Limited evolutionary rescue of locally adapted populations facing climate change Katja Schiffers1, Elizabeth C. Bourne2,3,4, Se´bastien Lavergne1, rstb.royalsocietypublishing.org Wilfried Thuiller1 and Justin M. J. Travis2 1Laboratoired’Ecologie Alpine, Universite´ Joseph Fourier,Grenoble 1, UMR-CNRS5553, BP53, 38041Grenoble Cedex 9,France 2Institute ofBiologicaland EnvironmentalSciences, UniversityofAberdeen,Zoology Building, TillydroneAvenue, Aberdeen AB242TZ,UK Research 3TheJames Hutton Institute, Craigiebuckler, AberdeenAB158QH,UK 4Institut fu¨r Biologie—Botanik, FreieUniversita¨t Berlin, Altensteinstrasse6,14195Berlin, Germany Cite this article: Schiffers K, Bourne EC, Lavergne S, Thuiller W, Travis JMJ. 2012 Dispersal is a key determinant of a population’s evolutionary potential. It Limited evolutionary rescue of locally adapted facilitatesthe propagation of beneficial alleles throughout the distributional 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, atthesametime, reduce fitnessthrough increasing http://dx.doi.org/10.1098/rstb.2012.0083 maladaptation. Here, we use a spatiallyexplicit, allelic simulation model to quantify how these equivocal effects of dispersal affect a population’s evo- One contribution of 15 to a Theme Issue lutionary response to changing climate. Individuals carry a diploid set of chromosomes, with alleles coding for adaptation to non-climatic environ- ‘Evolutionary rescue in changing mental conditions and climatic conditions, respectively. Our model results environments’. demonstratethattheinterplaybetweengeneflowandhabitatheterogeneity may decrease effective dispersal and population size to such an extent that Subject Areas: substantially reduces the likelihood of evolutionary rescue. Importantly, evolution evenwhenevolutionaryrescuesavesapopulationfromextinction,itsspatial rangefollowingclimatechangemaybestronglynarrowed,thatis,therescueis 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’sevolvabilityunderrapidenvironmentalchange. heterogeneity,migrationload,rapidadaptation 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:bufferingagainstnegativeeffectsofdeterioratinghabitatbypheno- typicplasticity[2–5],trackingsuitableclimatethroughrangeshifting[6,7]and adaptingtochangingconditionsbyrapidevolution[8,9].Someauthorssuggest thatmostspecieswillmorelikelyshifttheirdistributionalrangesorrespondby phenotypicplasticityratherthanadaptinsitutonewconditions[6,10].Thisis 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. & 2012TheAuthors.PublishedbytheRoyalSocietyunderthetermsoftheCreativeCommonsAttribution License http://creativecommons.org/licenses/by/3.0/, which permits unrestricted use, provided the original authorandsourcearecredited. adaptation—in assessments of the likely impacts of global fromthosethatundergotemporalchanges.Asimpleexample 2 changeon species abundance,distribution andpersistence. canillustratethisstatement.Manyplantpopulationsarelocally The theoretical foundations of adaptive dynamics have adaptedtovaryingabioticconditions(e.g.edaphicfactors)or rstb been established over the past decades by a growing biotic context (e.g. presence/absence of herbivores), but the .ro y numberofstudiesinthefieldsofpopulationandquantitative mosaic of this local adaptation will mostly be decoupled als o genetics. A key theorem states that the rate of adaptation is from currently changing climatic gradients. Under these cir- c ie predominantly driven by the amount of available additive cumstances,thecentralquestionis:howdothecontradictory ty p u genetic variance and the strength of environmental selec- effects of dispersal influence the evolutionary response of b lis tion [15,16]. In principle, given sufficient genetic variance, populationstoenvironmentalchange? h in populations should adapt to virtually any environmental Inthisstudy,weaddresstheabovequestionbyintegrat- g.o condition [17]. However, under natural conditions, an ing the key processes that have until now typically been rg often-complex interaction between demographic processes studiedseparately:theroleofdispersalasthemechanismdis- P h and evolutionary dynamics may result in failure of adap- tributing adapted alleles across populations and the il T tation and ultimate extinction of the population [18–20]. To feedbacks between dispersal and local adaptation. We do ra n s gain initial insights into such interactive processes, synthetic thiswithinthecontextofanallelicmodel,wherepopulation R approaches linking genetics with population demography genetics are coupled with population ecology by condition- So c are being applied increasingly frequently, addressing ques- ing demographic rates on the match of genetically variable B 3 tions on, e.g. the formation of species range edges [21–23] traits to environmental characteristics. We use our model to 6 8 : andinvasiondynamics[24,25],includinginvasiondynamics examine how the interplay between dispersal and local 2 0 1 inheterogeneous landscapes [26,27]. adaptationacrossspatiallyheterogeneoushabitatsinfluences 2 0 0 Inthecontextofeco-evolutionaryprocesses,dispersalisa the probability of evolutionary rescue of populations facing 8 3 keydeterminantofpopulationdynamics,owingtoitsimpact changing climatic conditions. We also examine how the on both spatial demography [28,29] and the speed of local geneticarchitectureofadaptivetraitsmodulatesthisinterplay. adaptation [29–31]. As a consequence, dispersal is likely to be crucial for evolutionary rescue. The main responsible mechanismisthespreadingofnewlyarising,beneficialalleles 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 asignificantlyhigherchanceofsurvivingaperiodofdeterior- response of populations to environmental change. The full atinggrowthconditionsandadaptingtothenewstate,when source code and an accompanying readme file are available dispersalallowedforgeneflowacrosssubpopulations. 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 Themodelorganismwehadinmindduringimplementa- undermostscenariosoflocaladaptation[36,37].Inaspatially 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(cid:2)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 termedmigrationload.Withanalyticalpredictionsandindi- of both axes are joined. Grid cells are characterized by two vidual-based simulations, Lopez et al. [37] have illustrated environmentalconditions: (i) localenvironmental 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)climaticconditions,e.g.maximalannualtemperature, Benhariraetal.[38]demonstratedthatinapatchypopulation, whichchangeduringthesimulatedperiod.Forsimplicity,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 eitherone 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 differinglocal conditions. environmentalconditions.Individualsarelocatedincontinu- Clearly, adaptation to heterogeneous habitat and tem- ousspaceandareassignedtothegridcellwithinwhichtheir poral changes in environmental conditions often occur x-and y-coordinatesfall. hand in hand [39], confronting populations with multiple Withineachgeneration,thefollowingprocessesaresimu- 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)dispersaloftheoffspring,(iii)selectionactingonthesurvi- 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 hardselectionforanindividual’sadaptationtoboth climatic conditions driving local adaptation of populations differ andlocalenvironmentalconditions. (a) Genetic architecture To gain sufficient computational efficiency, we do not 3 explicitly simulate the dispersal of pollen. Instead, we use Anumberofpreviousstudieshaveshownthattraitsaffecting species’ adaptation, particularly to climatic conditions, are the following algorithm. As for offspring dispersal, rstb usually polygenic. For example, 12 quantitative trait loci x/y-coordinates are chosen randomly in the neighbourhood .ro y have been identified for climatic adaptation in Arabidopsis ofthefocalindividual.Thematingpartneristhenrandomly als o drawn from all individuals inhabiting the grid cell within c thaliana[43],33forbud-flush,nineforautumncoldhardiness ie which the random position is located. In case the selected ty and nine for spring cold hardiness in Pseudotsuga menziesii p u grid cell is empty, the procedure is repeated up to 99 times. b [44](seealsoFalconer&Mackay[45]forageneraloverview). lis If all trials are unsuccessful, we assume the ovule not to h Onthebasisofthisinformation,wesimulatedgenomescom- in posedofn¼15lociforeachofthetwoconsideredtraits.To be fertilized. g.o Totestforpotentialundesirableeffectsofthissimplifica- rg representtwocontrastingscenariosoflinkage,weconsidered tion,wealsodevelopedimplementationofgametedispersal thegenome tobe composedeitherofone or several pairsof P h chromosomes.Inthefirstcase,alllociaresituatedonasingle thatismorepreciseinthesenseoflinkingfertilizationprob- il T chromosome and, as we do not allow for crossovers during ability to the exact distance between individuals. For each ran s recombination,thelociarefullylinked.Effectively,thiscould individual of the population, the probability of fertilizing a R also be considered a single locus with multiple alleles and specificovuleiscalculatedbasedontheinter-individualdis- Soc tances and theshape of thedispersal kernel. Followingthat, B pleiotropiceffects.Inthesecondcase,weassumetheopposite 3 the probabilityof no fertilization can be determined. Rescal- 6 possibleextremecaseofnolinkage.Thismaycorrespondtoa 8 : ing all resulting probabilities so that they add up to unity 2 situation where a genome is made of 30 chromosome pairs 0 1 eachcarryingasinglelocus,implyingcompletelyindependent thenallowssamplingofthepollendonorbyadrawofauni- 20 0 inheritanceofalleles.Or,thismightmimicasituationwhereall form randomnumberbetweenzero andunity. Comparisons 83 betweenthetwoapproachesshowedthattherearenoobvious thelociareonasingle(ormultiple)chromosome,butwithsuf- 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 crossovereventsthattheyareeffectivelyunlinked.Allelesare lessintensivemethod. 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 juvenilesurvivalprobability.Eachindividual’ssurvivalprob- unity[21–23,46]. abilityWiscalculatedastheproductofitsconditionrelated to climate W and its condition related to the local environ- C ment W . Both of these values, W , are functions of the (b) Simulated processes E C,E difference between the individual’s phenotype z , and C,E (i) Reproduction the optimal phenotype under the current climatic or local environmental conditions Q . They follow a normal Allindividualscanpotentiallybearoffspring.Thenumberof C,E distribution with maximum unityandvariancev2 : ovulesproducedbyeachindividualisdrawnfromaPoisson C,E distribution with average R¼100. Whether, and by which " ðz (cid:3)Q Þ# matingpartner,singleovulesarefertilizedismodelledstochas- WC;EðzÞ¼exp (cid:3) C;E2v2 C;E ; C;E tically with the probabilities of fertilization derived from the individuals’ distances and the shape of the pollen dispersal wherev2istraditionallyreferredtoasselectionstrength,but kernel(see§2b(ii)).Gametesarecomposedbyduplicatingpar- canalsobeinterpretedasameasureofthespecies’tolerance entalchromosomes,oneofeachhomologouspairbeingchosen tosuboptimalconditions,i.e.itsnichebreadth[40].Here,for randomly.Allelesmutatewithaprobabilityofm¼1027,which the default parameter settings, this value was fixed at 0.1, representstheaverageratefoundfortheannualplantspecies resulting in W ,0.01 and thus in a negative population C Arabidopsis thaliana [47–49]. The mutational effect, i.e. the growth rate (given the average number of offspring per amountbywhichtheallelicvalueischanged,isdrawnfrom individualis100)whentemperaturehaschangedbyapproxi- a zero-mean normal distribution with variance a2¼0.2, mately18C,assumingthephenotypeisfixed.Inanumberof approximatelyfittingempiricalobservations[47]. additionalruns,selectionstrengthwasreducedbyincreasing v2to 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 pollendispersalandoffspringdispersal.Botharecharacterized (similar to [39,51]): whenever the number of individuals bylognormal,isotropicdispersalkernelswithanaveragedis- within a grid cell exceeds its carrying capacity, K, resident tancedforbothgametesandoffspringandashapeparameter individuals are subjected to a density-dependent mortality of0.5.Thelognormaldistributionhasbeenfoundtoadequately with probabilityof survival¼12K/N. representbothlocalandlong-distancedispersal[50]. Offspring dispersal is simulated explicitly: dispersal dis- (c) Simulations tance and direction are chosen randomly with probabilities followingtheshapeofthedispersalkernel.Theoffspringisposi- Simulationswererun totesttheinteractiveeffectsof disper- tioned at the resulting x/y-coordinates, respecting torroidal sal, habitat heterogeneity and linkage on population boundaryconditions. dynamics and the likelihood of survival under climate Table 1. Parameter values for simulationruns. with no initial genetic variation showed that resulting 4 population parameters were not influenced by the chosen parameter description values startingconditions(seetheelectronicsupplementarymaterial, rstb figureS5).Forthemainanalysis,climatechangewassimulated .ro y V rate of climate shift twounits per 100 bykeepingthetemperatureconstantoverthefirst200gener- als o years ations and then gradually increasing it by 2.08C over the cie following 100 time-steps. After this period of change, ty H Hurstexponent 0.2 pu the new climatic conditions were assumed to be stable b h habitat 0,1,2,3, 4,5,6 lis H untiltheendof500simulationyears. h in heterogeneity g .o K carrying capacityper 5 rg grid cell 3. Results Ph il R mean numberof 100 In test runs without environmental change, population size, Tra n offspring average individual fitness and additive genetic variance sR D mean dispersal 0.05,0.1, 0.2, 0.4,0.8, were stable over time, unless mean dispersal distances were So c too small to ensure a sufficient number of fertilized ovules B distance 1.6, 3.2, 6.4 3 to keep growth rates higher than unity. When introducing a 6 8 d shape factor 0.5 : shape shift in climate, population size started to decline at the 2 0 1 dispersal kernel point where the average individual phenotype lagged so 2 0 L linkage between fully linked, free far behind the optimum Q that W,1/R. In simulations 083 wherethemutationratemwassettozero,populationsinev- loci recombination itablydied,becausestandinggeneticvariationalonedidnot M mutation rate per 1027 provideenoughscope forfulladaptationtonewconditions. locus Withthedefaultvalueform¼1027,anaveragefamilysizeof a2 variance of 0.2 100 and a carrying capacity around 5000 individuals, mutations occurred on average once per generation and mutational effect locus. In combination with the given variance of the muta- v2 selection strength 0.1,0.2 tional effect (a2)¼0.2 and a selection strength (v2)¼0.1, 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 thefixationofrare,largemutationscontributedtotheadap- distance of 6.4. Habitat heterogeneity h was controlled by tation process to the new conditions (results not shown), H 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, describedinHoltet 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- keptconstantacrosssimulations.Forallpossible112combin- egories of response (figure 1), before providing some detail ations of d, h and linkage, we ran 100 replicates, recording on howthe keyparametersinfluenced theoutcome. H population size over time and the population average and Complete evolutionary rescue occurred when there was a variance of individuals’ survival probabilities, W , as a sufficient number of beneficial mutations and when they C,E measurefortheirconditions. were able to spread unhampered across the landscape. This Landscapes were initialized with avalue of 258C for the class of response was typically characterized by an initial climaticconditionsandaHurstexponentof0.2forthefractal phaseduringwhich,astheclimatebegantochange,individ- distribution of local environmental conditions, their ampli- uals’survivalprobabilitiesdeclined.Subsequently,asoneor 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 thetotalpopulationsizefullyrecoveredandultimatelyindi- 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 Partialevolutionaryrescueoccurredunderconditionswhere conditions, but exhibited normally distributed additive gen- beneficialallelesarosebutwereunabletospreadowingtoinef- etic variation with a within-cell variance of 0.01. This value fective gene flowacross space.In this classof 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 reductioninthesuitablehabitatnicheforthepopulationsome- material, figures S1–S4). It has to be noted that allelic timesresultedinsubstantiallyreducedtotalpopulationsizes 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 waspersistent,lastinguntiltheendofsimulations,whichran waslow.However,comparisonswithadditionalsimulations for200generationsafterclimatechangeceased. (a) 1.5 5 1.0 rstb .ro y n 0.5 als of adaptatio 0 ocietypublish (b) evel 1.5 ing.o e l rg g a 1.0 aver Phil 00)/ 0.5 Tran 0 s 0 R ×1 0 S e ( oc z B si 3 (c) ulation 1.5 68:201 pop 1.0 2008 3 0.5 0 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 representthelevelofadaptationtoclimaticconditions, W,andlong dashedlines representthelevelofadaption,W,tolocal environmental conditions. Onthe 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(figure5a–c). and ultimatelyanon-viablepopulation (figure1c). With increasing spatial heterogeneity, there was also an increased likelihood that, when rescue occurred, it was only (a) Effects of dispersal and habitat heterogeneity partial.Thus,whilethepopulationhadatleastsomeprobability of surviving climate change through evolutionary rescue, the In accordance with our expectations based on previous landscapewasnotfullyoccupiedafterclimatechangeandthe studies[36,37],inaspatiallyheterogeneousenvironment,dis- total population size was substantially reduced (figure 5). persalgenerallyhadanegativeeffectonindividuals’levelsof Under a heterogeneity of h ¼5, the average relative popu- H adaptationto environmental conditions W (figure2). E lation size (of the surviving populations) at the end of the Inscenariosoffulllinkage,thelevelofadaptationincreased 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-changedensities(figure5c).Interestingly,theparameter dapted individuals and consequently higher averages for the valuesthatmaximizedtheprobabilityofrescuedidnotnecess- survivingfractionofthepopulation(resultsnotshown). arilyresultinamorecompleterescue.Forexample,whenh ¼ H 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 whendispersal¼0.4.Forthisscaleofdispersal,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 C sixth of their initial abundance. By contrast, when dispersal (figure 3). However, this pattern appeared to be more occurredacrossagreaterrange(e.g.dispersal¼2.5),thepopu- sensitive to stochastic effects than results regarding the lationssurvivedonly10percentofthetime,butthenrecovered adaptationto local environmental conditions. toanaverage50percentofinitialabundance. The likelihood of evolutionary rescue was strongly reduced oreven hindered fora range of dispersal distances, (b) Effect of linkage for which rapid adaptation would have been possible with- out local adaptation (figure 4). Because both high dispersal Theassumptionsregardingtheformoflinkagehadastrong distances,aswellasverylowdistances,decreasedtheprob- effect on the overall probability of evolutionary rescue. ability of evolutionary rescue, highest survival rates were Independent inheritance allowed for much fasteradaptation (a) (b) 6 6 1.00 rstb 5 .ro 0.95 ya ls o eity 4 0.90 ciety n p e u g b ero 0.85 lish et 3 in h g bitat 0.80 .org ha 2 P h 0.75 il T ra 1 n s 0.70 R S o c 0 B 1 2 3 4 5 6 1 2 3 4 5 6 36 8 dispersal distance dispersal distance :2 0 1 Figure2.Average valuesfor thelevelofadaptationtolocal environmental conditions,WE, during thephase oftemperaturerisefor (a)full linkage and (b)free 200 recombinationofloci.Depictedaretheaveragevaluesover100replicatesforallcombinationsofhabitatheterogeneityh andaveragedispersaldistancesdingrid 8 H 3 cell length. (a) (b) 6 0.60 5 0.55 y eit 4 n 0.50 e g o er 3 et 0.45 h at bit 2 0.40 a h 0.35 1 0.30 0 1 2 3 4 5 6 1 2 3 4 5 6 dispersal distance dispersal distance Figure3.Averagevaluesforthelevelofadaptationtoclimaticconditions,W,duringthephaseoftemperaturerisefor(a)fulllinkageand(b)freerecombination C of loci. Depicted are theaverage values over 100 replicates forall combinations of habitatheterogeneity h and average dispersal distances din grid cell length. H 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 likelihoodthatpopulationsadaptsufficientlyrapidlytochan- adaptation was strongly ameliorated (figure 4). However, ging environmental conditions is at the heart of research on the overall pattern of intermediate dispersal distances evolutionaryrescue. resulting in highest evolutionary potential was consistently Allelic simulation models, as used in this study, provide observedforboth 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 4. Discussion demographic processes. However, to date, most modelling 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. spatiallyandgeneticallyexplicit,andthat,asfaraspossible, For these species, in situ adaptation to changing climate is has been parametrized realistically for both genetic and likelytoprovidetheonlynaturalmeansofavoidingultimate demographic functions. (a) (b) 7 6 1.0 rstb 5 .ro y a 0.8 ls o eity 4 ciety n p e u g 0.6 b ero 3 lish et in h g bitat 2 0.4 .org a h P h il 1 0.2 Tra n s R S 0 0 oc 1 2 3 4 5 6 1 2 3 4 5 6 B 3 6 dispersal distance dispersal distance 8 : 2 Figure 4. Probabilityof full rescue depending on habitat heterogeneity hH and average dispersal distances d in grid cell length for (a) full linkage and (b) free 012 recombination of loci. Calculated from 100 simulation runs for each parameter combination. 00 8 3 (a) 0.8 0.4 e z n si 0 o ati (b) ul p o p e 0.8 v ati el d r 0.4 n a e u c 0 s e (c) of r y bilit a 0.8 b o pr 0.4 0 0 1 2 3 4 5 6 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 ¼0, (b) h ¼3, and (c) h ¼5. 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 reflectedbyreducedlevelsofadaptationtothelocalenviron- evolutionaryrescue,wherebyrapidadaptationsavesapopu- ment—leadtohighermortalityratesandanincreasedriskof lation from extinction, but both population size and its location extinction, hence a lower chance of rescue. On the geographicalrangemaybe substantiallyreduced. other hand, as argued and shown recently by Bell & Gonzalez [35], greater dispersal can be strongly beneficial, stabilizing selection for local environments would account 8 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,onecouldalsoexpectthatadaptiveresponsetochan- rstb byourresults,whenfocusingononlytheadaptationtotem- gingclimatewouldbereducedwhenrecombinationbetween .ro y porally changing climate and thus neglecting the distorting climate-relatedlocicanoccurateverygeneration,thusbreak- als o effects of migrationload. ing apart adaptive allele combinations and preventing the c ie The interplay of these double-edged consequences of populationfrombeingfullyrescued.Whetherandhowlink- ty p u gene flow leadsto the key resultsthat we emphasize in this age may facilitate or impede adaptation to changing b lis paper. When dispersal is high and habitat heterogeneous, environmental conditions could be further investigatedwith h in the number of viable offspring in each generation can be ourmodel,but is beyondthescope of this paper. g.o drastically reduced due to the arrival of many maladapted Clearly, a number of genetic, demographic and envir- rg juveniles.Atthepopulationlevel,thisisoflittleconsequence onmental settings that were neglected in this study can P h whentheclimateisstable,aslongasthenumberofsurviving modulate the effects of spatio-temporal variability on il T juvenilescanmaintainthepopulationinasteadystate.How- micro-evolutionary dynamics. Some of these are shortly ra n s ever, when the population needs to adapt to new climatic discussedin thefollowing. R conditions, the absolute number of beneficial mutations In terms of the genetic basis of adaptation, it has been So c becomes crucial. This number depends not only on the shown that the relative amount of genetic versus environ- B 3 mutation rate, but also on the number of potential recruits mental variability in individual phenotypes affects the 6 8 : that may carry these mutations and pass them on to sub- speed of adaptation and the likelihood of evolutionary 2 0 1 sequent generations. High rates of juvenile dispersal into rescue[39,53].Whiletheprobabilityofpopulationextinction 2 0 0 habitat to which they are ill-adapted reduces the effective isincreasedunderlowerheritabilityofthosetraitscontrolling 8 3 rate at which beneficial mutations on climate-related loci adaptationtotemporallychangingconditions,fortraitscon- can be fixed in the population (see Barton & Bengtsson trollingadaptationtospatialheterogeneity,lowheritabilities [52]). Ultimately, this interaction between dispersal, habitat andhighplasticitymayinsteadfacilitatepopulationsurvival: 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.Thissuggestthatevenunderhighdispersalscenarios, effective dispersal and the spread of beneficial alleles. populations previously adapted to spatially structured local Weakerselectionwillhaveapositiveinfluence onthesurvi- environmentsmayhavealowerchancetoadapttochanging val probabilityof populations as well, because the effects of regionalclimate. maladaptation are reduced. This effect is more pronounced Thesecondkeyresult—partialevolutionaryrescue—isin whenthehabitatisheterogeneous(seetheelectronicsupple- itsmechanismcloselylinkedtotheprocessdescribedabove. mentarymaterial, figureS6), becausethe 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.hardversussoftselection)[55]mightchangeevolutionary duetogeneticswampingbynewlyarrivedindividualscarry- dynamicssubstantially. ing alleles that are not adapted to local environmental Focusingondemographiceffectsonrapidadaptation,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 notapply,partlydecouplingevolutionaryfromdemographic survivingpopulations. 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 onpopulations’demographicrates.Itseemsthatlinkagedis- 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 effectsof dispersal hasto bereconsidered. 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 demonstrated in this study, spatial heterogeneity may even natural populations cannot be captured. Thus, we believe 9 accelerate adaptation to temporal change by increasing the that the type of allelic simulation model we applied in our geneticvarianceon which evolution can operate [42,59]. study will be needed, if we are to ultimately make robust rstb quantitative predictions on the likelihood of evolutionary .ro y rescue in particular populations or species. Here, we could als 5. Conclusion o show that the evolutionary potential of populations facing c ie deteriorating conditions might be overestimated when ty In pastyears, someremarkable studies have been published pu neglecting the effects of local adaptation to heterogeneous b identifying the genetic basis for variation in traits that are lis habitat characteristics. This finding will be important, h important for adaptation under climate change [60–64]. If in we are to understand under which conditions species will becauseincreasinghabitatdeteriorationwill leadtoreduced g.o total habitat availability, increased habitat fragmentation rg 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 Ph are likely to impede the ability of species to track their il the knowledge of the genetics underpinning adaptation to T preferredclimate. ra the level of population demography. In a recent study, ns R Chevin et al. [5] present a relatively simple evolutionary WethankOscarGaggiotti,Ire`neTill-BottraudandCarstenUrbachfor So modeltoassess—foragivencombinationofphenotypicvar- discussion during model development and implementation. 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