal. Both are characterized (similar to [39,51]): whenever the number of individuals by lognormal, isotropic dispersal kernels with an average dis- within a grid cell exceeds its carrying capacity, K, resident tance d for both gametes and offspring and a shape parameter individuals are subjected to a density-dependent mortality of 0.5. The lognormal distribution has been found to adequately with probability of survival ¼ 1 2 K/N. represent both local and long-distance dispersal [50]. Offspring dispersal is simulated explicitly: dispersal dis- tance and direction are chosen randomly with probabilities (c) Simulations following the shape of the dispersal kernel. The offspring is posi- Simulations were run to test the interactive effects of disper- tioned at the resulting x/y-coordinates, respecting torroidal sal, habitat heterogeneity and linkage on population boundary conditions. dynamics and the likelihood of survival under climate rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 with no initial genetic variation showed that resulting Table 1. Parameter values for simulation runs. population parameters were not influenced by the chosen starting conditions (see the electronic supplementary material, parameter description values figure S5). For the main analysis, climate change was simulated by keeping the temperature constant over the first 200 gener- V rate of climate shift two units per 100 ations and then gradually increasing it by 2.08C over the years following 100 time-steps. After this period of change, H Hurst exponent 0.2 the new climatic conditions were assumed to be stable h habitat 0, 1, 2, 3, 4, 5, 6 H until the end of 500 simulation years. heterogeneity K carrying capacity per 5 grid cell 3. Results R mean number of 100 In test runs without environmental change, population size, average individual fitness and additive genetic variance offspring were stable over time, unless mean dispersal distances were D mean dispersal 0.05, 0.1, 0.2, 0.4, 0.8, too small to ensure a sufficient number of fertilized ovules distance 1.6, 3.2, 6.4 to keep growth rates higher than unity. When introducing a d shape factor 0.5 shape shift in climate, population size started to decline at the point where the average individual phenotype lagged so dispersal kernel far behind the optimum Q that W, 1/R. In simulations L linkage between fully linked, free where the mutation rate m was set to zero, populations inev- loci recombination itably died, because standing genetic variation alone did not M mutation rate per 10 provide enough scope for full adaptation to new conditions. With the default value for m ¼ 10 , an average family size of locus 2 100 and a carrying capacity around 5000 individuals, a variance of 0.2 mutations occurred on average once per generation and mutational effect locus. In combination with the given variance of the muta- 2 2 v selection strength 0.1, 0.2 tional effect (a ) ¼ 0.2 and a selection strength (v ) ¼ 0.1, allelic dynamics resulted in a slow disruption of the initial normal distribution of allelic values (see the electronic sup- change (see table 1 for model parameters). The average dis- plementary material, figures S1–S4) during periods of persal distance d was set to 0.05 grid cell lengths for the stable climate. During phases of temperature rise, mainly first set of simulations and then repeatedly doubled up to a the fixation of rare, large mutations contributed to the adap- distance of 6.4. Habitat heterogeneity h was controlled by tation process to the new conditions (results not shown), modifying the range of possible local environmental con- leading to punctuated phases of rapid evolution as, for ditions from 0 units, i.e. no heterogeneity, to a maximum of example, described in Holt et al. [39]. six units in steps of 1. For testing the effect of linkage, the Population responses to rapid climate change fitted into two contrasting scenarios of complete versus no linkage three general classes, depending upon the values of some were compared. The remaining model parameters were key model parameters. We first describe the three main cat- kept constant across simulations. For all possible 112 combin- egories of response (figure 1), before providing some detail ations of d, h and linkage, we ran 100 replicates, recording on how the key parameters influenced the outcome. population size over time and the population average and Complete evolutionary rescue occurred when there was a variance of individuals’ survival probabilities, W ,asa sufficient number of beneficial mutations and when they C,E measure for their conditions. were able to spread unhampered across the landscape. This Landscapes were initialized with a value of 258C for the class of response was typically characterized by an initial climatic conditions and a Hurst exponent of 0.2 for the fractal phase during which, as the climate began to change, individ- distribution of local environmental conditions, their ampli- uals’ survival probabilities declined. Subsequently, as one or tude being controlled by h . The values assigned to h more beneficial mutations occurred and spread across the H H resulted in average differences between neighbouring cells landscape, the average individual’s fitness increased, of 0.03, 0.09, 0.15, 0.38, 0.9 and 1.46 units, respectively. The the total population size fully recovered and ultimately indi- spatial population was initialized by colonizing each grid viduals’ phenotypes were a good match to the new climate cell with three individuals. Individuals were, on average, conditions (figure 1a). optimally adapted to both climatic and local environmental Partial evolutionary rescue occurred under conditions where conditions, but exhibited normally distributed additive gen- beneficial alleles arose but were unable to spread owing to inef- etic variation with a within-cell variance of 0.01. This value fective gene flow across space. In this class of response, only corresponds approximately to the mutation–selection equi- fragments of what was previously fully occupied habitat librium reached after 1000 generations in previous test runs were populated following climate change. This effective under stable conditions (see the electronic supplementary reduction in the suitable habitat niche for the population some- material, figures S1–S4). It has to be noted that allelic times resulted in substantially reduced total population sizes values typically did not follow normal distributions at the following climate change (figure 1b). Importantly, this effect end of these runs, particularly when habitat heterogeneity was persistent, lasting until the end of simulations, which ran was low. However, comparisons with additional simulations for 200 generations after climate change ceased. rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 (a) 5 1.5 1.0 0.5 (b) 1.5 1.0 0.5 (c) 1.5 1.0 0.5 0 100 200 300 400 500 generations Figure 1. Three example runs depicting (a) full rescue, (b) partial rescue, and (c) population extinction. Solid lines represent population size, short dashed lines represent the level of adaptation to climatic conditions, W , and long dashed lines represent the level of adaption, W , to local environmental conditions. On the C E right-hand side the density of individuals is shown after 500 time-steps with darker values indicating higher densities. Extinction, due to the failure of evolutionary rescue, observed for intermediate values between 0.4 and 2 grid occurred when the frequency of beneficial mutations was cell units. Within that range, the peak of rescue probability too low. Under these conditions, individuals’ phenotypes depended on the level of habitat heterogeneity and shif- rapidly became very poorly matched to the prevalent ted towards shorter dispersal distances with increasing climatic conditions, resulting in lower offspring viability heterogeneity (figure 5a–c). and ultimately a non-viable population (figure 1c). With increasing spatial heterogeneity, there was also an increased likelihood that, when rescue occurred, it was only partial. Thus, while the population had at least some probability (a) Effects of dispersal and habitat heterogeneity of surviving climate change through evolutionary rescue, the In accordance with our expectations based on previous landscape was not fully occupied after climate change and the studies [36,37], in a spatially heterogeneous environment, dis- total population size was substantially reduced (figure 5). persal generally had a negative effect on individuals’ levels of Under a heterogeneity of h ¼ 5, the average relative popu- adaptation to environmental conditions W (figure 2). lation size (of the surviving populations) at the end of the In scenarios of full linkage, the level of adaptation increased simulation time was, across a broad range of dispersal dis- again for very high values of dispersal and heterogeneity tances, reduced to an average of around 50 per cent of pre- (figure 2a), owing to an increased mortality of strongly mala- climate-change densities (figure 5c). Interestingly, the parameter dapted individuals and consequently higher averages for the values that maximized the probability of rescue did not necess- surviving fraction of the population (results not shown). arily result in a more complete rescue. For example, when h ¼ On the other hand, model results also confirmed the 5, there was the greatest probability of population survival beneficial effect of dispersal on a population’s adaptation to when dispersal ¼ 0.4. For this scale of dispersal, however, sur- temporally changing conditions. This was demonstrated by viving populations were reduced on average to roughly one- increasing values of W with increasing dispersal distances sixth of their initial abundance. By contrast, when dispersal (figure 3). However, this pattern appeared to be more occurred across a greater range (e.g. dispersal ¼ 2.5), the popu- sensitive to stochastic effects than results regarding the lations survived only 10 per cent of the time, but then recovered adaptation to local environmental conditions. to an average 50 per cent of initial abundance. The likelihood of evolutionary rescue was strongly reduced or even hindered for a range of dispersal distances, for which rapid adaptation would have been possible with- (b) Effect of linkage out local adaptation (figure 4). Because both high dispersal The assumptions regarding the form of linkage had a strong distances, as well as very low distances, decreased the prob- effect on the overall probability of evolutionary rescue. ability of evolutionary rescue, highest survival rates were Independent inheritance allowed for much faster adaptation population size (×10 000)/average level of adaptation rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 (a) (b) 6 1.00 0.95 4 0.90 0.85 0.80 0.75 0.70 1 23 4 56 1 23 4 56 dispersal distance dispersal distance Figure 2. Average values for the level of adaptation to local environmental conditions, W , during the phase of temperature rise for (a) full linkage and (b)free recombination of loci. Depicted are the average values over 100 replicates for all combinations of habitat heterogeneity h and average dispersal distances d in grid cell length. (a)(b) 0.60 0.55 0.50 0.45 2 0.40 0.35 0.30 1 23 4 56 1 23 4 56 dispersal distance dispersal distance Figure 3. Average values for the level of adaptation to climatic conditions, W , during the phase of temperature rise for (a) full linkage and (b) free recombination of loci. Depicted are the average values over 100 replicates for all combinations of habitat heterogeneity h and average dispersal distances d in grid cell length. to both spatially (figure 2) and temporally changing con- extinction. Understanding the factors determining the ditions (figure 3) so that the negative effect of local likelihood that populations adapt sufficiently rapidly to chan- adaptation was strongly ameliorated (figure 4). However, ging environmental conditions is at the heart of research on the overall pattern of intermediate dispersal distances evolutionary rescue. resulting in highest evolutionary potential was consistently Allelic simulation models, as used in this study, provide observed for both scenarios. an ideal tool for integrating the available knowledge on eco-evolutionary dynamics from different organizational levels and to reflect the complex nature of adaptive and demographic processes. However, to date, most modelling 4. Discussion studies have been highly abstracted, for example, assuming Global environmental change is confronting natural popu- unrealistically high mutation rates and panmictic popula- lations simultaneously with rapid climate change and tions. Here, we have taken a first step towards quantitative increasing habitat loss and deterioration. The combination predictions of population response to environmental change of habitat fragmentation and limited dispersal will prevent by establishing an individual-based model that is both many populations from tracking suitable climate in space. spatially and genetically explicit, and that, as far as possible, For these species, in situ adaptation to changing climate is has been parametrized realistically for both genetic and likely to provide the only natural means of avoiding ultimate demographic functions. habitat heterogeneity habitat heterogeneity rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 (a)(b) 7 1.0 0.8 0.6 0.4 0.2 1 23 4 56 1 23 4 56 dispersal distance dispersal distance Figure 4. Probability of full rescue depending on habitat heterogeneity h and average dispersal distances d in grid cell length for (a) full linkage and (b)free recombination of loci. Calculated from 100 simulation runs for each parameter combination. (a) 0.8 0.4 (b) 0.8 0.4 (c) 0.8 0.4 dispersal distance Figure 5. Probability of evolutionary rescue ( partial and full rescue, solid lines) and relative population sizes ( population size at generation 500/K, extinctions excluded, dashed lines) in dependence on dispersal distance d for habitat heterogeneities of (a) h ¼ 0, (b) h ¼ 3, and (c) h ¼ 5. Results are based on 100 H H H simulation runs for full linkage of loci. The initial results of our model presented within this Considering the effects of dispersal on local adaptation paper demonstrate two potent key phenomena that we and environmental change separately, the results of our consider important, particularly under ongoing habitat model concur with existing studies on each topic. Under deterioration and fragmentation: first, the potentially com- habitat heterogeneity and local adaptation, dispersal typic- plex effects of dispersal for a population’s evolutionary ally has negative consequences for the average fitness response to both spatially heterogeneous habitats and [36,37]. Increased migration load—in our model output shifting climate. And second, the possibility for partial reflected by reduced levels of adaptation to the local environ- evolutionary rescue, whereby rapid adaptation saves a popu- ment—lead to higher mortality rates and an increased risk of lation from extinction, but both population size and its location extinction, hence a lower chance of rescue. On the geographical range may be substantially reduced. other hand, as argued and shown recently by Bell & habitat heterogeneity probability of rescue and relative population size rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 Gonzalez [35], greater dispersal can be strongly beneficial, stabilizing selection for local environments would account owing to its function in spreading favourable alleles across for most genetic load (i.e. for most fitness reduction). the populations’ distributional ranges. This was mirrored Second, one could also expect that adaptive response to chan- by our results, when focusing on only the adaptation to tem- ging climate would be reduced when recombination between porally changing climate and thus neglecting the distorting climate-related loci can occur at every generation, thus break- effects of migration load. ing apart adaptive allele combinations and preventing the The interplay of these double-edged consequences of population from being fully rescued. Whether and how link- gene flow leads to the key results that we emphasize in this age may facilitate or impede adaptation to changing paper. When dispersal is high and habitat heterogeneous, environmental conditions could be further investigated with the number of viable offspring in each generation can be our model, but is beyond the scope of this paper. drastically reduced due to the arrival of many maladapted Clearly, a number of genetic, demographic and envir- juveniles. At the population level, this is of little consequence onmental settings that were neglected in this study can when the climate is stable, as long as the number of surviving modulate the effects of spatio-temporal variability on juveniles can maintain the population in a steady state. How- micro-evolutionary dynamics. Some of these are shortly ever, when the population needs to adapt to new climatic discussed in the following. conditions, the absolute number of beneficial mutations In terms of the genetic basis of adaptation, it has been becomes crucial. This number depends not only on the shown that the relative amount of genetic versus environ- mutation rate, but also on the number of potential recruits mental variability in individual phenotypes affects the that may carry these mutations and pass them on to sub- speed of adaptation and the likelihood of evolutionary sequent generations. High rates of juvenile dispersal into rescue [39,53]. While the probability of population extinction habitat to which they are ill-adapted reduces the effective is increased under lower heritability of those traits controlling rate at which beneficial mutations on climate-related loci adaptation to temporally changing conditions, for traits con- can be fixed in the population (see Barton & Bengtsson trolling adaptation to spatial heterogeneity, low heritabilities [52]). Ultimately, this interaction between dispersal, habitat and high plasticity may instead facilitate population survival: heterogeneity and temporal environmental change leads to plasticity can buffer the negative effects of local malad- the observed reduction in the probability of evolutionary aptation, reduce mortality and thus allow for increased rescue. This suggest that even under high dispersal scenarios, effective dispersal and the spread of beneficial alleles. populations previously adapted to spatially structured local Weaker selection will have a positive influence on the survi- environments may have a lower chance to adapt to changing val probability of populations as well, because the effects of regional climate. maladaptation are reduced. This effect is more pronounced The second key result—partial evolutionary rescue—is in when the habitat is heterogeneous (see the electronic supple- its mechanism closely linked to the process described above. mentary material, figure S6), because the level of adaptation High habitat heterogeneity, subsequent migration load and to both climate and local conditions determine population decreased survival probability hamper the spatial spread of development in this case. Furthermore, a number of studies beneficial alleles, which may become locally abundant. The have demonstrated that characteristics of allelic effects such positive fitness effect of the beneficial mutation on climate- as epistatis or pleiotropy [54] and the nature of the selection related loci becomes overridden by the negative effects (i.e. hard versus soft selection) [55] might change evolutionary due to genetic swamping by newly arrived individuals carry- dynamics substantially. ing alleles that are not adapted to local environmental Focusing on demographic effects on rapid adaptation, the conditions. This is obviously most likely when habitat is characteristics and effects of dispersal and gene flow may strongly heterogeneous. Thus, when the resulting absolute need more detailed inspection. For example, gene flow by fitness of these individuals is lower than unity, beneficial pollen will affect adaptation processes differently compared alleles cannot spread throughout the distributional range of with gene flow by dispersal of seeds or individuals [37]. the population, thus preventing a species fully recovering First, the expected level of migration load is only half as its original geographical range following a shift in regional high for pollen as for seed dispersal, because just half the climate. In case the surviving subpopulations are too small number of maladapted alleles are placed into a new local to supply a sufficient amount of new mutations for adap- environment, leading to decreased mortality. Second, the tation to the conditions in the unpopulated space, we tend direct effect of shifting individuals between locations does to observe a quasi-stable fragmented distribution of the not apply, partly decoupling evolutionary from demographic surviving populations. dynamics. Apart from that, it has to be considered that dis- Our model also demonstrates that different ecological persal capabilities evolve rapidly themselves [56–58]. This traits—even though not genetically correlated—may interact adds another layer of complexity to forecasting population with the evolutionary dynamics, because they have dynamics in space and time, but should generally increase additional effects on individuals’ fitnesses and ultimately populations’ survival probabilities. Furthermore, the tree on populations’ demographic rates. It seems that linkage dis- types of population response—plasticity, adaptation and equilibrium between adaptive loci indeed has a prominent migration—are not mutually exclusive. Whenever popu- effect on the chance of evolutionary rescue. We found evo- lations are not limited in their distribution and tracking of lutionary rescue to be more likely under total genetic suitable habitat is possible, the balance between positive independence than under full linkage between adaptive and negative effects of dispersal has to be reconsidered. loci. These results are not straightforward given our model Finally, in the context of environmental conditions, it structure. First, we could have expected that under low should be noted that particularly when habitat is hetero- linkage between adaptive loci, the evolutionary response to geneous, the condition changing temporally may show shifting regional climate could be reduced, because variability across space. In this case, contrary to its effect rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 demonstrated in this study, spatial heterogeneity may even natural populations cannot be captured. Thus, we believe accelerate adaptation to temporal change by increasing the that the type of allelic simulation model we applied in our genetic variance on which evolution can operate [42,59]. study will be needed, if we are to ultimately make robust quantitative predictions on the likelihood of evolutionary rescue in particular populations or species. Here, we could show that the evolutionary potential of populations facing 5. Conclusion deteriorating conditions might be overestimated when In past years, some remarkable studies have been published neglecting the effects of local adaptation to heterogeneous identifying the genetic basis for variation in traits that are habitat characteristics. This finding will be important, important for adaptation under climate change [60–64]. If because increasing habitat deterioration will lead to reduced we are to understand under which conditions species will total habitat availability, increased habitat fragmentation be able to build upon this variation to respond to environ- and stronger spatial habitat heterogeneity, all of which mental change, an important next step is now to scale up are likely to impede the ability of species to track their the knowledge of the genetics underpinning adaptation to preferred climate. the level of population demography. In a recent study, Chevin et al. [5] present a relatively simple evolutionary We thank Oscar Gaggiotti, Ire`ne Till-Bottraud and Carsten Urbach for model to assess—for a given combination of phenotypic var- discussion during model development and implementation. Two iance, heritability, selection strength, growth rate and anonymous reviewers provided helpful comments on an earlier ver- sion of the manuscript. W.T. and S.L. acknowledge support from the plasticity—the critical rate of environmental change beyond European Research Council under the European Community’s Seventh which a population must decline and go extinct. This type Framework Programme FP7/2007-2013 grant agreement no. 281422, of analytical model allows for a rigid mathematical analysis and from by the French ‘Agence Nationale de la Recherche’ with the and can give valuable insights into the sensitivity and inter- project EVORANGE (ANR-09-PEXT-011). This research was sup- dependence of parameters. On the other hand, many of the ported by a Marie Curie Intra European Fellowship to K.S. within the European Community’s Seventh Framework Programme. typically complex dynamics of evolutionary processes in References 1. Bellard C, Bertelsmeier C, Leadley P, Thuiller W, 10. Ackerly D. 2003 Community assembly, niche 19. 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Limited evolutionary rescue of locally adapted populations facing climate change

Schiffers, Katja; Bourne, Elizabeth C.; Lavergne, Sébastien; Thuiller, Wilfried; Travis, Justin M. J.
Philosophical Transactions of the Royal Society B: Biological Sciences , Volume 368 (1610) – Jan 19, 2013
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Limited evolutionary rescue of locally adapted populations facing climate change 1 2,3,4 1 Katja Schiffers , Elizabeth C. Bourne ,Sebastien Lavergne , 1 2 rstb.royalsocietypublishing.org Wilfried Thuiller and Justin M. J. Travis Laboratoire d’Ecologie Alpine, Universite´ Joseph Fourier, Grenoble 1, UMR-CNRS 5553, BP 53, 38041 Grenoble Cedex 9, France Institute of Biological and Environmental Sciences, University of Aberdeen, Zoology Building, Tillydrone Avenue, Aberdeen AB24 2TZ, UK Research The James Hutton Institute, Craigiebuckler, Aberdeen AB15 8QH, UK Institut fu¨r Biologie—Botanik, Freie Universita¨t Berlin, Altensteinstrasse 6, 14195 Berlin, Germany Cite this article: Schiffers K, Bourne EC, Dispersal is a key determinant of a population’s evolutionary potential. It Lavergne S, Thuiller W, Travis JMJ. 2012 facilitates the propagation of beneficial alleles throughout the distributional Limited evolutionary rescue of locally adapted range of spatially outspread populations and increases the speed of adap- populations facing climate change. Phil tation. However, when habitat is heterogeneous and individuals are locally Trans R Soc B 368: 20120083. adapted, dispersal may, at the same time, reduce fitness through increasing http://dx.doi.org/10.1098/rstb.2012.0083 maladaptation. Here, we use a spatially explicit, allelic simulation model to quantify how these equivocal effects of dispersal affect a population’s evo- lutionary response to changing climate. Individuals carry a diploid set of One contribution of 15 to a Theme Issue chromosomes, with alleles coding for adaptation to non-climatic environ- ‘Evolutionary rescue in changing mental conditions and climatic conditions, respectively. Our model results environments’. demonstrate that the interplay between gene flow and habitat heterogeneity may decrease effective dispersal and population size to such an extent that substantially reduces the likelihood of evolutionary rescue. Importantly, Subject Areas: even when evolutionary rescue saves a population from extinction, its spatial evolution range following climate change may be strongly narrowed, that is, the rescue is only partial. These findings emphasize that neglecting the impact of non- Keywords: climatic, local adaptation might lead to a considerable overestimation of a allelic model, dispersal, gene flow, habitat population’s evolvability under rapid environmental change. heterogeneity, migration load, rapid adaptation Author for correspondence: 1. Introduction Katja Schiffers e-mail: [email protected] Facing one of the most drastic global changes in the Earth’s history, a funda- mental objective of current ecological and evolutionary research is to understand and predict species’ responses to changing environmental con- ditions [1]. Three key types of response may ameliorate the threat of extinction: buffering against negative effects of deteriorating habitat by pheno- typic plasticity [2–5], tracking suitable climate through range shifting [6,7] and adapting to changing conditions by rapid evolution [8,9]. Some authors suggest that most species will more likely shift their distributional ranges or respond by phenotypic plasticity rather than adapt in situ to new conditions [6,10]. This is mainly because plasticity and range shifting may be substantially faster in matching phenotypic preferences with environmental conditions than evo- lutionary processes. Nonetheless, a number of species have been shown to adapt with remarkable rapidity in response to environmental change [11,12], and numerous studies have identified heritable population differentiation in ecologically relevant traits, providing indirect evidence for the potential of adaptive evolution over ecological time-scales [8,13,14]. It thus seems impera- Electronic supplementary material is available tive to consider the role of evolutionary rescue—the phenomenon of once at http://dx.doi.org/10.1098/rstb.2012.0083 or declining populations evolving back to positive growth by evolutionary via http://rstb.royalsocietypublishing.org. & 2012 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0/, which permits unrestricted use, provided the original author and source are credited. rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 adaptation—in assessments of the likely impacts of global from those that undergo temporal changes. A simple example change on species abundance, distribution and persistence. can illustrate this statement. Many plant populations are locally The theoretical foundations of adaptive dynamics have adapted to varying abiotic conditions (e.g. edaphic factors) or been established over the past decades by a growing biotic context (e.g. presence/absence of herbivores), but the number of studies in the fields of population and quantitative mosaic of this local adaptation will mostly be decoupled genetics. A key theorem states that the rate of adaptation is from currently changing climatic gradients. Under these cir- predominantly driven by the amount of available additive cumstances, the central question is: how do the contradictory genetic variance and the strength of environmental selec- effects of dispersal influence the evolutionary response of tion [15,16]. In principle, given sufficient genetic variance, populations to environmental change? populations should adapt to virtually any environmental In this study, we address the above question by integrat- condition [17]. However, under natural conditions, an ing the key processes that have until now typically been often-complex interaction between demographic processes studied separately: the role of dispersal as the mechanism dis- and evolutionary dynamics may result in failure of adap- tributing adapted alleles across populations and the tation and ultimate extinction of the population [18–20]. To feedbacks between dispersal and local adaptation. We do gain initial insights into such interactive processes, synthetic this within the context of an allelic model, where population approaches linking genetics with population demography genetics are coupled with population ecology by condition- are being applied increasingly frequently, addressing ques- ing demographic rates on the match of genetically variable tions on, e.g. the formation of species range edges [21–23] traits to environmental characteristics. We use our model to and invasion dynamics [24,25], including invasion dynamics examine how the interplay between dispersal and local in heterogeneous landscapes [26,27]. adaptation across spatially heterogeneous habitats influences In the context of eco-evolutionary processes, dispersal is a the probability of evolutionary rescue of populations facing key determinant of population dynamics, owing to its impact changing climatic conditions. We also examine how the on both spatial demography [28,29] and the speed of local genetic architecture of adaptive traits modulates this interplay. adaptation [29–31]. As a consequence, dispersal is likely to be crucial for evolutionary rescue. The main responsible mechanism is the spreading of newly arising, beneficial alleles 2. The model throughout a population’s distributional range [32–35]. In a recent study, Bell & Gonzalez [35] empirically tested these We developed an allelic, spatially explicit and individual- theoretical predictions with an experiment on bakers yeast: based simulation model to investigate the interactive effects they demonstrated that spatially structured populations had of gene flow and local adaptation on the evolutionary a significantly higher chance of surviving a period of deterior- response of populations to environmental change. The full ating growth conditions and adapting to the new state, when source code and an accompanying readme file are available dispersal allowed for gene flow across subpopulations. as electronic supplementary material, and a maintained ver- In contrast to its beneficial effect for rapid adaptation sion of the model is downloadable from http://www.katja- under temporally changing conditions, dispersal is known schiffers.eu/docs/allele_model.zip. to have an overall negative influence on population fitness The model organism we had in mind during implementa- under most scenarios of local adaptation [36,37]. In a spatially tion was a bisexual, annual plant species with xenogamous heterogeneous environment, mismatches between immi- breeding system. Population dynamics take place within a grants’ genotypes and the environmental conditions at their continuous region of 32  32 grid cells. To avoid arbitrary destination locations result in a reduction in overall fitness, edge effects, the area is simulated as a torus, i.e. the edges termed migration load. With analytical predictions and indi- of both axes are joined. Grid cells are characterized by two vidual-based simulations, Lopez et al. [37] have illustrated environmental conditions: (i) local environmental conditions how, under gene flow through both pollen and seed move- such as edaphic parameters or particular biotic settings, ment, migration load increases with the degree of habitat which follow a fractal distribution and are stable over time; heterogeneity. In a further theoretical study, Alleaume- and (ii) climatic conditions, e.g. maximal annual temperature, Benharira et al. [38] demonstrated that in a patchy population, which change during the simulated period. For simplicity, we distributed across an environmental gradient, intermediate assume climate to be homogeneous across space. Each grid rates of dispersal optimized fitness. This was the result of a cell can support a number of individuals, the maximal trade-off between some dispersal having benefits in terms number given by the local carrying capacity, which is con- of purging deleterious alleles, especially from smaller mar- stant across the region. Individuals are diploid, carrying ginal populations, and increasing dispersal resulting in two copies of either one or several chromosomes coding for higher migration load owing to gene flow between patches an individual’s level of adaptation to climatic and local of differing local conditions. environmental conditions. Individuals are located in continu- Clearly, adaptation to heterogeneous habitat and tem- ous space and are assigned to the grid cell within which their poral changes in environmental conditions often occur x- and y-coordinates fall. hand in hand [39], confronting populations with multiple Within each generation, the following processes are simu- sources of potential maladaptation. However, the few exist- lated: (i) reproduction with mutation, recombination, gamete ing studies investigating population responses to a spatially dispersal and subsequent death of the parental generation, and temporally changing optimum focus predominantly on (ii) dispersal of the offspring, (iii) selection acting on the survi- a single environmental variable [40–42]. Such an approach val probabilities of the juveniles, and (iv) density-dependent neglects a situation that is likely to be very common in nat- mortality. Selection takes the form of density-independent, ural conditions, that is where the spatially heterogeneous hard selection for an individual’s adaptation to both climatic conditions driving local adaptation of populations differ and local environmental conditions. rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 To gain sufficient computational efficiency, we do not (a) Genetic architecture explicitly simulate the dispersal of pollen. Instead, we use A number of previous studies have shown that traits affecting the following algorithm. As for offspring dispersal, species’ adaptation, particularly to climatic conditions, are x/y-coordinates are chosen randomly in the neighbourhood usually polygenic. For example, 12 quantitative trait loci of the focal individual. The mating partner is then randomly have been identified for climatic adaptation in Arabidopsis drawn from all individuals inhabiting the grid cell within thaliana [43], 33 for bud-flush, nine for autumn cold hardiness which the random position is located. In case the selected and nine for spring cold hardiness in Pseudotsuga menziesii grid cell is empty, the procedure is repeated up to 99 times. [44] (see also Falconer & Mackay [45] for a general overview). If all trials are unsuccessful, we assume the ovule not to On the basis of this information, we simulated genomes com- be fertilized. posed of n ¼ 15 loci for each of the two considered traits. To To test for potential undesirable effects of this simplifica- represent two contrasting scenarios of linkage, we considered tion, we also developed implementation of gamete dispersal the genome to be composed either of one or several pairs of that is more precise in the sense of linking fertilization prob- chromosomes. In the first case, all loci are situated on a single ability to the exact distance between individuals. For each chromosome and, as we do not allow for crossovers during individual of the population, the probability of fertilizing a recombination, the loci are fully linked. Effectively, this could specific ovule is calculated based on the inter-individual dis- also be considered a single locus with multiple alleles and tances and the shape of the dispersal kernel. Following that, pleiotropic effects. In the second case, we assume the opposite the probability of no fertilization can be determined. Rescal- possible extreme case of no linkage. This may correspond to a ing all resulting probabilities so that they add up to unity situation where a genome is made of 30 chromosome pairs then allows sampling of the pollen donor by a draw of a uni- each carrying a single locus, implying completely independent form random number between zero and unity. Comparisons inheritance of alleles. Or, this might mimic a situation where all between the two approaches showed that there are no obvious the loci are on a single (or multiple) chromosome, but with suf- differences at the level of evolutionary or demographic ficient distance between the loci and sufficient frequency of dynamics. We thus chose the former, computationally much crossover events that they are effectively unlinked. Alleles are less intensive method. described by continuous values and are additive within and between loci, i.e. neither epistatic nor pleiotropic effects are considered. Individuals’ phenotypes are directly determined (iii) Selection by their genotypes, that is, environmental effects on pheno- Selection acts on population demography by modulating types are neglected, and heritability is thus assumed to be juvenile survival probability. Each individual’s survival prob- unity [21–23,46]. ability W is calculated as the product of its condition related to climate W and its condition related to the local environ- ment W . Both of these values, W , are functions of the E C,E (b) Simulated processes difference between the individual’s phenotype z , and C,E the optimal phenotype under the current climatic or local (i) Reproduction environmental conditions Q . They follow a normal C,E All individuals can potentially bear offspring. The number of distribution with maximum unity and variance v : C,E ovules produced by each individual is drawn from a Poisson "# distribution with average R ¼ 100. Whether, and by which ðz  Q Þ C;E C;E W ðzÞ¼ exp  ; C;E mating partner, single ovules are fertilized is modelled stochas- 2v C;E tically with the probabilities of fertilization derived from the individuals’ distances and the shape of the pollen dispersal where v is traditionally referred to as selection strength, but kernel (see §2b(ii)). Gametes are composed by duplicating par- can also be interpreted as a measure of the species’ tolerance ental chromosomes, one of each homologous pair being chosen to suboptimal conditions, i.e. its niche breadth [40]. Here, for randomly. Alleles mutate with a probability ofm ¼ 10 , which the default parameter settings, this value was fixed at 0.1, represents the average rate found for the annual plant species resulting in W , 0.01 and thus in a negative population Arabidopsis thaliana [47–49]. The mutational effect, i.e. the growth rate (given the average number of offspring per amount by which the allelic value is changed, is drawn from individual is 100) when temperature has changed by approxi- a zero-mean normal distribution with variance a ¼ 0.2, mately 18C, assuming the phenotype is fixed. In a number of approximately fitting empirical observations [47]. additional runs, selection strength was reduced by increasing v to 0.2. (ii) Dispersal (iv) Density-dependent mortality There are two phases of dispersal in each generation cycle: We assume a simple ceiling form of density dependence pollen dispersal and offspring dispersal. Both are characterized (similar to [39,51]): whenever the number of individuals by lognormal, isotropic dispersal kernels with an average dis- within a grid cell exceeds its carrying capacity, K, resident tance d for both gametes and offspring and a shape parameter individuals are subjected to a density-dependent mortality of 0.5. The lognormal distribution has been found to adequately with probability of survival ¼ 1 2 K/N. represent both local and long-distance dispersal [50]. Offspring dispersal is simulated explicitly: dispersal dis- tance and direction are chosen randomly with probabilities (c) Simulations following the shape of the dispersal kernel. The offspring is posi- Simulations were run to test the interactive effects of disper- tioned at the resulting x/y-coordinates, respecting torroidal sal, habitat heterogeneity and linkage on population boundary conditions. dynamics and the likelihood of survival under climate rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 with no initial genetic variation showed that resulting Table 1. Parameter values for simulation runs. population parameters were not influenced by the chosen starting conditions (see the electronic supplementary material, parameter description values figure S5). For the main analysis, climate change was simulated by keeping the temperature constant over the first 200 gener- V rate of climate shift two units per 100 ations and then gradually increasing it by 2.08C over the years following 100 time-steps. After this period of change, H Hurst exponent 0.2 the new climatic conditions were assumed to be stable h habitat 0, 1, 2, 3, 4, 5, 6 H until the end of 500 simulation years. heterogeneity K carrying capacity per 5 grid cell 3. Results R mean number of 100 In test runs without environmental change, population size, average individual fitness and additive genetic variance offspring were stable over time, unless mean dispersal distances were D mean dispersal 0.05, 0.1, 0.2, 0.4, 0.8, too small to ensure a sufficient number of fertilized ovules distance 1.6, 3.2, 6.4 to keep growth rates higher than unity. When introducing a d shape factor 0.5 shape shift in climate, population size started to decline at the point where the average individual phenotype lagged so dispersal kernel far behind the optimum Q that W, 1/R. In simulations L linkage between fully linked, free where the mutation rate m was set to zero, populations inev- loci recombination itably died, because standing genetic variation alone did not M mutation rate per 10 provide enough scope for full adaptation to new conditions. With the default value for m ¼ 10 , an average family size of locus 2 100 and a carrying capacity around 5000 individuals, a variance of 0.2 mutations occurred on average once per generation and mutational effect locus. In combination with the given variance of the muta- 2 2 v selection strength 0.1, 0.2 tional effect (a ) ¼ 0.2 and a selection strength (v ) ¼ 0.1, allelic dynamics resulted in a slow disruption of the initial normal distribution of allelic values (see the electronic sup- change (see table 1 for model parameters). The average dis- plementary material, figures S1–S4) during periods of persal distance d was set to 0.05 grid cell lengths for the stable climate. During phases of temperature rise, mainly first set of simulations and then repeatedly doubled up to a the fixation of rare, large mutations contributed to the adap- distance of 6.4. Habitat heterogeneity h was controlled by tation process to the new conditions (results not shown), modifying the range of possible local environmental con- leading to punctuated phases of rapid evolution as, for ditions from 0 units, i.e. no heterogeneity, to a maximum of example, described in Holt et al. [39]. six units in steps of 1. For testing the effect of linkage, the Population responses to rapid climate change fitted into two contrasting scenarios of complete versus no linkage three general classes, depending upon the values of some were compared. The remaining model parameters were key model parameters. We first describe the three main cat- kept constant across simulations. For all possible 112 combin- egories of response (figure 1), before providing some detail ations of d, h and linkage, we ran 100 replicates, recording on how the key parameters influenced the outcome. population size over time and the population average and Complete evolutionary rescue occurred when there was a variance of individuals’ survival probabilities, W ,asa sufficient number of beneficial mutations and when they C,E measure for their conditions. were able to spread unhampered across the landscape. This Landscapes were initialized with a value of 258C for the class of response was typically characterized by an initial climatic conditions and a Hurst exponent of 0.2 for the fractal phase during which, as the climate began to change, individ- distribution of local environmental conditions, their ampli- uals’ survival probabilities declined. Subsequently, as one or tude being controlled by h . The values assigned to h more beneficial mutations occurred and spread across the H H resulted in average differences between neighbouring cells landscape, the average individual’s fitness increased, of 0.03, 0.09, 0.15, 0.38, 0.9 and 1.46 units, respectively. The the total population size fully recovered and ultimately indi- spatial population was initialized by colonizing each grid viduals’ phenotypes were a good match to the new climate cell with three individuals. Individuals were, on average, conditions (figure 1a). optimally adapted to both climatic and local environmental Partial evolutionary rescue occurred under conditions where conditions, but exhibited normally distributed additive gen- beneficial alleles arose but were unable to spread owing to inef- etic variation with a within-cell variance of 0.01. This value fective gene flow across space. In this class of response, only corresponds approximately to the mutation–selection equi- fragments of what was previously fully occupied habitat librium reached after 1000 generations in previous test runs were populated following climate change. This effective under stable conditions (see the electronic supplementary reduction in the suitable habitat niche for the population some- material, figures S1–S4). It has to be noted that allelic times resulted in substantially reduced total population sizes values typically did not follow normal distributions at the following climate change (figure 1b). Importantly, this effect end of these runs, particularly when habitat heterogeneity was persistent, lasting until the end of simulations, which ran was low. However, comparisons with additional simulations for 200 generations after climate change ceased. rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 (a) 5 1.5 1.0 0.5 (b) 1.5 1.0 0.5 (c) 1.5 1.0 0.5 0 100 200 300 400 500 generations Figure 1. Three example runs depicting (a) full rescue, (b) partial rescue, and (c) population extinction. Solid lines represent population size, short dashed lines represent the level of adaptation to climatic conditions, W , and long dashed lines represent the level of adaption, W , to local environmental conditions. On the C E right-hand side the density of individuals is shown after 500 time-steps with darker values indicating higher densities. Extinction, due to the failure of evolutionary rescue, observed for intermediate values between 0.4 and 2 grid occurred when the frequency of beneficial mutations was cell units. Within that range, the peak of rescue probability too low. Under these conditions, individuals’ phenotypes depended on the level of habitat heterogeneity and shif- rapidly became very poorly matched to the prevalent ted towards shorter dispersal distances with increasing climatic conditions, resulting in lower offspring viability heterogeneity (figure 5a–c). and ultimately a non-viable population (figure 1c). With increasing spatial heterogeneity, there was also an increased likelihood that, when rescue occurred, it was only partial. Thus, while the population had at least some probability (a) Effects of dispersal and habitat heterogeneity of surviving climate change through evolutionary rescue, the In accordance with our expectations based on previous landscape was not fully occupied after climate change and the studies [36,37], in a spatially heterogeneous environment, dis- total population size was substantially reduced (figure 5). persal generally had a negative effect on individuals’ levels of Under a heterogeneity of h ¼ 5, the average relative popu- adaptation to environmental conditions W (figure 2). lation size (of the surviving populations) at the end of the In scenarios of full linkage, the level of adaptation increased simulation time was, across a broad range of dispersal dis- again for very high values of dispersal and heterogeneity tances, reduced to an average of around 50 per cent of pre- (figure 2a), owing to an increased mortality of strongly mala- climate-change densities (figure 5c). Interestingly, the parameter dapted individuals and consequently higher averages for the values that maximized the probability of rescue did not necess- surviving fraction of the population (results not shown). arily result in a more complete rescue. For example, when h ¼ On the other hand, model results also confirmed the 5, there was the greatest probability of population survival beneficial effect of dispersal on a population’s adaptation to when dispersal ¼ 0.4. For this scale of dispersal, however, sur- temporally changing conditions. This was demonstrated by viving populations were reduced on average to roughly one- increasing values of W with increasing dispersal distances sixth of their initial abundance. By contrast, when dispersal (figure 3). However, this pattern appeared to be more occurred across a greater range (e.g. dispersal ¼ 2.5), the popu- sensitive to stochastic effects than results regarding the lations survived only 10 per cent of the time, but then recovered adaptation to local environmental conditions. to an average 50 per cent of initial abundance. The likelihood of evolutionary rescue was strongly reduced or even hindered for a range of dispersal distances, for which rapid adaptation would have been possible with- (b) Effect of linkage out local adaptation (figure 4). Because both high dispersal The assumptions regarding the form of linkage had a strong distances, as well as very low distances, decreased the prob- effect on the overall probability of evolutionary rescue. ability of evolutionary rescue, highest survival rates were Independent inheritance allowed for much faster adaptation population size (×10 000)/average level of adaptation rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 (a) (b) 6 1.00 0.95 4 0.90 0.85 0.80 0.75 0.70 1 23 4 56 1 23 4 56 dispersal distance dispersal distance Figure 2. Average values for the level of adaptation to local environmental conditions, W , during the phase of temperature rise for (a) full linkage and (b)free recombination of loci. Depicted are the average values over 100 replicates for all combinations of habitat heterogeneity h and average dispersal distances d in grid cell length. (a)(b) 0.60 0.55 0.50 0.45 2 0.40 0.35 0.30 1 23 4 56 1 23 4 56 dispersal distance dispersal distance Figure 3. Average values for the level of adaptation to climatic conditions, W , during the phase of temperature rise for (a) full linkage and (b) free recombination of loci. Depicted are the average values over 100 replicates for all combinations of habitat heterogeneity h and average dispersal distances d in grid cell length. to both spatially (figure 2) and temporally changing con- extinction. Understanding the factors determining the ditions (figure 3) so that the negative effect of local likelihood that populations adapt sufficiently rapidly to chan- adaptation was strongly ameliorated (figure 4). However, ging environmental conditions is at the heart of research on the overall pattern of intermediate dispersal distances evolutionary rescue. resulting in highest evolutionary potential was consistently Allelic simulation models, as used in this study, provide observed for both scenarios. an ideal tool for integrating the available knowledge on eco-evolutionary dynamics from different organizational levels and to reflect the complex nature of adaptive and demographic processes. However, to date, most modelling 4. Discussion studies have been highly abstracted, for example, assuming Global environmental change is confronting natural popu- unrealistically high mutation rates and panmictic popula- lations simultaneously with rapid climate change and tions. Here, we have taken a first step towards quantitative increasing habitat loss and deterioration. The combination predictions of population response to environmental change of habitat fragmentation and limited dispersal will prevent by establishing an individual-based model that is both many populations from tracking suitable climate in space. spatially and genetically explicit, and that, as far as possible, For these species, in situ adaptation to changing climate is has been parametrized realistically for both genetic and likely to provide the only natural means of avoiding ultimate demographic functions. habitat heterogeneity habitat heterogeneity rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 (a)(b) 7 1.0 0.8 0.6 0.4 0.2 1 23 4 56 1 23 4 56 dispersal distance dispersal distance Figure 4. Probability of full rescue depending on habitat heterogeneity h and average dispersal distances d in grid cell length for (a) full linkage and (b)free recombination of loci. Calculated from 100 simulation runs for each parameter combination. (a) 0.8 0.4 (b) 0.8 0.4 (c) 0.8 0.4 dispersal distance Figure 5. Probability of evolutionary rescue ( partial and full rescue, solid lines) and relative population sizes ( population size at generation 500/K, extinctions excluded, dashed lines) in dependence on dispersal distance d for habitat heterogeneities of (a) h ¼ 0, (b) h ¼ 3, and (c) h ¼ 5. Results are based on 100 H H H simulation runs for full linkage of loci. The initial results of our model presented within this Considering the effects of dispersal on local adaptation paper demonstrate two potent key phenomena that we and environmental change separately, the results of our consider important, particularly under ongoing habitat model concur with existing studies on each topic. Under deterioration and fragmentation: first, the potentially com- habitat heterogeneity and local adaptation, dispersal typic- plex effects of dispersal for a population’s evolutionary ally has negative consequences for the average fitness response to both spatially heterogeneous habitats and [36,37]. Increased migration load—in our model output shifting climate. And second, the possibility for partial reflected by reduced levels of adaptation to the local environ- evolutionary rescue, whereby rapid adaptation saves a popu- ment—lead to higher mortality rates and an increased risk of lation from extinction, but both population size and its location extinction, hence a lower chance of rescue. On the geographical range may be substantially reduced. other hand, as argued and shown recently by Bell & habitat heterogeneity probability of rescue and relative population size rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 Gonzalez [35], greater dispersal can be strongly beneficial, stabilizing selection for local environments would account owing to its function in spreading favourable alleles across for most genetic load (i.e. for most fitness reduction). the populations’ distributional ranges. This was mirrored Second, one could also expect that adaptive response to chan- by our results, when focusing on only the adaptation to tem- ging climate would be reduced when recombination between porally changing climate and thus neglecting the distorting climate-related loci can occur at every generation, thus break- effects of migration load. ing apart adaptive allele combinations and preventing the The interplay of these double-edged consequences of population from being fully rescued. Whether and how link- gene flow leads to the key results that we emphasize in this age may facilitate or impede adaptation to changing paper. When dispersal is high and habitat heterogeneous, environmental conditions could be further investigated with the number of viable offspring in each generation can be our model, but is beyond the scope of this paper. drastically reduced due to the arrival of many maladapted Clearly, a number of genetic, demographic and envir- juveniles. At the population level, this is of little consequence onmental settings that were neglected in this study can when the climate is stable, as long as the number of surviving modulate the effects of spatio-temporal variability on juveniles can maintain the population in a steady state. How- micro-evolutionary dynamics. Some of these are shortly ever, when the population needs to adapt to new climatic discussed in the following. conditions, the absolute number of beneficial mutations In terms of the genetic basis of adaptation, it has been becomes crucial. This number depends not only on the shown that the relative amount of genetic versus environ- mutation rate, but also on the number of potential recruits mental variability in individual phenotypes affects the that may carry these mutations and pass them on to sub- speed of adaptation and the likelihood of evolutionary sequent generations. High rates of juvenile dispersal into rescue [39,53]. While the probability of population extinction habitat to which they are ill-adapted reduces the effective is increased under lower heritability of those traits controlling rate at which beneficial mutations on climate-related loci adaptation to temporally changing conditions, for traits con- can be fixed in the population (see Barton & Bengtsson trolling adaptation to spatial heterogeneity, low heritabilities [52]). Ultimately, this interaction between dispersal, habitat and high plasticity may instead facilitate population survival: heterogeneity and temporal environmental change leads to plasticity can buffer the negative effects of local malad- the observed reduction in the probability of evolutionary aptation, reduce mortality and thus allow for increased rescue. This suggest that even under high dispersal scenarios, effective dispersal and the spread of beneficial alleles. populations previously adapted to spatially structured local Weaker selection will have a positive influence on the survi- environments may have a lower chance to adapt to changing val probability of populations as well, because the effects of regional climate. maladaptation are reduced. This effect is more pronounced The second key result—partial evolutionary rescue—is in when the habitat is heterogeneous (see the electronic supple- its mechanism closely linked to the process described above. mentary material, figure S6), because the level of adaptation High habitat heterogeneity, subsequent migration load and to both climate and local conditions determine population decreased survival probability hamper the spatial spread of development in this case. Furthermore, a number of studies beneficial alleles, which may become locally abundant. The have demonstrated that characteristics of allelic effects such positive fitness effect of the beneficial mutation on climate- as epistatis or pleiotropy [54] and the nature of the selection related loci becomes overridden by the negative effects (i.e. hard versus soft selection) [55] might change evolutionary due to genetic swamping by newly arrived individuals carry- dynamics substantially. ing alleles that are not adapted to local environmental Focusing on demographic effects on rapid adaptation, the conditions. This is obviously most likely when habitat is characteristics and effects of dispersal and gene flow may strongly heterogeneous. Thus, when the resulting absolute need more detailed inspection. For example, gene flow by fitness of these individuals is lower than unity, beneficial pollen will affect adaptation processes differently compared alleles cannot spread throughout the distributional range of with gene flow by dispersal of seeds or individuals [37]. the population, thus preventing a species fully recovering First, the expected level of migration load is only half as its original geographical range following a shift in regional high for pollen as for seed dispersal, because just half the climate. In case the surviving subpopulations are too small number of maladapted alleles are placed into a new local to supply a sufficient amount of new mutations for adap- environment, leading to decreased mortality. Second, the tation to the conditions in the unpopulated space, we tend direct effect of shifting individuals between locations does to observe a quasi-stable fragmented distribution of the not apply, partly decoupling evolutionary from demographic surviving populations. dynamics. Apart from that, it has to be considered that dis- Our model also demonstrates that different ecological persal capabilities evolve rapidly themselves [56–58]. This traits—even though not genetically correlated—may interact adds another layer of complexity to forecasting population with the evolutionary dynamics, because they have dynamics in space and time, but should generally increase additional effects on individuals’ fitnesses and ultimately populations’ survival probabilities. Furthermore, the tree on populations’ demographic rates. It seems that linkage dis- types of population response—plasticity, adaptation and equilibrium between adaptive loci indeed has a prominent migration—are not mutually exclusive. Whenever popu- effect on the chance of evolutionary rescue. We found evo- lations are not limited in their distribution and tracking of lutionary rescue to be more likely under total genetic suitable habitat is possible, the balance between positive independence than under full linkage between adaptive and negative effects of dispersal has to be reconsidered. loci. These results are not straightforward given our model Finally, in the context of environmental conditions, it structure. First, we could have expected that under low should be noted that particularly when habitat is hetero- linkage between adaptive loci, the evolutionary response to geneous, the condition changing temporally may show shifting regional climate could be reduced, because variability across space. In this case, contrary to its effect rstb.royalsocietypublishing.org Phil Trans R Soc B 368: 20120083 demonstrated in this study, spatial heterogeneity may even natural populations cannot be captured. Thus, we believe accelerate adaptation to temporal change by increasing the that the type of allelic simulation model we applied in our genetic variance on which evolution can operate [42,59]. study will be needed, if we are to ultimately make robust quantitative predictions on the likelihood of evolutionary rescue in particular populations or species. Here, we could show that the evolutionary potential of populations facing 5. Conclusion deteriorating conditions might be overestimated when In past years, some remarkable studies have been published neglecting the effects of local adaptation to heterogeneous identifying the genetic basis for variation in traits that are habitat characteristics. This finding will be important, important for adaptation under climate change [60–64]. If because increasing habitat deterioration will lead to reduced we are to understand under which conditions species will total habitat availability, increased habitat fragmentation be able to build upon this variation to respond to environ- and stronger spatial habitat heterogeneity, all of which mental change, an important next step is now to scale up are likely to impede the ability of species to track their the knowledge of the genetics underpinning adaptation to preferred climate. the level of population demography. In a recent study, Chevin et al. [5] present a relatively simple evolutionary We thank Oscar Gaggiotti, Ire`ne Till-Bottraud and Carsten Urbach for model to assess—for a given combination of phenotypic var- discussion during model development and implementation. Two iance, heritability, selection strength, growth rate and anonymous reviewers provided helpful comments on an earlier ver- sion of the manuscript. W.T. and S.L. acknowledge support from the plasticity—the critical rate of environmental change beyond European Research Council under the European Community’s Seventh which a population must decline and go extinct. This type Framework Programme FP7/2007-2013 grant agreement no. 281422, of analytical model allows for a rigid mathematical analysis and from by the French ‘Agence Nationale de la Recherche’ with the and can give valuable insights into the sensitivity and inter- project EVORANGE (ANR-09-PEXT-011). This research was sup- dependence of parameters. On the other hand, many of the ported by a Marie Curie Intra European Fellowship to K.S. within the European Community’s Seventh Framework Programme. typically complex dynamics of evolutionary processes in References 1. Bellard C, Bertelsmeier C, Leadley P, Thuiller W, 10. Ackerly D. 2003 Community assembly, niche 19. 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Philosophical Transactions of the Royal Society B: Biological Sciences – Pubmed Central

Published: Jan 19, 2013

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