Mutation surfing and the evolution of dispersal during range expansions

doi:10.1111/j.1420-9101.2010.02123.x Mutation surfing and the evolution of dispersal during range expansions J. M. J. TRAVIS*, T. MÜNKEMÜLLER* &O.J.BURTON* *Zoology Building, Institute of Biological and Environmental Sciences, University of Aberdeen, Scotland, UK Laboratoire d Ecologie Alpine, Université J. Fourier, Grenoble, France Keywords: evolution; evolvability; invasion; range shifting. Abstract A growing body of empirical evidence demonstrates that at an expanding front, there can be strong selection for greater dispersal propensity, whereas recent theory indicates that mutations occurring towards the front of a spatially expanding population can sometimes surf to high frequency and spatial extent. Here, we consider the potential interplay between these two processes: what role may mutation surfing play in determining the course of dispersal evolution and how might dispersal evolution itself influence mutation surfing? Using an individual-based coupled-map lattice model, we first run simulations to determine the fate of dispersal mutants that occur at an expanding front. Our results highlight that mutants that have a slightly higher dispersal propensity than the wild type always have a higher survival probability than those mutants with a dispersal propensity lower than, or very similar to, the wild type. However, it is not always the case that mutants with very high dispersal propensity have the greatest survival probability. When dispersal mortality is high, mutants of intermediate dispersal survive most often. Interestingly, the rate of dispersal that ultimately evolves at an expanding front is often substantially higher than that which confers a novel mutant with the greatest probability of survival. Second, we run a model in which we allow dispersal to evolve over the course of a range expansion and ask how the fate of a neutral or nonneutral mutant depends upon when and where during the expansion it arises. These simulations highlight that the success of a neutral mutant depends upon the dispersal genotypes that it is associated with. An important consequence of this is that novel mutants that arise at the front of an expansion, and survive, typically end up being associated with more dispersive genotypes than the wild type. These results offer some new insights into causes and the consequences of dispersal evolution during range expansions, and the methodology we have employed can be readily extended to explore the evolutionary dynamics of other life history characteristics. Introduction There is a growing interest in the evolutionary dynamics of populations that are expanding their ranges (see reviews by Hänfling & Kollmann, 2002; Lambrinos, Correspondence: Justin M. J. Travis, Zoology Building, Institute of Biological and Environmental Sciences, University of Aberdeen, Tillydrone Avenue, Aberdeen, AB24 2TZ, Scotland, UK. Tel.: +44 1224 274483; fax: +44 1224 272396; e-mail: justin.travis@ abdn.ac.uk 2004; Hastings et al., 2005; Phillips et al., 2010). Studies have demonstrated that a range of life history characteristics can come under strong selection at an expanding front (selfing-rates Daehler, 1998; resistance to herbivores Garcia-Rossi et al., 2003; dispersal behaviour Simmons & Thomas, 2004; Phillips et al., 2006) and that, at least in some cases, their evolution can modify the spread dynamics (e.g. Simmons & Thomas, 2004; Phillips et al., 2006). Population geneticists have often used spatial patterns of genetic diversity within a species 2656

Mutation surfing and dispersal evolution 2657 existing range to make inferences about its past history, and recent work suggests that observed phylogeographic patterns may, in many cases, be mainly determined by the initial colonization wave (Biek et al., 2007; Excoffier & Ray, 2008). Simulation models have demonstrated that initially rare alleles or novel mutations can sometimes reach high frequency and spatial extent by surfing the wave of range expansion (e.g. Edmonds et al., 2004; Klopfstein et al., 2006; Travis et al., 2007; Miller, 2010) and it has been suggested that by better understanding and accounting for the genetic dynamics of range expanding populations, we will be able to improve our interpretation of current patterns of genetic diversity (Excoffier & Ray, 2008). Here, we seek to link life history evolution with the population genetics of range expansion by constructing an individual-based model that combines features from previous models investigating the evolution of dispersal (e.g. Travis & Dytham, 2002; Travis et al., 2009) with those developed to investigate the mutation surfing phenomenon (e.g. Klopfstein et al., 2006; Travis et al., 2007). One interesting result to have emerged from theory focussing on the population genetics of species undergoing range expansion (recently reviewed by Excoffier et al., 2009) is that neutral and nonneutral mutations that arise on the edge of a range expansion sometimes surf on the wave of advance and can reach much higher spatial extent and overall density than they would within a stationary population. This process highlights very clearly the roles of stochasticity and founder effects in driving the genetic dynamics at range fronts. The mutation surfing dynamic can have important consequences for evolutionary dynamics: Burton & Travis (2008a) demonstrated that the likelihood of fitness peak shifting (a population crossing from suboptimal fitness peak via a fitness valley to a global optimum) can be considerably more likely during range expansions because of increased frequency of deleterious alleles towards the front. However, although it is now clear that the dynamics of novel mutations are quite different at an expanding front than within a stable range, there has yet to be any work that has explicitly considered consequences of mutation surfing for life history evolution. Here, we ask how mutation surfing might influence the evolution of dispersal during range expansion. Dispersal is a key life history characteristic playing a central role in a population s ecological and evolutionary dynamics (Bowler & Benton, 2005), so it should be of little surprise that there has been considerable effort devoted to understanding what determines different dispersal strategies (e.g. Perrin & Goudet, 2001; Travis & Dytham, 2002; Poethke et al., 2003; see Bowler & Benton, 2005; Ronce, 2007 for recent reviews). Dispersal often carries considerable costs that constrain its evolution regardless of whether they are because of the increased energetic demands associated with movement between patches (Zera & Mole, 1994; Stobutzki, 1997), are because of increased predation risk (Belichon et al., 1996; Yoder et al., 2004) or are because of the risk of not finding suitable habitat (Travis et al., 2010). That dispersal is ubiquitous, despite these often considerable costs, indicates that strong selective forces must be acting to favour movement between patches. Dispersal can evolve as a means of reducing kin competition (Gandon, 1999; Ronce et al., 2000; Bach et al., 2006) or inbreeding depression (Gandon, 1999; Perrin & Mazalov, 1999). Additionally, selection favours greater dispersal when temporal environmental variability (McPeek & Holt, 1992; Travis, 2001) and or demographic stochasticity (Travis & Dytham, 1998; Cadet et al., 2003) increase. By increasing colonization and reinforcement, dispersal enables regional population despite the frequent population crashes and extinctions that both high temporal environmental variability and demographic stochasticity can generate (Olivieri et al., 1995; Metz & Gyllenberg, 2001; Parvinen et al., 2003). During periods of range expansion, selection pressure on dispersal can be very different to that acting on individuals in a stationary population. At an expanding margin, there will generally be strong selection favouring increased dispersal as there are considerable fitness benefits of being amongst the earliest colonists of a new patch. This is both predicted by theoretical models (e.g. Travis & Dytham, 2002; Phillips et al., 2008; Burton et al., 2010), and observed to be the case both in invasive species (e.g. Phillips et al., 2006) and in populations undergoing range expansions in response to climate change (e.g. Thomas et al., 2001; Hughes et al., 2003; Darling et al., 2008; Léotard et al., 2009). As a range expansion proceeds, increases in dispersal propensity towards the expanding front lead to an accelerating rate of range expansion. In this paper, we are interested in the interplay between life history evolution and the genetics of range expansion. The evolution of a life history strategy during the course of a range expansion may influence the phylogeographic pattern that emerges. Here, we consider how dispersal evolution can be expected to alter the likely fate of mutants that occur close to an expanding front. Will the survival probability and expected spatial spread of a novel mutant that occurs at the beginning of an expansion be different to that which occurs later when dispersal evolution may have occurred? In addition to influencing the population genetics of range expansion, life history evolution will itself be impacted by those genetic dynamics. Mutations arising towards the expanding front that influence life history characteristics will be subjected to the same founder effects and strong genetic drift as any other mutants. Excoffier & Ray (2008) suggest that selection for increased dispersal propensity must be very strong at a wave front in order for it to overcome drift. Here, we will use our modelling framework to explore this issue in greater detail, considering how the fate (including survival and surfing probabilities) of a mutant depends upon the mutant s

2658 J. M. J. TRAVIS ET AL. dispersal propensity relative to the wild type and how this varies according to key parameters including carrying capacity, intrinsic population growth rate and the mortality cost associated with dispersing. The model The model is an extension of recent studies investigating the dynamics of neutral (Edmonds et al., 2004; Klopfstein et al., 2006) and nonneutral (Travis et al., 2007; Burton & Travis, 2008b; Münkemüller et al., in press) mutations arising at expanding range margins. As in these previous models, we simulate asexual, haploid individuals and assume a population with discrete, nonoverlapping generations. The key extension that we make here is to allow individuals to carry a gene that determines their dispersal propensity. In doing this, our model links the methods used in the recent mutation surfing literature with methods widely employed in tackling questions related to the causes and consequences of dispersal evolution (Hovestadt et al., 2001; Travis & Dytham, 2002; Bach et al., 2007; Travis et al., 2009). Below, we provide a detailed description of our model before describing the simulation experiments that we have conducted with it. Spatial dynamics Each generation consists of two parts: within patch dynamics and dispersal between patches. The within patch dynamics are simulated using an individual-based version of the discrete-time Hassell & Comins (1976) model. Each individual present at time, t, gives birth to a number of offspring drawn at random from the Poisson distribution with mean: k(1 + an t ) )b where a =(k 1 b ) 1) K. Here, k is the intrinsic rate of increase, K is the subpopulation (or deme) equilibrium density, and b describes the form of competition. In all simulations, we use K = 20. For generality, we include the parameter b here, although in all the results that we present, we set b = 1, describing pure contest competition. Drawing from a Poisson distribution to determine the number of offspring born to an individual generates demographic stochasticity, a key contributing factor in the evolution of dispersal. Dispersal occurs immediately after the within patch dynamics. Each individual carries a gene, d, that directly determines its probability of emigrating. Thus, an individual with gene, d = 0.35 will disperse with probability 0.35. Emigrating individuals have a probability, m, of dying during dispersal. Those that survive dispersal move with equal probability to one of the four patches that adjoin the individual s natal patch. We use a reflecting boundary along the x axis and a wrapped boundary for y essentially we are simulating the dynamics of an invasion proceeding from one end of a cylinder towards the other. All individuals carry two unlinked genes, one that determines their dispersal propensity and the other a neutral marker. Offspring inherit both genes from their single parent. In simulations where we allow dispersal to evolve, mutation to the dispersal gene, d, occurs with probability, mut. In all cases where we simulate dispersal evolution, mut = 0.001. A single mutation modifies d by an amount drawn at random from the normal distribution with mean = 0.0 and standard deviation = 0.1. If a mutation results in d > 1.0, d = 1.0 and similarly if d < 0.0, d = 0.0. The simulation experiments The fate of dispersal mutants In the first simulation experiment, we explore the potential role of mutation surfing in driving the evolution of dispersal. In this experiment, we introduce a single dispersal mutation into the expanding front of a population that is fixed for a different dispersal propensity. By repeating this for mutants with different dispersal propensity, we can determine the probability that a dispersal mutant will survive and spread according to its dispersal characteristics and that of the wild type. However, before running simulations within which we introduce a novel dispersal mutant to an expanding front, we had to determine baseline dispersal probabilities to use for the initial wild-type population. Rather than making a purely arbitrary choice, we decided to use the dispersal probabilities of a population in a stationary range as our starting point. We note here that kin competition is always present in our model so we always expect to obtain nonzero emigration rates. Also, the strength of kin competition increases with increasing k and we thus expect higher emigration rates to evolve when k is higher. For all combinations of intrinsic rate of increase, (k = 1.5,3.0,4.5), and for probabilities of dying during dispersal, (m = 0.0 ) 0.9), we ran the model on a 25 row by 25 column grid for 10 000 generations and observed the mean dispersal probabilities in the final generation; 10 000 generations were found to be sufficiently long for a quasi-equilibrium rate of dispersal to have been reached. We repeated this process twenty times for each combination of parameters. This involved 1140 simulations (20 replicates of each of 57 parameter combinations). From the total pool of 57 combinations of parameter values for which we obtained mean evolved dispersal strategies in a stationary population, we selected six combinations that we would use in subsequent simulations (Fig. 1 and see Table 1). This way we defined properties of six virtual example species. Each of these six virtual species is, in turn, used as a wild type in subsequent simulations where the survival and surfing of mutations are explored. Our method is extremely similar to those used previously to explore surfing dynamics (e.g. Klopfstein et al., 2006; Travis et al., 2007) but, in our case, the mutant that is introduced

Mutation surfing and dispersal evolution 2659 Fig. 1 A simplified schematic of surfing dynamics for the two different simulation experiments (left vs. right column). In the first experiment, we are interested in determining how a single mutation to dispersal propensity fares when introduced into a population fixed for another dispersal propensity. A population of the wild-type dispersal propensity expands from the left-hand size of the grid into black, unoccupied space. A single dispersal mutant is introduced into cell X and its spatial abundance over time is illustrated by the numbers in the cells. In the second experiment (right column), we are interested in how dispersal evolution impacts the survival and surfing of neutral mutations. Now, dispersal rates are allowed to evolve and a novel, neutral mutant is introduced into cell X. This mutant inherits its dispersal rate from its wildtype parent. In this second experiment, there can be spatial variability in dispersal propensity and, in general, we expect higher dispersal propensity to evolve at the front (in this schematic, higher mean dispersal propensity is illustrated by lighter shading of the cells). The numbers in the cells, in this case, refer to the numbers of mutants present. Table 1 The six different property combinations used in the further simulation experiments. We recorded the full distribution of evolving dispersal rates for all combinations of three different intrinsic rates of increase (k) and two different dispersal mortality rates (dispmort) in a static landscape. Combination k dispmort Mean (dispwild) SD (dispwild) 1 1.5 0.1 0.189 0.047 2 1.5 0.6 0.044 0.019 3 3.0 0.1 0.220 0.045 4 3.0 0.6 0.043 0.019 5 4.5 0.1 0.222 0.045 6 4.5 0.6 0.044 0.019 influences the dispersal propensity of an individual. At the beginning of each simulation, we initialized a grid of 300*25 cells with 20 wild types in the 5*25 leftmost demes. Dispersal rates of these initial individuals were identical and were set to the mean dispersal rate that evolved in the static landscape. As soon as the expanding front reached deme <20,12>, a mutation with a new dispersal rate, dispmut, was introduced. No other mutations to dispersal occur in this experiment. Simulations were repeated 1000 times. Here, we are interested in asking how likely it is that mutants with different dispersal propensities survive, how likely they are to surf and what their survival and surfing might mean for the range expansion. Thus, we record the success of mutants 300 timesteps after introduction with regard to survival and surfing and, additionally, throughout the simulation, we record the distance that the whole population has travelled. We consider two forms of surfing, surfing anywhere on the expanding front and surfing at the rightmost point of the front. In the first case, an individual of the mutant type simply has to be present in one of the subpopulations on the leading edge of the range expansion, whereas to qualify as the more stringent second case, a mutant has to occur in the furthest right occupied cell (i.e. not just anywhere on the leading edge but in the most advanced subpopulation). The fate of neutral mutants when dispersal is allowed to evolve We ran a second simulation experiment to explore how the evolution of dispersal is likely to influence the fate of a novel, neutral mutation that arises at the expanding front. At the beginning of each of these simulations, we initialized a grid of 1500*25 cells with 20 wild types in the 5*25 leftmost demes. Dispersal rates for each initialized individual were drawn randomly from those that

Evolved dispersal rate 0.0 0.2 0.4 0.6 0.8 2660 J. M. J. TRAVIS ET AL. evolved in the static landscape (as described previously). Thus, there was some initial variability in dispersal within the introduced population. Also, in these simulations, mutations to dispersal propensity occur at rate mut. A single neutral mutant was introduced at a specified time, introtime, after initialization but always at the very front of the expanding wave. Simulations were repeated 1000 times. As in the first set of simulations, we record the success of the mutant in terms of both its probability of survival and of surfing. Throughout each simulation, we also record both the evolved dispersal propensities and the extent of population range expansion. Finally, to establish the equilibrium emigration rate at an expanding front, we ran simulations where a range was allowed to expand for 10 000 generations. These simulations were started using exactly the same method as in the second set of simulations. At each generation, we calculated the mean emigration rate of those individuals within three columns of the furthest forward individual. This was repeated 1000 times for each of the six parameter combinations (see Table 1). Results In a stationary population, the evolved dispersal strategy depends upon K, k and the probability of mortality associated with movement (see Fig. 2). Higher dispersal propensities evolve for lower K (not shown), lower dispersal mortalities and for higher k. In our model, dispersal mortality is the parameter that exerts the greatest influence. These results are in agreement with previous theory (e.g. Travis & Dytham, 1998; Ronce et al., 2000; Bowler & Benton, 2005). The fate of dispersal mutants The fate of a novel dispersal mutant that arises at an expanding front depends upon its dispersal propensity relative to the wild type (Fig. 3). We observe some survival of mutants of most dispersal propensities (Fig. 3a) except for species C2, which has a low reproductive rate and high dispersal mortality. For this species, mutants with d > 0.5 never survive. In all cases, mutants that have a slightly higher dispersal propensity than the wild type have a higher survival probability than those mutants with a dispersal propensity lower than, or very similar to, the wild type. However, when we consider mutants of even higher dispersal propensity, the pattern is less consistent. For the three species that suffer lower dispersal mortality (C1, C3 and C5), survival probability of a mutant increases to an asymptote as the dispersal propensity of the mutant increases. This is not the case for the other three species, for which the highest survival probability is for mutants of intermediate dispersal propensity. The pattern is similar when the probability of mutant surfing is considered (Fig. 3b). For the three Reproduction rate 1.5 3 4.5 0.0 0.2 0.4 0.6 0.8 Dispersal mortality Fig. 2 Adaptive dispersal rates in stationary populations. Dispersal mortality and reproduction rate influence evolved dispersal. The black boxes indicate the six different combinations used in the further simulation experiments (cf. Table 1). Each point shows the mean from 20 replicate simulations. In all cases, the results are for K = 20 on a 25 by 25 lattice. The model was run for 10 000 generations, plenty of time for a stable dispersal rate to evolve. species with lower dispersal mortality, surfing probability increases to an asymptote as the dispersal propensity of the mutant increases, whereas for the other three species, it increases up to intermediate rate of dispersal, beyond which mutant survival declines. Whereas some mutants of lower dispersal propensity than the wild type survive for 300 timesteps, very few surf for long (compare Fig. 3a with Fig. 3b). When we consider the extent of population spread attained when different dispersal mutants are introduced, we observe a right-shift in the pattern with higher dispersal propensities yielding the highest spread rates than were found to have the highest survival or surfing probabilities. For example, when we consider species C6, mutants of d = 0.25 are the most likely to survive and surf, whereas mutants of d = 0.6 result in populations spreading the most. Thus, the most likely dispersal mutant to survive and even to surf is not necessarily the one that will result in the greatest range expansion. At this point, it is worth comparing the results shown in Fig. 3 with those in Fig. 4, where the results of the third set of simulations are shown. Interestingly, the emigration rate that is ultimately selected at an expanding front (Fig. 4) is close to that which maximizes the rate of spread (compare results shown in Fig. 4 with those in Fig. 3). In all cases, the evolutionary stable frontal strategy is much closer to that which maximizes the rate of spread than it is to the dispersal mutant that is the most likely to initially survive at the beginning of a range expansion. It is informative to consider the temporal dynamics of survival and surfing; these clearly illustrate important

Mutation surfing and dispersal evolution 2661 (a) Survival probability 0.0 0.2 0.4 0.6 0.8 C2, C4, C6 C1 C3, C5 Evolved dispersal rate C1 C3 C5 C2 C4 C6 0 2000 4000 6000 8000 10 000 Time (b) Surfing probability (c) Spread distance 0 50 000 150 000 0.0 0.2 0.4 0.6 0.8 C1 C3 C5 C2 C4 C6 Fig. 4 Evolution of dispersal rates at the wave front (three front columns) during range expansion (simulations with evolution). (Initial dispersal rates for each initialized individual were drawn randomly from those that evolved in the static landscape.) high dispersal mortality (dispmort = 0.6, combinations C2, C4, C6) and low dispersal mortality (dispmort = 0.1 combinations C1, C3, C5); low reproduction rates (k = 1.5, combinations C1, C2), medium reproduction rates (k = 3.5, combinations C3, C4) and high reproduction rates (k = 4.5, combinations C5, C6). Surviving mutants with lower dispersal propensity typically do not surf for long (Fig. 5c,d) and very few are found in the cell at the furthest advanced position of range expansion for any period of time. However, a very different temporal pattern is seen for mutants with higher dispersal propensity. Over time, we find that an ever increasing proportion of surviving, more dispersive mutants are also surfing and, additionally, that an increasing proportion of those surfing mutants are present within the furthest advanced subpopulation. The fate of neutral mutants when dispersal is allowed to evolve Dispersal rate, mutant Fig. 3 The fate of the mutation after 300 timesteps of range expansion depends on dispersal rates, reproduction rates and dispersal mortality (simulations without evolution). For high dispersal mortality (dispmort = 0.6, combinations C2, C4, C6) survival, surfing and spread distance peak at low dispersal rates of the mutant, for low dispersal mortality (dispmort = 0.1 combinations C1, C3, C5), it is vice versa. Low reproduction rates reduce survival, surfing and spread (k = 1.5, combinations C1, C2). Vertical grey lines mark dispersal rates of the wild type (straight line for combinations C2, C4, C6, dashed line for combination C1 and pointed-dashed line for combinations C3, C5). differences between mutants whose dispersal propensity is lower than the wild type compared to mutants whose dispersal propensity is higher than the wild type. For illustrative purposes, the fate of two neutral mutations is shown in Fig. 6. In the first case, a novel mutation initially increases in abundance before declining close to extinction at around time = 240 (Fig. 6a). However, at this time, a mutation increasing dispersal propensity occurs to one of the mutant individuals (see the rapid increase in mutant s mean dispersal propensity Fig. 6b) and following this, the mutant population size grows rapidly. By time = 390, the mutant totally dominates the range expanding population. Contrast this with the example shown in Fig. 6c,d. Here, the mutant increases in density to the point where it is equally abundant as the wild type. However, at about time = 250, the wild type acquires a more dispersive mutation and this leads to the eventual exclusion of the mutant. There is some indication that the mutant itself acquires a mutation for greater dispersal, but this is insufficient to rescue it from extinction. The two exam-

2662 J. M. J. TRAVIS ET AL. (a) Dispersal mortality = 0.6 Dispersal mortality = 0.1 (b) Survival probability 0.0 0.2 0.4 0.6 (c) (e) 0.0 0.2 0.4 0.6 (d) (f) Dispersal rate, mutant Dispersal rate, mutant (c) (d) Fate of mutant Fate of mutant (e) 50 100 200 300 Time 50 100 200 300 Time (f) Survival probability Surfing-somewhere Surfing-rightmost 50 100 200 300 Time 50 100 200 300 Time Fig. 5 The fate of the mutation over 300 timesteps of range expansion depends on dispersal rate and dispersal mortality. Shown are selected time-series for the same simulations presented in Fig. 3 (plot a and b, selected parameter combinations are marked, reproduction rate is 3.0, vertical lines mark mean dispersal rates of the wild types). A lower dispersal rate of the mutant compared to the wild-type results in a decreasing surfing probability compared to survival probability over time (plot c and d). However, if the dispersal rate of the mutant is higher, it is vice versa. Over time, almost all surviving mutations surf (plot c and d) and surfing does not only occur somewhere at the front but at rightmost (plot e and f). ples shown here are both cases where the mutant survives for a substantial period of time but we emphasize that, because of stochastic effects, in many cases, the mutant goes extinct very rapidly. The example results shown in Fig. 7 indicate that the success of a neutral mutant is likely to depend upon the dispersal genotypes that it is associated with. One consequence of this is that novel mutants that arise at the front of an expansion, and survive, typically end up being associated with more dispersive genotypes than the wild type (Fig. 7). An interesting related question is whether the fate of a neutral mutant changes over the course of an invasion throughout which there is a gradual increase in dispersal propensity (as observed in Fig. 4). Our results suggest that the probability that a neutral mutant survives for 300 timesteps is largely independent of when it occurs in relation to the onset of range expansion (Fig. 8a). However, there is clear evidence that a new mutation s probability of surfing with the range advance is greater when an expansion has already been proceeding for longer (Fig. 8b). While this general effect is true for each of our six species, it is more pronounced when the reproduction rate is greater. It is worth highlighting that the difference in surfing probability can be substantial; for example, in simulations using species C6, the probability of surfing roughly doubles from 0.07 when the novel mutant is introduced at the onset of range expansion to over 0.15 if it is introduced when time > 100.

Mutation surfing and dispersal evolution 2663 (a) Density (b) Evolved dispersal rate (c) Density (d) Evolved dispersal rate 0 200 400 600 0.4 0.6 0.8 0.0 0.2 0 200 400 600 0.0 0.2 0.4 0.6 0.8 Mutant Wild Place of introduction 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 x-direction Fig. 6 Example results for a surfing mutation (plot a and b) and a surviving but not surfing mutation (plot c and d) after 300 timesteps in simulations with evolution. The surfing mutation occupies the complete wave of expansion from the point of introduction to the front and has much higher evolved dispersal rates. However, if the mutation survives but does not surf, it is vice versa. The wild type has higher densities and higher dispersal rates at the front. Density is the sum of individuals present across the 25 columns. These results are for combination 2 of the parameter values with mut = 0.001. The expansion occurs on a 25 by 500 cell lattice. Evolved dispersal rate 0.0 0.2 0.4 0.6 0.8 Discussion Wild Mutant 0.1 0.6 Dispersal mortality Fig. 7 Overall, evolving dispersal rates of the mutant tend to be higher than those evolving for the wild type. Boxplots aggregate results after 300 timesteps for all simulated times of introduction and all different reproduction rates. There has been considerable recent interest in the process coined mutation surfing, and numerous studies have now explored the dynamics of neutral and nonneutral mutations that arise at an expanding range (e.g. Edmonds et al., 2004; Klopfstein et al., 2006; Burton & Travis, 2008b; Hallatschek & Nelson, 2008). Here, we have extended the general method to explore how mutation surfing both influences, and is influenced by, the evolution of a key life history characteristic, the propensity to disperse. It is well established that dispersal should be selected upwards during a range advance (e.g. Cwynar & Macdonald, 1987; Travis & Dytham, 2002; Phillips et al., 2006), but previous theory has tended to seek the evolutionary stable dispersal strategy at the front (e.g. Travis et al., 2009; Burton et al., 2010). In contrast, rather than focussing on simply identifying the evolutionary optimal strategy, we have concentrated on determining the likelihoods that mutants of different dispersal propensities will survive and surf. We believe that this offers a useful new perspective on the evolution of dispersal during range expansions. There are potentially important consequences of this effect. In this discussion, we will first seek to explain our results before considering their implications in terms of improving our understanding of the spatial dynamics of past, current and future range expansions. Unsurprisingly, mutants conferring lower emigration propensity than has evolved in a stationary range have very low surfing probabilities; they are highly unlikely to remain for long on the front as the wild-type individuals are more dispersive. Interestingly, however, these low dispersal mutants frequently survive for substantial periods. This is explained by the fact that mutants are introduced into a low-density region at an expanding front. This provides an opportunity for the mutants to gain a foothold and obtain reasonable local abundance

2664 J. M. J. TRAVIS ET AL. (a) Survival probability (b) Surfing probability 0.0 0.2 0.4 0.6 0.00 0.05 0.10 0.15 0 200 400 600 800 1000 1200 C1 C3 C5 C2 C4 C6 0 200 400 600 800 1000 1200 Time of introduction Fig. 8 The fate of the mutation after 300 timesteps of range expansion depends on the time of introduction and the combination of species properties (simulations with evolution). Early times of introduction result in comparable survival (plot a) but in a much reduced surfing probability (plot b). High dispersal mortality (dispmort = 0.6, combinations C2, C4, C6) and low reproduction rates (k = 1.5, combinations C1, C2) reduce survival and surfing. even when they do not become long-term surfers. This process is clearly illustrated in Fig. 5c,d: here, large proportions of the introduced mutants remain somewhere along the expanding front for several generations and, even once they have fallen away from the front, they have accumulated sufficient numbers and selection is sufficiently weak that they often persist for a substantial period of time. Mutants conferring somewhat higher emigration propensity than the wild type suffer similar immediate probabilities of stochastic extinction as those conferring lower emigration, but they are much more likely to reach and remain on the leading edge of the range expansion and utilize the easily accessible resources. Once they have reached the leading edge, almost all survive (Fig. 5e,f) as they are extremely unlikely to be caught and out-competed by the less-dispersive wild type. When the cost of dispersal is high, there is a clear intermediate optimum in terms of the dispersal propensity that is most likely to survive and surf. This is simply because, for mutants of very high emigration rate, the mortality burden (because of dispersal) compromises their viability. A particularly interesting feature of the results is that the dispersal propensity that ultimately evolves on an expanding front is often substantially higher than that which is most likely to initially survive (and surf) at the beginning of a range expansion. For example, for species C4, emigration rate eventually reaches 0.55 in an expanding range (Fig. 4), a rate that is substantially higher than that which optimizes either survival or surfing in the early stages of range expansion (Fig. 3). This highlights that we should expect dispersal to evolve in a stepwise or gradual fashion during range expansions. Even if it is possible for a single mutation to yield an extremely dispersive individual, our results suggest that it is more likely that initial changes in dispersal are relatively small, because it is these mutants that have the highest survival probability. Travis et al. (2009) demonstrated the importance of intergeneration effects in terms of determining the outcome of evolution at an expanding front; a strategy that does not maximize individual lifetime reproductive success thrives because, on average, it leaves a greater number of long-term descendants. For a high emigration mutant, the cost of dispersal mortality will often reduce the expected number of children or grandchildren (and may consequentially reduce the mutant s immediate chances of survival) but the mutant may, nonetheless, have an increased mean expected number of, for example, great, great, great grandchildren. While a higher dispersal mutant may have a lower chance of surviving, if it survives, it is likely to be very successful by surfing on the front. The contrast in our results between the emigration propensity that optimizes survival and that which eventually evolves is a consequence of this balance between short- and long-term fitness. Other than in the very early stages of range expansion, the evolution of increased dispersal during a range expansion has relatively minor effects on the probability that a neutral mutation will survive or surf (time of introduction after the start of range expansion has no strong effect, Fig. 8). This is unsurprising given previous findings that have shown both survival and surfing probabilities are largely insensitive to the emigration rate (Travis et al., 2007). We attribute the increase in surfing probability that is observed in the very early phases of range expansion (Fig. 8) to the population dynamics at the front rather than any evolved shift in dispersal. Immediately after the range has started expanding, there will be a relatively straight edge to the front, and most of the patches will be close to carrying capacity. There will be many individuals close to the front and thus, a single neutral mutant introduced at this stage will have a lower probability of surfing the front than one that occurs on the front once range expansion is established. Once established, the front tends to be irregular and there are

Mutation surfing and dispersal evolution 2665 far fewer individuals close to the front. Under these conditions, a single mutant has a far higher probability of surfing. Burton & Travis (2008b) demonstrated that the shape of an expanding front can introduce spatial heterogeneity into surfing probabilities for novel mutants. Similarly, temporal variation in the shape of the front may introduce temporal heterogeneity in surfing probabilities. Because of the surfing dynamic, mutations can survive and attain substantial spatial extent (Edmonds et al., 2004; Klopfstein et al., 2006; Travis et al., 2007). Our work demonstrates that the same is true for mutations that influence a key life history trait, dispersal. An implication of this finding is that there may be increased variation in life history strategies between regions that have been recently colonized. In general, we expect an erosion of genetic diversity during range expansion (e.g. Austerlitz et al., 1997; Hallatschek & Nelson, 2008). However, Excoffier et al. (2009) highlighted both empirical (Hallatschek et al., 2007) and theoretical (Excoffier & Ray, 2008) work suggesting that a range expansion can result in distinct sectors, each characterized by different distinct (neutral) genotypes and suggest that these sectors may, under some conditions, be temporally stable. Thus, while range expansions may reduce local diversity, they may simultaneously result in considerable between-region variability. We suggest that the same is likely to be true for mutations that influence life histories and highlight the need for further work to test whether stable sectors in life history traits may be an outcome of range expansions. We anticipate that, in addition to being dependent upon the spatial scale of dispersal (Excoffier et al., 2009), the stability of these sectors may also critically depend upon the rate at which novel mutations arise and the strength of selection acting upon them during both the expansion and the stationary phase. Dispersal is just one of many life history traits that are likely to come under strong selection during a period of range expansion (Burton et al., 2010), and the methods we describe in this paper can readily be applied to increase our understanding of how other characteristics should evolve. For example, mating strategy is anticipated to evolve such that Allee effects are reduced. In plants, we would expect selection to favour a decrease in self-incompatibility at an expanding front (Daehler, 1998). As models are developed to explore the evolution of a greater range of life history traits during range expansion, it is important that we not only determine the evolutionary stable strategy but consider how this strategy might be reached. It is also important that we increase our understanding of how range expansions might leave sometimes persistent spatial patterns of life histories in their wake. In some cases, it may be that we are looking for selective explanations for spatial variation in life histories when, in reality, the patterns may be generated by the genetic dynamics of range expansion (e.g. Excoffier et al., 2009). A major limitation to further improving our understanding, and ultimately predictive capability, of the evolution of life histories during range expansion is the paucity of information on the genetic architecture underlying life history traits. However, advances in quantitative genetics are beginning to reveal these details (e.g. Haag et al., 2005) and we should seek to develop models that can incorporate this additional complexity. The interplay between dispersal traits and mutation surfing has potentially consequences for another area that is gaining increased attention, the inference of dispersal characteristics from spatial genetic data. Both for plants (e.g. Austerlitz et al., 2004; Bittencourt & Sebbenn, 2007) and animals (e.g. Coulon et al., 2004; Keogh et al., 2007), genetic data have been used to make inferences about the nature of dispersal. There are at least two interesting issues in relation to the genetic dynamics of range expansion. First, the inferential power is likely to be reduced because of the surfing dynamic, at least if it is not accounted for in the modelling framework. Second, and more interestingly, is the question of whether it should be possible to infer past dispersal evolution from current patterns of spatial genetic variation. In recent work, Ray & Excoffier (2010) have made some initial progress using a Bayesian approach with spatial genetic data to infer the degree of long distance dispersal during past range expansion. With sufficiently high-quality genetic data, it may become possible to use similar methods to infer spatio-temporal changes in demographic parameters, which would offer enormous potential in terms of ultimately being able to parameterize and run models incorporating the life history evolution that we know is so important in many range expansions. Acknowledgements JMJT thanks both NERC and BiodivERsA for partially funding this work. OJB was supported by BBSRC funding. Three anonymous referees provided constructive comments that helped improve the manuscript. 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