The significant role of post-pairing male behavior on the evolution of male preferences and female traits | Communications Biology – Nature.com

Trade-off between mate guarding and seeking additional mating

Unlike previous modeling studies on male mate choice (e.g., refs. 7,9), we include a post-pairing stage into our population genetic models that allows choosy males to have different strategies during this period. We assume that when a female chooses a male mate, reproduction occurs during which the male mate faces different post-pairing trade-offs. We first consider an intuitive trade-off between allocating effort to seeking additional mating and defending within-pair paternity (e.g., through mate guarding24,34,35 or territory defense36). In this model, males contribute nothing but gametes to the offspring (which can be interpreted as all males contributing equally in paternal care).

We assume two loci denoted P and T in our model. The first locus P determines the male preference, while T determines the expression of a female signaling trait. Specifically, we assume P2 males have a preference to mate with T2 females pre-pairing. However, it does not mean that all P2 males would mate with their preferred T2 females due to the competition with other males. And if T1 females choose to mate with P2 males, the preference for T2 females might drive those P2 males to reduce their investment in breeding within social pair (e.g., reducing their effort to mate guarding or paternal care as we explored in this study), which in turn enables them to have more effort to seeking additional matings.

We consider a pre-pairing life stagesimilar to previous models7,9. The life cycle starts by male courtship. We assume that males with the preference P2 allele are 1 + a times more likely to court preferred females (T2) than unpreferred (T1) females (at a ratio of (1 + a):1, respectively). All males compete for limited mating opportunities in the population depending on their courtship efforts (see Eqs.4, 5 in Methods). For analytical tractability, we assume polygyny in our model to ensure all females having equal mating success, and the females choose their mate based on the males courtship effort. Empirical studies have indicated that polygynous species may also engage in EPCs, causing the males to face a severe risk of cuckoldry in nature (e.g.,37,38).

After mating, a post-pairing life stage occurs, during which both males and females may engage in EPCs. We assume the ratios of within-pair offspring produced by females of different genotypes are determined by their male mates mateguarding investment. Specifically, P1 males (i.e., without preferences) would allocate a fixed effort to mate guarding, by which their female mates would engage in EPCs also at a fixed probability (denoted by ). For those females that have EPCs, we further assume that they would produce a proportion of extra-pair offspring. Therefore, the female mates of P1 males can produce extra-pair and within-pair offspring at expected proportions of and 1 , respectively. For analytical simplicity, we use a parameter (instead of 1) to represent the proportion of within-pair offspring that can be fertilized by P1 males, implying that their female mates would produce a proportion 1 of extra-pair offspring in general. For P2 males, we assume they would have a variable post-pairing behavior that depends on the phenotypes of their social mates. When they mate with unpreferred T1 females, P2 males are prone to reduce their mateguarding effort to seek additional matings15, and as a result, can only fertilize a reduced proportion () of within-pair offspring (see Eq.6 in Methods). However, they would act in a similar way to P1 males when they mate with the preferred T2 females.

We also assume P1 males would allocate fixed effort to seek EPCs (denoted by e), so do P2 males when they mate with the preferred T2 females. For P2 males that mate with unpreferred T1 females, however, they can spend additional effort (e.g., longer time and/or more energy) to seek EPCs (denoted by e + e), because of their reduced mate guarding investment. After within-pair and extra-pair copulations, females then begin to produce offspring. We delineate the full model construction processes and the detailed model analysis in the Methods.

Contrary to previous modeling outcomes that consider only a pre-pairing life stage7, our model reveals a line of neutrally stable polymorphic equilibria (Fig.1 and Supplementary Fig.1) whereby male preference and the female trait could evolve and be maintained polymorphically when the following condition is met (detailed description of each symbol can be found in Table1):

$$frac{varDelta e}{e} > frac{varDelta theta }{1-theta }$$

(1)

where (frac{varDelta e}{e}) represents the relative increase in fitness gained from additional mating by P2 males when they mate with unpreferred T1 females, and(frac{varDelta theta }{1-theta }) represents the relative loss of paternity. The equilibria of this model represents a balance between the competition for preferred T2 females, which selects against choosy P2 males7, and the selection for P2 males due to their potential for increased extra-pair paternity from additional mating to outperform within-pair paternity loss when they mate with unpreferred T1 females. Thus, an increased value of (frac{varDelta e}{e}) generally has a positive effect on the equilibrium frequencies of both the P2 and T2 alleles (Fig.1a).

a Effect of the relative increase in fitness gained from additional mating by P2 males ((frac{varDelta e}{e})). The three lines in this graph represent different values of (varDelta e). b Effect of different strengths of male preference (a). The parameters behind those lines satisfy (frac{varDelta e}{e} > frac{varDelta theta }{1-theta }), where (frac{varDelta e}{e}) represents the relative increase in fitness gained from additional mating by P2 males when they mate with unpreferred T1 females, (frac{varDelta theta }{1-theta }) represents the relative loss of paternity. For both panels, (e) = 0.8, (varDelta theta =0.1), and = 0.8. We set a = 1 in (a) and (varDelta e=0.7) in (b).

From condition (1), we can see that male preference (a) has no effect on determining the existence of stable polymorphic equilibria. However, a stronger male preference (a) can effectively hinder the evolution of male preference and female trait (i.e., resulting in lower equilibrium frequencies of P2 and T2, see Fig.1b). Intuitively, when male preference (a) is stronger, the effect of direct negative selection on the male preference would be increased. Additionally, since choosy P2 males will be less likely to mate with unpreferred T1 females in this case (i.e., under a stronger male preference), it thus may lead to a much lower chance of benefitting from additional mating, further resulting in a reduced stable frequency of the male preference P2 allele (Fig.1b).

Simulations indicated that initial frequencies of the P2 and T2 alleles determine the evolutionary outcome in this basic model (Supplementary Fig.1). The near vertical evolutionary trajectories mean that very little evolution occurs in the female T2 trait allele because all females have the same mating success regardless of the locus T. The female trait evolves only because of the indirect selection from the genetic correlation between the female trait and the male preference9, as we find that a positive linkage disequilibrium between the loci P and T arises soon (Supplementary Fig.2). Furthermore, we numerically confirmed that the linkage disequilibrium between the two loci at the line of polymorphic equilibria is always positive. The alleles P2 and T2 (and P1 and T1) are therefore associated along this line. Two mechanisms contribute to this association. First, P2 males show preferences to mate T2 females pre-pairing, resulting in nonrandom mating (i.e., it would be more likely to have P2 male-T2 female pairs than random mating). Second, when P2 males mate with unpreferred T1 females, they would reduce their guarding effort to look for extra-pair mating, resulting in a portion of offspring produced by the social pair (i.e., P2 male-T1 female) being replaced by extra-pair paternity (which could be with P1 males), while the P2 males get a chance to produce extra-pair offspring with T2 females through extra-pair mating. These two mechanisms thus enable P2 males to have a higher probability of producing offspring with T2 females than with T1 females, resulting in the positive linkage disequilibrium.

Here we also consider another possible post-pairing trade-off for males, which is between seeking additional mating and providing paternal care to ensure offspring survival and quality22. In this model, we assume males of all genotypes allocate the same effort to mate guarding, and thereby females will have the same probability to be involved in EPCs. For simplicity, we assume all females produce a proportion of within-pair offspring and a proportion 1 of extra-pair offspring. For choosy P2 males, we assume they will reduce their care investment in reproduction within social pair by a proportion, , when they mate with unpreferred T1 females, which translates to a reduction in fecundity. As a trade-off, they can allocate more efforts (i.e., e + e) to seeking additional mating (see Methods). In this case, the T2 female trait allele is more beneficial than the T1 allele due to the fecundity selection caused by male preference, i.e., T1 females (those without the trait) will suffer from a direct fitness loss when they mate with P2 males.

In this model, we find that the male preference locus always remains polymorphic when

$$frac{varDelta e}{e} > frac{bdelta theta }{(1+b)(1-theta )}$$

(2)

is met. Moreover, the T2 female trait allele always becomes fixed within the population (Fig.2b). Similar to the condition (1) in our first model, we can see that condition (2) also examines the fitness change in P2 males when paired with T1 females. The expression on the left-hand side represents the relative increase in extra-pair fitness due to increased effort. The expression on the right-hand side represents the relative loss in within-pair fitness due to reduced parental investment. When the condition is not met, both male preference and female trait can still evolve when the initial frequencies of the P2 and T2 alleles are relatively high (Fig.2a). In both cases, a high frequency of preference is maintained only when both the preference and the trait alleles start at relatively high frequencies, with the preference locus evolving downward for the majority of starting conditions (Fig.2). This is because under a higher frequency of the P2 allele, choosy P2 males not only face stronger competition pre-pairing, but also are more likely to gain a smaller amount of fitness from additional matings due to reduced paternal care investment by the social father, while their loss of within-pair fecundity remains constant. We also find that when the condition (2) is met, the frequency of the P2 allele would generally increase under a small initial value (Fig.2b). In this case, relatively low competition for additional mating might enable choosy P2 males to gain enough fitness from EPCs to outcompete the selection on pre-pairing mate preference and the paternity loss of within-pair fecundity.

a When condition (2), i.e., (frac{varDelta e}{e} , < , frac{bdelta theta }{(1,+,b)(1,-,theta )}) is met, the model may evolve to an equilibrium point on the line of ({t}_{2}=1) or on the line of ({p}_{2}=0), depending on the initial frequencies. b When (frac{varDelta e}{e} > frac{bdelta theta }{(1+b)(1-theta )}) is met, it would always evolve to an equilibrium point on the line of t2 = 1. The arrowhead curves show the evolutionary trajectories under different initial states (p2 and t2 are set as 0.1, 0.5, and 0.9, respectively). We set (varDelta e=0.1) in (a) and (varDelta e=0.8) in (b). For all runs, the other parameters are: (e=0.8), (a=1.5), (varDelta theta =0.1), (delta =0.1), (b=0.8), and (theta =0.8). .

Since expressing a signaling trait is costly to females39, we investigate whether such a costly female signal can also evolve through post-pairing behavior of choosy males. Specifically, we assume T2 females would suffer from a viability cost7, denoted by a coefficient sf. The life cycle starts with a viability selection on females (see Methods) and follows the same processes from the previous two models.

Firstly, the female trait allele is always lost from the population when there is a trade-off between mate guarding and seeking additional matings for choosy males (Supplementary Fig.3). Under the trade-off between care investment within social pair and seeking additional matings, however, both male preference and the costly female trait can still be maintained polymorphically under certain parameter values. Specifically, a relatively large reduction in care investment by P2 males that mate with T1 females (i.e., ) and/or a low cost of female trait suffered by T2 females (i.e., sf) play fundamental roles in driving the evolution, i.e., requiring

$$delta , > , {s}_{f}(1+1/b)$$

(3)

otherwise the female trait cannot evolve (Fig.3; Supplementary Note1). From the above condition, we can deduce that the female viability cost (i.e., sf) needs to be lower than (frac{bdelta }{1,+,b}), which represents the relative change of offspring produced in a single pair of T1 female and P2 male due to the reduction in paternal care. Under condition (3), there will always be a neutrally stable line of equilibria on t2 = 1 (see Supplementary Fig.4a), enabling the evolution of both male preference and the female trait.

The equilibria are given in the form of (p2, t2, D), where p2 and t2 represent the frequency of the allele P2 and S2 at each equilibrium, and D represents the corresponding linkage disequilibrium. Regions indicated in blue represent the conditions for local stability of (0, 0, 0). Equilibrium (1, 0, 0) is stable in the red color region. The region indicated in yellow represents the conditions required for local stability of an equilibrium point of ((frac{varDelta e(1,+,b)(1,-,theta ),-,bedelta theta }{varDelta ebdelta }), 0, 0). The brown region in the left panel (when ({s}_{f} < 1-theta) is satisfied) represents the conditions for a stable polymorphic equilibrium. The vertical black line shows the threshold value of when (delta ={s}_{f}(1+1/b)). In the region on the right side of this line, the model may also evolve to an equilibrium point on the line of ({t}_{2}=1) depending on the initial frequencies (e.g., Supplementary Fig.4a). Detailed conditions required for different equilibria stability can be found in the Supplementary Note1. Numerical results of the internal equilibrium (allele frequencies and linkage disequilibrium between the two loci P and T) can be found in the Supplementary Fig.5. We set ({s}_{f}=0.05) and (theta =0.7) in (a), ({s}_{f}=0.2) and (theta =0.85) in (b). The other parameters are: (b=0.8), (e=0.8).

Furthermore, when the relative fitness increase of (frac{varDelta e}{e}) is larger than (frac{bdelta theta }{(1,+,b)(1,-,{s}_{f},-,theta )}) (and sf < 1 is met), the model may also reach a stable polymorphic equilibrium (the brown color region in Fig.3a illustrates when the male preference and female trait are kept polymorphic in the population). In this instance, the evolutionary outcome is either an equilibrium point on the line of t2 = 1, or the polymorphic equilibrium point, depending on the initial frequencies (Supplementary Fig.4a).

We find that the linkage disequilibrium between the P and T loci is always positive at the polymorphic equilibrium (Supplementary Fig.5). It thus represents that the alleles P2 and T2 (and P1 and T1) are still associated under the trade-off between male paternal care and seeking additional mating. Note that in this model, P2 males would reduce their paternal care investment when they mate with unpreferred T1 females, resulting in a declined number of surviving offspring. Therefore, in combine with nonrandom mating pre-pairing, P2 males can also have a higher probability of producing offspring with T2 females, but a lower probability with T1 females than do P1 males, resulting in a positive linkage disequilibrium. In addition, numerical analysis indicates that the parameter space that allows the existence of the stable polymorphic equilibrium is larger when the strength of male preference (a) is higher (Supplementary Fig.5).

The costs of preferences have long been known to influence evolutionary outcomes in sexual selection models whereby some extra benefit from mate choice is required to enable the evolution of a costly female choice40,41. Here we also investigate whether male preference and female trait can still evolve when both are costly. For simplicity, we assume choosy P2 males also suffer from a viability cost7, denoted by a coefficient of sm and that viability selection for the male preference happens before sexual selection (see Methods). The subsequent sexual selection and reproduction processes are the same as the previous basic models.

Intriguingly, we found that the model may still have a stable polymorphic equilibrium under the post-pairing trade-off between care investment within social pair and seeking additional mating (Fig.4). Similar to the model with costly female traits described in the previous section, a relatively large reduction in care investment and a very low cost of the female trait are essential in generating a polymorphic equilibrium, i.e., requiring (delta , > , {s}_{f}(1+1/b)), and ({s}_{f} , < , 1-theta) (see Supplementary Note2 for detailed conditions required for the stabilities of different equilibria). Furthermore, when the gain in fitness from additional mating is relatively large compared to the loss of within-pair paternity and viability costs, the polymorphic equilibrium would become the only stable point (illustrated by the brown color regions in Fig.4a, b; and see Supplementary Note2). When the cost of male preference (sm) is also limited, satisfying ((1-{s}_{f})(1-{s}_{m}) > theta), then polymorphic equilibrium can be achieved under a limited reduction in care (), and also under a small increase in effort toward additional mating (e) (Fig.4a, comparing to Supplementary Fig.6), which should be biologically meaningful. Furthermore, either a higher proportion of paternity loss (i.e., under a smaller value of ) or lower costs to male preference (sm) and/or female trait (sf) can effectively extend the parameter range that favors a stable internal equilibrium generally (Supplementary Fig.7). As before, we find that the linkage disequilibrium between the P and T loci is still positive at the polymorphic equilibrium (Supplementary Fig.8). Numerical analyses also indicate that a weak male preference (a) can have a dramatically positive effect on the equilibrium frequency of the allele T2 (Supplementary Fig.8).

The color definitions for local stabilities are the same as Fig.3. Regions indicated in blue, red and yellow represent the conditions for the local stability of equilibria (0, 0, 0), (1, 0, 0) and ((frac{varDelta e(1,+,b)(1,-,{s}_{m})(1,-,theta ),-,e(bdelta theta ,+,{s}_{m}(1,+,b,-,bdelta theta ))}{(varDelta e(1,-,{s}_{m}),-,e{s}_{m})({s}_{m}(1,+,b(1,-,delta )),+,bdelta )}), 0, 0), respectively. The stable polymorphic equilibrium exists in the brown color region in (a) and (b). Detailed conditions required for local stability of different equilibria can be found in Supplementary Note2. Numerical results of the internal equilibrium (allele frequencies and linkage disequilibrium between the two loci P and T) can be found in the Supplementary Fig.8. We set ({s}_{f}=0.05), ({s}_{m}=0.05) and (theta =0.7) in (a), ({s}_{f}=0.05), ({s}_{m}=0.25) and (theta =0.8) in (b), ({s}_{f}=0.17), ({s}_{m}=0.05) and (theta =0.85) in (c), and ({s}_{f}=0.15), ({s}_{m}=0.15) and (theta =0.9) in (d). The other parameters are: (b=0.8), e = 0.8, (a=2).

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The significant role of post-pairing male behavior on the evolution of male preferences and female traits | Communications Biology - Nature.com

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