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Colour polymorphism torn apart by opposing positive
frequency-dependent selection, yet maintained in
space
Swanne P. Gordon
1
*, Hanna Kokko
2
, Bibiana Rojas
1
, Ossi Nokelainen
1,3
and
Johanna Mappes
1
1
Centre of Excellence in Biological Interactions, Department of Biological and Environmental Sciences, University of
Jyv€
askyl€
a, yv€
askyl€
a, Finland;
2
Institute of Evolutionary Biology and Environmental Studies, University of Zurich,
Zurich, Switzerland; and
3
Department of Zoology, University of Cambridge, Cambridge, UK
Summary
1. Polymorphic warning signals in aposematic species are enigmatic because predator learning
and discrimination should select for the most common coloration, resulting in positive fre-
quency-dependent survival selection.
2. Here, we investigated whether differential mating success could create sufficiently strong
negative frequency-dependent selection for rare morphs to explain polymorphic (white and
yellow) warning coloration in male wood tiger moths (Parasemia plantaginis).
3. We conducted an experiment in semi-natural conditions where we estimated mating success
for both white and yellow male moths under three different morph frequencies.
4. Contrary to expectations, mating success was positively frequency-dependent: white morph
males had high relative fitness when common, likewise yellow morph males had high relative
fitness when instead they were common. We hence built a model parameterized with our data
to examine whether polymorphism can be maintained despite two sources of positive fre-
quency dependence. The model includes known spatial variation in the survival advantage
enjoyed by the yellow morph and assumes that relative mating success follows our experimen-
tally derived values. It predicts that polymorphism is possible under migration for up to
approximately 20% exchange of individuals between subpopulations in each generation.
5. Our results suggest that differential mating success combined with spatial variation in
predator communities may operate as a selection mosaic that prevents complete fixation of
either morph.
Key-words: aposematism, coloration, mating success, modelling, predation, sexual selection,
spatial mosaic
Introduction
A fundamental question in evolutionary biology is what
processes drive the origin and maintenance of genetic
polymorphisms in the wild. Polymorphisms indicate the
potential for unusual types of selection because they devi-
ate from simpler cases where one genotype has a consis-
tent advantage over another and natural selection drives
the winning type to fixation (Calsbeek, Bonvini & Cox
2010). If a genotype’s relative fitness improves with its rel-
ative frequency (positive frequency dependence), polymor-
phisms typically cannot be explained: here selection acts
against rare alleles, and the population is consequently
expected to evolve towards one of alternative stable states
but not towards a stable polymorphism (Mallet & Joron
1999; Lehtonen & Kokko 2012). Negative frequency
dependence on the other hand has the opposite effect: a
genotype is selected against when common and selected
for when rare, making it easier to maintain polymor-
phisms (Sinervo & Lively 1996). Gene flow, that links
populations undergoing spatially heterogeneous selection,
can also make alternative morphs persist within an envi-
ronment: in this case, a locally suboptimally performing
morph can avoid extinction because of continual immigra-
tion from elsewhere, where it is selected for (divergent
selection, Gray & McKinnon 2007).
*Correspondence author. E-mail: swanne.gordon@jyu.fi
©2015 The Authors. Journal of Animal Ecology ©2015 British Ecological Society
Journal of Animal Ecology 2015 doi: 10.1111/1365-2656.12416
Being easily measured and tracked, animal colours rep-
resent some of the best-studied examples of trait polymor-
phisms (McKinnon & Pierotti 2010). Colours are often
strongly linked to fitness in many different contexts such
as crypsis (Steward 1977; Rothschild 1981; Endler &
Greenwood 1988) and thermoregulation (Clusella-Trullas,
Van Wyk & Spotila 2007; Hegna et al. 2013). Colour is
also often used a warning signal of unprofitability (Poul-
ton 1890; Cott 1940; Stevens & Ruxton 2012), and in this
context, theoretical expectations (Servedio 2000; Endler &
Mappes 2004) as well as empirical studies (review, Allen
1988; Mallet & Barton 1989; Borer et al. 2010) point to
positive frequency-dependent survival selection. It is easier
for predators to learn to discriminate against signals that
are not only highly recognizable and memorable, but also
common (‘strength in numbers’); this selects against poly-
morphism (Mu
¨ller 1878; Mallet & Joron 1999; Lindstr€
om
et al. 2001; Rowland et al. 2007). This renders it enig-
matic why numerous polymorphic aposematic colour sig-
nals from a range of taxa are known in nature (e.g.
O’Donald & Majerus 1984; Nokelainen et al. 2012; Rojas
& Endler 2013).
Recent research has investigated the effect of various
processes that can maintain polymorphisms and hence
also impact prey fitness. In many cases, these mechanisms
are not mutually exclusive and instead work in concert to
achieve polymorphisms (S
anchez-Guill
en et al. 2011).
These range from spatio-temporal variation in predation
(Endler & Rojas 2009; Stevens & Ruxton 2012; Noke-
lainen et al. 2014) or sexual selection (Maan & Cummings
2009; Nokelainen et al. 2012) to frequency-dependent
selection (Svensson, Abbott & Hardling 2005; Olendorf
et al. 2006). Gene flow (Rosenblum 2006) and genetic
drift (Hoffman et al. 2006; Gray & McKinnon 2007) add
to the mix of effects that can impact the stability of
polymorphisms.
Research on colour polymorphisms in aposematic spe-
cies has focused on the role of predator learning and
signal evolution, due to the strong selection exerted by
the high cost of conspicuousness when predators are naive
(Lindstr€
om et al. 2001; Mappes et al. 2014). Here, we
show that full understanding into the maintenance of
warning colour polymorphisms may require considering
multiple forces and their interaction. Our particular inter-
est lies in understanding potential trade-offs between nat-
ural and sexual selection (Kotiaho et al. 1998; Maan &
Cummings 2009; Nokelainen et al. 2012; Cummings &
Crothers 2013; Finkbeiner, Briscoe & Reed 2014) and in
the arguably understudied interaction of frequency-depen-
dent selection and gene flow (Joron & Iwasa 2005; Cals-
beek, Bonvini & Cox 2010).
Colour in aposematic organisms may serve multiple
functions: thermoregulation, defence against predators
and mate attraction. This highlights the possibility that
both natural and sexual selection can be frequency-de-
pendent (Gray & McKinnon 2007; Sinervo & Calsbeek
2006; Roulin & Bize 2007), and it is known from gen-
eral theory that when different types of frequency
dependence interact, the diversity of dynamic outcomes
can be far greater than predicted under one source of
selection only (Sinervo & Calsbeek 2006). Here, we com-
bine information from a mating experiment with pub-
lished estimates of survival selection in order to examine
their interaction and the potential role of frequency-de-
pendent selection on the maintenance of colour poly-
morphism in an aposematic organism. The results aim
to confirm an idea previously expressed by Roulin &
Bize (2007): it is difficult to explain polymorphisms if
the common morph derives a mating advantage, but in
a spatially structured population, some degree of gene
flow could potentially counteract the predicted loss of
genetic variation. Interestingly, a modelling study of a
particular colour polymorphism –Mu
¨llerian mimicry –
shows that too high gene flow can again break down a
polymorphism, because the system then effectively
behaves like one unit with averaged parameter values
(Joron & Iwasa 2005). We therefore also include a mod-
elling component to investigate the range of dispersal
values that could protect a polymorphism in a system
where natural and sexual selection interact and also vary
spatially.
Our study species is the aposematic wood tiger moth
(Parasemia plantaginis). Males of this species exhibit dis-
crete wing coloration on both local and on a broad geo-
graphical scale (Hegna, Galarza & Mappes 2015).
European populations feature two distinct genetic male
morphs, yellow and white (Galarza et al. 2014). In Fin-
nish populations, the more conspicuous yellow male
morph has been shown to have greater warning signal
efficacy, such that viability selection mediated by preda-
tion favours this morph (Nokelainen et al. 2012, 2014).
White adult males, on the other hand, sometimes appear
to have better mating success than yellow males, espe-
cially in instances where mating incurs high costs (Noke-
lainen et al. 2012). However, mating success has so far
only been evaluated in a context of equal frequency of
both morphs, and under small laboratory conditions as
opposed to more natural settings. To test for the effects
of potential frequency dependence in the context of sex-
ual selection, we conducted an experiment in semi-natu-
ral conditions where we estimated mating success under
three different morph frequencies. We next integrate our
data from this experiment with known estimates of pre-
dation against both morphs in a simple spatial model.
The combination of both mating experiment and model
is based on the suggested trade-off between natural and
sexual selection described above driving the evolution
and maintenance of colour polymorphism in our system.
This trade-off is particularly interesting and unexplored
in a case where both natural and sexual selection are
potentially frequency-dependent in aposematic organisms,
as never before has variation in frequency dependence
across fitness components been considered in this con-
text.
©2015 The Authors. Journal of Animal Ecology ©2015 British Ecological Society, Journal of Animal Ecology
2S. P. Gordon et al.
Materials and methods
study system
The wood tiger moth system (Parasemia plantaginis) is well stud-
ied in terms of the evolution of warning signals (e.g. Ojala, Lind-
str€
om & Mappes 2007; Lindstedt, Lindstr€
om & Mappes 2009;
Lindstedt et al. 2010; Nokelainen et al. 2012, 2014; Nokelainen,
Lindstedt & Mappes 2013). Wood tiger moths are easy to rear
and maintain in a laboratory setting and can be collected and
manipulated with relative ease in semi-wild or wild conditions.
They overwinter as larvae in the wild and naturally go through
one generation a year per life cycle. Adult wood tiger moths are
capital breeders and hence do not feed (but drink) during adult-
hood. Although laboratory-reared female–male ratio at eclosion
is very close to the 50 : 50 ratio, in the field the operational sex-
ratio is much more male biased (Gordon et al. In prep.). This is
likely based on the fact that females in the laboratory live on
average only a few days, whereas males can live up to two weeks
(Santostefano & Mappes, In prep.), which likely reflect their life
span differences in wild. Adult females are also conspicuous,
avoided by bird predators, and, unlike the discrete coloration in
males, exhibit a continuous range of wing coloration from yellow
to orange and to red (Lindstedt et al. 2011). Like most moths,
mature female moths emit a sexual pheromone call to attract
males. Once fertilized, wood tiger moth females can lay approxi-
mately 300 eggs in one clutch (Ojala, Lindstr€
om & Mappes
2007). Females appear choosy, as males attempting to mate can
be rejected if not preferred by females (pers. obs.). All wood tiger
moths used in the enclosure experiment (see below) were labora-
tory-raised from stock collected from wild moths caught in Fin-
land in 2010 and reared under greenhouse conditions at the
University of Jyv€
askyl€
a for multiple generations (for more details
on laboratory rearing see Lindstedt, Lindstr€
om & Mappes 2008).
enclosure experiment
In order to examine the effect of frequency-dependent selection
on mating in wood tiger moths, we ran a large-scale outdoor
enclosure experiment in Konnevesi research station of the
University of Jyv€
askyl€
a (Finland), from 4 July 2012 until 24 July
2012. A 20 m 930 m (3 m high) enclosure was divided into six
separate cage compartments, approximately 6 m 910 m each.
The floor of each compartment was open with natural foliage,
and the top and two of the sides were made of white mesh, open
to natural light. The other two sides were covered with a plastic
green tarp to block visual contact between the cages and to limit
the spread of mating pheromones exuded by the calling females.
We performed 10 individual runs, each involving three treat-
ments: a balanced morph ratio (12 white males and 12 yellow
males); a white-biased treatment (16 white males and eight yellow
males); and a yellow-biased treatment (16 yellow males and eight
white males). Every male and female used in the entire experi-
ment was individually marked using a paint dot on the underside
of both the top and bottom portion of the fore and hind wing.
Each run used 24 virgin males and five virgin females per treat-
ment (in order to closely mimic natural male-biased sex ratios in
the wild), totalling 72 males and 15 females per run. Treatments
within each run were randomly assigned to three of the six
compartments, and all males and females used in each run were
randomly assigned to their treatment. However, to achieve the
desired sample sizes, some unmated males had to be re-used in
the next subsequent run. To see whether this logistical constraint
had an effect, we analysed the mating success of each male cate-
gorized as na
€
ıve vs. re-used; we found no effect (for white male
morphs: effect =0294 0436, z=674, P=0500; and for
yellow morph: effect =0018 0460, z=0038, P=0970). In
total, we used 720 male measurements of which 590 involved
na
€
ıve males and 130 were re-used.
The five females were tethered to a string in an open Styrofoam
box (one female per box), which allowed them to move and fly
but not escape the box. Behavioural assessments of the females
prior to and during the experiment did not reveal any changes in
behaviours that would limit them from escaping harassment from
males if they so chose (Rojas et al. In prep.), and tethering them
allowed us the opportunity to count all their eggs reliably. If free
female choice was, however, impacted negatively by tethering, this
impact should be spread equally across all three treatments.
The boxes, that offered protection from the wind and rain,
were placed at equidistant points around the corners of every
cage. Females were allowed to acclimatize for approximately one
hour. Given past information on ideal mating times in these
moths (S. Gordon pers. obs.), males were then released in the
middle of each cage at approximately 4:00 pm. All moths were
collected again at 8:00 am the next morning. The time window
hence includes the time when matings naturally occur in this spe-
cies (Nokelainen et al. 2012). Cages were watched from the
beginning to the end of each run by one observer in each cage.
Data about general hourly weather conditions, moth behaviours
and the ID’s of mated pairs upon the onset of mating were col-
lected by observers. Because females may mate multiply, the total
number of matings was not fixed. Males, however, were only
found to mate maximally once, with a few exceptions: there were
two double matings involving each one Y and one W male mated
to same female, and one mating of the same white male to two
females. As males were individually marked and identified after
the onset of every mating, we could confidently assign paternity
to all matings (except for the doubly mated pair, where we were
able to assign paternity to the most likely father based on the col-
oration of the adult offspring for the basis of analyses). At the
end of each experimental run, all mated females were brought to
the greenhouse at the University of Jyv€
askyl€
a and their egg num-
ber and hatching success were measured.
statistical analyses
Male age and size
As females may choose males based on differences in age and
size, we first calculated the spread of male characteristics across
treatments to assess any bias the assignment of individuals into
treatments may have produced. We used pupal weight as a good
proxy for adult weight (as adults do not eat). We ran an ANOVA
with age (days since pupation) and pupa weight as response vari-
ables and treatment by morph interaction as explanatory factors
(using function ‘aov’ in Program Rv215, 2013).
Mating success
We measured the mating success of the W and the Y morph
using generalized linear mixed effect models, first combined, and
then separately (one for each morph). In each model, the number
©2015 The Authors. Journal of Animal Ecology ©2015 British Ecological Society, Journal of Animal Ecology
Positive frequency dependence and polymorphism 3
of matings in each cage was the response variable (binomial vari-
able where 1 is mated and 0 means not mated in all cases). Pupa
weight, male age and treatment (and their interaction) were the
explanatory variables. We included enclosure cage as a random
effect to account for the non-independence of matings within
each enclosure.
Fitness
The relative fitness of individual males (estimated morph siring
success) was calculated as simply a measure of the proportion of
larval recruits (out of the total number of enclosure recruits) that
were sired by each male (i.e. proportional to its contribution to the
next generation) relative to the total number of males in the focal
enclosure. It was obtained by dividing the number of hatched lar-
vae sired by a given male by the total number of hatched larvae in
each enclosure. This led to every male in each of the 30 unique
enclosures having a measure of relative fitness. We then again ran
a binomial generalized linear mixed effect model (morphs were not
also separated as above because here there were no significant
three-way interactions) where fitness was the response variable.
Morph frequency (treatment), morph and their interaction were
the explanatory variables, age and pupa weight were added covari-
ates, and enclosure compartment was a random effect.
Results
effect of male age and sizes
Yellow males used in the experiment tended to be
younger than white males (ANOVA F
1,701
=14610,
P<0001), yet this effect was not different between treat-
ments (F
2, 701
=0223, P=0800). The same pattern was
found for pupal weight, which was smaller for yellow
males (ANOVA F
1,706
=9367, P=0002), yet equally so for
all treatments (F
2,706
=0273, P=0761). Due to this,
both male age and pupa weight were included as covari-
ates in all analyses.
mating success
The model for mating success of white male moths
showed a significant positive effect of weight (model effect
size =0016 0006, z=2722, P=0006) but none of
age (effect size =0011 0044, z=0242, P=0809) or
treatment (P>07867). The model for the mating success
of yellow males likewise showed a significant effect of
weight (effect size =00323 0011, z=0011, P=
0002), treatment (driven by this morph’s significantly
lower mating success in the white-biased treatment, see
below; effect size =6404 3181, z=2013, P=0044)
and a significant interaction between weight and
treatment: yellow males had lower mating success in the
white-biased treatment (no difference in the yellow-biased
treatment), with large males suffering more from this
effect (effect size =0038 0017, z=2191,
P=0028). Age was also an insignificant covariate in the
model for mating success of yellow males (effect
size =0040 0050, z=0803, P=0422).
We should note that the model combining both morphs
model showed comparable results for age and size, but
had no overall effect of morph (effect size of White
morph vs. Yellow morph =4640 2692, z =1728,
P=0085). The only significant interactions were a white-
biased treatment by morph interaction (model effect
size =8886 3995, z =2224, P=0026); that is, the
yellow morph had significantly lower mating success in
the white-biased treatment, driven mainly by larger males
doing worse in this regard (significant weight by white-bi-
ased treatment by yellow morph interaction: effect
size =0052 0022, z=2403, P=00163).More
importantly, however, a Type III Chi-square ANOVA shows
an overall significant effect of the three-way interaction
between morph, weight and treatment (Chi-sq =585,
P=005), implying that morphs responded differently to
all aspects we were evaluating (treatment and weight).
Therefore, for greater clarity, we will only focus on the
separated morph model results in the discussion.
fitness
Fitness, which consider the mating success as well as
the ultimate offspring sired hatching success, show that
the yellow male morph have significantly lower fitness in
the white-biased treatment compared to the other treat-
ments (Fig. 1). This result is opposite for the white male
morph. Analyses found no significant differences between
treatments (t=1318, P=0188), but a significant treat-
ment 9morph interaction (t=2214, P=0027). Age
was again insignificant in the model (t=0206,
P=0837), whereas weight was significant (t=3195,
P=0002).
In order to better examine whether the differences
between morphs in both high-frequency treatments were
significant, we ran a similar model but excluded the bal-
anced ratio treatment. Results show that in the white-bi-
ased treatment, yellow males have marginally lower fitness
compared to white males (1408 0792, t=1777,
P=0076), while this pattern was reversed in the yellow-
biased treatment (2292 0998, t=2295, P=0022).
modelling the consequences
Our results surprisingly indicate positively frequency-de-
pendent mating success: males of the white morph had
high relative fitness when common, likewise yellow males
had high relative fitness when they formed the majority of
the males (Fig. 2). As both natural and sexual selection
therefore appear positively frequency-dependent, the most
straightforward theoretical prediction is that a population
should evolve towards one of two possible alternative
equilibria (Lehtonen & Kokko 2012): either white only or
yellow only. The existence of large geographic areas with
polymorphisms therefore led us to consider the role of
spatially varying selection, for which there is evidence
based on variation in bird communities (Nokelainen et al.
©2015 The Authors. Journal of Animal Ecology ©2015 British Ecological Society, Journal of Animal Ecology
4S. P. Gordon et al.
of matings in each cage was the response variable (binomial vari-
able where 1 is mated and 0 means not mated in all cases). Pupa
weight, male age and treatment (and their interaction) were the
explanatory variables. We included enclosure cage as a random
effect to account for the non-independence of matings within
each enclosure.
Fitness
The relative fitness of individual males (estimated morph siring
success) was calculated as simply a measure of the proportion of
larval recruits (out of the total number of enclosure recruits) that
were sired by each male (i.e. proportional to its contribution to the
next generation) relative to the total number of males in the focal
enclosure. It was obtained by dividing the number of hatched lar-
vae sired by a given male by the total number of hatched larvae in
each enclosure. This led to every male in each of the 30 unique
enclosures having a measure of relative fitness. We then again ran
a binomial generalized linear mixed effect model (morphs were not
also separated as above because here there were no significant
three-way interactions) where fitness was the response variable.
Morph frequency (treatment), morph and their interaction were
the explanatory variables, age and pupa weight were added covari-
ates, and enclosure compartment was a random effect.
Results
effect of male age and sizes
Yellow males used in the experiment tended to be
younger than white males (ANOVA F
1,701
=14610,
P<0001), yet this effect was not different between treat-
ments (F
2, 701
=0223, P=0800). The same pattern was
found for pupal weight, which was smaller for yellow
males (ANOVA F
1,706
=9367, P=0002), yet equally so for
all treatments (F
2,706
=0273, P=0761). Due to this,
both male age and pupa weight were included as covari-
ates in all analyses.
mating success
The model for mating success of white male moths
showed a significant positive effect of weight (model effect
size =0016 0006, z=2722, P=0006) but none of
age (effect size =0011 0044, z=0242, P=0809) or
treatment (P>07867). The model for the mating success
of yellow males likewise showed a significant effect of
weight (effect size =00323 0011, z=0011, P=
0002), treatment (driven by this morph’s significantly
lower mating success in the white-biased treatment, see
below; effect size =6404 3181, z=2013, P=0044)
and a significant interaction between weight and
treatment: yellow males had lower mating success in the
white-biased treatment (no difference in the yellow-biased
treatment), with large males suffering more from this
effect (effect size =0038 0017, z=2191,
P=0028). Age was also an insignificant covariate in the
model for mating success of yellow males (effect
size =0040 0050, z=0803, P=0422).
We should note that the model combining both morphs
model showed comparable results for age and size, but
had no overall effect of morph (effect size of White
morph vs. Yellow morph =4640 2692, z =1728,
P=0085). The only significant interactions were a white-
biased treatment by morph interaction (model effect
size =8886 3995, z =2224, P=0026); that is, the
yellow morph had significantly lower mating success in
the white-biased treatment, driven mainly by larger males
doing worse in this regard (significant weight by white-bi-
ased treatment by yellow morph interaction: effect
size =0052 0022, z=2403, P=00163).More
importantly, however, a Type III Chi-square ANOVA shows
an overall significant effect of the three-way interaction
between morph, weight and treatment (Chi-sq =585,
P=005), implying that morphs responded differently to
all aspects we were evaluating (treatment and weight).
Therefore, for greater clarity, we will only focus on the
separated morph model results in the discussion.
fitness
Fitness, which consider the mating success as well as
the ultimate offspring sired hatching success, show that
the yellow male morph have significantly lower fitness in
the white-biased treatment compared to the other treat-
ments (Fig. 1). This result is opposite for the white male
morph. Analyses found no significant differences between
treatments (t=1318, P=0188), but a significant treat-
ment 9morph interaction (t=2214, P=0027). Age
was again insignificant in the model (t=0206,
P=0837), whereas weight was significant (t=3195,
P=0002).
In order to better examine whether the differences
between morphs in both high-frequency treatments were
significant, we ran a similar model but excluded the bal-
anced ratio treatment. Results show that in the white-bi-
ased treatment, yellow males have marginally lower fitness
compared to white males (1408 0792, t=1777,
P=0076), while this pattern was reversed in the yellow-
biased treatment (2292 0998, t=2295, P=0022).
modelling the consequences
Our results surprisingly indicate positively frequency-de-
pendent mating success: males of the white morph had
high relative fitness when common, likewise yellow males
had high relative fitness when they formed the majority of
the males (Fig. 2). As both natural and sexual selection
therefore appear positively frequency-dependent, the most
straightforward theoretical prediction is that a population
should evolve towards one of two possible alternative
equilibria (Lehtonen & Kokko 2012): either white only or
yellow only. The existence of large geographic areas with
polymorphisms therefore led us to consider the role of
spatially varying selection, for which there is evidence
based on variation in bird communities (Nokelainen et al.
©2015 The Authors. Journal of Animal Ecology ©2015 British Ecological Society, Journal of Animal Ecology
4S. P. Gordon et al.
flectance) have been found to actually attract attacks by
these predators (Lyytinen et al. 2001; Lyytinen, Lind-
str€
om & Mappes 2004). On the other hand, dunnocks
(Prunellidae) tend to avoid white male moths and gener-
ally forage closer to the ground level in shaded boreal for-
ests. White coloration might be a more effective warning
signal in these circumstances because they have much
higher luminance values compared to the yellow morph
(Galarza et al. 2014).
model using both predation and mating
results
We consequently built our model assuming that the 60
sites sampled above represent the range of naturally
occurring spatial variation in morph-specific viabilities, as
estimated in Nokelainen et al. 2014. We considered a
world consisting of 60 patches, each producing 50 off-
spring in each generation. We only tracked the dynamics
of males, that is we assume that male offspring morph
frequencies are proportional to the frequency with which
males of each morph become sires (this only requires
assuming that inheritance via females does not bias pat-
terns of inheritance in either direction).
Given that differential predation based on wing colour
occurs during the adult time period, morph ratios are not
necessarily constant and the model needs to track morph
frequencies at the time when siring occurs. Having no pre-
cise information of this time dependency, we use the fol-
lowing logic to simulate the most likely pattern. Denote
by b
i
the survival advantage of the yellow morph in a cur-
rent patch i(e.g. if site 13 has b
13
=121 then in this site
a yellow individual’s daily risk of dying is 1/1121, that is
a fraction 089 of that of a white individual). Conse-
quently, if a local population starts with w
0
whites and y
0
yellows (the subscript 0 denoting that no male has had
the time to die yet), the probability that the next death
targets a yellow male is (y
0
/b)/[(y
0
/b)+w
0
], and the comple-
mentary probability that the next removed male is white
is w
0
/[(y
0
/b)+w
0
]. Thus, if a uniformly distributed random
number in the range [0,1] falls below (y
0
/b)/[(y
0
/b)+w
0
], we
subtract one individual from the local y(thus y
1
=y
0
–1,
w
1
=w
0
), and otherwise from the local w(thus y
1
=y
0
,
and w
1
=w
0
–1). We repeat this procedure until no males
of either morph are alive.
We then assume that females largely mate when mates
are numerous (i.e. mostly when the season is not nearly
over yet) and choose the mating time index of each female
by rounding down a random number that is exponentially
distributed with mean (y
0
+w
0
)/10. This result, denoted t,
describes that a female mates at a point in time when t
males have died and y
t
and w
t
are consequently still avail-
able for matings. The female mating time is thus designed
to follow mate availability, and the factor 10 was set to
make the proportion of females that attempt to mate when
no males are alive negligibly low (for y
0
+w
0
50 which
according to our assumptions is the approximate size of
local populations, this probability –i.e. the probability
that the exponential distribution with mean (y
0
+w
0
)/10
produces a value that exceeds y
0
+w
0
, the number of deaths
it takes for all males to have died –is approximately
045 910
5
). We assume that these exceedingly rare late
females in reality mate with the last available male, while
noting that our results remain virtually unchanged if we
instead assume that they completely fail to mate, as the
siring success this late in the season contributes minimally
to the mating success of either of the male morphs.
Populations were initiated such that 250 yellow and 250
white males were distributed randomly across the 60
patches, to yield initial patch-specific y
0
and w
0
values.
The above procedure was then used within each subpopu-
lation to determine siring times for 50 surviving offspring
per patch (for those patches that had at least one male;
we thus implicitly evoke density dependence: each occu-
pied patch is equally productive). We equate survival with
maturation.
The morph identity of each of the 50 sires was deter-
mined based on y
t
and w
t
at the siring time t, such that
Prob foffspring is yellowg¼ x
xþ1xðÞeaxþb:
Here, x=y
t
/(y
t
+w
t
) is the proportion of yellows in the
current population of potential sires. The parameters a
and bdefine the relative mating success advantage of
whites, determined by a least-squares regression of log
(mean eggs sired by white
mean eggs sired by yellow), values taken from the empirical part
of this paper against the treatment xvalues (x=1/3, 1/2
and 2/3) used in the experiments. Because a few females
mated once with a yellow and once with a white male, we
computed three different values for aand b, to cover the
entire range of uncertainty caused by this behaviour: (i)
the first regression assumed that these females all con-
tributed only to their white mate’s success, (ii) the second
assumed that these females all contributed only to their
yellow mate’s success, and (iii) the third assumed that
these females had half their eggs sired by the white mate,
and half by the yellow mate.
This procedure of determining offspring morph was
repeated across all patches. We then assumed that a pro-
portion dof offspring disperse, and others stay in their
current patch. A dispersed offspring was assumed to land
in any other than its natal patch. Dispersal completed a
generation, and the entire procedure was then run for
1000 generations for a variety of different values of d, for
each of the assumptions (i), (ii) and (iii).
model results
We depict a large collection of single-run outcomes at
generation 1000 rather than averaging over several repli-
cates per parameter value. The latter approach would not
be able to distinguish between a scenario with alternative
non-polymorphic equilibria and a protected polymor-
©2015 The Authors. Journal of Animal Ecology ©2015 British Ecological Society, Journal of Animal Ecology
6S. P. Gordon et al.
phism (e.g. 05 could then, confusingly, mean either
equally many ‘yellow fix’ and ‘white fix’ cases, or all runs
having stabilized at a yellow-white polymorphism). Our
approach shows that a polymorphism would never be
maintained if the populations were assumed panmictic
(d=1) or, more generally, if the dispersal rate dexceeded
approximately 02 (Fig. 2). The model then mostly pre-
dicts that the yellow morph disappears, but this conclu-
sion proved sensitive to how we assumed paternity to be
divided in those cases when a female mated multiply. If
we made the yellow-favouring assumption, then some-
times the yellow morph fixed (Fig. 2), and polymorphism
also prevailed at slightly higher values of dthan in the
other cases.
When dispersal was less frequent (d<02), the model’s
behaviour was consistent across a large range of dispersal
rates and also across the different assumptions regarding
multiple mating. Both morphs persisted, with no clear
trend other than that if a morph was assumed to gain
more paternity with doubly mated females in our estima-
tion of aand b, this morph was able to shift its frequency
somewhat upwards from the scenario of equal paternity
(the difference between the open and filled symbols in
Fig. 2). Thus, we predicted an approximate 1 : 1 morph
ratio when we made the yellow-favouring assumption,
approximately 40% yellow males when we made the equal
paternity assumption, and approximately 30% yellow
males when we made the white-favouring assumption.
Discussion
Aposematism is assumed, and in many organisms shown,
to be under positive frequency-dependent selection leading
to monomorphism (Mallet & Barton 1989; Lindstr€
om
et al. 2001). In our study system, the wood tiger moth,
the more conspicuous yellow male morph, survives as a
whole better against predators than the white male morph
(Nokelainen et al. 2012). However, it appears that this
survival advantage is dependent on the local predator
community (Nokelainen et al. 2014). In our case, this is
important because male fitness proves to have not only
one (predation), but potentially two (predation and sexual
selection) positively frequency-dependent components.
Our enclosure experiment shows that white males have
an advantage over yellow males in mating probabilities,
but this appears to occur only at high frequencies of white
males. However, when we analyse overall individual fit-
ness, both morphs have an advantage when common that
disappears when at a balanced ratio. These results may
overall suggest some sampling artefact where there is a
higher probability of finding higher quality males in the
high-frequency morph group. However, this reason seems
unlikely because aspects of male quality shown to affect
mating success in the past (male age and size) were
already included in our analyses to test their effects; and
only male age had a small treatment effect (and only in
the Y-biased treatment). Instead, two plausible and not
mutually exclusive reasons could be responsible for our
results.
First, both morphs could trade off on certain aspects of
reproduction. For example, yellow males have low mating
success when in white male-dominated environments, but
compensate for this by siring more eggs and having a
higher hatching success of offspring compared to white
males (see Appendix S1, Supporting Information). This
difference in strategy could be related to morph-related
differences in fitness-related traits we have not measured
here. For example, a recent study found that white wood
tiger moth males fly for longer stretches of time, whereas
yellow males tend to focus their flying around the peak
calling activity of female moths (Rojas et al. In review).
This is probably due to the white males compensating
their less efficient signal to predators by increased to flight
to escape predation attempts, or yellow males being lim-
ited in flight because of physiological limitations from
producing their more efficient, yet costly chemical defence
(Rojas et al. unpublished data). Regardless of the specific
reason that difference in flight activity between the two
morphs may lead to disproportionate chances for the
white morph to achieve more matings, especially when
common, and in return select over time for the yellow
males who leave more sired eggs once they achieve mat-
ing.
Secondly, wood tiger moths may display flexible mating
preferences, depending on morph frequencies, which
would have led to our results. Sampling of natural popu-
lations shows that most populations of wood tiger moths
have an admixture of both morphs (Hegna, Galarza &
Mappes 2015). For example, in Finland alone, there are
populations that are white dominated (such as in Central
Finland where much of our laboratory stock in this
experiment was taken from) and others that are yellow
dominated (Southern Finland), and much gene flow
occurs between populations (Nokelainen et al. 2012;
Galarza et al. 2014). Adaptive coloration also varies spa-
tially as well as temporally in our system, and viability
strongly favours one morph over the other via predation,
immunocompetence response to disease (Nokelainen,
Lindstedt & Mappes 2013) and potentially other pres-
sures. This may make it adaptive to avoid mating with
rare morphs, potentially explaining why female wood
tiger moths in our experiment appear to either choose
mates (or lay more eggs) for the male morph with the
more common phenotype (i.e. the morph with seemingly
higher viability). Short-lived polyandrous species like
wood tiger moths may easily track male morph frequen-
cies via the social interactions that occur between calling
females and courting males (McLain 2005; Westerman
et al. 2014).
Some examples of flexible mate choice have been con-
firmed experimentally, and in each case, its occurrence is
linked with systems that have natural variations in morph
frequencies. For example, female soldier beetles (Chauliog-
nathus pennsylvanicus) possess flexible mate preferences
©2015 The Authors. Journal of Animal Ecology ©2015 British Ecological Society, Journal of Animal Ecology
Positive frequency dependence and polymorphism 7
flectance) have been found to actually attract attacks by
these predators (Lyytinen et al. 2001; Lyytinen, Lind-
str€
om & Mappes 2004). On the other hand, dunnocks
(Prunellidae) tend to avoid white male moths and gener-
ally forage closer to the ground level in shaded boreal for-
ests. White coloration might be a more effective warning
signal in these circumstances because they have much
higher luminance values compared to the yellow morph
(Galarza et al. 2014).
model using both predation and mating
results
We consequently built our model assuming that the 60
sites sampled above represent the range of naturally
occurring spatial variation in morph-specific viabilities, as
estimated in Nokelainen et al. 2014. We considered a
world consisting of 60 patches, each producing 50 off-
spring in each generation. We only tracked the dynamics
of males, that is we assume that male offspring morph
frequencies are proportional to the frequency with which
males of each morph become sires (this only requires
assuming that inheritance via females does not bias pat-
terns of inheritance in either direction).
Given that differential predation based on wing colour
occurs during the adult time period, morph ratios are not
necessarily constant and the model needs to track morph
frequencies at the time when siring occurs. Having no pre-
cise information of this time dependency, we use the fol-
lowing logic to simulate the most likely pattern. Denote
by b
i
the survival advantage of the yellow morph in a cur-
rent patch i(e.g. if site 13 has b
13
=121 then in this site
a yellow individual’s daily risk of dying is 1/1121, that is
a fraction 089 of that of a white individual). Conse-
quently, if a local population starts with w
0
whites and y
0
yellows (the subscript 0 denoting that no male has had
the time to die yet), the probability that the next death
targets a yellow male is (y
0
/b)/[(y
0
/b)+w
0
], and the comple-
mentary probability that the next removed male is white
is w
0
/[(y
0
/b)+w
0
]. Thus, if a uniformly distributed random
number in the range [0,1] falls below (y
0
/b)/[(y
0
/b)+w
0
], we
subtract one individual from the local y(thus y
1
=y
0
–1,
w
1
=w
0
), and otherwise from the local w(thus y
1
=y
0
,
and w
1
=w
0
–1). We repeat this procedure until no males
of either morph are alive.
We then assume that females largely mate when mates
are numerous (i.e. mostly when the season is not nearly
over yet) and choose the mating time index of each female
by rounding down a random number that is exponentially
distributed with mean (y
0
+w
0
)/10. This result, denoted t,
describes that a female mates at a point in time when t
males have died and y
t
and w
t
are consequently still avail-
able for matings. The female mating time is thus designed
to follow mate availability, and the factor 10 was set to
make the proportion of females that attempt to mate when
no males are alive negligibly low (for y
0
+w
0
50 which
according to our assumptions is the approximate size of
local populations, this probability –i.e. the probability
that the exponential distribution with mean (y
0
+w
0
)/10
produces a value that exceeds y
0
+w
0
, the number of deaths
it takes for all males to have died –is approximately
045 910
5
). We assume that these exceedingly rare late
females in reality mate with the last available male, while
noting that our results remain virtually unchanged if we
instead assume that they completely fail to mate, as the
siring success this late in the season contributes minimally
to the mating success of either of the male morphs.
Populations were initiated such that 250 yellow and 250
white males were distributed randomly across the 60
patches, to yield initial patch-specific y
0
and w
0
values.
The above procedure was then used within each subpopu-
lation to determine siring times for 50 surviving offspring
per patch (for those patches that had at least one male;
we thus implicitly evoke density dependence: each occu-
pied patch is equally productive). We equate survival with
maturation.
The morph identity of each of the 50 sires was deter-
mined based on y
t
and w
t
at the siring time t, such that
Prob foffspring is yellowg¼ x
xþ1xðÞeaxþb:
Here, x=y
t
/(y
t
+w
t
) is the proportion of yellows in the
current population of potential sires. The parameters a
and bdefine the relative mating success advantage of
whites, determined by a least-squares regression of log
(mean eggs sired by white
mean eggs sired by yellow), values taken from the empirical part
of this paper against the treatment xvalues (x=1/3, 1/2
and 2/3) used in the experiments. Because a few females
mated once with a yellow and once with a white male, we
computed three different values for aand b, to cover the
entire range of uncertainty caused by this behaviour: (i)
the first regression assumed that these females all con-
tributed only to their white mate’s success, (ii) the second
assumed that these females all contributed only to their
yellow mate’s success, and (iii) the third assumed that
these females had half their eggs sired by the white mate,
and half by the yellow mate.
This procedure of determining offspring morph was
repeated across all patches. We then assumed that a pro-
portion dof offspring disperse, and others stay in their
current patch. A dispersed offspring was assumed to land
in any other than its natal patch. Dispersal completed a
generation, and the entire procedure was then run for
1000 generations for a variety of different values of d, for
each of the assumptions (i), (ii) and (iii).
model results
We depict a large collection of single-run outcomes at
generation 1000 rather than averaging over several repli-
cates per parameter value. The latter approach would not
be able to distinguish between a scenario with alternative
non-polymorphic equilibria and a protected polymor-
©2015 The Authors. Journal of Animal Ecology ©2015 British Ecological Society, Journal of Animal Ecology
6S. P. Gordon et al.
sity of Jyv€
askyl€
a were also kind to read and comment on earlier versions
of this manuscript. Funding was provided by the Academy of Finland via
the Centre of Excellence in Biological Interactions (Project: 2100000256 to
J.M. and Project: 21000027441 to S.G.).
Data accessibility
Data available from the Dryad Digital Repository: http://dx.doi.org/
10.5061/dryad.nn493 (Gordon et al. 2015).
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Supporting Information
Additional Supporting Information may be found in the online version
of this article.
Appendix S1. Egg number and hatching success.
©2015 The Authors. Journal of Animal Ecology ©2015 British Ecological Society, Journal of Animal Ecology
10 S. P. Gordon et al.
