Which cues are sexy? The evolution of mate preference in sympatric species reveals the contrasted effect of adaptation and reproductive interference

Abstract Mate preferences may target traits (a) enhancing offspring adaptation and (b) reducing heterospecific matings. Because similar selective pressures are acting on traits shared by different sympatric species, preference-enhancing offspring adaptation may increase heterospecific mating, in sharp contrast with the classical case of so-called “magic traits.” Using a mathematical model, we study which and how many traits will be used during mate choice, when preferences for locally adapted traits increase heterospecific mating. In particular, we study the evolution of preference toward an adaptive versus a neutral trait in sympatric species. We take into account sensory trade-offs, which may limit the emergence of preference for several traits. Our model highlights that the evolution of preference toward adaptive versus neutral traits depends on the selective regimes acting on traits but also on heterospecific interactions. When the costs of heterospecific interactions are high, mate preference is likely to target neutral traits that become a reliable cue limiting heterospecific matings. We show that the evolution of preference toward a neutral trait benefits from a positive feedback loop: The more preference targets the neutral trait, the more it becomes a reliable cue for species recognition. We then reveal the key role of sensory trade-offs and the cost of choosiness favoring the evolution of preferences targeting adaptive traits, rather than traits reducing heterospecific mating. When sensory trade-offs and the cost of choosiness are low, we also show that preferences targeting multiple traits evolve, improving offspring fitness by both transmitting adapted alleles and reducing heterospecific mating. Altogether, our model aims at reconciling “good gene” and reinforcement models to provide general predictions on the evolution of mate preferences within natural communities.


Impact summary
Mate preferences are widespread throughout the animal kingdom and generate powerful selective forces impacting the diversification of traits and species.The evolution of such preferences has been the focus of multiple theoretical and empirical studies and intense scientific debates.The evolution of mate preference (a) enhancing offspring fitness and (b) reducing heterospecific mating have been mostly studied separately, except in the specific case of preference for so-called ''magic traits'' that increase both offspring survival and species divergence.However, in many cases, the evolution of traits in sympatric species generates conflicting evolutionary forces acting on preferences.On one hand, enhanced offspring survival promotes preference toward locally adaptive traits and may thus lead to convergent evolution of traits among sympatric species.On the other hand, the evolution of similar traits in sympatric species may generate costly heterospecific sexual interactions promoting preference toward traits that diverge between species.Here, we thus build a general mathematical model to investigate the evolutionary factors determining which and how many traits are targeted by mate choice.We especially determine whether preferences will likely target adaptive versus neutral traits.Our model highlights that the evolution of preferences for adaptive versus neutral traits in sympatric species depends not only on within-species mating opportunities but also on the niche overlap between species, tuning heterospecific interactions.By jointly considering (a) the selection regimes acting on the targeted traits within species, as well as (b) interactions with other species living in sympatry, our theoretical study provides a general framework reconciling these research fields.

Introduction
The evolution of mate preference plays a major role in diversifying traits (Chouteau et al., 2017) and species (Stre et al., 1997).Nevertheless, we still know little about the evolutionary factors determining the traits preferentially targeted by preferences.Preferences target traits displayed by the parents, but their evolution may depend on the indirect fitness benefit brought to the offspring carrying locally adapted traits (Neff & Pitcher, 2005).The evolution of mate preference depends not only on intraspecific competition but also on the ecological interactions with sympatric species.When species occur in sympatry, sexual interactions with heterospecifics (Gröning & Hochkirch, 2008) can lead to fitness reduction because of limited survival in the resulting hybrids (Merrill et al., 2012), but also because of costly heterospecific courtship and rivalry.These fitness costs generated by heterospecific interactions can promote mate preferences targeting traits that differ between species (McPeek & Gavrilets, 2006;Yamaguchi & Iwasa, 2013).The evolution of preferences may thus depend on both (a) the selection regimes acting on the targeted traits within species and (b) the distribution of these traits in other species living in sympatry.Such multifactorial selection acting on the different traits displayed by males may then favor the evolution of female preferences targeting several traits.Preference for multiple cues may improve some components of fitness in the offspring and/or limit heterospecific matings (Candolin, 2003).
However, by contrast with classical ''magic'' traits under disruptive selection (Servedio et al., 2011), natural selection frequently promotes similar traits in different sympatric species (e.g., in mimetic species, Sherratt 2008).Indirect fitness benefits enjoyed by the offspring may promote preference increasing the risk of heterospecific matings (e.g., Gumm & Gabor 2005;Higgie & Blows 2007).Preference targeting multiple traits may then improve offspring fitness by both transmitting adapted alleles and reducing heterospecific mating (Candolin, 2003).However, several constraints might limit the number of traits targeted by preference (Iwasa & Pomiankowski, 1994;Pomiankowski & Iwasa, 1993;Schluter & Price, 1993).The number of available partners displaying the preferred combination of traits may also impact the evolution of preference for multiple traits.The cost of choosiness associated with rejecting unpreferred males by choosy females may increase when the number of targeted traits grows.The complex cognitive processes involved may also limit the evolution of preference for multiple traits (Crapon de Caprona and Ryan, 1990).
Here, we propose a general mathematical framework to predict the trait targeted by mate choice, when preferences for locally adapted traits increase heterospecific mating.We use mathematical modeling to investigate the evolution of preference based on multiple traits, assuming sensory trade-offs impacting the relative perception of different mating cues.We study the evolution of preference toward two evolving traits (T 1 and T 2 ) shared by a pair sympatric species (A and B).We assume that selection regimes acting on traits increase species similarity.We aim at identifying how selection regimes acting on the targeted traits, as well as reproductive interference between species, favor (a) preference for locally adapted trait versus trait reducing heterospecific mating and (b) preference for single versus multiple traits.

Model overview
We consider two sympatric species (A and B) and assume that individuals from both species display two traits that female preferences could target.We assume that both traits are controlled by independent haploid loci (called T 1 and T 2 , respectively), with two possible alleles 0 or 1 at each locus.For the sake of simplicity, we assume that alleles 0 or 1 code for trait values 0 or 1, respectively.We fix the genotypic distribution in species B by assuming that all individuals carry the allele 1 at both trait loci.We assume that a parameter  modulates the strength of female preferences.The loci P 1 and P 2 then determine the value of traits T 1 and T 2 , respectively, preferred by females.Female preference can target either or both traits (T 1 and T 2 ) displayed by the males: A preference locus M controls the relative level of attention paid by the female toward trait T 1 versus trait T 2 expressed by males.We thus introduced  as the relative preference weighting, modulating the level of attention on either trait (Figure 1).We assume that a resident and mutant allele can occur at locus M with different values of  ( r and  m ).We then study the evolution of the relative preference weighting in focal species A. Assuming nonoverlapping generations and relying on an adaptive dynamics framework, we investigate the fixation of new mutant alleles and estimate the equilibrium relative preference weighting ( * ).The ancestral relative preference weighting is given by  t 0 .
The evolution of the relative preference weighting depends on the survival of the produced offspring.We thus assume that the traits T 1 and T 2 displayed by the individuals can modify their survival.s 1 and s 2 gives the selective advantages of allele 1 at locus T 1 and T 2 , respectively.We assume that s 1 ≥ 0 and s 2 ≥ 0 so that natural selection acts within species A promotes similarity with species B (recall that allele 1 is fixed for both traits in species B).We also assume that females can encounter and have sexual interactions with heterospecifics.Such sexual interactions lead to fitness costs but do not produce any viable offspring.
To model a sensory trade-off acting on preferences, we also assume that the level of attention on one trait diminishes the attention on the alternative one.We investigate several shapes of this trade-off tuned by the parameter a (Figure 1).Finally, we assume that after refusing a mating opportunity females may not encounter another male with a probability c, leading to a cost of choosiness.We investigate how the cognitive trade-off and the costs of choosiness impact the evolution of the direction of preference, which might lead to a preference for either a single or multiple traits.

Selection regime acting on the displayed traits
We assume that individuals display two different traits T 1 and T 2 , each controlled by a single biallelic locus.We assume that the traits T 1 and T 2 displayed by the individuals can modify their survival.Let  = {0, 1} 5 , be the set of all genotypes at loci T 1 , T 2 , P 1 , P 2 , and M. We define f i and f ′ i as the frequencies of genotype i ∈  in the focal species before and after a step of natural selection acting on survival, respectively.The resulting frequency after selection, f ′ i is then given by where w i is the fitness of an individual of genotype i during natural selection, and the mean fitness w is a normalization term to ensure that genotype frequencies sum to 1 after selection.
We recall that s 1 and s 2 are the selective advantages of allele 1 at locus T 1 and T 2 , respectively.The fitness component due to the natural selection of an individual of genotype i is thus given by: where (T 1 ) i and (T 2 ) i refer to the allele (0 or 1) an individual of genotype i carries at loci T 1 and T 2 , respectively (following Kirkpatrick et al., 2002).For example, (T 1 ) i = 1 and (T 2 ) i = 0 for an individual carrying allele 1 at locus T 1 and allele 0 at locus T 2 .

Reproductive success depending on female preference on traits displayed by males
Preference based on multiple traits Females generally use both traits in mate choice but may vary in their relative attention given to trait T 1 versus trait T 2 .This relative attention depends on the relative preference weighting parameter .
Alleles at locus M determine the relative preference weighting: allele 0 (resp.1) is associated with the value  r (resp. m ).Translating into an equation, the relative preference weighting of a female of genotype j is thus given by: where (M) j is the allele (0 or 1) at locus M in genotype j.We assume that a cognitive trade-off, described by the function f, also impacts the relative attention to the two traits.f(1 -) and f() determine the attention on trait T 1 and T 2 where a ∈ [0, +∞) and The function f is non-decreasing, so attention on one trait diminishes attention on the alternative trait.Moreover, f(0) = 0 and f(1) = 1, so the female choice relies on a single trait in the two extreme cases.The parameter a tunes the shape of the trade-off function f (Figure 1): selection acting on the preferred traits.Here, we assume two sympatric species, A and B, depicted in this scheme as butterfly species with different wing shapes.
The individuals can display two traits, T 1 and T 2 , represented by the forewing and hindwing colors as an example.We study the coevolution of the trait values (0 or 1, shown as intense versus light color of the wings) and the preference in species A. We assume that all individuals in species B displayed the trait value 1 (intense color) at both traits.We assume a selection step, promoting trait value 1 at both traits in species A, increasing similarity with species B, where value 1 is fixed for both traits.We then assume a reproduction step, where the mating success of the different individuals in species A depends on the traits and preferences carried by males and females.In particular, females of species A may attempt costly and unfertile sexual interactions with males of species B depending on their preferences.(B) Genetic basis of preference.Depending on the genotype at locus M, females modulate their level of attention toward either trait displayed by males (relative preference weighting ).We also assume that the level of attention on one trait diminishes the attention on the alternative one.We investigate several shapes of this trade-off tuned by the parameter a.
• when a = 1, f is linear, leading to a linear trade-off, where the female attention on traits 1 (resp.2) is proportional to 1 - (resp.).• when a < 1, f is concave, leading to a weak trade-off between attention toward the two male traits.Females can thus use both traits for mate choice.• when a > 1, f is convex, leading to a strong trade-off in female attention between the two traits.Females focusing on one trait largely ignore the alternative trait, and intermediate values of  lead to poor attention to both traits.
Therefore, when a female of genotype j encounters a male of genotype k, she accepts the male with probability where 1 {.} is the indicator function that returns 1 if the condition in the subscript is realized and 0 otherwise.The mating probability for a pair composed of a female with genotype j and a male with genotype k depends on the match between the female's preferred traits (given by (P 1 ) j and (P 2 ) j ) and the male's traits values (given by (T 1 ) k and (T 2 ) k ).When the female does not prefer the male traits (either (P 1 ) j ≠ (T 1 ) k or (P 2 ) j ≠ (T 2 ) k ), the female tends to reject the male.The parameter  quantifies the strength of female preference.

Mating process
We assume that females can mate at most once.We assume that each female sequentially meets males in a random order.These males can be either conspecifics or heterospecifics (see Figure 2 for an illustration of the mating process).At each encountering event, the female may accept the male with a probability depending on her preference and on the traits displayed by the encountered male.
Given that a female of genotype j encounters a male uniformly at random, T(j) gives the realized probability that a female of genotype j accepts a conspecific (Otto et al., 2008): where N and Ñ are species A and B densities, respectively.T(j) depends on (a) the probability of encountering a conspecific versus a heterospecific male, (b) on the distribution of traits within conspecific males, and (c) on female preference.
A female of genotype j may also accept a heterospecific male with a probability where c ri ∈ [0, 1] modulates the probability for the female to accept heterospecific males.This parameter may capture the effect of other unmodeled traits the females can assess and tune the strength of reproductive interference.We assume a same genetic Figure 2. Illustration of the mating process.We assume that females can mate at most once.We assume that each female meets sequentially random males, which can be either conspecifics or heterospecifics.At each encounter, the female accepts or rejects the male with a probability depending on the female's preference and the male's traits.After an encounter, a female accepts a conspecific (resp.heterospecific) male with probability T (resp.T ri ).If a female engages in heterospecific mating, she produces totally unviable offspring.Because females mate at most once, a female engaged in a heterospecific mating cannot recover the associated fitness loss.Moreover, we assume that females refusing a mating opportunity can encounter another male with a probability of 1 -c.We interpret c as the cost of choosiness.
architecture of traits in species A and B, f k is the frequency of genotype k in species B. We assume that the allele 1 is fixed at both trait loci (T 1 and T 2 ) in species B. We assume that heterospecific crosses produce totally unviable offspring.Because females mate at most once, a female engaged in a heterospecific mating cannot recover the associated fitness loss.
However, we assume that females refusing a mating opportunity encounter another male with a probability of 1 -c.We interpret c as the cost of choosiness.The probability that a female of genotype j mates with a conspecific male is thus given by where ((1-T(j)-T ri (j))(1-c)) n is the probability that a female of genotype j rejects the n males she first encounters and then encounters an (n + 1) -th male.

Mating success of a pair
We now compute the mating success of a pair.Knowing that a female of genotype j has mated with a conspecific male, the probability that this male is of genotype k is given by The contribution to the next generation of a mating between a female of genotype j and a male of genotype k m j,k is thus given by the product of (a) the probability that a female of genotype j mates with a conspecific male (j) with (b) the probability the female mates with a male of genotype k knowing that the female has mated with a conspecific male Φ(j, k) Genotypic frequencies after reproduction in the focal species then depend on the contribution to the next generation of the different crosses between females and males of genotype j and k, respectively, described by m j,k , for all j and k in .We note m the mean value of this contribution across all mating pairs The frequency after reproduction of genotype i in species A is then given by where (i, j, k) the probability that a mating between a female of genotype j and a male of genotype k produces an offspring of genotype i. (i, j, k) describes the segregation of alleles during reproduction.We assume recombination between female and male haplotypes.The offspring inherits any of the two recombined haplotypes with a probability one half.

Mutation
We assume that mutations occur at loci T 1 , T 2 , P 1 , and P 2 within offspring with probability u T 1 , u T 2 , u P 1 , and u P 2 , respectively.
We summarize all the model's variables and parameters in Supplementary Table A1.

Invasion analyses
In an adaptive dynamics framework, we study the invasion of a rare mutant at locus M associated with the value of relative preference weighting  m in a resident population where the resident allele codes for the value  r .We assume that the mutation has a small effect, so that  r - m is small.Before the mutant introduction, we assume that genotypic frequencies at loci T 1 , T 2 , P 1 , and P 2 evolve toward equilibrium allelic frequency values named P * T 1 , P * T 2 , P * P 1 , and P * P 2 .Initially, we assume no genetic association.For the parameters space explored in this study, the initial allele frequencies have no impact on the evolutionary dynamics (see Supplementary Appendix A2).Studying mutant invasion for all possible resident populations, we estimate the different types of singular relative preference weightings numerically (Geritz et al., 1998;Rousset, 2004): • Continuously stable relative preference weighting: The model predicts a convergent evolution toward this gamma value, and once this value is reached, any mutant associated with other gamma value will then fail to invade.• Evolutionary repeller: The model predicts that the evolution of gamma will always strongly depart from this value.• Branching point: The model predicts a convergent evolution toward this gamma value, but once this value is reached, mutants associated with other gamma value will invade, leading to polymorphism (never observed in this study).
We determine the equilibrium relative preference weighting ( * ), that is, the continuously stable relative preference weighting reached by the dynamics that may depend on ancestral preference ( t 0 ).By default, we assume that ancestral preference equally targets both traits ( t 0 = 1/2).

QLE analysis
Assessing mutant invasion would first require estimating the 2 4 -1 = 15 equilibrium genotypic frequencies at loci T 1 , T 2 , P 1 , and P 2 in the resident population (with the resident allele fixed at locus M).Then, the 2 5 -1 = 31 genotypic frequencies at loci T 1 , T 2 , P 1 , P 2 , and M would need to be tracked down throughout the generations following mutant introduction, to determine whether the mutant allele invades.To simplify the model analyses, we perform a quasi-linkage equilibrium (QLE) analysis.The QLE approach allows to analytically estimate the change in allele frequencies and in genetic associations (Kirkpatrick et al., 2002).Under the QLE hypotheses, the genetic associations quickly reach their equilibrium value (Nagylaki, 1993), so they can be approximated by their equilibrium value (Kirkpatrick et al., 2002).Using the estimated change of allele frequencies at loci T 1 , T 2 , P 1 , and P 2 under QLE approximation, we compute the equilibrium allele frequencies at these loci before mutant introduction.We then use the sign of the change of mutant allele frequency in the resident population under QLE approximation to assess mutant invasion.We compute the selection gradient S by rewriting the approximated change of mutant frequency under QLE (given in Equation A10) where  =  m - r is the effect of the mutant allele on the relative preference weighting.When the selection gradient is positive (resp.negative), selection promotes the evolution of preference toward the trait T 2 (resp.T 1 ).Using the selection gradient S, we can disentangle the relative effects of the different selection pressures acting on the evolution of the relative preference weighting.We decompose the selection gradient in four terms where S os , S or , S ri , and S c (those expressions are given in Equations A21, A22, A16, and A18) capture the effect of offspring survival, offspring reproductive success, reproductive interference, and cost of choosiness on mutant fitness, respectively.More precisely, S os and S or capture the indirect fitness benefit of producing offspring carrying locally adapted and sexy traits, respectively.S ri and S c capture the direct fitness benefit for a female of reducing heterospecific mating and the cost of choosiness.
The QLE analysis assumes that selection is weak and recombination is strong compared to selection.In line with this hypothesis, we assume that s 1 , s 2 , , c ri , and c are of order  with  being small and recombination rates of order 1.We also assume that mutation rates are of order .We perform the QLE analysis using Wolfram Mathematica 12.0 and provide detailed results of these analyses in Supplementary Appendix A1.
To check the robustness of specific results, we also run numerical analyses, relaxing the QLE assumptions (e.g., Supplementary Figure A5).

Default parameters
If not specified, we use the following parameter values:

''Good genes'' versus reinforcement
To explore the evolution of preference-enhancing offspring fitness versus reducing heterospecific mating, we computed the equilibrium value of the relative preference weighting  * when assuming that natural selection acts on trait T 1 , increasing similarity with species B (s 1 > 0), while the trait T 2 is neutral (s 2 = 0).We investigate different strengths of natural selection acting on trait T 1 (s 1 ) and reproductive interference (c ri ) (Figure 3).

The neutral trait becomes a reliable cue for species recognition
Assuming that the two species do not sexually interact (c ri = 0), the model predicts that female preference will target the trait under selection T 1 (Figure 3).In contrast, assuming reproductive interference between the two sympatric species promotes the evolution of preference targeting the neutral trait T 2 .A female of species A prefers trait value 0 (Supplementary Figure A2), reducing sexual interaction with males from species B always displaying the trait value 1 (see Equation A6).Sexual selection thus increases the phenotypic divergence with heterospecific (see Equation A1), making the neutral trait T 2 a more reliable cue for species recognition in species A.
Figure 4C confirms that the selective advantage owing to reproductive interference rises when the resident preference tends to target the neutral trait.When preference toward the neutral trait T 2 increases, the stronger sexual selection enhances the phenotypic divergence with heterospecific (Supplementary Figure A3), making T 2 a more reliable cue for species recognition.Then in an adaptive dynamic framework, during the recurrent fixation of mutant alleles, a positive feedback loop promotes preference toward the neutral trait T 2 .As long as natural selection is strong relative to reproductive interference, females from species A prefer males with the allele 1 at the trait under selection (Supplementary Figure A2), also displayed by the males of the sympatric species B. However, when reproductive interference is strong relative to natural selection, female preference targets the neutral trait T 2 reducing heterospecific mating rather than enhancing offspring fitness.  .We fixed the level of reproductive interference (c ri = 0.0025) and assume that trait T 1 is under natural selection (s 1 = 0.02), while trait T 2 is neutral (s 2 = 0).We assume the cost of choosiness (c = 0.001).When the line is green (resp.purple), the corresponding evolutionary force (offspring survival, offspring reproductive success, reproductive interference, and cost of choosiness) promotes the evolution of preference toward the neutral selection T 2 (resp.the trait under selection T 1 ).The more intense the color, the more intense the selection.

Species interaction limits preference enhancing offspring fitness
Figure 4A reveals that the selective benefit of producing adapted offspring decreases when resident preference targets the trait under selection.When preference toward the trait under selection T 1 increases, the stronger sexual selection reduces the genetic diversity (Supplementary Figure A3).As most males displayed the well-adapted trait value 1 (Supplementary Figure A3), the advantage of preference toward the trait under selection decreases.By contrast with the evolution of the preference toward the neutral trait, a negative feedback loop limits the evolution of preference toward the trait under selection.
Moreover, the selective benefit of producing sexy sons promotes preference toward the neutral trait (Figure 4B and Supplementary Figure A4).Because natural selection strongly reduces the phenotypic diversity at trait T 1 , almost all males display the sexy trait value at T 1 (Supplementary Figure A3).By contrast, males exhibiting the trait value 0 at the neutral trait T 2 benefit from a sexual selection advantage compared to other males.Female preference toward males exhibiting this trait values at trait T 2 is then further advantaged through an indirect benefit gained by their sexier sons (see Equation A19).The ''sexy son'' advantage promotes the neutral trait T 2 if the strength of reproductive interference is sufficiently high and promotes preference for the trait value 0 at the neutral trait T 2 (Supplementary Figure A4).This enhanced ''sexy son'' advantage associated with female preferences toward neutral compared to adaptive traits can explain why preference toward cues reducing heterospecific mating can preferentially evolve.
Figure 3 suggests that reproductive interference should be weak for preference targeting the trait under selection T 1 to evolve.However, our analyses rely on the hypothesis that all evolutionary forces are weak.Supplementary analyses, relaxing the weak selection hypothesis, show that preference targeting the trait under selection T 1 can still evolve for larger values of reproductive interference, pending strong natural selection relative to reproductive interference (Supplementary Figure A5).

Evolution of preference for multiple traits enhancing offspring fitness and reducing heterospecific mating
Nevertheless, the contrasted selective pressures may promote the evolution of preference toward both traits, therefore jointly enhancing offspring fitness and reducing heterospecific mating.
We thus test which values of cost of choosiness (c) and shapes of the trade-off function f (through the parameter a) allow the evolution of preference for multiple traits.

Without species interactions, the cost of choosiness promotes ancestral preference
Assuming no interaction between species (c ri = 0), the model predicts that preference will almost always target the trait under selection T 1 (Supplementary Figure A6).Nevertheless, when the ancestral preference targets the neutral trait T 2 and assumes a low sensory trade-off, the cost of choosiness can maintain preference toward the neutral trait T 2 (Supplementary Figure A6b).

Ancestral single trait preference can limit the evolution of preference for multiple traits
We then investigate the effect of ancestral preferences on the evolution of relative preference weighting expressed in females.We compare ancestral preferences targeting: equally both traits ( t 0 = 0.5), mainly the trait under selection or the neutral trait ( t 0 = 0.01 or  t 0 = 0.99).
Figure 5A-C show that preferences are biased toward ancestral preference.Interestingly, ancestral preference influences the evolution of mate preference when substantial trade-offs and cost of choosiness are assumed.Under a strong trade-off, preference based on both traits effectively leads to poor attention toward both traits.This lack of attention toward both cues, therefore, creates a fitness valley preventing the switch of female attention from one trait to the alternative one.When female choice is mainly based on one trait ancestrally, positive selection promoting choice for the alternative trait may not be powerful enough to cross this fitness valley.
Figure 4D indicates that the cost of choosiness also favors the evolution of preference toward the ancestrally most preferred trait because this trait is then likely to be highly prevalent in the males suitable for reproduction.Mate choices mainly target the already preferred trait and then benefit from a reduced cost of choosiness (see Equation A17).
Moreover, when the ancestral preference mostly targets one trait, Figure 4B indicates that sexual selection promotes preference for this trait.When a trait is already sexy, females carrying a mutant allele increasing their attention on this trait are likely to produce more sexy sons.
These mechanisms explain why the evolution of preference strongly depends on the ancestral traits, as observed in Figure 5. Interestingly, Figure 5B also shows that when the ancestral preference equally targets both traits, preference targeting the trait under selection is favored.However, this may depend on the strength of the sensory trade-off and the cost of choosiness.= 0.01), (B) equally both traits ( t 0 = 0.5), and (C) mainly trait T 2 ( t 0 = 0.99).We assume reproductive interference (c ri = 0.0025), that trait T 1 is under natural selection (s 1 = 0.02) and trait T 2 is neutral (s 2 = 0).multiple traits.This preference enhances offspring fitness and reduces heterospecific mating by using the trait under selection and the neutral trait, respectively.More substantial cognitive trade-offs or cost of choosiness prevent the evolution of such preference for multiple traits.Interestingly, a linear trade-off (log(a) = 0) leads to preference based on a single trait.A concave tradeoff (a < 1) is thus necessary for the evolution of preference for multiple traits.

Low cost of choosiness and weak sensory trade-off allow the evolution of preference for multiple traits
The cost of choosiness and the sensory trade-off promote single trait preference targeting the adaptive trait When ancestral preference equally targets both traits, a strong sensory trade-off promotes preference toward adaptive traits (Figure 5).When assuming a large sensory trade-off (a > 1), the ancestral preference leads to poor attention toward both traits.This poor attention toward male traits limits the previously described ''sexy sons'' effect that promotes preference toward the neutral trait (Supplementary Figure A7).
A large cost of choosiness also promotes single-trait preference targeting the trait under natural selection T 1 , assuming that ancestral preference equally targets both traits.Indeed natural selection acting on trait T 1 reduces phenotypic diversity in species A and, therefore, reduces the cost of choosiness associated with preference based on the trait T 1 in this species (see Equation A17and Supplementary Figure A8).
In contrast, an intermediate cost of choosiness allows the evolution of a preference for multiple traits with biased attention toward the neutral trait T 2 (Figure 5).When the cost of choosiness is not too high, the ''sexy son'' advantage obtained through slightly biased attention toward the neutral trait balances it.However, the preference for the adaptive trait becomes more advantageous when the cost of choosiness further increases: Such preference alleviates the cost of choosiness, thus favoring the single trait preference targeting the trait T 1 when the cost of choosiness becomes too large.

Connecting ''good genes'' with reinforcement
To explore the impact of natural selection acting on mating cues shared with other sympatric species on the evolution of female preferences, we computed the equilibrium value of the relative preference weighting  * for different strengths of (a) natural selection at trait T 1 and T 2 (s 1 and s 2 ) and of (b) levels of reproductive interference (c ri ).

Without species interactions, the trait under stronger selection is sexy
As expected, Figure 6A shows that without species interactions (c ri = 0), female preference mainly targets the trait under stronger selection.Furthermore, Figure 6A also highlights that in the absence of reproductive interference, preference for multiple traits is likely to emerge when both traits are under strong selection.The impact of variation in mutation rates at the different loci is described in Supplementary Figure A9.

Assuming reproductive interference, the trait under lower selection becomes sexy
By contrast, assuming reproductive interference with species B (c ri > 0), females from species A mainly target a single trait.When natural selection on the trait T 1 and T 2 is low, the effect of reproductive interference prevents the evolution of preference toward the traits under the strongest selection (Figure 6B) because such preference increases the risk of heterospecific mating.Preference toward this trait indeed increases the frequency of the allele 0 at this locus, enhancing the reliability of this trait as a cue preventing heterospecific matings, since allele 1 is fixed at both traits in species B. When reproductive interference further increases (Figure 6C, the parameter space under which a trait can become a reliable cue-limiting heterospecific mating increases.Finally, Figure 6B and 6C also show that when natural selection acting on the traits T 1 and T 2 is very high, preference targets again the trait under the strongest selection, highlighting how natural selection may override the effect of reproductive interference.
Altogether our results show the relevance of jointly considering the effect of natural selection acting on mating cues within species, but also on the cues displayed in sympatric species to understand the evolution of mate choice.

Discussion
Evolutionary biologists have extensively studied the evolution of mate preferences in the light of the ''good genes'' hypothesis (Puurtinen et al., 2009) or the context of reinforcement (Servedio & Noor, 2003).By jointly considering (a) the selection regimes acting on the targeted traits within species, as well as (b) interactions with other species living in sympatry, our theoretical study provides a general framework reconciling these research fields.
We focused on natural selection regimes shared between sympatric species promoting species similarity and increasing risks of reproductive interference.For example, in the spadefoot toad, a preference for mating call increases the number of eggs fertilized in choosy females.However, it leads to reproductive interference because of the similarity of calls between sympatric species (Pfennig, 2000).Our approach drastically differs from classical studies on reinforcement, focusing on ''magic traits'' that are under disruptive selection between species (Servedio et al., 2011).Because ''magic traits'' are honest signals of both local adaptation and species identity, antagonistic selection regimes are not involved in the evolution of mate preferences in such a framework.Here, we investigate conflicting selections acting on the evolution of mate preferences.
We show that depending on the relative strength of natural selection and reproductive interference, females may prefer traits under natural selection, improving offspring fitness, or neutral traits, reducing heterospecific mating.Selection promotes preferences for traits under natural selection only when natural selection is strong relative to reproductive interference.Our results also show that conflicting selection may promote the evolution of preference for multiple traits.Preferences targeting multiple traits may improve offspring fitness by both transmitting adapted alleles and reducing heterospecific mating.For example, in field crickets of the genus Teleogryllus, females target both (a) cuticular hydrocarbons, providing fitness benefits to their offspring (Berson & Simmons, 2019) and (b) male calling song (Hill et al., 1972) that differentiates sympatric species (Moran et al., 2020).
Nevertheless, the cost of choosiness limits the evolution of such preference and can change the trait mainly targeted by female choice.The cost of choosiness promotes preference based on naturally selected traits rather than traits allowing species recognition.As natural selection erodes phenotypic diversity, preference based on traits allowing species recognition leads to stronger opportunity cost, promoting preference targeting the naturally selected traits.However, when the cost of choosiness is more limited, our model highlights that female preference may then preferentially target traits that differ from other species.For example, in Heliconius butterflies, where females are usually mated rapidly after emergence because of a high density of suitable males, female preference has been shown to target chemical cues differentiating sympatric species (González-Rojas et al., 2020).
Our model assumes that traits allowing limiting heterospecific mating are neutral.However, selective constraints may also act on traits used as species recognition cues.For instance, variation in such cues may influence their detection probability by predators: The conspicuousness of a trait may enhance the identification by sexual partners but may, in turn, also increase parasitism and predation risks (observed on visual, acoustic, and olfactory cues in numerous organisms reviewed in Zuk & Kolluru, 1998).Increasing costs of sexual trait conspicuousness may theoretically promote the display of combinations of cryptic traits allowing recognition (Johnstone, 1995), therefore promoting preference toward multiple cues.
Our results also highlight how indirect fitness benefits and/or reproductive interference can promote female preference for multiple traits.The evolution to such a preference occurs only when the cognitive trade-off is weak.Multiple traits-based mate choice may thus preferentially evolve in species where multiple sensory systems allow such cognitive integration.Nevertheless, due to evolutionary trade-offs, the development of sensory systems is frequently associated with the regression of others (Barton et al., 1995;Nummela et al., 2013).Moreover, physical constraints may generate sensory trade-offs.For example, a visual system model of the surfperch reveals a trade-off in the performance between luminance and chromatic detection because of the limited numbers of the different types of cones in the eyes (Cummings, 2004).Neural integration of multiple information may also be limited, generating trade-offs in using multiple traits in decisions.In the swordtail fish Xiphophorus pygmaeus, females prefer a visual or an olfactory trait when experimenters expose them to the variation of only one out of the two traits in the potential mates.However, when both traits vary in potential mates, females do not express preference (Crapon de Caprona and Ryan, 1990), suggesting that sensory trade-off limits the use of multiple traits in preference.
Nevertheless, several alternative decision mechanisms may reduce cognitive trade-offs.For example, sequential/hierarchical mate preference, whereby targeted traits are processed in a hierarchical order, efficiently produces a decision, even considering many traits (Gigerenzer et al., 1999).Sequential mate preference is common (e.g., Eddy et al., 2012;Gray, 2022;Shine & Mason, 2001) and may allow the evolution of preference for multiple traits.Sequential mate choice may emerge because some traits are visible at long distances (such as color or calls).In contrast, others are perceived only at short distances (such as oviposition site guarded by males or male-emitted pheromones) (e.g., Candolin & Reynolds, 2001;López & Martín, 2001;Mérot et al., 2015).
The distance at which choosers perceive different traits may play a key role in reproductive isolation (Moran et al., 2020).Females using a cue for species recognition detectable at a short distance may have already spent time and energy or need to deploy substantial efforts to avoid heterospecific mating.Therefore, females may still suffer from increased costs associated with reproductive interference, even if they eventually manage to avoid mating with heterospecific males (Gröning & Hochkirch, 2008).Hence, reproductive interference may promote preferencetargeting traits detected from far distances that efficiently reduce heterospecific interactions.
Reproductive isolation between species also depends on the niche of individuals of both species.Mating may preferentially occur between individuals sharing the same niche leading to niche-based assortative mating.Niche segregation may play a key role in the evolution of reproductive isolation.In two treefrog species, differing by their mating call (Park et al., 2013), different spatial and temporal segregations in calling and resting places during the breeding period increase reproductive isolation (Borzée et al., 2016).As well as sequential mate preference, niche segregation may efficiently participate in reproductive isolation without generating a trade-off with a preference for other traits.
Our study shows how natural and sexual selection may have a conflicting influence on the evolution of mate choice, specifically on the emergence of for multiple traits in sympatric species.Our study highlights the importance of (a) identifying the tradeoff limiting attention toward different traits and (b) estimating the strength of the cost of choosiness to understand what traits are likely to be targeted by preference.

Figure 1 .
Figure 1.Schematic description of the model.(A) Life cycle.The evolution of the preference may depend on the interactions between species and natural

Figure 3
Figure3also indicates that natural selection promotes preference toward the trait under selection T 1 .As long as natural selection is strong relative to reproductive interference, females from species A prefer males with the allele 1 at the trait under selection (Supplementary FigureA2), also displayed by the males of the sympatric species B. However, when reproductive interference is strong relative to natural selection, female preference targets the neutral trait T 2 reducing heterospecific mating rather than enhancing offspring fitness.

Figure 3 .
Figure 3. Evolution of relative preference weighting toward a trait under selection T 1 or a neutral trait T 2 ( * ), depending on the strength of natural selection acting on trait T 1 (s 1 ) and the strength of reproductive interference (c ri ) when T 2 is neutral (s 2 = 0).

Figure 4 .
Figure 4. Decomposition of the fitness gradient into terms associated with (A) offspring survival (S os ), (B) offspring reproductive success (S or ), (C) reproductive interference (S ri ), and (D) cost of choosiness (S c ), depending on the resident relative preference weighting value ( r ).We fixed the level of reproductive interference (c ri = 0.0025) and assume that trait T 1 is under natural selection (s 1 = 0.02), while trait T 2 is neutral (s 2 = 0).We assume the cost of choosiness (c = 0.001).When the line is green (resp.purple), the corresponding evolutionary force (offspring survival, offspring reproductive success, reproductive interference, and cost of choosiness) promotes the evolution of preference toward the neutral selection T 2 (resp.the trait under selection T 1 ).The more intense the color, the more intense the selection.

FigureFigure 5 .
Figure5Ashows that a weak cognitive trade-off (log(a) < 0) and low cost of choosiness (c) allow the evolution of preference for

Figure 6 .
Figure 6.Evolution of relative preference weighting toward traits T 1 or T 2 ( * ), depending on the strength of natural selection acting on trait T 1 and T 2 (s 1 and s 2 ), for different strengths of reproductive interference (c ri ).We assume (A) c ri = 0, (B) c ri = 0.01, and (C) c ri = 0.02.