mutation surfing and the evolution of dispersal during range expansions

Mutation surfing and the evolution of dispersal during rangeexpansions

J. M. J. TRAVIS*, T. MUNKEMULLER*� & O. J. BURTON*

*Zoology Building, Institute of Biological and Environmental Sciences, University of Aberdeen, Scotland, UK

�Laboratoire d’Ecologie Alpine, Universite J. Fourier, Grenoble, France

Introduction

There is a growing interest in the evolutionary dynamics

of populations that are expanding their ranges (see

reviews by Hanfling & Kollmann, 2002; Lambrinos,

2004; Hastings et al., 2005; Phillips et al., 2010). Studies

have demonstrated that a range of life history character-

istics can come under strong selection at an expanding

front (selfing-rates – Daehler, 1998; resistance to herbi-

vores – 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’

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

ª 2 0 1 0 T H E A U T H O R S . J . E V O L . B I O L . 2 3 ( 2 0 1 0 ) 2 6 5 6 – 2 6 6 7

2656 J O U R N A L C O M P I L A T I O N ª 2 0 1 0 E U R O P E A N S O C I E T Y F O R E V O L U T I O N A R Y B I O L O G Y

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.

doi:10.1111/j.1420-9101.2010.02123.x

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 expan-

sion 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 undergo-

ing 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 muta-

tion 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. How-

ever, 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 evolu-

tion 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 dis-

persal 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 popu-

lation 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; Leotard 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 addi-

tion 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, consid-

ering how the fate (including survival and surfing

probabilities) of a mutant depends upon the mutant’s

Mutation surfing and dispersal evolution 2657


J O U R N A L C O M P I L A T I O N ª 2 0 1 0 E U R O P E A N S O C I E T Y F O R E V O L U T I O N A R Y B I O L O G Y

dispersal propensity relative to the wild type and how

this varies according to key parameters including carry-

ing 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; Munkemuller 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 + aNt))b where a = (k1 ⁄ 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 proba-

bility 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 distribu-

tion 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 mutantsIn the first simulation experiment, we explore the

potential role of mutation surfing in driving the evolu-

tion 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 propen-

sity. 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 probabil-

ities 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 kand 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 suffi-

ciently 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

2658 J. M. J. TRAVIS ET AL.



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 muta-

tions 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 strin-

gent 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 allowedto evolveWe 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 initial-

ized individual were drawn randomly from those that

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 wild-

type 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 evolv-

ing 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




evolved in the static landscape (as described previously).

Thus, there was some initial variability in dispersal

within the introduced population. Also, in these simu-

lations, 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 simula-

tions, we record the success of the mutant in terms of

both its probability of survival and of surfing. Through-

out 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 indi-

viduals 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 repro-

ductive 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

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 popula-

tion 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 expand-

ing 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

0.0 0.2 0.4 0.6 0.8

0.0

0.2

0.4

0.6

0.8

Dispersal mortality

Evo

lved

dis

pers

al r

ate

Reproduction rate1.534.5

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.




differences between mutants whose dispersal propensity

is lower than the wild type compared to mutants whose

dispersal propensity is higher than the wild type.

Surviving mutants with lower dispersal propensity typ-

ically 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 allowedto evolve

For illustrative purposes, the fate of two neutral muta-

tions is shown in Fig. 6. In the first case, a novel

mutation initially increases in abundance before declin-

ing 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 dom-

inates 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-

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

Surv

ival

pro

babi

lity

C2,

C4,

C6

C3,

C5

C1

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

Surf

ing

prob

abili

ty

0.0 0.2 0.4 0.6 0.8 1.0

050

000

150

000

Spre

ad d

ista

nce

C2C4C6

C1C3C5

Dispersal rate, mutant

(a)

(b)

(c)

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 dis-

persal 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).

0 2000 4000 6000 8000 10 000

0.0

0.2

0.4

0.6

0.8

1.0

Time

Evo

lved

dis

pers

al r

ate

C2C4C6

C1C3C5

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).




ples shown here are both cases where the mutant

survives for a substantial period of time but we empha-

size 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 propen-

sity (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.

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6


Surv

ival

pro

babi

lity

(c)

(e)

(a)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6


(d)

(f)

(b)

50 100 200 300

0.0

0.2

0.4

0.6

0.8

1.0

Time

(c)

50 100 200 300

0.0

0.2

0.4

0.6

0.8

1.0

Time

Survival probabilitySurfing-somewhereSurfing-rightmost

(d)

50 100 200 300

0.0

0.2

0.4

0.6

0.8

1.0

Time

Fate

of

mut

ant

Fate

of

mut

ant

(e)

50 100 200 300

0.0

0.2

0.4

0.6

0.8

1.0

Time

(f)

Dispersal mortality = 0.6 Dispersal mortality = 0.1

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 simu-

lations 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).




Discussion

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 evolu-

tionary 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 poten-

tially 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

Den

sity

0 100 200 300 400 500

020

040

060

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MutantWild

Evo

lved

dis

pers

al r

ate

0 100 200 300 400 500

0.0

0.2

0.4

0.6

0.8(b)

Den

sity

0 100 200 300 400 500

020

040

060

0(c)

Evo

lved

dis

pers

al r

ate

0 100 200 300 400 500

0.0

0.2

0.4

0.6

0.8

x-direction

(d)

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.

Dispersal mortality

Evo

lved

dis

pers

al r

ate

0.0

0.2

0.4

0.6

0.8

0.1 0.6

WildMutant

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.




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 some-

where 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 pro-

pensity 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 viabil-

ity. 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 exam-

ple, 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

0 200 400 600 800 1000 1200

0.0

0.2

0.4

0.6

Surv

ival

pro

babi

lity

(a)

0 200 400 600 800 1000 1200

0.00

0.05

0.10

0.15

Surf

ing

prob

abili

ty

C2C4C6

C1C3C5

(b)

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.




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 empir-

ical (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 antici-

pated 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 strat-

egy 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 demo-

graphic parameters, which would offer enormous

potential in terms of ultimately being able to parameter-

ize 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 construc-

tive comments that helped improve the manuscript.

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Received 9 July 2010; revised 26 August 2010; accepted 1 September

2010




mutation surfing and the evolution of dispersal during range expansions

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