MATING UNPLUGGED: A MODEL FOR THE EVOLUTION OF MATING PLUG (DIS-)PLACEMENT

Authors


ABSTRACT

Mating plugs are male-derived structures that may impede female remating by physically obstructing the female genital tract. Although mating plugs exist in many taxa, the forces shaping their evolution are poorly understood. A male can clearly benefit if his mating plug secures his paternity. It is unclear, however, how plug efficacy can be maintained over evolutionary time in the face of counteracting selection on males’ ability to remove any plugs placed by their rivals. Here, I present a game-theory model and a simulation model to address this problem. The models predict that evolutionarily stable levels of mating-plug efficacy should be high when (1) the number of mating attempts per female is low; (2) the sex ratio is male-biased, and (3) males are sperm-limited. I discuss these results in the light of empirical data.

Many traits of male animals can be explained in terms of their contribution to two key aspects of male reproductive success: mating success and paternity (also called pre- and postcopulatory success; Andersson 1994; Simmons 2001). Some traits may enhance both aspects simultaneously: for example, relatively large body size may allow a male to gain access to females, thus enhancing mating success, and to keep other males at bay, thus securing paternity (Borgia 1979; Schuett 1997; Lewis et al. 2000). Other traits may influence mating success and paternity in opposite directions, leading to a trade-off between the two. Mate-guarding, for example, may secure a male's paternity at a cost of time and effort that could otherwise be spent seeking further females (e.g., Hasselquist and Bensch 1991; Schubert et al. 2009). Moreover, if a male prevents a female from remating, this will necessarily reduce the mating success of any potential future mates of that female. This creates a negative feedback between mating success and paternity at the population level (Queller 1997; Webb et al. 1999; Fromhage et al. 2007), fuelling an evolutionary tug-of-war between adaptations to increase paternity on the one hand and adaptations to increase mating success on the other hand (Parker 1984). Notable adaptations in this context are mating plugs (copulatory plugs), male-derived structures that can impede female remating by physically obstructing the female genital tract (Parker 1970; for other possible functions of mating plugs, see Ramm et al. 2005). Although mating plugs occur in a wide range of taxa, including mammals, birds, reptiles, amphibians, and especially arthropods (Drummond 1984; Eberhard 1996; Gomendio et al. 1998; Baer et al. 2001; Simmons 2001; Uhl et al. 2010), the forces shaping their evolution are poorly understood. A male can clearly benefit if his mating plug secures his paternity. It is less clear, however, how plug efficacy can be maintained over evolutionary time in the face of counteracting selection on males’ ability to remove any plugs placed by their rivals. This susceptibility to active removal by subsequent males sets mating plugs apart from other forms of paternity protection such as seminal proteins (Chapman et al. 2003) or anti-aphrodisiacs (Andersson et al. 2000) that hinder female remating. In the only theoretical account available to date, Parker (1984) treated mating-plug evolution as an example of the “opponent-independent costs game” (Parker 1979, 1983), which can be summarized as follows: individuals engage in pairwise asymmetric interactions; the winner of an interaction is determined by role-specific “armament” levels (e.g., mating plug quality versus mating plug removal ability); the winner obtains a role-specific payoff; each individual pays the cost of its “armament,” regardless of the outcome of an interaction. Although Parker's (1984) approach was an important step in exploring the logical possibilities of mating-plug evolution, it has two limitations. First, it relies on arbitrary payoff values, whereas several authors have since argued that, to ensure a model's internal consistency, payoffs are best derived from an explicit account of reproduction (Grafen 1987; Houston and McNamara 2005; Kokko et al. 2006). Second, Parker's (1984) prediction that “we would expect to see some cases in which a second male is able to overcome a first male's investment in remating prevention, and some cases where he fails to remate with mated females” does not identify any ecological parameters that may be relevant in this context.

Here I present a model of mating-plug evolution based on an explicit account of male reproductive success. Mating plugs exist in two main types: those formed by amorphous secretions and those formed by male genital fragments (Birkhead and Moller 1998). Because the abilities to place or remove mating plugs are likely to make different demands on a male's phenotype, I assume that these traits are subject to some kind of trade-off. The details of this trade-off are likely to differ between plug types. For example, if plugs are formed from male genital fragments (the Genital Fragment Case), this may reduce a male's capacity to mate in the future (Uhl et al. 2010), generating a trade-off between plug size, unplugging skills, and remating capacity. Alternatively, if mating plugs are formed from male secretions (the Secretory Plug Case), a given unit of resource may contribute either to the plug or to the ejaculate (e.g., Orr 1995), generating a trade-off between plug production, ejaculate production, and unplugging skills. Throughout, I use the term “ejaculate” to refer to nonplug substances only, although by a broader definition a secretory plug might be considered to be part of the ejaculate. I also consider the simplest case (the Basic Case) where a trade-off involves only plug size versus unplugging skills.

Using this framework, I predict evolutionarily stable levels of mating-plug efficacy in relation to the frequency of male–female encounters, the sex ratio, and males’ ability to replenish sperm reserves between matings.

Game-Theory Model

Consider a large population with an adult sex ratio of R males per female. During a mating season, each female experiences N mating attempts from different males, so that each male makes N/R attempts. A given attempt may be successful or not. Successful attempts are defined as involving the transfer of an ejaculate, after which the male places a mating plug on the female genital region. A male strategy is characterized by the quality x of the mating plugs produced (plug size), by its ability y to remove a predecessor's plug (unplugging skills), and by its ejaculate size z. These variables are in the range 0<x<1; 0<y<1; 0<z<1 and their relation to each other depends on the specific trade-off considered (see below). Following a game-theory approach (Maynard Smith 1982), I consider that almost all males in the population use the same strategy [inline image, inline image, inline image], called the “resident” strategy, which is challenged by a rare mutant using the alternative strategy [x, y, z]. Mating attempts with virgin females invariably succeed, whereas mating attempts with nonvirgin females may or may not succeed, depending on the previous male's plug size and the present male's unplugging skills. Specifically, if a mutant male attempts to mate with a female that was plugged by a resident, the mutant succeeds with probability

image(1)

Conversely, I define “plug efficacy” as the probability 1–inline image that a mating attempt with a nonvirgin female fails. Equation (1) was chosen because it has the following properties: (1) mating probability decreases with the previous male's plug size in a decelerating manner (Fig. 1A), (2) mating probability increases with the current male's unplugging skills in a decelerating manner (Fig. 1B); (3) parameter α (plugging ease) provides a combined measure of the effectiveness of plugging and the ineffectiveness of unplugging, reflecting the idea that factors such as morphology and female behavior may make plugging easier in some species than in others; (4) parameter β>0 ensures that mating attempts succeed by default if both plug size and unplugging skills tend to zero. Results shown use β= 0.1, which ensures that a male's investment in plugging needs to be at least on the order of a few percent of his resource budget to have an appreciable effect. However the model is robust with respect to β, yielding qualitatively similar results for β= 0.01 and β= 0.5 (not shown). The decelerating curvatures shown in Figure 1 reflect the idea that improving a trait's performance may often become more difficult at high performance levels: if a male already invests heavily in plugging, then investing still more may have a relatively weak effect on plug performance. Similarly, if he already invests heavily in unplugging, then investing still more may have a weak effect on unplugging performance. Although I assume for simplicity that mating attempts succeed in an all-or-nothing fashion, it is worth noting that in nature there is also the possibility of mating plugs being partly removed, allowing partial sperm transfer.

Figure 1.

Mating probability as a function of a focal male's unplugging skills (held fixed at y = 0.5 in panel A) and his predecessor's plug size (held fixed at x = 0.5 in panel B), for different levels of plugging ease α.

Consider a female that experiences her ith mating attempt, which is performed by a mutant male. Using this event as a reference point in time, it will be convenient to refer to earlier and later events as the female's past and future, respectively. If the female is nonvirgin (i.e., i>0), her probability of having received inline image ejaculates in the past is given by a binomial distribution as

image(2)

This takes into account that the first attempt per female always succeeds, so that inline image further matings must have occurred during i – 2 subsequent attempts (with individual success probability inline image) to add up to inline image past matings in total. Assuming that the focal attempt succeeds, the probability that this female will have inline image future matings is given by

image(3)

Here, the first row represents the probability that none of the (N – i) future attempts succeeds. In the second row, inline image is the probability that all future attempts fail until the jth future attempt. Given that the jth future attempt succeeds (with probability inline image), a binomial distribution specifies the probability that furtherinline image matings occur during the remaining N – i – j attempts to add up to inline image future matings in total. The reason for distinguishing between future mating attempts that occur before or after the first successful (jth) future attempt is that the female still has the mutant plug up to that point, and a resident plug afterwards. If a mutant is the ith male to make a mating attempt with a given female, his expected paternity from this attempt is given by

image(4)

The first row of equation (4) refers to a mutant that mates with a virgin female. The expression inline image is the probability that the female mates only with the mutant, granting him full paternity. To the right of this expression, the summation sign accounts for all possible nonzero numbers of future matings, inline image, granting paternity inline image to the mutant. This formulation implies that sperm compete for fertilizations according to a fair raffle (Parker 1998). In the second row of equation (4), inline image is the probability that the mutant's focal attempt succeeds; the first summation sign accounts for all possible numbers E of competing resident ejaculates; and the second summation sign accounts for all combinations of past and future matings that add up to a given E (where E = Epast+ Efut). Assuming that all mating attempts have equal chances to be in the ith position of a female's mate-encounter sequence, mutant fitness is given by

image(5)

Because of a fundamental link between male and female fitness (Fisher 1930), resident male fitness is always equal to 1/R, which can be verified by setting inline image and inline image in equation (5). Assuming a trade-off between plugging and unplugging skills, such that inline image (the Basic Case), I model ejaculate size in two alternative ways: without sperm limitation, ejaculate size is constant, z =inline image, implying that each male's sperm reserves are replenished between matings. With sperm limitation, each male has a fixed sperm supply (e.g., Michalik et al. 2010), so that his ejaculate size is inversely proportional to his expected number of matings. A male's expected number of matings is given by

image(6)

where N/R is his number of mating attempts, and the expression in square brackets is his success probability per attempt: here, 1/N is a male's probability of being the first to mate with a female, in which case he has guaranteed success, whereas the probability of not being the first is (1 – 1/N), in which case he has success with probability inline image. Taking the inverse of this expression, ejaculate size is given by

image(7)

To find evolutionarily stable strategies (ESSs, Maynard Smith 1982), I used the following iterative method. Beginning with an arbitrary resident strategy, I compared fitness between residents and mutants that differed by a small strategy change. Specifically, I compared the resident strategy inline image with mutant strategies inline image and inline image, where inline image is a small unit of resource. The mutant (if any) having the highest fitness was then defined as the new resident strategy. Repeated until convergence for given parameter settings, this procedure always led to the same locally stable strategy from different starting conditions, suggesting that the model has a single ESS.

Simulations

To relax the assumption of a monomorphic resident population, and to explore more complex trade-offs, I performed individual-based simulations as follows. A population contains F females and R·F males. Each individual carries three haploid loci, each of which encodes a trait (see below) that is expressed in males only. Each iteration of the simulation proceeds through the following stages.

MATING

Females and males are randomly arranged to form inline image pairs. In each pair, the male attempts to mate with the female, succeeding to do so with a probability as specified by equation (1).

MORTALITY

To ensure that both sexes have similar expected life spans, the sex ratio among individuals that die at any given time step is constrained to R. Individuals that die at a given time step are selected by two criteria: (1) all individuals that have reached their maximum number of matings or matings attempts die; (2) if the sex ratio among these individuals differs from R, then a suitable number of additional members of the underrepresented sex die, where each individual's probability of death is proportional to age (number of time steps since birth). Parameter N specifies the maximum number of mating attempts per female.

REPRODUCTION

Each female produces 2(1 + R) offspring at the end of its life. Paternity for each offspring is independently determined by a fair raffle among the ejaculates received by its mother. Each offspring receives a set of alleles by unlinked Mendelian inheritance. Then its alleles mutate with independent probability μ, such that new allelic values are drawn from a bounded normal distribution centered around the previous value (with standard deviation σ for loci 1 and 3, and standard deviation σm for locus 2; see below). Offspring are stored in a pool from which new adults are recruited to replace the dead. The offspring pool contains a maximum of F + RF individuals; excess numbers are eliminated by discarding randomly chosen offspring.

Males are subject to one of the following trade-offs.

BASIC CASE

This case is similar to the game theory model. Locus 1 is initialized as a random number between 0 and 1 that encodes a male's investment in unplugging skills (y). Plug size is given by x = 1 – y. Locus 2 is initialized as a random integer between 1 and 100 that encodes a male's mating capacity, m, defined as the maximum number of matings that he is capable of performing given unlimited mating opportunities. This formulation creates a trade-off between the amount of any finite resources expended in each mating and the maximum number of matings that can be performed. With sperm limitation, a male's ejaculate size is given by z = 1/m. Without sperm limitation, ejaculate size is given by z = 1.

GENITAL FRAGMENT CASE

This case is similar to the Basic Case, except that the size of an individual mating plug is given by x = (1 – y)/m. This generates a trade-off between plug size and mating capacity.

SECRETORY PLUG CASE

This case is similar to the Genital Fragment Case, except that it uses an additional variable, Z (encoded by locus 3; initialized as a random variable between 0 and 1), to specify how resources are allocated between mating plug production and ejaculate production. A male's ejaculate size is given by z = (1 – y)Z/m. Plug size is given by x = (1 – y)(1– Z)/m.

Results shown are arithmetic means across 10 replicate simulations per parameter combination. Each replicate ran for 5000 iterations, by which time an equilibrium was reached. Settings: F = 100; μ= 0.05; σ= 0.1.

Results and Discussion

In almost all cases, the number of mating attempts per female (N) is negatively associated with mating plug efficacy (Figs 2A, 3–5). There are three intuitive reasons for this: First, low N implies that mating attempts with virgin females make up a relatively large proportion of all mating attempts. Because mating attempts with virgin females require no unplugging skills to be successful, they reduce, when common, the need for males to invest in unplugging. Second, high N implies that there are many mating opportunities per male, selecting for high male mating capacity. If a trade-off exists between mating capacity and plug size (as is true in the Genital Fragment and Secretory Plug Case, but not in the Basic Case), high male mating capacity decreases plug size (Figs. S2–S4) and hence plug efficacy (Figs. 3–5). Third, high N increases the intensity of sperm competition. In the Secretory Plug Case, this selects for high ejaculate production (Fig. 3G–I) as predicted by previous theory (Parker et al. 1997; Parker and Ball 2005; Fromhage et al. 2008). High ejaculate production undermines plug efficacy by directing resources away from (un)plugging (Fig. S2). Only in the Basic Case with sperm limitation, plug efficacy remains high at any value of N (Figs. 2 and S1), providing an example of the more general finding that sperm limitation enhances plug efficacy (compare Fig. 4 versus Fig. 5). This finding can be explained as follows: whereas sperm-limited males can increase their number of matings only at the cost of transferring fewer sperm in each mating (resulting in a weak incentive for multiple mating), sperm-replenishing males do not incur this cost, resulting in a strong incentive for multiple mating. A male can increase his mating frequency by emphasizing his unplugging skills. Thus, by generating a strong incentive for multiple mating, sperm replenishment undermines plug efficacy.

Figure 2.

ESS plug efficacy in the game theory model, with or without sperm limitation. R = 1.

Figure 3.

Simulation model, Secretory Plug Case. Plug efficacy, mating capacity, and ejaculate production, as found for various parameter combinations of N, α, R.

Figure 4.

Simulation model, Genital Fragment Case without male sperm limitation. Plug efficacy and male mating capacity, as found for various parameter combinations of N, α, R.

Figure 5.

Simulation model, Genital Fragment Case with sperm limitation. Plug efficacy and male mating capacity, as found for various parameter combinations of N, α, R.

For a given value of N, plug efficacy is higher at a higher sex ratio R (males/females) (Figs. 3A–C, 4A–C, and 5A–C). This result arises because higher R implies that there are fewer mating opportunities per male. This selects for low mating capacity m (Figs. 3D–F, 4D–F, and 5D–F), whereby males can produce larger plugs (Figs S2A–C, S3A–C, and S4A–C).

In the Genital Fragment Case, high plug efficacy is associated with high plug size and low unplugging skills (Figs. 4A–C, 5A–C, S3, and S4). This implies a negative relationship between plug size and unplugging skills, such as might be expected given a trade-off between plugging versus unplugging. In the Secretory Plug Case, by contrast, high plug efficacy is associated with both high plug size and high unplugging skills (Figs. 3A–C and Figs. S2A–F, D–F). This pattern arises because the extent to which males invest in ejaculate production (Fig. 3G–I) relates negatively to their investment in (un)plugging.

Although the present study considers several possible trade-offs, it is worth noting that there are still other possibilities. For example, instead of modeling unplugging skills as a “structural” trait that requires a one-time investment during development, as I have done here, one could model costs of unplugging as an increasing function of the number and quality of the mating plugs that are being removed. The latter alternative might be more appropriate for species in which mating plug removal requires large amounts of time and energy.

Empirical testing of the present model's predictions requires comparisons across species or populations. For example, one could test for a negative relationship between plug efficacy and estimates of mate-encounter rate, or for a positive relationship between plug efficacy and the extent of male sperm limitation. Sperm limitation could be established by showing a lack of sperm production during the reproductive period (Michalik et al. 2010), or by measuring to what extent ejaculate size and (experimentally manipulated) male mating rate are negatively correlated. Because N and R have counteracting effects in the present model, empirical tests should ideally aim to estimate both of these parameters, and to test their effects while controlling for each other.

A number of studies provide support for the assumption that variation in plug size underlies variation in plug efficacy. Polak et al. (2001) showed that the probability of a future copulation in female Drosophila hibisci flies increased sharply with an experimental decrease in plug size. Similarly, natural variation in plug size negatively predicted female remating in the spider Agelena limbata (Masumoto 1993) and the butterfly Atrophaneura alcinous (Matsumoto and Suzuki 1992). Moreover, Simmons (2001) showed that increases in male expenditure on the mating plug are associated with reductions in female remating across butterfly species. Evidence for the costliness of secretory mating-plug production comes from rodents, where the accessory glands involved in plug production (as well as the plugs produced) are larger in species thought to face a high degree of sperm competition (Ramm et al. 2005). Similarly, in fungus-growing ants, males of monogynous species (defined as having only one queen per colony) have large accessory glands that produce a mating plug, whereas males of polygynous species have smaller accessory glands and lack plugs (Hosken et al. 2009).

Compared to the numerous descriptions of mating plugs across taxa, traits facilitating the removal of mating plugs have been described relatively rarely. This may be because the structures used for plug removal typically serve more than one purpose. For example, the shovel-like copulatory organs in papilionid butterflies appear to allow plug penetration and/or removal (Matsumoto and Suzuki 1992; Orr 1995).

Mating plugs that do not prevent female remating may serve alternative functions, such as stimulation of sperm transport (Ramm et al. 2005), prevention of sperm loss (Woyciechowski et al. 1994) protection from sperm desiccation (Huber 1995), or female fecundity stimulation (Timmermeyer et al. 2010; for theoretical accounts of fecundity stimulation in a context of sperm competition, see Cameron et al. 2007; Alonzo and Pizzari 2010). The mating plug of the honey bee even appears to promote female remating, although the adaptive value of this remains unclear (Wilhelm et al. 2011). Ineffective mating plugs may also exist temporarily when a mating system is not in evolutionary equilibrium. This may be the case after a sudden evolutionary improvement of unplugging skills, or after females have evolved a counter-adaptation against plugging. The latter has been suggested for the spider genus Nephila, in which genital fragment plugs are effective in at least one species (Fromhage and Schneider 2006) but not in others (Schneider et al. 2008; Kuntner et al. 2009). More generally, although the present model has focused on male strategies, it is clear that females too can play an active role in mating-plug placement and/or removal. If females incur costs from being plugged (e.g., Sauter et al. 2001; Arnqvist and Rowe 2005), they may evolve the ability to eject plugs (Lorch et al. 1993; Eberhard 1996; Koprowski 1992). Conversely, if females benefit from plugs (e.g., nutritional benefits or reduced harassment rates), they may assist in mating plug placement (Knoflach 1998; Aisenberg and Eberhard 2009). Regarding the present model, we can envisage such variation in terms of different levels of “plugging ease” (α). In species where females are selected to resist plugging, α should be low; in species where females benefit from plugging, α should be high. Ultimately it would be desirable to integrate the study of mating plug evolution with the question of what determines female evolutionary interests in the first place. In view of the complex nature of female evolutionary interests (which are shaped by an interplay between ecology, genetics, morphology, physiology and behavior; Eberhard 1996; Zeh and Zeh 2003; Arnqvist and Rowe 2005), this remains a major challenge for the future.


Associate Editor: P. Stockley

ACKNOWLEDGMENTS

I thank A. Houston, J.M. Schneider, P. Michalik, and G. Uhl for helpful comments on the manuscript. I dedicate this article to the memory of A. Seitz.

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