1 INTRODUCTION

If selection can only exploit the best of the immediately available alternative phenotypes, how can novel ecological strategies evolve in already well-adapted organisms? This has traditionally been envisaged as the problem of peak shifts across the metaphorical ‘fitness landscape’ (Wright, 1931). When the environment remains stable, in order to move from one adaptive peak (i.e. local optimum) to another, populations must first transverse a fitness valley, inhabited by intermediate and typically maladaptive phenotypes. To overcome this problem, genetic drift is often invoked as a means by which populations may cross these fitness valleys (Coyne & Orr, 2004; Mallet, 2010; Wright, 1931). However, when the traits in question are under positive frequency-dependent selection, an additional complication is added: as peaks are defined by the abundance of its corresponding phenotype, new ‘unexplored’ peaks only become available once already populated by a substantial number of (initially maladapted) individuals.

Aposematic warning patterns, which are commonly assumed to be under strong positive frequency-dependent selection, can represent considerable fitness peaks in the adaptive landscape (Borer et al., 2010; Chouteau et al., 2016; Gordon et al., 2021; Lindstrom et al., 2001; Mallet et al., 1990; Merrill et al., 2012). Because predators learn to associate particular patterns with unpleasant experiences, an individual's risk of predation should decrease as the local density of its warning pattern increases (Müller, 1879; Sherratt, 2008). This can lead to the convergence of warning patterns of different prey species sharing a habitat, a process coined ‘Müllerian mimicry’ (Müller, 1879). However, although naively we might expect a single warning pattern to emerge, warning patterns are often very diverse within a community (Briolat et al., 2019).

The establishment of entirely new warning signals under positive frequency-dependent selection via predators is problematic. One possibility is that during periods of relaxed selection (which might conceivably result from an extreme meteorological events, such as a hurricane, or a reduction in predators due to disease), drift may allow new variants to rise above a threshold density until mimicry selection takes over (Mallet, 2010; Mallet & Joron, 1999; Sherratt, 2006). Another possibility is that a model in which predators learn to avoid unpalatable prey only after sampling a fixed number is overly simplistic. For example, if predators are neophobic and generally avoid prey with unfamiliar phenotypes, novel signalling phenotypes might be favoured when they are rare (Aubier & Sherratt, 2015). A third possibility is that warning patterns might be multifunctional so that their evolution is not solely governed by purifying frequency dependent processes induced by predators (Briolat et al., 2019).

Sex-specific selection provides a mechanism by which ecological diversity may be promoted (Bonduriansky, 2011). Ecological adaptations, including strategies to exploit resources within the environment or avoid predators, are typically—though not always—shared between the sexes. Viability selection is normally expected to push ecological phenotypes towards a shared optimum. Sex-specific selection on the other hand may produce different adaptive optima for the two sexes (Andersson, 1994; Arnqvist & Rowe, 2005). This can result, for example, from requirements imposed on females to produce offspring or the need for males to find receptive mates (Bateman, 1948; De Lisle, 2019). The existence of sex-specific optima can also lead to sexually antagonistic selection, and rapid evolution, even in opposition to viability selection (Arnqvist & Rowe, 2005). For example, males may evolve strategies that increase their likelihood of securing mates. If these strategies impose costs on females, females may in turn evolve strategies to circumvent these male tactics, leading to further selection on males and so on. If such interlocus sexually antagonistic selection involves ecologically relevant traits, this might result in peak shifts across the viability fitness landscape.

Heliconius butterflies provide an excellent opportunity to empirically address these questions. Since Bates (1862) first described mimicry theory, studies of these butterflies have made a substantial contribution to our understanding of adaptation (Merrill et al., 2015). Distasteful Heliconius are well known for their bright warning patterns, which are often associated with Müllerian mimicry. These warning patterns are an important ecological adaptation in Heliconius, and predator-induced selection coefficients for the most common local patterns are strong (Mallet et al., 1990). Despite this, Heliconius butterflies exhibit a striking diversity of alternative warning patterns (Bates, 1862; Merrill et al., 2015). Individual species often vary in warning pattern across their range, leading to distinct geographical colour pattern types, and in some cases, such as in H. cydno, H. numata and H. doris, polymorphisms exist within single geographical populations. In addition, multiple warning patterns frequently coexist within a single geographical community. A given Heliconius species may then join many distinct mimicry rings according to local context, leading to the well-documented mosaic of warning patterns observed across the Neotropics (Brown, 1976). Spatial variation in local predator and prey communities shape a rugged adaptive landscape, crucial to the maintenance of warning signal diversity.

In addition to warning potential predators, Jocelyn Crane (1955) demonstrated that the bright warning patterns of Heliconius stimulate male courtship in the 1950s. Since then, numerous experiments have repeatedly shown that male Heliconius generally prefer females that share their own warning pattern over that of other conspecific morphs or closely related species (e.g. Hausmann et al., 2021; Jiggins et al., 2001, 2004; Kronforst et al., 2006; Merrill et al., 2014, 2019; Merrill, Gompert, et al., 2011; Merrill, Van Schooten, et al., 2011; Sánchez et al., 2015). It seems likely that competition between males drives these genetically determined local preferences, as the ability to efficiently locate potential mates within a visually complex environment would be beneficial (Merrill et al., 2019). In addition, because male Heliconius make a considerable reproductive investment in the form of a nutrient-rich spermatophore (Boggs, 1981), selection to avoid wasting time pursuing hetero-specifics or producing unfit hybrids may also be involved (Jiggins et al., 2001; Merrill et al., 2019). However, previously mated females may suffer fitness costs if these cues lead to disturbance by males during oviposition or foraging. These costs would be augmented by the fact that, although individual Heliconius are long lived (up to 6 months), female re-mating is a rare event in most species (Walters et al., 2012). These female-specific costs could conceivably set the stage for interlocus sexual conflict, leading to an arms race between warning pattern and male preferences and rapid evolution when patterns are released from constraints imposed by aposematism (e.g. after a local reduction in predation; see also Gavrilets & Waxman, 2002). Ultimately, this could be an additional factor explaining warning pattern diversification.

To explore how costs imposed on females by male attraction to warning patterns might contribute to pattern diversification in Heliconius, we first implemented individual-based simulations. Across a vast parameter space, we tested (i) if the presence of such female costs can favour the evolution of novel patterns as opposed to drift acting without sexual conflict, (ii) which parameters are most relevant for such dynamics to occur, and (iii) how the genetic architecture of male attraction traits might affect the speed at which novel patterns increase in frequency. Due to very strong positive frequency selection acting on warning pattern in Heliconius (e.g. Mallet & Barton, 1989) and following others (Mallet, 2010; Mallet & Joron, 1999), we assume a period of locally relaxed predation (perhaps resulting from meteorological events or the spread of avian diseases). However, our simulations allow us to test to what extent the required period of relaxed selection depends on other biologically relevant parameters. We then performed experiments to begin to test these ideas by disrupting warning patterns of mated Heliconius females with marker pens or by introgressing a novel colour pattern allele from a closely related species. We subsequently tested the hypotheses that (i) males interact less frequently with females with disrupted patterns, (ii) females lay fewer eggs in the presence of males and that (iii) this effect is less pronounced for females with experimentally disrupted patterns.

2 MODEL AND METHODS

2.1 Individual-based simulations

We first give a brief overview of the entire model, which specifically considers the biology of Heliconius butterflies and is broadly based on that of Duenez-Guzman et al. (2009) and informed by the broader literature, before focusing on the details in the sections below (see also Figure 1). Individuals inhabit one of 384 patches arranged on a 94 × 4 torus, and can differ from one another in sex, colour pattern (expressed in both sexes) and attraction to these patterns (only expressed in males). Both colour pattern and preference phenotype can evolve across the whole population, but with the exception of a single novel colour pattern mutation, new mutations can only arise at preference loci. By tracking the fate of a novel warning pattern allele, introduced at the beginning of each simulation, we were able determine the effects of sexual conflict, in addition to variation in other parameters likely to influence the evolutionary processes involved. Within each patch, colour pattern is under positive frequency-dependent selection because predators stop eating adult butterflies of a certain pattern once a threshold number has been sampled within that patch. Mating between any given female and any given male also depends on (female) colour pattern, as well as the male's preference phenotype, which is determine by a (variable) number of unlinked diallelic loci. In simulations in which it is included, sexual conflict arises because females are disturbed by males during oviposition (reducing the number of offspring they produce), and the probability that any given female is disturbed by any given male depends on (female) colour pattern and the male's preference phenotype. Finally, we tested for the effects of genetic drift by greatly reducing the number of eggs laid by all females, thereby imposing a bottleneck, across a subset of 80 central patches, including that where the novel pattern allele was introduced.

2.1.1 Arena

Individuals live, breed and die within a rectangular arena of 96 × 4 patches with uniform habitat, each representing ~1 km² of forest. This arena is divided between 80 central patches, and the remaining 304 peripheral patches (see Figure 1a). To reduce boundary effects, the arena is wrapped into a torus.

2.1.2 Genetics of individual pattern and preference phenotypes

Individuals are sexual, diploid and have discrete sexes (determined by segregation of sex chromosomes). Both warning pattern and male mating preferences are genetically determined, and all loci are assumed to be autosomal and segregate independently (Merrill et al., 2015). Many years of research have established that major colour pattern elements in Heliconius are controlled by just a few Mendelian loci (reviewed in McMillan et al., 2020). Although a handful of genes may differentiate colour pattern races, here we are explicitly interested in the spread of individual colour pattern alleles and so consider just a single locus. As such, individuals have a single diallelic locus determining variation in a warning pattern element (with alleles A, a), which is expressed in both sexes: The derived novel allele A is dominant over the ancestral allele a, reflecting strong dominance observed at Heliconius colour pattern loci (McMillan et al., 2020). To account for mating preferences, we assume the existence of two additive quantitative characters p_a and p_n, controlling males' attraction towards females of the ancestral and novel pattern, respectively. Both traits p_a and p_n, are scaled between 0 and 1 and are each controlled by N unlinked diallelic loci with equal effects (Figure S1). Alleles have dominance relationships so that alleles increasing attraction towards the respective pattern elements are dominant over those that reduce attraction.

2.1.3 Life cycle

The life cycle consists of five stages per generation (see Figure 1a): (1) age-related mortality; (2) frequency-dependent selection of adults due to predation; (3) production of offspring; (4) mating; and (5) dispersal. In contrast to a previous model from Duenez-Guzman et al. (2009), our model incorporates overlapping generations. This increases the biological realism of the model as Heliconius are long lived and breed throughout their adult life. Newly eclosed adults are assigned as age = 0 and their age increases by 1 each generation. Individuals with age > 4 are removed from the population at the beginning of each generation.

2.1.4 Predation

Predation is modelled implicitly through a patch-specific learning threshold, where predators stop eating individuals with a certain pattern once the learning score Q is reached (following Duenez-Guzman et al., 2009). The learning process for each pattern occurs by each individual eaten within a patch contributing 1 to the corresponding learning score for the patch. The learning score for each patch is reset every generation and no evolution in predators is allowed. In the 80 central patches of the arena, predation is initially relaxed for time T (i.e. no individuals are eaten in these patches for the first T generations).

2.1.5 Sexual conflict and reproduction

Offspring can be produced by previously mated females, regardless of whether she subsequently encounters a male or not (though an encounter can subsequently allow disturbance when sexual conflict is present, see below). We assume that during oviposition, the chance that a female encounters a male depends on the probability of encountering any particular male (e) and the number of males within the patch (m):

$$c=1-{\left(1-e\right)}^m$$(1)

In a scenario of sexual conflict, during an encounter, a female may then either be disturbed or not, and hence lay an egg or not. The probability that an encounter between any given male and any given female leads to a disturbance by the male depends on the attraction R of this male to the female. Disturbance is then a two-step process, first depending on the probability of encounter and then on the probability of attraction. Following Duenez-Guzman et al. (2009), R is dependent on the male's preference trait p and a parameter α, which is positive and measures the strength of attraction to female patterns. Large values of α imply strong attraction to colour and smaller values imply weaker attraction. The smaller α, the less will R differ between males with different preference traits (Figure S1). R for a pair of males i with preference p_x and female j with pattern type x (x being either a [ancestral] or n [novel]) is:

$$R_{i,j}=\mathit{exp}\left[\alpha \times \left({p_i}_{x_j}-0.5\right)\right]$$(2)

The probability that an encounter leads to a disturbance is equal to R_i,j divided by the maximum possible value of R (where p = 1), i.e.:

$$\mathit{exp}\left[\alpha \times \left({p_i}_{x_j}-1\right)\right]$$(3)

The total number of eggs (which directly translates to offspring), B, for a patch is Poisson-distributed with mean b. b is independent of male disturbance and limited only by available oviposition sites and female egg-laying attempts are repeated until B is reached. Gametes producing an egg are randomly hit by mutation. Asides from the initial colour pattern mutation, mutations only occur at loci affecting attraction to patterns, at a constant rate of μ per locus per individual per generation (no double mutations of a locus within an individual during the same generation are allowed). Maternal and paternal alleles recombine freely.

2.1.6 Mating

Mating occurs between individuals of the same patch. We assume females only mate once and continue to lay eggs at a constant rate throughout their lives. Males are assigned to unmated females with relative probabilities equal to their attraction to patterns displayed by females (female choice is not present), which is calculated following equation (2). The majority of females mate immediately after eclosion (and before dispersal); however, because each male can only mate 4 times per generation (mating is costly to Heliconius males) females may remain unmated if a patch by chance has >4 times more unmated females than males and then may be mated during subsequent generations. However, although the costs of not mating are significant, this risk of not mating will be extremely low. Assuming that within each patch on average 1/5 of females are newly eclosed (and therefore have had no opportunity to mate), there will, on average, be 5 males (each of which can mate 4 times per generation) for every receptive female (which only mate once during their life time). As such, on average only a very small cost will be imposed on females with patterns that are less attractive to local males. These likely trivial costs imposed on less attractive females, due to the unusual case where such females do not mate, probably reflects the situation in the wild, where empirical data suggest that the frequency of unmated females is vanishingly small (probably because most females are mated very quickly after eclosion; Walters et al., 2012).

2.1.7 Dispersal

Finally, newly produced individuals disperse. We assume that each individual migrates to one of the eight neighbouring patches or stays in its native patch with the same probability 1/9.

2.1.8 Implementation

We implemented our model as individual-based simulations in R (R Core Team, 2019). To efficiently simulate the process of female egg laying and disturbance by male (by avoiding to individually simulate each egg laying attempt), we made use of the fact that the combined number of eggs placed by females of a patch was independent of male disturbance. During each iteration and per patch, R for each possible female–male pair was computed and scaled to the maximum possible value of R (where p = 1). The mean of these values equals the average probability of male encounters leading to disturbance, d. The expected proportion of eggs laid after male encounter, among all those without disturbance, P, is hence:

$$P=\frac{c\times \left(1-d\right)}{c\times \left(1-d\right)+1-c}$$(4)

The number of eggs laid after encounter (but without disturbance) with a male was drawn from a Poisson distribution with mean b×P, and number of eggs without encounter from a separate Poisson distribution with mean b×(1 − P). The number of eggs laid after encounters with disturbance is of course = 0. Mated females within a patch were randomly assigned to the available eggs laid without encounter. However, unattractive females, who are less likely to be harassed, were more likely to contribute to eggs laid with encounter (but no disturbance). The relative probability of a female within a patch being assigned to those eggs equalled 1—mean attractiveness of this female to all males in the patch (as calculated following equation (2)). In this way females that are relatively less attractive compared with other females in her patch will be assigned more eggs.

We ran all simulations with equal starting conditions. The arena was initially populated with 114 individuals (57 mated females and 57 males) per patch, which was a population size similar to the equilibrium population size. Ages were distributed equally over patches and sexes within a patch and ranged from 0 to 5 (as typical for the beginning of a new generation). All individuals were initially homozygous (aa) for the recessive ancestral pattern and homozygous (aa) for the recessive ancestral allele at loci for attraction to the novel pattern (i.e. minimum attraction to the novel pattern in males). Also, all individuals were homozygous (AA) for the dominant ancestral allele at loci for attraction to the ancestral pattern (i.e. maximum attraction to the ancestral pattern in males). Throughout, the mutation rate for attraction loci, μ was set at 10⁻⁵.

At the beginning of each subsequent simulation run (i.e. at generation 1), a colour pattern mutation was introduced into a randomly chosen individual of age 0 within one of the 80 central patches, where predation was initially reduced (so that it was heterozygous Aa). The fate of the introduced mutation was then followed until it was lost from the population, or when 2500 generations were reached. During each generation, the number of eggs laid by females within one patch, B, was drawn from a Poisson distribution, with mean b = 20. However, for a subset of simulation runs, a bottleneck was imposed within the 80 central-most patches for the first five generations to increase the effects of drift, where b = 0.5.

2.1.9 Parameter space

We systematically varied the predator learning threshold (Q); the number of generations that predators were absent from the central patches of the arena (T); whether or not a bottleneck was imposed on the central patches in the first generations; the sex of the first mutant; the number of loci affecting each colour attraction trait in males (N); the strength of colour attraction in males (α); and whether sexual conflict was present (i.e. possible disturbance by males during egg laying) or not (reference baseline). In simulation runs where sexual conflict was present, we also varied the probability of encounter between a specific female and male (e). Additionally, we always noted the position in the arena where the first mutant occurred. Different settings for the parameters are shown in Table 1, together with the expected relative difference in number of offspring sired by a novel patterned female versus an ancestrally patterned female, as dependent on α and e (assuming a patch containing males typical for the first generation with minimum attraction to novel and maximum attraction to ancestral pattern). An average of 1000 iterations were run for each of the 720 parameter combinations. 576 of these parameter combinations included sexual conflict and 144 did not. Numbers of heterozygous and homozygous individuals at each locus in central and non-central patches were recorded during each simulated generation and stored in a sparse matrix (Bates & Maechler, 2019). Scripts to run the model are available in the supplementary R Markdown.

TABLE 1. Simulation parameters and their settings.

Parameter symbol	Meaning	Default values
Q	Learning threshold	1; 2; 4
T	Predator presence	10; 100
—	Bottleneck	No; Yes
—	Sex of first mutant	Female; Male
N	Loci attraction	1; 5; 10
α	Strength attraction	1; 3
—	Sexual conflict	No; Yes
e	Probability of encounter	0.001; 0.0025; 0.005; 0.01

If sexual conflict present
e	0.001	0.001	0.0025	0.0025	0.005	0.005	0.01	0.01
α	1	3	1	3	1	3	1	3
Δ eggs	+2.9%	+4.3%	+7.2%	+10.4%	+14.1%	+19.8%	+27.2%	+36.0%

• Note: Parameters shown at the top were systematically varied across simulation runs, with the exception of parameter e (probability of encounter between specific female and male), which was only varied if sexual conflict was present. Below, for each combination of e and α (strength of male attraction to female pattern), and assuming a patch containing males typical for the first generation with minimum attraction to novel and maximum attraction to ancestral pattern, the expected relative difference in number of offspring sired by a novel patterned female versus an ancestrally patterned female is shown.

2.1.10 Statistical analysis

All analyses were conducted in R (R Core Team, 2019). Scripts are available in the supplementary R Markdown. Numeric covariates (i.e. Q, T N, α, e; see Table 1 for annotation) were transformed into ordered factors. We tested which of the simulation parameters affects the probability of the novel warning pattern allele surviving until generation 2500 (at which point simulations were always ended) using GLMs with binomial error structure (i.e. success = allele remains in population, always identical with going to (near) fixation; failure = allele disappears from population). In cases of perfect separation (where an independent variable perfectly predicts the dependent variable and the likelihood of the model is not defined), the predictors in question were excluded from the models and their effect instead tested with binomial tests (correcting p-values with the Bonferroni method). Stepwise forward-model selection based on AIC via the MASS package (Venables & Ripley, 2002) was used to find the model that explained the data best, maximally allowing for two-way interactions. To test for the effect of genetic architecture of male attraction traits on number of generations until the novel warning pattern went to near fixation (allele frequency = 0.95; only considering runs where the novel pattern survived), we fitted a GLM with Poisson error structure with number of loci coding for each attraction trait (N) as fixed effect. Estimated marginal means for the different predictors were extracted using the emmeans package (Lenth, 2019). The same package was used to perform Type III ANOVA to test for significance among fixed effects. Resulting p-values were corrected for multiple testing using the Bonferroni method. R² values were calculated using the dominanceanalysis package (Bustos Navarrete & Soares, 2020).

3 RESULTS

3.1 Simulation results

3.1.1 Sexual conflict facilitates the evolution of novel warning patterns

We ran simulations across 720 different parameter combinations (each replicated ~1000 times). The novel pattern quickly disappeared from the population in all 144 000 simulation runs where sexual conflict could not contribute to the diversification of warning patterns (Figure 2a). The novel pattern allele only survived in simulations which included both, sexual conflict and the maximum period of relaxed predation (i.e. T = 100 generations; Figure 2a). The novel allele persisted in 2865 of 288 000 simulations fulfilling these two criteria (i.e. 1%), and in each of these it also increased in frequency to near or complete fixation (Figure S4). By far, the most important additional parameter in these simulations was the probability of a male–female encounter (e), which explained 64% of the variance (Figure 2b): Asides from 2 simulation runs (with a value of 0.005), probability of encounter (e) had to be at 0.01 for the novel pattern allele to be retained. However, stepwise model selection also revealed that strength of male attraction to colour (α), predator learning threshold (Q), presence of a bottleneck in the central patches during the first generations (bottleneck), sex of the first mutant (sex), as well as the interactions bottleneck × α, bottleneck × Q, bottleneck × sex, and α × Q, also all significantly affected the retention of the novel allele (Figure 2b and Table S2). Overall, the most promising combination of parameter settings included sexual conflict, Q = 1, T = 100, no bottleneck, female first mutant, N = 10, α = 3 and e = 0.01, where the novel allele was retained in 26% of runs (Table S1). This is perhaps unsurprising as these are the conditions under which we might intuitively expect any benefits experienced by females with novel patterns to have the greatest effect: increased probability of encounter between males and females (e), and a greater strength of attraction intuitively suggests that costs due to disturbance experienced by ancestral colour patterns will be at their greatest; a large number of generations before predators return (T) will allow the greatest chance for the novel pattern to spread sufficiently to overcome the (here low) learning threshold (Q); and the small effect size of individual preference loci (~large number of loci, N) will slow the evolution of male counter adaptions, which will oppose the spread of the novel allele. Perhaps less intuitive is the lack of bottleneck favouring the spread of the novel allele, which likely reflects a greater importance of deterministic process than drift in our simulations. We also found that the novel allele was more likely to survive when the initial mutation occurred in one of the most central patches (i.e. far away from active predation, Figure S2). Indeed, the eventual fate of the novel pattern allele seemed to be largely determined during these first generations of relaxed predation in the central patches, as its frequency at generation 100 was closely correlated with future retention or loss of the allele (Figure S3).

3.1.2 Male attraction to colours tracks warning pattern evolution

Overall, the mean frequency of alleles causing male attraction to the novel pattern closely tracked the frequency of the novel pattern allele, but lagged behind some generations, as typically expected during chase-away selection (Figure 3a, see also Supplementary Animation). The magnitude of this lag depended on the genetic architecture of male attraction traits, with more complex architectures (i.e. more preference loci) generating a greater discrepancy between pattern and male attraction to this pattern (Figure S4). In contrast, the mean frequency of alleles determining attraction to the ancestral pattern changed very little (Figure 3a; note that male attraction to the two pattern types was controlled by independent loci): Across simulation runs, the average male was at no point more attracted to the novel than to the ancestral pattern (Figure S5). Therefore, once the novel pattern exceeded the frequency of the ancestral pattern, both mimicry selection and selection imposed by disturbance by males acted in the same direction for a period of time, both favouring for the novel pattern (Figure S5).

3.1.3 Genetic architecture of male attraction influences the speed at which novel pattern alleles spread in simulations with sexual conflict

Although the number of loci encoding attraction phenotypes was not retained in our model testing for survival of the novel pattern allele, it did have a strong effect on how fast the novel pattern allele's frequency increased in the population, in cases where it persisted (Figure 3b and S6). With just one locus determining attraction to each pattern, simulation runs required on average ~ 600 generations longer to reach a frequency of 0.95 of the novel pattern allele compared to simulation runs with 5 loci (z-test: z = 394.812, p < 0.001) or 10 loci (z-test: z = 375.969, p < 0.001). Surprisingly, simulation runs with 5 or with 10 loci did not differ much from each other in this respect (and the trend was even slightly reversed, z-test: z = −20.558, p < 0.001). These differences were observed across all possible combinations of the other simulation parameters (see supplementary R Markdown).

3.2 Empirical results

3.2.1 Warning patterns influence male disturbance of mated Heliconius erato females

In Experiment 1, we carried out observations for 58 individual females, including 30 experimental butterflies with disrupted warning patterns, and 28 butterflies subjected to one of the two control treatments (14 of each). After removing outliers (five experimental and four control individuals, see Figure S9 and Supplementary Methods), females with intact warning patterns were harassed more often (i.e. males directed more hovering courtship or chasing behaviours towards them) than those with disrupted patterns (Figure 4a, F ratio = 13.34, df = 1, p < 0.001; inclusion of the outliers did not qualitatively affect the results: Figure S9A, F ratio = 6.24, df = 1, p = 0.013). In Experiment 2, we carried out observations for 45 individual females, including 20 experimental butterflies with yellow-red forewing pattern, and 25 control butterflies with yellow forewing pattern. Overall, males were much more responsive than in Experiment 1, which may reflect differences between the species tested or conditions under which the two experiments were conducted (i.e. insectary site). Surprisingly, including all individuals, females with experimental pattern were harassed more often (i.e. males directed more hovering courtship or chasing behaviours towards them) than those with control pattern (Figure S9B, F ratio = 4.54, df = 1, p = 0.033), though this trend was no longer significant when outliers (two experimental and one control individual) were removed (Figure 4c, F ratio = 3.61, df = 1, p = 0.058). However, for yellow-red females with measurements of the band sizes available (12 of the 18 from Figure 4c), we found that male–female interactions (hovering courtship or chasing), which might cause disturbance, decreased as the size of the red band increased (Figure S10A, z-test for slope ≠ 0: z = 2.566, p = 0.010), whereas the size of the yellow band had no effect (Figure S10B, z-test: z = 0.116, p = 0.908).

3.2.2 Male presence reduces the number of eggs laid by females

There was considerable variation in the number of eggs laid, both, between experimental periods (i.e. males present and males absent) for individual females, as well as between females (Figure 4b,d). Nonetheless, in both experiments, females laid fewer eggs in the presence of males (Experiment 1, including females without warning pattern treatment: F ratio = 5.83, df = 1, p = 0.016 (Figure 4b); Experiment 2: F ratio = 12.49, df = 1, p < 0.001 [Figure 4d]). Over a two-day period, females in the presence of males laid ~0.73 [CI: 0.14–1.32] fewer eggs in Experiment 1 (a reduction in 13%; GLMM estimate without male = 5.45, with male = 4.72) and 1.70 [CI: 0.74–2.66] fewer eggs in Experiment 2 (a reduction of 19%; GLMM estimate without male = 8.86, with male = 7.15). However, we found no evidence of an interaction between the presence of males and warning pattern treatment on the number of eggs laid (Experiment 1: F ratio = 1.110, df = 1, p = 0.291; Experiment 2: F ratio = 0.005, df = 1, p = 0.943). Hatching success, measured for a subset of females in Experiment 2, was also unaffected by male presence (Figure S11).

4 DISCUSSION

The warning patterns of Heliconius butterflies have become a textbook example of natural selection (e.g. Barton et al., 2007; Futuyama & Kirkpatrick, 2017), but the origins of their considerable diversity remain problematic. We explored whether sex-specific selection might contribute to the evolution of novel warning patterns. Using individual-based simulations, we have shown that drift alone is unlikely to account for the spread of novel warning pattern alleles under our model conditions. Instead our simulations suggest that disturbance of previously mated females by males attracted to their bright warning patterns—in association with periods of initially relaxed predation—could facilitate the spread of novel pattern alleles. We also showed that genetic architecture of male attraction traits can influence how quickly a novel pattern may spread through the population, as it determines how fast males adapt their corresponding mating preferences. Data from insectary experiments also provide some support that sexual conflict can facilitate the spread of novel patterns: The presence of males reduced short-term female fecundity, highlighting that unwanted male attention may well favour the evolution of female defensive traits in Heliconius. However, we found no evidence in our experiments that novel warning patterns mitigate female-specific costs.

In our simulations, we considered a large parameter space to investigate which variables may facilitate the spread of novel warning pattern alleles. Notably, in all 144 000 simulations without sexual conflict, the novel allele was rapidly lost from the population, regardless of other parameter values. In contrast, among the remaining 576 000 simulations where sexual conflict was present, the novel allele was retained in ~0.5% of runs. Despite the striking diversity of warning patterns in Heliconius, the spread of a novel pattern allele is presumably a rare event, so even this apparently modest increase could make a substantial difference across 12 million years (Kozak et al., 2015) of Heliconius diversification. Overall, our simulations suggest that drift acting in isolation may be unlikely to facilitate the evolution of novel warning patterns, and that sex-specific selection may be an important, previously unrecognized factor.

Alongside a potential role for sex-specific selection, our simulations also suggest that increased periods of relaxed predation and high probabilities of encounter between mated females and males are important factors determining the fate of novel pattern alleles. Periods of relaxed predation have frequently been invoked as a necessary prerequisite for the spread of novel warning patterns in aposematic butterflies (Mallet, 2010; Mallet & Joron, 1999). In our simulations, the maximum period of relaxed predation, i.e. T = 100 generations, was required for the novel allele to spread, which given a Heliconius generation time of ~1 month might equate to ~8 years. It is difficult to know whether the kinds of events we have suggested, including extreme weather or the spread of avian diseases, might permit a sufficient drop in predation for such a period. Nevertheless, during the course of Heliconius colour pattern evolution, such periods of locally reduced selection are conceivable. Our simulations also clearly show that the sexual conflict could increase the chance of novel pattern evolution. High population density (leading to increased probabilities of encounter) has also been shown theoretically to drive diversification through interlocus sexual conflict (Gavrilets, 2000). Notably, in two of our simulations runs, the novel pattern persisted with a moderate encounter probability between females and males. This suggests that even at lower encounter rates, sexual conflict can contribute to the evolution of novel warnings patterns.

Of course, the interpretation of our simulations must depend on how likely its parameters reflect reality. The benefits that we introduced to females with novel patterns in our simulations (during relaxed predation; see Table 1) are broadly comparable to the higher fecundity experienced by females in the absence of males in our empirical data. However, although a great deal is now known of Heliconius biology (Jiggins, 2017; Merrill et al., 2015), making them an excellent subject for exploration with individual-based simulations, it is important to note that we still know little about their predators, both in terms of population densities or learning functions (Jiggins, 2017). Similarly, although Heliconius can exist in high densities, this—to our knowledge—has not been systematically assessed.

Another important caveat of our simulation results relates to the spatial set-up of our model. In particular, might this promote the fixation of the novel allele under the sexual conflict scenario? We consider this to be unlikely. Instead, because increased density likely increases the chance for male disturbance (see above), and that the novel allele is introduced to the central patches, where the bottleneck (i.e. a reduced number of individuals) is also introduced, if anything we would expect the opposite. It would be interesting to further explore how spatial structure influences the spread of warning pattern alleles, though this is beyond the scope of our current study.

In evolutionary arms-races, adaptations in one party are contested by counter-adaptations in the other (Arnqvist & Rowe, 2005). The genetic architecture underlying these adaptations can play a crucial role during these dynamics, as it may affect how fast one party can distance itself, or conversely catch up, to the other party. Our simulations show that male preferences rapidly track changes in female wing pattern cue, and that very simple genetic architectures speed up this process. This in turn decreases the speed at which the novel pattern allele spreads across the population, as female benefits from novel patterns are reduced when male interest in this pattern increases. However, this does not affect whether or not the novel pattern eventually reaches high frequencies in our simulations. The final fate of the novel pattern allele in our simulations seems to be largely determined in the first generations after its occurrence, during which the novel pattern is at very low frequency in the population, and hence, there is not yet strong selection for increased attraction to this pattern.

We modelled attraction of males to novel or ancestral patterns with two independent traits, controlled by different sets of loci (following Duenez-Guzman et al., 2009). Alleles that reduce attraction to the ancestral pattern did not markedly increase in frequency in any of our simulations. Males in our simulations suffered few costs from being attracted to females. This seems reasonable considering the sparsity of receptive Heliconius females in the wild, securing access to which possibly outweighs costs associated with attraction to the wrong female (Estrada & Jiggins, 2008). In our simulations, this meant that a reversal in disturbance probability of differently coloured females never occurred (i.e. the novel pattern was never harassed more than the ancestral pattern). If both attraction traits were controlled by the same loci (i.e. an increase in attraction to the novel pattern requires a decrease in attraction to the ancestral pattern), this might lead to such reversals and possibly increase the probability for colour polymorphisms to occur. Both this, and the influence of increased male costs, would be interesting questions for further empirical and theoretical work, but is beyond the scope of the current study.

Both our experiments support the hypothesis that male presence is costly for mated females, at least in the short term, as shown by a reduction in eggs laid. Although we cannot rule out the possibility that competition between females and males over food resources, as opposed to disturbance by males (e.g. hovering courtship and chasing behaviours), accounts for this reduction in laying rate, we consider this unlikely. In our experiments, butterflies were provided with multiple flowers and feeders (similar to cages housing much larger number of butterflies, where average laying rates per butterfly are within the same range), and it seems unlikely that this was a limiting resource. Although it has not previously been shown experimentally, Heliconius researchers frequently keep mated females separate from males to increase egg yield (independent of overall butterfly density). We therefore consider it more likely that disturbance by males, interrupting females during egg laying or during foraging or scouting for host plants, explains our data. In support of this view, the reduction in the eggs laid was more pronounced in Experiment 2, in which we also observed much higher levels of male–female interactions (despite having only a single male with each female).

Heliconius erato and H. timareta females respectively laid on average 13% and 19% fewer eggs when males were present. Female Heliconius only lay a few eggs per day, and if consistent across a female's reproductive life (up to several months), this would represent a significant reduction in fitness. Notably, this is comparable to per locus estimates of selection acting on warning pattern due to predation (albeit at the lower end; e.g. per locus s = 0.13–0.40 in H. erato and H. melpomene, Mallet et al., 1990). Once again, extrapolation of our results to natural populations must be treated with some caution. In particular, the activity and density of individuals in our insectary enclosures might not reflect the situation in the wild. For example, wild Heliconius males often show much higher activity than captive individuals (potentially leading to high rates of encounter between females and males). Local abundance of Heliconius in the wild can be very high, and interactions frequent, but there is considerable variation in density between sites (Merrill, pers. obs.). As such, it is unclear whether the densities in our insectary experiments reflect those in natural populations and this remains an important caveat. Nevertheless, given the large effective population sizes of many Heliconius species, even a relatively small fitness cost resulting from male disturbance could have significant effects on the evolution of associated traits (like warning pattern).

Although our experiments reveal that male presence can reduce short-term female fecundity, they provide only limited evidence for a key prediction of our hypothesis: That novel warning patterns should mitigate costs resulting from disturbance by males. H. erato females with disrupted patterns did receive less attention from males; however, there was no effect of pattern treatment on short term female fecundity (i.e. number of eggs laid with males present). In our experiments with H. timareta, we found no evidence that novel patterns reduce disturbance by males (indeed, there is some evidence that males are more interested in females with the red band) or that warning pattern affects the number of eggs laid with males present.

Despite this, it is perhaps premature to rule out a role of sexual conflict as a factor contributing to the evolution of novel warning patterns. The increased interest of males directed towards females with intact patterns observed in our first experiment, mirrors previous experiments testing male attraction to population-specific warning patterns in H. erato (e.g. Finkbeiner et al., 2014; Merrill et al., 2014; Muñoz et al., 2010). Indeed, our warning pattern manipulation of H. erato demophoon creates a similar phenotype to H. e. chestertonii (see Figure 1b), which Muñoz et al. (2010) have shown to be less attractive to neighbouring, red-banded populations of H. erato. Why the differences in interactions we observed do not translate into differences in female short-term fecundity is not immediately clear. One possibility is that anti-aphrodisiac pheromones, transferred from males to females during mating (Gilbert, 1976), which have also been hypothesized to reduce disturbance by male (Estrada et al., 2011), may mitigate any detectable costs associated with initial male interest. Another possibility is that our experiments simply lack power, especially considering the large variation in the number of eggs laid.

The results of our experiments with H. timareta may simply reflect the lack of strong differences in visual attraction. In particular, mate choice experiments with H. t. linaresi males—which were run concurrently with experiments reported here—revealed that males show only very weak preferences for the conspecific yellow pattern over a yellow-red pattern, as used in the present study (Hausmann et al., 2021). Recently, it has also become apparent that the composite colour patterns of H. heurippa may not be the target of differences in male attraction between different species of Heliconius (Mavárez et al., 2021). We initially chose to study these taxa because introgressing a red band into H. t. linaresi recreates a H. heurippa-like pattern (see Figure 1b) and is thought to reflect the evolutionary history of this putative hybrid species. We consider the initial acquisition of colour pattern alleles through hybridization and introgression an especially likely scenario affecting the kinds of dynamics we describe here. A stronger effect of warning pattern in mitigating fecundity loss due to male presence may be observed if repeating our experiments with other Heliconius species that are known to show stronger colour-based mate choice, such as H. melpomene (Merrill et al., 2019). Further experiments across a broader range of populations would be important to robustly test a role for sexual conflict in driving warning pattern divergence in Heliconius.

The rise of a new variant at an ecologically relevant locus due to interlocus sexual conflict is a challenging concept, especially if it is at the same time constrained by positive frequency dependent natural selection (e.g. Briolat et al., 2019; Sherratt, 2008). As the new variant will be less advantageous for one sex than the other (in our example, males with novel warning pattern suffer higher costs than females), an additional component of (intralocus) sexual conflict is introduced, where male and female adaptations at the same locus are in conflict (Schenkel et al., 2018). Such combined effects can hinder, but possibly also induce antagonistic coevolution between males and females (Pennell et al., 2016; Pennell & Morrow, 2013). A role for sex-specific selection driving divergence in primarily ecological traits has been suggested previously (Bonduriansky, 2011). In poison frogs, it seems that sexual selection due to female preferences for bright colours has contributed to inter-population differences in warning signals (Maan & Cummings, 2009). Similarly, evidence suggests that disturbance by male drives phenotypic diversity in colour in damselflies (Svensson et al., 2005). Although there seems to be little evidence that these damselfly colour morphs are ‘ecologically relevant’ (i.e. affecting an individual's survival due to interaction with heterospecific individuals, or the abiotic environment but see Svensson et al., 2020; Willink & Svensson, 2017), diversity appears to enhance population performance more generally by reducing overall fitness costs to females from sexual conflict (Takahashi et al., 2014). Among Papilio butterflies, which are often female-limited Batesian mimics, non-mimetic ‘male-like’ females might exist to avoid unwanted attention of males. In P. dardanus, males do indeed prefer to approach mimetic over non-mimetic (male-like) females (Cook et al., 1994). Similarly, disturbance of Alba morph females may contribute to the maintenance of polymorphism in Colias butterflies (Nielsen & Watt, 2000). Our study contributes to this body of work by explicitly testing for fitness effects resulting from sexual conflict relating to an ecological trait.

In conclusion, our theoretical results suggest that drift alone might be unlikely to drive diversification of warning patterns. However, once these patterns are additionally involved in mate choice, and the two sexes have different reproductive strategies (e.g. males are adapted to mate as often as they can, while females are not), sexual conflict can arise and contribute to warning pattern diversification. The speed at which novel patterns increase in frequency will then depend on the genetic architecture underlying adaptations in the sexes arising from this arms race. In addition, although strong dominance is frequently observed at Heliconius colour pattern loci (McMillan et al., 2020), and this will greatly aid the spread of novel a novel alleles under any if the scenarios we have explored, further work could further explore the evolution of recessive alleles. Our empirical results show that females can indeed suffer fitness costs from unwanted male attention, but this was not mitigated by females displaying unusual patterns. The failure of detecting such interaction could be caused by a number of factors, the most likely of which is that colour-based preferences of males in the taxa we used are not strong enough to see a clear effect. Future work may repeat these experiments with taxa that are known to show stronger colour-based mate choice.

AUTHOR CONTRIBUTIONS

Alexander E. Hausmann: Conceptualization (equal); formal analysis (lead); investigation (equal); methodology (equal); software (lead); writing – original draft (lead). Marilia Freire: Formal analysis (equal); investigation (equal); methodology (equal); writing – review and editing (equal). Sara A. Alfthan: Investigation (supporting). Chi-Yun Kuo: Formal analysis (supporting); investigation (supporting); supervision (supporting). Mauricio Linares: Funding acquisition (supporting); project administration (supporting); resources (equal). Owen McMillan: Funding acquisition (supporting); project administration (supporting); resources (supporting); supervision (supporting). Carolina Pardo-Diaz: Funding acquisition (supporting); project administration (equal); resources (equal); supervision (supporting); writing – review and editing (supporting). Camilo Salazar: Funding acquisition (supporting); project administration (equal); resources (equal); supervision (supporting); writing – review and editing (supporting). Richard M. Merrill: Conceptualization (lead); formal analysis (supporting); funding acquisition (lead); investigation (supporting); methodology (equal); project administration (lead); resources (equal); supervision (lead); writing – original draft (supporting); writing – review and editing (lead).

CONFLICT OF INTEREST

The authors have no conflict of interest to declare.