Selection on Female Remating Interval Is Influenced by Male Sperm Competition Strategies and Ejaculate Characteristics

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Selection on female remating interval is influenced by male sperm competition strategies and ejaculate characteristics

Suzanne H. Alonzo1 and Tommaso Pizzari2 rstb.royalsocietypublishing.org 1Department of Ecology and Evolutionary Biology, Yale University, New Haven, CT 06517, USA 2Department of Zoology, Edward Grey Institute, University of Oxford, Oxford OX1 3PS, UK

Female remating rate dictates the level of sperm competition in a population, and extensive research has focused on how sperm competition generates Research selection on male ejaculate allocation. Yet the way ejaculate allocation strategies in turn generate selection on female remating rates, which ultimately Cite this article: Alonzo SH, Pizzari T. 2013 influence levels of sperm competition, has received much less consideration Selection on female remating interval is despite increasing evidence that both mating itself and ejaculate traits affect influenced by male sperm competition multiple components of female fitness. Here, we develop theory to examine how the effects of mating on female fertility, fecundity and mortality interact strategies and ejaculate characteristics. Phil to generate selection on female remating rate. When males produce more fer- Trans R Soc B 368: 20120044. tile ejaculates, females are selected to mate less frequently, thus decreasing http://dx.doi.org/10.1098/rstb.2012.0044 levels of sperm competition. This could in turn favour decreased male ejaculate allocation, which could subsequently lead to higher female remating. One contribution of 14 to a Theme Issue When remating simultaneously increases female fecundity and mortality, females are selected to mate more frequently, thus exacerbating sperm ‘The polyandry revolution’. competition and favouring male traits that convey a competitive advantage even when harmful to female survival. While intuitive when considered Subject Areas: separately, these predictions demonstrate the potential for complex coevolu- behaviour, evolution tionary dynamics between male ejaculate expenditure and female remating rate, and the correlated evolution of multiple male and female reproductive traits affecting mating, fertility and fecundity. Keywords: sexual selection, sperm allocation, polyandry, sexual conflict, mathematical model 1. Introduction Author for correspondence: Parker recognized two major evolutionary implications of female polyandry. Suzanne H. Alonzo First, when females have the opportunity of mating with multiple males, ejacu- e-mail: [email protected] lates can compete over the fertilization of a set of ova, a process known as ‘sperm competition’ [1]. Second, polyandry causes potential for a conflict of fitness interests between the female and her prospective mates with respect to different reproductive decisions, such as the rate at which a female should mate with new males, differential female sperm selection for fertilization, and differential parental investment [2,3]. Here, we focus on conflict over female remating and investigate the consequences of male traits involved in sperm competition for female fitness and selection on female remating behaviour. Extensive research has focused on understanding sperm competition as a component of sexual selection and an evolutionary agent of traits involved in mating and fertilization [4–6]. This work has shown that in several species the outcome of sperm competition is influenced by male investment in traits, such as the number of viable sperm delivered by an ejaculate [7–12], and/or the rate at which sperm are retained in the fertilizing pool [13–16]. The energetic demands of ejaculate production are sufficiently high that males must trade off ejaculate expenditure with investment in other reproductive traits [4,17,18]. An extensive theoretical framework has been developed to examine the evolution of male strategies of economic ejaculate allocation under varying levels of sperm competition [4,19]. A subset of sex allocation theory [20], ejaculate economic theory, is a powerful tool to understand variation in ejaculate expenditure in the light of sperm competition at multiple levels, from

macroevolutionary responses across species to facultative As far as we are aware, no theory has examined explicitly 2 responses within individual males [19,21]. As a result, we how female remating rate is expected to respond to effects of sbryloitpbihn.r hlTasRScB38 20120044 368: B Soc R Trans Phil rstb.royalsocietypublishing.org have an ever increasing appreciation of the effect of female mating and male ejaculate allocation on female fitness. Here, remating behaviour on male ejaculate allocation strategies. we address this gap by presenting new theory to examine However, the opposite causality of this relationship has selection on female remating rate in response to patterns of received surprisingly less consideration. Theory has exam- male sperm investment and ejaculate characteristics. We ined how a presumed net negative effect of mating on first develop a general framework for thinking about the female survival may affect the evolution of female mating various interacting factors that influence selection on preferences and remating rate [22–25]. Reality is likely to female remating rate. We then consider if and when feed- be more complex, however, because remating and ejaculates backs may arise between female remating rate and male comprise multiple integrated traits, such as sperm, nuptial adaptations to sperm competition. All else being equal, gifts and seminal fluid components. The way in which increased selection on female remating will shorten female these individual traits interact to affect female fitness and in remating intervals which will increase the level of sperm turn generate selection on female remating behaviour competition, while prolonged female remating intervals will remains largely unresolved and theoretically unexplored relax competition among ejaculates. The evolution of female (but see [26]). Yet, this baseline understanding is a necessary remating interval therefore has direct consequences for first step towards being able to predict the coevolution of sperm competition, which may drive selection on both multiple male and female reproductive traits affecting male and female traits involved in mating, fertilization and mating, fertility and fecundity. sperm competition. Consequently, it is important to examine This gap in theory is particularly problematic considering how male traits affect selection on female mating patterns the increasing empirical evidence that mating and ejaculate as a first step in predicting the coevolutionary dynamics traits can have a considerable impact on female fitness, of female and male traits involved in mating, sperm mostly through their influence on fertilization success, competition and fertilization. female fecundity and longevity [27]. First, the traditional assumption that female reproductive success is not sperm limited has come under increasing scrutiny, and mounting 2. A general life-history model of selection on evidence suggests that a single ejaculate might not be necessarily sufficient to guarantee maximal fertilization success female remating interval [19,28–31]. Depletion of female sperm stores occurs through Here, we examine how positive and negative effects of a range of mechanisms, including sperm use during fertiliza- mating and ejaculate characteristics interact to affect selection tion, the progressive loss of sperm from female sperm storage on female remating rate. We first describe a general life- sites (in internal fertilizers) or from the vicinity of the ova (in history model, extended to consider these effects. We then external fertilizers), and the rate at which post-meiotic sperm derive a more specific version of this model to make predic- senescence leads to sperm mortality, progressive loss of fertil- tions regarding how female survival costs of remating izing function, and loss of zygotic viability following interact with sperm depletion and male effects on female fertilization by ageing sperm [32,33]. Sperm limitation may fecundity to determine selection on female remating rate. be a particularly relevant aspect of an ejaculate’s fertilizing Both of these formulations (equations (2.1) and (3.1)) make efficiency in both external fertilizers [30,34–36] and internal the following assumptions: we assume that reproduction fertilizers, where prolonged sperm storage may impair fertil- (i.e. mating and offspring production) occurs continuously ity and zygote viability through sperm senescence [33]. (rather than seasonally) but that mating and offspring pro- Second, increasing evidence indicates that the number of duction do not occur simultaneously (i.e. females alternate eggs produced by a female (fecundity) can be influenced by between mating and producing offspring). In addition, our non-sperm components of an ejaculate, or other male traits discrete time life-history model is based on the assumption associated with mating. For example, the spermatophylax that each single mating event is followed by one or more of certain orthopterans [37,38] and the ejaculate of several offspring-producing bouts (the number of which determines lepidopterans contain nutrients that can directly influence the remating interval). Finally, for simplicity, we assume that the fecundity of a female [39]. Similarly, accessory gland prod- females control whether or not they mate, and that females ucts, such as ovulin and the sex peptide of male Drosophila adopt a single remating interval. In other words, we do not melanogaster, interact intimately with the female reproductive consider here the possibility that female remating interval, tract to generate a transient stimulation of the female ovipos- survival, fecundity or fertility depend on female age or ition rate [40]. In other species, male stimulation of female other state variables (but see [49]) or that other female traits fecundity can be mediated by specialized behaviours associated or behaviours might evolve with female remating interval. with mating, such as the provision of nuptial gifts, courtship While these possibilities are biologically plausible under feeding and sexual cannibalism [41]. Finally, mating often some conditions, exploring these effects is beyond the scope reduces female longevity (e.g. [42] but see [43]). Mating may of this study. We first focus on how female remating interval be costly to females because of the inherent risk or energetic affects female fitness, and do not examine selection on, or costs of mating. However, it is also known that male genitalia variation in, other female traits or behaviours. and behaviours (such as mate guarding) involved in sperm A female’s expected reproductive success in a given time competition can increase female mortality [44–46]. In particu- period will depend on the probability she will survive (S) lar, ejaculate products such as seminal fluid compounds have from birth to the current offspring-producing time period, been increasingly implicated in mating costs. For example, her fecundity in this offspring-producing period (F, the D. melanogaster accessory gland peptides can shorten female number of eggs produced) and her fertility at this time (P, lifespan, and impose net fitness costs on females [47,48]. the probability her eggs will be fertilized; see table 1 for a Downloaded from http://rstb.royalsocietypublishing.org/ on January 29, 2017

Table 1. Definitions for key variables and parameters used in the model. 3 sbryloitpbihn.r hlTasRScB38 20120044 368: B Soc R Trans Phil rstb.royalsocietypublishing.org general W(t) female lifetime expected fitness t number of offspring-producing bouts since the last mating m number of mating events t remating interval (the number of offspring-producing bouts between mating events) T maximum number of offspring-producing bouts (can be infinite) survival S(t,m,t) probability of survival from birth to time period mt þ t s probability of survival between offspring-producing time bouts m survival cost per mating, 1 – m is the probability of surviving each mating event fertility N(t,m,t) quantity of viable sperm stored by a female at time t since the last mating m P(t,m,t) probability of fertilization t time periods since the last mating n quantity of viable sperm received from a male at each mating p proportion of stored sperm remaining after each new mating event d the proportion of sperm lost or depleted between offspring-producing periods r fertilization rate fecundity F(t,m,t) female fecundity f baseline female fecundity (without male effect) f maximum effect of mating on female fecundity r proportion of f remaining following each time period since last mating

description of key variables and parameters). Consider a survival, fertility and fecundity. In general, we would reproductively mature female, and let m represent the expect female fertility (i.e. the probability of fertilization) to number of times she has mated, t, the number of offspring- decline with time since mating. The rate of decline will producing bouts between mating events and t, the number depend on a number of biological factors, such as the of offspring-producing time periods since the last mating number and quality of sperm received from the male as event. We are interested in how variation in S, F and P well as patterns of female sperm storage and usage. While (arising from variation in t, m and t) affect selection on the fertility will usually decline as remating rate decreases, remating interval (t). Let T represent the maximum number remating rate and the time since last mating can have both of offspring-producing bouts or time periods (which could positive and negative effects on female survival and fecund- under some conditions be infinite). The expected lifetime ity [50]. Selection on female remating interval will therefore reproductive success of a female (W(t)) is the sum of her depend on the complex balance between these multiple expected reproductive success across all time periods positive and negative effects of mating. (where she first mates and then produces offspring for t time periods before mating and producing offspring again). This yields 3. A more specific example of selection on dXT=te Xt WðtÞ¼ Sðt; m; tÞPðt; m; tÞFðt; m; tÞ; ð2:1Þ female remating interval m¼1 t¼1 The equation (2.1) is neither intended nor able to yield specific predictions. Instead, it captures the multiple effects where the notation dT/te indicates a ‘ceiling function’ which that mating may have on female fitness. In order to make rounds up to the next integer. If the maximum number of off- more quantitative predictions, we need to make specific spring-producing bouts (T ) is not an integer multiple of the assumptions about how survival, fertility and fecundity are number of offspring-producing bouts between matings (t), affected by male ejaculate characteristics and female remating the summation will include term(s) for after the end of the rate. Consider the following biological scenario: imagine that maximum lifespan where those terms will have the value each mating event carries an immediate additional risk of of zero. This is simply a life-history model of female fitness mortality (m), where 1 – m gives the probability of surviving extended to examine the fitness effects of female remating each mating (which is assumed here to be static rather than interval (t) and consider the effects of fecundity (F) and fer- a function of time since mating or the number of mating tility (P) on reproductive success separately (given the events). Let s represents the baseline probability of surviving assumptions outlined above). The relative fitness of a particu- between offspring-producing periods, independent of mating lar remating interval will depend on how mating affects (assumed to be static as well). We will assume as above that Downloaded from http://rstb.royalsocietypublishing.org/ on January 29, 2017

4 activity mate produce offspring mate produce offspring sbryloitpbihn.r hlTasRScB38 20120044 368: B Soc R Trans Phil rstb.royalsocietypublishing.org survival s s ..s s s ..s 1 – m 1 – m ...... offspring pf pf pf pf pf pf

time period t t = 1 2 ... t = 1 2 ... t (offspring producing)

matings m m+1

Figure 1. The structure of the specific life-history model of female remating interval. Female lifetime expected reproductive success depends on female remating interval (t), the probability of surviving a mating event (1 – m) and each offspring-producing bout (s), and the probability of fertilization ( p) and fecundity ( f ) within each offspring-producing bout. The life history represented here yields equation (3.1). See text for further details on the assumptions of the model and the derivation of the fitness function. females produce offspring in discrete reproductive bouts matings ( p,figure2a). Females therefore ‘accumulate’ sperm (or time periods) and that they may mate between these as they mate with multiple males over their lifetime. Let bouts, where t represents the number of offspring-producing N(t,m,t) represent the number of viable sperm stored by a bouts between mating events (figure 1). female that has survived m mating events, with t reproductive Female expected lifetime reproductive success then becomes bouts between each mating and whose last mating occurred t

dXT=te Xt time units ago where m ðm1Þtþt ðtÞ¼ ð mÞ ð ; ; tÞ ð ; ; tÞ; ð : Þ t ðtþtÞ W 1 s P t m F t m 3 1 Nðt; m; tÞ¼nð1 dÞ þ npð1 dÞ m¼1 t¼1 þþnpðm1Þð1 dÞððm1ÞtþtÞ where, as in equation (2.1), the notation dT/te indicates a Xm ‘ceiling function’ which rounds up to the next integer. If the ¼ npði1Þð1 dÞðði1ÞtþtÞ: ð3:2Þ maximum number of offspring-producing bouts (T ) is not i¼1 an integer multiple of the number of offspring-producing Over time, there will be a balance between the input of bouts between matings (t), the summation will include new viable sperm (determined by n and t) and the loss terms after the end of the maximum lifespan which will of viable sperm (determined by p and d, figure 2a). Note have the value of zero. From this equation, one can see that that this equation assumes that sperm begin to decline in via- (as in the more general case presented above) the optimal bility and availability immediately after mating (such that remating interval will be determined by a balance between N(1,1,t) ¼ n(1 – d) rather than n). This is consistent with the the negative effect of mating on survival (e.g. m), the positive idea that females store sperm and a delay exists between effects of mating on fertility (e.g. changes in P with t) and the mating and the first bout of fertilization and offspring way in which male traits and remating rate affect female production. For species for which this is not a reasonable fecundity (e.g. how F changes with t, m and t). Next, we assumption, t would be replaced with t – 1 in equation (3.2). derive specific equations that capture how female fecundity This has little quantitative and no qualitative effect on the and fertility are affected by remating rate and male ejaculate outcome of the model. traits, under the assumption that mating itself is costly (as While this sperm storage scenario represents only one represented in equation (3.1)). option of multiple biologically plausible scenarios, it allows for the entire continuum between no storage ( p ¼ 0) and com- plete storage ( p ¼ 1), and therefore captures a broad range of (a) Sperm storage and depletion dynamics and species. All else being equal, females will be We assume that the amount of viable sperm available to a more sperm limited as p decreases (figure 2a,b). It is worth female declines between mating events due to sperm noting that remating by a female always decreases the expected depletion (e.g. the rate at which sperm become unavailable share of paternity of her previous mates, as long as some of or inviable over time). The dynamics of sperm storage (and their sperm remain viable. Therefore, conflict between the use) between mating events will also influence the total sexes with respect to paternity and female remating always amount of viable sperm available to a female. exists at some level as long as the sperm of a male has non- Here, we consider the scenario where female sperm stor- zero probability of fertilization if the female does not mate age capacity does not limit the maximum quantity of viable again with another male. Our analyses focus on how the effects sperm available for fertilization and where a proportion ( p) of mating on female fecundity, fertility and survival interact to of the remaining sperm from each earlier ejaculate is removed shape selection on female remating interval. at each new mating (where 0 , p , 1). Here, the total amount of viable sperm stored is determined by the number of new sperm delivered by the current insemination (n), the pro- (b) Female fertility portion of sperm lost or depleted between time periods (d) The probability of an egg being fertilized is typically an and the proportion of viable sperm remaining from earlier asymptotically increasing function of the number of viable Downloaded from http://rstb.royalsocietypublishing.org/ on January 29, 2017

(a) given in equation (3.2) (figure 2c). In equation (3.3), 5 erNðt;m;tÞ represents the probability that all of the available sbryloitpbihn.r hlTasRScB38 20120044 368: B Soc R Trans Phil rstb.royalsocietypublishing.org viable sperm will fail to fertilize the egg (i.e. the probability

) 200 t no fertilization occurs based on a Poisson distribution where the mean number of ‘events’ is l ¼ rN(t,m,t)). The par- 150 ameter r represents the relative number of sperm required for fertilization and will vary among species depending, for example, on mode of fertilization [30]. Equation (3.3) implies 100 viable sperm, N ( t , m generally that (all else being equal) the probability that an egg will be fertilized declines with time since mating (t), and the rate of decline is determined by the relative value 20 40 60 80 100 of parameters r, d and n, which determine the amount of time (b) 500 sperm needed for fertilization, the rate of sperm depletion following insemination, and the total amount of viable sperm a 400 p = 1 female obtains at each mating, respectively (figures 2c and 3a). Our analyses focus on how the number of viable sperm 300 received at each mating and the rate of sperm depletion (represented by n and d, respectively), are predicted to affect selection on female remating interval. 200 p = 0.5 asymptotic sperm storage 100 p = 0.01 (c) Female fecundity We consider the possibility that mating and/or ejaculate traits 0 5 10 15 20 can have gonadotropic effects on female fecundity (see §2). (c) female remating interval, t Here, we consider the situation where mating has an acute

) 1.0

t effect on average female fecundity, such that expected fecundity (F(t)) depends on time since last mating (t). This captures 0.8 the biological case where female fecundity is increased by mating, for example, owing to resources obtained from the 0.6 male at mating. Let f represents the baseline fecundity of the female without any male effect, f, the maximum effect of 0.4 mating on female fecundity (which could be positive or negative as long as 2 f , f)andr gives the proportion of that 0.2 effect on fecundity that is lost per time period since mating.

probability of fertilization, P ( t , m Female fecundity F(t) can then range between f and f þ f depending on time since last mating (t), such that 0 20 40 60 80 100 time FðtÞ¼f þ frt1: ð3:4Þ

Figure 2. The dynamics of sperm storage. (a) The number of viable sperm We focus on cases where there is either no effect of mating available to a female varies over time (and here time is determined by the time on fecundity (f ¼ 0) or a positive effect of mating on fecund- since last mating (t), number of mating events (m), the remating interval (t), such ity (f . 0; figure 3b). In general, we ask how large the that total time ¼ t m þ t), the number received at each mating (n), the positive effect on fecundity must be to outweigh the negative proportion depleted per time period (d), and the proportion that remain after each effects of mating on female survival. This allows us to deter- new mating event ( p). (a–c) Black lines represent p ¼ 0.01, dashed lines p ¼ 0.5 mine the degree to which male traits that affect female and grey lines p ¼ 1,andresultsshownareford ¼ 0.1, n ¼ 100 and t ¼ 5. fecundity have secondary effects on female mating behaviour (b) Females that have mated multiple times reach an asymptotic maximum level of (i.e. propensity to remate) and thus sperm competition sperm storage which depends on remating interval (t), proportion of sperm (figure 3c). We also ask how these costs and benefits of retained ( p) and sperm depletion (d, mathematically this is given by finding the mating interact with male ejaculate characteristics such as t limit of equation (3.2) for t ¼ 0asm!1 or n=ð1 pð1 dÞ Þ: (c)The the number of viable sperm delivered and the rate of sperm probability of fertilization P(t,m,t) varies with the number of available sperm and depletion to determine selection on female remating rate. In fertilization rate (shown here for N(t,m,t)from(a)andr ¼ 0.01). the future, this framework would also enable one to consider alternative scenarios where fecundity might vary with the number of matings (m), time since reproductive maturity (mt þ t) or remating interval (t) directly. sperm available to a female at the time of fertilization [7,11,12]. The probability of fertilization (P(t,m,t)) at any time (t) since the last mating will depend on the amount of viable sperm stored by the female (N(t,m,t), given in equation 4. Results of the specific model (3.2)) and can be represented by the general equation It is not possible to solve the above equations analytically. It is, Pðt; m; tÞ¼1 erNðt;m;tÞ; ð3:3Þ however, possible to calculate female fitness and find the remating interval (t) that maximizes female reproductive where r represents the rate at which sperm encounter and fer- success for any given set of parameters. We present the results tilize eggs, and the number of available sperm (N(t,m,t)) is of these numerical analyses both graphically and verbally Downloaded from http://rstb.royalsocietypublishing.org/ on January 29, 2017

(a) 1.0 delivered by an ejaculate and the rate of sperm depletion 6 from the female sperm stores, (ii) male/ejaculate effects on sbryloitpbihn.r hlTasRScB38 20120044 368: B Soc R Trans Phil rstb.royalsocietypublishing.org 0.8 female fecundity, and (iii) the interactive effects of female sperm depletion and male/ejaculate fecundity effects.

) 0.6 t (a) Female responses to the number of viable sperm 0.4 P ( t,m, and sperm depletion 0.2 For simplicity, we first examine the effect of sperm viability

probability of fertilization, and costs of mating in isolation. Consider the situation where mating has no direct effect on female fecundity (i.e. F ¼ f and 0462 810 f ¼ 0), but carries a risk of mortality for females (m . 0). Selec- (b) 2.0 tion on remating interval will then be determined by the joint effect of mating mortality costs (m) and sperm limitation (represented by the initial number of sperm inseminated (n)and 1.5 the rate of sperm depletion following mating (d)) on female fitness. In this case, the only benefit of mating is in avoiding 1.0 sperm depletion. All else being equal, the optimal remating interval is predicted to increase as the survival cost of mating (m) increases (figure 4). For a given value of m, decreasing 0.5

female fecundity, F ( t ) the amount of sperm a female receives per mating also selects for more frequent mating (figure 4, compare panels from left to right), as does more rapid sperm depletion (figure 4, compare 0462 810within each panel from bottom to top). The pattern of sperm (c) storage (figure 4, compare across rows) has very little quantita-

) 30 tive effect when sperm numbers and quality are relatively high. t When sperm limitation is high (e.g. low n or r and high d), 25 however, greater sperm storage ( p large) is predicted to 20 favour shorter remating intervals (figure 4, far left column). One might expect lower storage to favour shorter intervals, 15 all else being equal, since lower storage reduces the amount 10 of sperm available (figure 2b). Our analyses indicate that the survival cost of mating is only outweighed by the fertility 5 benefits of mating when sperm storage (and the associated

lifetime expected fitness, W ( potential for high fertility) is high. Perhaps surprisingly, greater 20 4 6 8 10 sperm storage by females can therefore favour shorter remating female remating interval t intervals, particularly in species where sperm is limiting. It is important to note that even if females achieve their optimal Figure 3. Female fertility, fecundity and fitness as a function of remating remating interval, they are predicted to tolerate striking interval. (a) The probability of fertilization declines with time since last reductions in fertility when mating comes at a cost to female mating. The rate of decline is determined by the total amount of sperm survival (e.g. for the optimal remating rate of t ¼ 9givenby received per mating (n) and the proportion of sperm (d) that are depleted or the black line in figure 3c, the associated female’s expected fer- ¼ become inviable between each offspring-producing period (black line n tilization rate is predicted to drop from 100 per cent to ¼ ¼ ¼ 1000, d 0.25; grey line n 100, d 0.5). Solid lines represent limited approximately 50 per cent before she will mate again, as ¼ storage ( p 0.01), while dashed lines represent nearly unlimited storage shown in figure 3a by the solid black line). ( p ¼ 0.99) (b) Female fecundity may be unaffected (black line, f ¼ 0) or increase with mating (grey line f ¼ 1, r ¼ 0.25). (c) Female lifetime expected reproductive success is determined by fertilization, mortality and (b) Female responses to effects of remating interval fecundity (for both lines f ¼ 1, r ¼ 0.01, T ¼ 1000 and s ¼ 0.99, other on fecundity parameters as given for (a) and (b)). Although low and high levels of sperm We now consider how the effect of mating on female fecund- storage scenarios are shown (dashed and solids lines as in (a)), they mostly ity influences selection on female remating interval. In all of overlap for cases with moderate to low sperm limitation and thus have little the cases discussed below, we assume that female mortality effect on female expected fitness. rate increases with shorter remating intervals (i.e. mating is costly to females, m . 0) and the probability of fertilization (P) decreases over the remating interval (i.e. d . 0). When (MATHEMATICA code available on request). In all cases, we mating increases female fecundity, remating intervals are pre- assume some survival costs of mating exist (i.e. m . 0). dicted to be shorter than in the absence of a fecundity effect Although the quantitative results we report are specific to (figure 5). Thus, while male stimulation of female fecundity the equations described earlier, the general patterns persist may be selected for in males, it may also increase sperm com- as long as the basic biology remains that fertility declines petition as it favours more frequent mating by females. As the with sperm depletion and mating can be both beneficial and magnitude of the fecundity effect increases (i.e. f increases costly to females. We now consider selection on female remat- relative to f ), the predicted effect on female remating interval ing intervals in response to: (i) number of viable sperm increases as well, with greater fecundity effects selecting for Downloaded from http://rstb.royalsocietypublishing.org/ on January 29, 2017

increasing sperm number 7 sbryloitpbihn.r hlTasRScB38 20120044 368: B Soc R Trans Phil rstb.royalsocietypublishing.org n = 10 n = 100 n = 1000

0.8 5 5

0.6 5 p

10 10 0.01 15 0.4 15 15 20 25 25 30 rate of sperm depletion ( d ) 0.2 40 10 30 35 20 25 20 45 increasing sperm storage

0.8 5 5 5 0.6 p

10 10 =

0.50 15 0.4 15 15 20 25 30 0.2 25

rate of sperm depletion ( d ) 40 10 30 35 20 25 20 45

0.8 5 5 5 p

0.6 0.99 10 10 15 0.4 15 15 20 25 30

rate of sperm depletion ( d ) 25 0.2 20 30 40 10 20 35 45 0.80.60.40.2 0.80.60.40.2 0.80.60.40.2 survival cost per mating (µ) survival cost per mating (µ) survival cost per mating (µ) Figure 4. Sperm number and quality affect female remating interval: in the absence of any male effects on fecundity, selection on female remating interval depends on the survival costs of mating (shown on the horizontal axis) and sperm limitation (captured by the sperm depletion (d) on the vertical axis, sperm number (n) from left to right and sperm storage ( p) from top to bottom). For all f ¼ 1, f ¼ 0, r ¼ 0.1, T ¼ 100 and s ¼ 0.99.

shorter remating intervals. Similarly, when the fecundity Fecundity effects are predicted to have the largest relative effects attenuate rapidly (r large), shorter remating intervals effect on remating intervals when sperm limitation is low. are favoured, all else being equal. Examination of the duration of the fecundity (r) effect reveals an interaction (c) Male per ejaculate allocation effects on female between the cost of mating and effects of mating on female fecundity: for low costs of mating (m small), the predicted remating interval optimal female remating interval is shorter when the fecund- The optimal female remating interval depends on an inter- ity effect is short-lived (r small, figure 5 dashed lines) than action between the number of sperm received per mating when it is long-lasting (r large, figure 5 solid lines). This (n), the rate of decline in fertility (d), the effect of remating pattern is reversed, however, at higher costs of mating, with interval on female fecundity (f and r), and the mortality long-lasting fecundity effects favouring shorter remating inter- cost of mating (m), which will depend on the total and relative vals than short-lived fecundity effects (figure 5, thin solid per ejaculate allocation by males. While both increased allo- lines). All else being equal, positive effects of mating favour cation to sperm quality (in terms of duration of viability d) shorter remating intervals. The magnitude of this effect, how- and quantity (n) are expected to select for longer female ever, depends on an interaction between the cost of mating remating intervals, it is likely that a trade-off exists between and the duration of the influence of mating on fecundity. these ejaculate traits, such that increases in quantity may Downloaded from http://rstb.royalsocietypublishing.org/ on January 29, 2017

fecundity effect: 8 no effect 25 20120044 368: B Soc R Trans Phil rstb.royalsocietypublishing.org small, short t small, long 20 large, short

15 large, long

5 female optimal remating interval,

0.05 0.10 0.15 0.20 0.25 survival cost per mating (µ) Figure 5. Selection on female remating interval depends on the effect of mating on fecundity and male allocation to sperm and other ejaculate characteristics. Each line represents the optimal female remating interval as a function of the cost of mating for a specific set of parameter values. Positive effects of mating on fecundity favour shorter female remating intervals, all else equal (no effect (thick black line), f ¼ 0; small fecundity effect (thin black lines), f ¼ 1; large fecundity effect (grey lines), f ¼ 5; long-lasting effects (thin solid lines), r ¼ 0.8; short-lived effects (thin dashed lines), r ¼ 0.2). Results are shown for f ¼ 1, d ¼ 0.1, n ¼ 100, r ¼ 0.1, T ¼ 1000, s ¼ 0.99 and p ¼ 0.5. trade off with quality and vice versa for a given per ejaculate mating and ejaculate traits interact to affect multiple com- allocation. Similarly, while increased allocation to fecundity ponents of female fitness. We show that, in general, greater effects will favour shorter female remating intervals, all else female survival costs associated with mating select for longer being equal, increased allocation to traits that affect the cost remating intervals (and thus lower remating rates) in females. of mating will favour longer female remating intervals. However, the magnitude and direction of selection depends Thus, while the effect of each male ejaculate trait is relatively on an interaction between fertilization dynamics due to sperm intuitive in isolation, the expected coevolutionary dynamics depletion rates, the number of viable sperm received by a between multiple make ejaculate traits and female remating female and the effect of mating on female fecundity and survi- interval is less clear. At present, it is impossible to predict val. If changes in female mating behaviour select for changes in these dynamics without greater knowledge of how multiple male ejaculate characteristics, complex feedback dynamics may male ejaculates evolve simultaneously in response to female result. Predicting these coevolutionary dynamics will require remating rate and how evolutionary ‘tugs of war’ between greater knowledge of how female remating affects the multiple male and female traits are resolved. correlated evolution of multiple male ejaculate traits. For example, if males respond to sperm competition by investing preferentially in sperm numbers at the expense of sperm longevity [57,58], the net effect on female mating inter- 5. Discussion val will depend on the relative change in these two traits, as The realization that strong selection may exist on both males increased sperm number favours longer remating intervals and females with respect to mating frequency has catalysed while decreased longevity favours shorter intervals (figure 4). theoretical interest in the coevolutionary dynamics of remating In contrast, if higher levels of sperm competition select instead [3,22,25,47,49,51–53]. When the direction of selection on for greater total investment in ejaculates, then high remating mating differs between males and females, an evolutionary rates may favour increased sperm quantity and quality [59], conflict over mating decisions arises between the sexes, which then further selects for longer remating intervals (and which may influence both male and female behaviour and may subsequently lead to selection on males for decreased allo- reproductive traits [3,44]. Unfortunately, the field remains cation to ejaculates). Whether these dynamics lead to stable strongly polarized. On the one hand, coevolutionary models intermediate remating rates and ejaculate allocation or an that explore sexual conflict over remating often ignore unstable arms race will depend on the degree to which males dynamics of male ejaculate allocation underpinning selection and females determine remating interval (‘power of winning’ on female remating. On the other hand, models of ejacu- [3]) as well as how selection shapes evolutionary male late economics often ignore the dynamic inter-dependence responses to sperm competition and the underlying genetics between male ejaculate allocation and female remating behav- of traits affecting mating, fertilization and fecundity [60]. iour, and either assume fixed remating rates [54] or assume We have predicted how female remating interval is that remating rates change exclusively owing to selection on expected to evolve in response to male ejaculate characteristics. males [55,56]. The objective of this paper was to provide Other female traits—related to sperm storage, fertilization effi- a theoretical framework for understanding how fitness ciency and egg production—likely also experience selection effects associated with mating and multiple ejaculate traits arising from male ejaculate characteristics. The evolution of simultaneously shape selection on female remating intervals. female remating will therefore also depend on the magnitude Our results illustrate how selection on female remating of selection on and rate of evolution of these related female intervals changes in response to the complex ways in which traits. Further theory and empirical data on the genetic Downloaded from http://rstb.royalsocietypublishing.org/ on January 29, 2017

covariances among multiple male and female traits will be female coevolution may therefore depend on specific biological 9 needed to predict the correlated evolution of the many male details of how mating, fertilization and fecundity arise. sbryloitpbihn.r hlTasRScB38 20120044 368: B Soc R Trans Phil rstb.royalsocietypublishing.org and female traits involved in mating and fertilization. We show that selection on female remating interval, Another way to think about the combined effects of determined by multiple fitness effects associated with mating on female fitness is to ask whether a positive or nega- mating, represents an alternative and intuitive—but so far tive relationship between reproductive output (fertility times neglected—evolutionary pathway to both reductions and fecundity) and survival as a function of remating interval increases in the level of sperm competition of a population. exists. This is somewhat similar to asking whether an inter- Two key points emerge from these results. action is parasitic, mutualistic or altruistic [61,62]. When all First, it is important to interpret empirical evidence for effects are negative (e.g. fertility, fecundity and female survi- antagonistic male ‘manipulation’ of females and sexual conflict val all decrease with increased remating rate) then selection over mating due to decreased survival cautiously as only will clearly favour decreased female remating rates and con- under a net lifetime fitness cost will conflict over remating flict between the sexes with respect to remating rate will be interval truly exist. For example, if mating increases fecundity likely to arise. When a combination of positive and negative or sperm depletion occurs quickly, females may be selected to effects exists, then individual costs of mating may be evident mate as often as possible and experience low survival. We also even if evolutionary conflict (e.g. differences in the direction find that females may experience large apparent costs of of selection with respect to female remating, [63]) over mating mating even at the predicted optimal remating interval for is not. Further empirical data on the covariance between females. Therefore, costs of mating alone do not necessarily specific male traits and individual aspects of female fitness indicate that females are in conflict with males over remating (e.g. survival, fecundity and fertility) may yield important interval, and female remating in the presence of mating costs insights into net selection on female remating rate and the to female survival is not necessarily indicative of males ‘win- feedback between female remating rate and selection on ning’ the battle over remating rate (note that the absence of specific male traits involved in sperm competition. sexual conflict over remating rates does not eliminate potential Traditionally, strategies of male ejaculate expenditure for conflict over female sperm utilization and other reproduc- have been considered assuming fixed levels of sperm compe- tive decisions). These predictions are consistent with a recent tition. More recently, a few studies have considered ejaculate meta-analysis showing that females often experience net posi- expenditure strategies evolving dynamically with male tive fitness effects of multiple mating, selecting for more effects. For example, Parker & Ball [64] proposed a popu- frequent mating in many species [27]. lation model in which the level of sperm competition was Second, the results of our study influence our understand- proportional to the number of matings a male achieves, so ing of mating systems evolution. Spatio-temporal variation in that the costs of gaining a mating and male ejaculate expend- female availability has been traditionally explained in terms of iture are inter-related. Consistent with traditional ejaculate patterns of distribution of reproductive resources and female economic theory (equation (3.3)), the model by Parker & potential reproductive rates [66]. However, our results show Ball [64] predicts higher ejaculate expenditure with increasing that variation in remating rates may also emerge as an intrinsic risk of sperm competition in a population. However, in property of sexual selection on male mating traits that also another ‘consistent’ model in which number of mating dic- influence female fecundity and survival. These dynamics are tates ejaculate expenditure, Williams et al. [55] argue that further influenced by species-specific aspects of reproductive higher sperm allocation will necessarily lead males to mate physiology, ecology and evolutionary history that, in the con- less frequently, thus resulting in lower levels of sperm com- text of our model, can generate predictable variation among petition. A recent theoretical study by Fromhage et al. [65] species and populations with respect to patterns of mating. demonstrated that these divergent predictions can be recon- Therefore, the evolution of mating systems and selection on ciled by considering female mating behaviour, and showed female remating rate will interact to determine patterns of that when females are able to resist mating beyond an arbitrary female availability and male reproduction in ways not captured threshold, mating frequency in the population can become by existing theory on the evolution of mating systems. decoupled from patterns of male sperm allocation justifying predictions by Parker & Ball [64]. However, when males are able to This research was supported by grants from the Royal Society of London (to S.H.A. and T.P.), the Natural Environment Research impose mating on females, mating frequency becomes intimately Council (to T.P.), the National Science Foundation (to S.H.A.), a Visit- linked with male sperm allocation leading to the scenario pre- ing Senior Research Fellowship from Jesus College Oxford (to S.H.A.) dicted by Williams et al. [55]. Predictions regarding male and and Yale University (to S.H.A.).

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