Mutation surfing and the evolution of dispersal during range expansions
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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
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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
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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
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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
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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.
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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).
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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
Dispersal rate, mutant
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
Dispersal rate, mutant
(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).
2662 J. M. J. TRAVIS ET AL.
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
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
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
0
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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.
Mutation surfing and dispersal evolution 2663
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
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
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.
2664 J. M. J. TRAVIS ET AL.
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
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
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.
References
Austerlitz, F., JungMuller, B., Godelle, B. & Gouyon, P.H. 1997.
Evolution of coalescence times, genetic diversity and structure
during colonization. Theor. Popul. Biol. 51: 148–164.
Austerlitz, F., Dick, C.W., Dutech, C., Klein, E.K., Oddou-
Muratorio, S., Smouse, P.E. & Sork, V.L. 2004. Using genetic
markers to estimate the pollen dispersal curve. Mol. Ecol. 13:
937–954.
Bach, L.A., Thomsen, R., Pertoldi, C. & Loeschcke, V. 2006. Kin
competition and the evolution of dispersal in an individual-
based model. Ecol. Modell. 192: 658–666.
Bach, L.A., Ripa, J. & Lundberg, P. 2007. On the evolution of
conditional dispersal under environmental and demographic
stochasticity. Evol. Ecol. Res. 9: 663–673.
Mutation surfing and dispersal evolution 2665
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
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
Belichon, S., Clobert, J. & Massot, M. 1996. Are there differences
in fitness components between philopatric and dispersing
individuals? Acta Oecologica – International Journal of Ecology 17:
503–517.
Biek, R., Henderson, J.C., Waller, L.A., Rupprecht, C.E. & Real,
L.A. 2007. A high-resolution genetic signature of demographic
and spatial expansion in epizootic rabies virus. Proc. Natl. Acad.
Sci. USA 104: 7993–7998.
Bittencourt, J.V.M. & Sebbenn, A.M. 2007. Patterns of pollen
and seed dispersal in a small, fragmented population of the
wind-pollinated tree Araucaria angustifolia in southern Brazil.
Heredity 99: 580–591.
Bowler, D.E. & Benton, T.G. 2005. Causes and consequences of
animal dispersal strategies: relating individual behaviour to
spatial dynamics. Biol. Rev. 80: 205–225.
Burton, O.J. & Travis, J.M.J. 2008a. The frequency of fitness
peak shifts is increased at expanding range margins because of
mutation surfing. Genetics 179: 941–950.
Burton, O.J. & Travis, J.M.J. 2008b. Landscape structure and
boundary effects determine the fate of mutations occurring
during range expansions. Heredity 101: 329–340.
Burton, O.J., Phillips, B.L. & Travis, J.M.J. 2010. Trade-offs and
the evolution of life-histories during range expansion. Ecol.
Lett. 13: 1210–1220.
Cadet, C., Ferriere, R., Metz, J.A.J. & van Baalen, M. 2003. The
evolution of dispersal under demographic stochasticity. Am.
Nat. 162: 427–441.
Coulon, A., Cosson, J.F., Angibault, J.M., Cargnelutti, B., Galan,
M., Morellet, N., Petit, E., Aulagnier, S. & Hewison, A.J.M.
2004. Landscape connectivity influences gene flow in a roe
deer population inhabiting a fragmented landscape: an indi-
vidual-based approach. Mol. Ecol. 13: 2841–2850.
Cwynar, L.C. & Macdonald, G.M. 1987. Geographical variation
of Lodgepole Pine in relation to population history. Am. Nat.
129: 463–469.
Daehler, C.C. 1998. Variation in self-fertility and the reproduc-
tive advantage of self-fertility for an invading plant (Spartina
alterniflora). Evol. Ecol. 12: 553–568.
Darling, E., Samis, K.E. & Eckert, C.G. 2008. Increased seed
dispersal potential towards geographic range limits in a Pacific
coast dune plant. New Phytol. 178: 424–435.
Edmonds, C.A., Lillie, A.S. & Cavalli-Sforza, L.L. 2004. Muta-
tions arising in the wave front of an expanding population.
Proc. Natl. Acad. Sci. USA 101: 975–979.
Excoffier, L. & Ray, N. 2008. Surfing during population expan-
sions promotes genetic revolutions and structuration. Trends
Ecol. Evol. 23: 347–351.
Excoffier, L., Foll, M. & Petit, R.J. 2009. Genetic consequences
of range expansions. Annu. Rev. Ecol. Evol. Syst. 40: 481–
501.
Gandon, S. 1999. Kin competition, the cost of inbreeding and
the evolution of dispersal. J. Theor. Biol. 200: 345–364.
Garcia-Rossi, D., Rank, N. & Strong, D.R. 2003. Potential for self-
defeating biological control? Variation in herbivore vulnera-
bility among invasive Spartina genotypes. Ecol. Appl. 13: 1640–
1649.
Haag, C.R., Saastamoinen, M., Marden, J.H. & Hanski, I. 2005. A
candidate locus for variation in dispersal rate in a butterfly
metapopulation. Proc. R. Soc. Lond. B Biol. Sci. 272: 2449–
2456.
Hallatschek, O. & Nelson, D.R. 2008. Gene surfing in expanding
populations. Theor. Popul. Biol. 73: 158–170.
Hallatschek, O., Hersen, P., Ramanathan, S. & Nelson, D.R.
2007. Genetic drift at expanding frontiers promotes gene
segregation. Proc. Natl. Acad. Sci. USA 104: 19926–19930.
Hanfling, B. & Kollmann, J. 2002. An evolutionary perspective
of biological invasions. Trends Ecol. Evol. 17: 545–546.
Hassell, M.P. & Comins, H.N. 1976. Discrete-time models for
2-species competition. Theor. Popul. Biol. 9: 202–221.
Hastings, A., Cuddington, K., Davies, K.F., Dugaw, C.J., Elmen-
dorf, S., Freestone, A., Harrison, S., Holland, M., Lambrinos,
J., Malvadkar, U., Melbourne, B.A., Moore, K., Taylor, C. &
Thomson, D. 2005. The spatial spread of invasions: new
developments in theory and evidence. Ecol. Lett. 8: 91–101.
Hovestadt, T., Messner, S. & Poethke, H.J. 2001. Evolution of
reduced dispersal mortality and ‘fat-tailed’ dispersal kernels in
autocorrelated landscapes. Proc. R. Soc. Lond. B Biol. Sci. 268:
385–391.
Hughes, C.L., Hill, J.K. & Dytham, C. 2003. Evolutionary trade-
offs between reproduction and dispersal in populations at
expanding range boundaries. Proc. R. Soc. Lond. B Biol. Sci. 270:
S147–S150.
Keogh, J.S., Webb, J.K. & Shine, R. 2007. Spatial genetic
analysis and long-term mark-recapture data demonstrate
male-biased dispersal in a snake. Biol. Lett. 3: 33–35.
Klopfstein, S., Currat, M. & Excoffier, L. 2006. The fate of
mutations surfing on the wave of a range expansion. Mol. Biol.
Evol. 23: 482–490.
Lambrinos, J.G. 2004. How interactions between ecology and
evolution influence contemporary invasion dynamics. Ecology
85: 2061–2070.
Leotard, G., Debout, G., Dalecky, A., Guillot, S., Gaume, L.,
McKey, D. & Kjellberg, F. 2009. Range expansion drives
dispersal evolution in an equatorial three-species symbiosis.
PLoS ONE 4: e5377.
McPeek, M.A. & Holt, R.D. 1992. The evolution of dispersal in
spatially and temporally varying environments. Am. Nat. 140:
1010–1027.
Metz, J.A.J. & Gyllenberg, M. 2001. How should we define
fitness in structured metapopulation models? Including an
application to the calculation of evolutionarily stable dispersal
strategies. Proc. R. Soc. Lond. B Biol. Sci. 268: 499–508.
Miller, J.R. 2010. Survivial of mutations arising during inva-
sions. Evol. Appl. 3: 109–121.
Munkemuller, T., Travis, J.M.J., Burton, O.J., Schiffers, K. &
Johst, K. in press. Density regulated population dynamics and
conditional dispersal alter the fate of mutations occurring at
the front of an expanding population. Heredity, doi: 10.1038/
hdy.2010.107.
Olivieri, I., Michalakis, Y. & Gouyon, P.H. 1995. Metapopulation
genetics and the evolution of dispersal. Am. Nat. 146: 202–228.
Parvinen, K., Dieckmann, U., Gyllenberg, M. & Metz, J.A.J.
2003. Evolution of dispersal in metapopulations with local
density dependence and demographic stochasticity. J. Evol.
Biol. 16: 143–153.
Perrin, N. & Goudet, J. 2001. Inbreeding, kinship, and the
evolution of natals dispersal. In: Dispersal (J. Clobert, E.
Danchin, A.A. Dhondt & J.D. Nichols, eds), pp. 123–142.
Oxford University Press, Oxford.
Perrin, N. & Mazalov, V. 1999. Dispersal and inbreeding
avoidance. Am. Nat. 154: 282–292.
Phillips, B.L., Brown, G.P., Webb, J.K. & Shine, R. 2006.
Invasion and the evolution of speed in toads. Nature 439: 803–
803.
2666 J. M. J. TRAVIS ET AL.
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
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
Phillips, B.L., Brown, G.P., Travis, J.M.J. & Shine, R. 2008.
Reid’s paradox revisited: the evolution of dispersal kernels
during range expansion. Am. Nat. 172: S34–S48.
Phillips, B.L., Brown, G.P. & Shine, R. 2010. Life-history
evolution in range-shifting populations. Ecology 91: 1617–
1627.
Poethke, H.J., Hovestadt, T. & Mitesser, O. 2003. Local extinc-
tion and the evolution of dispersal rates: causes and correla-
tions. Am. Nat. 161: 631–640.
Ray, C. & Excoffier, L. 2010. A first step toward inferring levels
of long distance dispersal during past expansions. Mol. Ecol.
Resour. 10: 902–914.
Ronce, O. 2007. How does it feel to be like a rolling stone? Ten
questions about dispersal evolution. Annu. Rev. Ecol. Evol. Syst.
38: 231–253.
Ronce, O., Gandon, S. & Rousset, F. 2000. Kin selection and
natal dispersal in an age-structured population. Theor. Popul.
Biol. 58: 143–159.
Simmons, A.D. & Thomas, C.D. 2004. Changes in dispersal
during species’ range expansions. Am. Nat. 164: 378–395.
Stobutzki, I.C. 1997. Energetic cost of sustained swimming in the
late pelagic stages of reef fishes. Mar. Ecol. Prog. Ser. 152: 249–
259.
Thomas, C.D., Bodsworth, E.J., Wilson, R.J., Simmons, A.D.,
Davies, Z.G., Musche, M. & Conradt, L. 2001. Ecological and
evolutionary processes at expanding range margins. Nature
411: 577–581.
Travis, J.M.J. 2001. The color of noise and the evolution of
dispersal. Ecol. Res. 16: 157–163.
Travis, J.M.J. & Dytham, C. 1998. The evolution of dispersal in a
metapopulation: a spatially explicit, individual-based model.
Proc. R. Soc. Lond. B Biol. Sci. 265: 17–23.
Travis, J.M.J. & Dytham, C. 2002. Dispersal evolution during
invasions. Evol. Ecol. Res. 4: 1119–1129.
Travis, J.M.J., Munkemuller, T., Burton, O.J., Best, A., Dytham,
C. & Johst, K. 2007. Deleterious mutations can surf to high
densities on the wave front of an expanding population. Mol.
Biol. Evol. 24: 2334–2343.
Travis, J.M.J., Mustin, K., Benton, T.G. & Dytham, C. 2009.
Accelerating invasion rates result from the evolution of
density-dependent dispersal. J. Theor. Biol. 259: 151–158.
Travis, J.M.J., Smith, H.S. & Ranwala, S.M.W. 2010. Towards a
mechanistic understanding of dispersal evolution in plants:
conservation implications. Divers. Distrib. 16: 690–702.
Yoder, J.M., Marschall, E.A. & Swanson, D.A. 2004. The cost of
dispersal: predation as a function of movement and site
familiarity in ruffed grouse. Behav. Ecol. 15: 469–476.
Zera, A.J. & Mole, S. 1994. The physiological costs of flight
capability in wing-dimorphic crickets. Res. Popul. Ecol. 36: 151–
156.
Received 9 July 2010; revised 26 August 2010; accepted 1 September
2010
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