Impact of male alternative reproductive tactics on female costs of sexual conflict under variation in operational sex ratio and population density

Abstract Sexual conflict over mating rate is both pervasive and evolutionarily costly. For females, the lifetime reproductive fitness costs that arise through interactions with potential mates will be influenced by the frequency of such interactions, and the fitness cost of each interaction. Both of these factors are likely to be influenced by variation in operational sex ratio (OSR) and population density. Variation in OSR‐ and density‐dependent male alternative reproductive tactics (ARTs) may be particularly important if the fitness costs that females experience vary with the reproductive tactics that males express. Using a simple model, we consider several examples of OSR‐ and/or density‐dependent variation in male ARTs and the frequency of male–female interactions, and find that variation in the expression of male ARTs has the potential to augment or diminish the costs of frequent male interactions for females. Accurately documenting variation in the expression of male ARTs and associated female fitness costs will benefit future work in this area.


| INTRODUCTION
Sexual reproduction often entails conflict, as reproductive partners frequently differ in their evolutionary interests (Parker, 1979). One area where such conflict is widely observed and has been greatly investigated is mating rate; whereas females may require relatively few matings to maximize fitness, in many species a male's fitness increases with his mating frequency (Andersson, 1994;Arnqvist & Rowe, 2005;Chapman, Arnqvist, Bangham, & Rowe, 2003;Gavrilets, Arnqvist, & Friberg, 2001;Parker, 2006). For example, in the case of two previously mated individuals encountering one another, selection may favor a male that remates, but a female that does not (Parker, 1979). The outcome of such an interaction can result in both direct and indirect fitness costs or benefits for the male or the female (Holland & Rice, 1998;Parker, 1979Parker, , 2006. Direct fitness costs to females resulting from conflict interactions have been of particular empirical and theoretical interest. Such costs can result in selection for traits that allow females to avoid direct fitness costs when interacting with males, and can therefore be drivers of evolutionary change (Clutton-Brock & Parker, 1995;Parker, 1979Parker, , 2006Rowe, Arnqvist, Sih, & Krupa, 1994). Furthermore, because the mean reproductive successes of males and females are necessarily equivalent in a population with a 1:1 sex ratio, direct fitness costs to females will also limit male fitness, and can depress the fitness of the entire population (Rankin, Dieckmann, & Kokko, 2011).
Intrasexual reproductive competition may select for more than one alternative to obtaining fertilizations. When expressed as discrete phenotypes in either males or females, these alternatives are better known as alternative reproductive tactics (ARTs) (Gross, 1996;Brockmann, 2001; reviewed by Shuster & Wade, 2003;. Alternative reproductive tactics are expected to evolve whenever they allow individuals to increase their fitness beyond what could be achieved by conventional tactics, and examples of male ARTs are plentiful (reviewed in . Prior to copulation, male ARTs may take the form of territorial versus satellite and/or floating individuals, courting versus noncourting, guarding versus searching, or bourgeois versus parasite individuals, among others . As alternative solutions to the problem of obtaining female mates, it is conceivable that male ARTs could entail different fitness costs for females. For example, water strider males exhibit both courtship and coercion in pursuing mates, the former posing fewer direct costs to females than the latter (Arnqvist, 1997). The implication of such differences in female's costs for systems with intraspecific variation in male ARTs has not been explored until recently (Alonzo, 2008;Reichard, Le Comber, & Smith, 2007;Weir, 2012). Explicit consideration of such effects will help increase our understanding of the impact of sexual conflict on individuals and populations.
Two factors known to influence the expression of male ARTs are operational sex ratio (the ratio of potentially receptive males to receptive females at any one time, OSR; Emlen, 1976;Jirotkul, 1999a) and population density (Jirotkul, 1999b;Rowe et al., 1994;Tomkins & Brown, 2004). Although efforts are frequently made to examine the independent effects of OSR and population density on mating behavior (Alonso-Pimentel & Papaj, 1996;Jirotkul, 1999a,b;de Jong, Wacker, Amundsen, & Forsgren, 2009;Wacker et al., 2013), together the two determine the encountered number of potential competitors and potential mates (Emlen & Oring, 1977;Kokko & Rankin, 2006), and thus both influence perceived levels of mate competition and mate availability. Actual relationships between OSR or population density and the frequency of male ARTs may be complex, and will vary from system to system (Aronsen et al., 2013;Knell, 2009;Kokko & Rankin, 2006;Weir, Grant, & Hutchings, 2011). Furthermore, OSR and population density are unlikely to vary completely independently of one another.
Not only are the two metrics linked to one another through numbers of individuals; it is also possible that individuals will respond to one factor in such a way that it induces change in the other (e.g., secondary sex ratio variation in response to increased population density in red deer; Kruuk, Clutton-Brock, Albon, Pemberton, & Guinness, 1999).
Whatever the underlying mechanism, given the extent to which varying sex ratios and population densities result in temporal and spatial variation in the expression of male ARTs, we should expect similar variation in any female fitness costs associated with these two factors.
Increased male-encounter rates due to high population densities and/or male-biased sex ratios are expected to increase female fitness costs associated with remating and/or resistance, and decrease the marginal benefits of remating for females (Härdling & Kaitala, 2005;Kokko & Rankin, 2006). However, if the expression of density-and OSR-dependent male ARTs alters the cost of different male interactions for females, then there may also be an indirect relationship between population-level factors and direct fitness costs to females. Although several empirical studies have examined female fitness costs relating to male ARTs (Johnson & Brockmann, 2010;Reichard et al., 2007;Watters, 2005), few have considered these costs in conjunction with OSR-and/or density-dependent effects (Weir, 2012) or the compounded effects of mate-encounter rate on female fitness. We introduce here a theoretical framework that we hope will assist in further investigations of the relationships between population states, mating behavior, and female costs. We present a simple model linking OSR and population density to the number of costly male interactions experienced by an individual female, and then examine the resulting female conflict costs in a two male ARTs system under a variety of parameter values. In particular, our model distinguishes potential quantitative effects (variation in the number of male encounters) from qualitative effects (variation in the type of male behavior encountered). We consider this model an important first step toward a better understanding of how variation in population-level factors can influence coevolutionary dynamics between males and females; future research will need to investigate the ways in which selection on females could impact male ARTs, under such variation in conditions.

| Female fitness costs
For the purposes of our model, we assume that a female experiences some net direct fitness cost (or benefit) as a result of each interaction she has with a male, and that those costs accumulate in an additive fashion over the course of a given time period (e.g., the reproductive season). These costs are considered to be direct fitness costs to the female in that they decrease her lifetime reproductive success, either through decreasing her lifespan, and/or through decreasing her net reproductive output. If males express different alternative reproductive tactics, and subsequently differ in the direct fitness costs they impose on females, we can weight those costs by how often females encounter different male tactics. The net fitness cost of male-female interactions for the female during that time period, then, is given by where c i is the mean net female fitness cost arising from an interaction with a male expressing tactic i (i.e., the male-interaction cost), n i is the number of interactions the female has with a male (or males) expressing tactic i during the time period, and T is the total number of male tactics in the system. It should be noted that here we are interested in quantifying direct costs to females due to interactions with males. In practice, a female who encounters zero males during the current time period (and who has no access to viable sperm stored from encounters during previous time periods) will experience essentially infinite costs due to an inability to reproduce. Such a female would also experience zero male-interaction costs, however.
Male-interaction costs may be any real number; we have chosen to represent female fitness costs using positive values in order to make them easier to visualize. Therefore, if the female experiences a net fitness benefit as a result of interacting with a male instead of a net fitness cost, c i would be <0. (1) If we assume that the probability that a female encounters and interacts with a particular male is independent of the tactic he is expressing (i.e., the probability of interacting with a female i is the same for all males), then equation 1 may be restated as: where m i is the proportion of males that express tactic i, and n is the total number of male interactions that the female experiences during the time period of interest. For a system in which male reproductive tactics are plastic rather than fixed, this is equivalent to assuming that each time a female encounters and interacts with a male, he expresses one of the existing tactics with some known probability (m i ).
In a system with two male reproductive tactics (tactic 1 and tactic 2), equation 2 may be restated as:

| Population density-and OSR-dependent variation in female fitness costs
As (2) F I G U R E 1 OSR-dependent variation in expression of male ARTs, and related female fitness costs. Solid line represents proportion of males expressing alternative tactic 1 (m 1 ); the proportion of males expressing alternative tactic 2 (not shown) is the inverse of this curve. i, The expression of male tactic 1 does not vary with OSR; ii, expression of male tactic 1 increases with OSR; iii, expression of male tactic 1 decreases with OSR; iv, expression of male tactic 1 reaches its maximum at intermediate levels of OSR. The dotted line shows resulting female fitness costs as a function of OSR, when the male-interaction cost associated with tactic 1 is twice than of tactic 2 (c 1 = 1, c 2 = 0.5), and when females interact with one male during the time period of interest (n = 1)

OSR
Female fitness costs C f figures in this paper can be found in Appendix S1 (Appendix S2 is an editable doc. file).
Next, we will consider what happens when the number of male-female interactions varies. Modeling male-female interaction and/or encounter rates realistically can be a complicated endeavor (Hutchinson & Waser, 2007). In addition to determining male and female densities, OSR and population density may also affect population spatial structure, mate searching behavior, and individual movement patterns (Kokko & Rankin, 2006), making the relationship between male-female interaction rates and population parameters complex. For the sake of simplicity, we will consider situations in which number of in-

| Combining ARTs and population drivers
The combined effects of (a) male response to OSR and (b) the population-level determinants of male-female interaction rates on female fitness costs can be seen in Figure 3. Here, we apply the four patterns of variation in male ARTs (described in i, ii, iii, and iv) to situations with either density and/or OSR-dependent male-female interaction rates. This yields eight surfaces representing variation in direct, costs are still relatively high as long as population density is also high.
These results are based on a relatively moderate ratio between maleinteraction costs (i.e., c 1 = 1 and c 2 = 0.5). As the relative difference of male-interaction costs increases, so will the impact of variation in expression of male ARTs on net female fitness costs. Nonetheless, such effects will be most apparent when the number of male-female interactions is high rather than low.
Third, whether we choose to calculate the number of male-female interactions based on male density or OSR will have strong qualitative effects on net female fitness costs. If male-female interaction rates are density-dependent, low population densities will have a moderating effect on the costs females experience as a result of male ARTs. If male-female interaction rates are instead a function of OSR, females can experience high fitness costs even when male densities are low, as long as OSR is high.
Fourth, we have assumed that interactions with males will have a net fitness cost for females, whereas such interactions might instead be beneficial (e.g., due to nuptial gifts, or other benefits of polyandry). (4) Thus, the sign for c i could be positive or negative. How exactly these differences might play out in the real world is not clear, but we would not expect the resultant fitness surfaces to necessarily mirror one another due to the fact that fitness benefits and costs can be bounded differently from one another. For example, benefits from serial nuptial gifts may be saturating (i.e., nonadditive), whereas energetic costs from serial harassment may be linear (or asymptote at a far greater distance from the origin than the former). Investigating the nature of variation in female fitness benefits versus costs in relation to OSR-or density-dependent male ARTs is a potentially fruitful topic for future theoretical work.
Finally, we can ask what this modeling exercise might tell us about mating conflict in theory and in nature. If we were to construct a full ESS, two-sex model, it is clear that the use of simple, context-free female-cost constants could be problematic. We have shown that such costs can vary from near zero to very high depending upon population values. The surfaces that we have deduced are only moderately complex, however, which suggests that simple functions could easily replace those worrisome constants. Given that our approach provides estimates of direct, net fitness costs to females across a gradient of male tactics, we can now also estimate fitness costs (and benefits) that might arise if female reproductive tactics were to evolve, and subsequent evolutionary responses by males that could move the population to a different position along the gradient.
In terms of empirical studies of mating conflict, our model illustrates the potential significance of variation in both the expression of male ARTs and the number of male-female interactions when it comes to estimating the impact of OSR-dependent male ARTs on female fitness. If a male ART that imposes direct fitness costs on females is more prevalent when male-female interaction rates are high (e.g., at a high OSR or high population density), females will experience higher male interaction related fitness costs than predicted by male-interaction rates alone. If the reverse is true (i.e., the male ART that is associated with higher male-interaction costs for females is less frequent at a high OSR/population density), then plasticity in male reproductive tactics could in fact mitigate the cost of frequent male-female interactions for females. Our model suggests that the relative magnitude of the male-interaction costs associated with the different male reproductive tactics would influence overall patterns of variation in female fitness costs, whereas absolute differences in male-interaction costs would determine the scale of those costs. For any pattern of OSRdependent variation in male ARTs (e.g., Figure 1), if the ratio of c 1 :c 2 is held constant, the relative difference between net female fitness costs at any two OSR (or population densities) will also remain constant.
The greater the relative difference in male-interaction costs, the more abrupt the variation in net female fitness costs as the relative representation of the two male tactics changes. As the absolute magnitude of male-interaction costs increases, so will net female fitness costs.
In our model, we consider only the potential for female costs to arise out of male-female interactions. If such costs exist, females may be under selection to express OSR-or density-dependent tactics that reduce the fitness costs of interacting with males (Parker, 2006). For example, females may become more aggressive toward males when operational sex ratios are high, or may avoid interacting with males under high-density conditions by altering their spatial (e.g., residence time) and/or temporal (e.g., emergence) overlap. Sex ratio and population density may also impact female fitness via female densities, and the costs of intrasexual competition could offset or outweigh maleinteraction-related fitness costs for females (Smith, 2007;Smith & Sargent, 2006). Finally, males may also experience divergent fitness costs when they express different reproductive tactics (Christenson  Goist, 1979;Gross, 1996;Lucas & Howard, 1995;Smith, Schrank, & Brockmann, 2013;Vahed, 2007). Differential fitness of males and females could potentially alter OSR and population density in the next reproductive time frame, leading to carry over effects of populationlevel variation.

| CONCLUSION
We have presented a simple model examining the potential effects of variation in OSR and population density on female fitness costs due to interactions with males. Specifically, we investigate how differences in the female fitness costs associated with male alternative reproductive tactics might interact with variation in the frequency of male-female interactions. Other work has drawn attention to the importance of considering both variation in the probability of particular male reproductive behaviors, as well as variation in the opportunity for behavior (i.e., male-female encounter rates), when interpreting observed frequencies of male reproductive tactics (de Jong et al., 2012). Here, we show that variation in probability and opportunity can have an important impact on female fitness, because together they determine number of costly interactions. These predictions are for the most part intuitive, and provide a clear demonstration of how fitness costs due to one-on-one interactions can be greatly mitigated or exacerbated by existing population factors.
Despite the intuitive nature of our model, we conclude by highlighting some issues that may not be obvious: (1) OSR can impact costs to females by impacting both expression of ARTs and the number of interactions with males, resulting in nonlinear cost functions and (2) male-interactions costs to females are not monotonic with regard to OSR. If males adjust to the less costly ART with increasing OSR, female fitness costs will maximize at some intermediate value of OSR even if interaction rates increase (e.g., Figure 3biii).

ACKNOWLEDGMENTS
Thank you to the Roitberg lab for helpful feedback, as well as to R.
Ydenberg and three anonymous reviewers for valuable comments on an earlier draft of the manuscript. This work was made possible by financial support from the Natural Science and Engineering Research Council of Canada to BR, and DGAPA-UNAM and CONACyT (Mexican government) sabbatical grants to AC-A.
F I G U R E 3 Variation in female fitness costs associated with OSR-dependent male ARTs. The solid surfaces represent female fitness costs when the number of male interactions per female is directly proportional to (a) male density (ρ m ; see Figure 2i), or (b) the operational sex ratio (OSR; see Figure 2ii). The relationships between the expression of male ARTs and OSR correspond to those shown in Figure 1: i, the expression of male tactic 1 does not vary with OSR (m 1 = m 2 = 0.5); ii, expression of male tactic 1 increases with OSR; iii, expression of male tactic 1 decreases with OSR; iv, expression of male tactic 1 reaches its maximum at intermediate levels of OSR. Female fitness costs associated with the first male tactic are assumed to be twice that of the second (c 1 = 1; c 2 = 0.5). The transparent surfaces represent female fitness costs associated with male ARTs when the number of male-female interactions is independent of either OSR or population density and constant (n = 1); these surfaces are therefore identical within each column of the figure. Dotted lines in Figure 1i-iv show the two-dimensional equivalent of these transparent surfaces