Behavioral Ecology Advance Access originally published online on June 11, 2004
Behavioral Ecology 2004 15(5):715-721; doi:10.1093/beheco/arh046
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Male brood care without paternity increases mating success
a Animal Ecology, Ecology Building, 223 62 Lund, Sweden b Department of Biology, Box 3000, FIN-90014 University of Oulu, Finland
Address correspondence to R. Härdling. E-mail: roger.hardling{at}zooekol.lu.se.
Received 27 March 2003; revised 19 August 2003; accepted 9 September 2003.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHE MODELRESULTSDISCUSSIONAPPENDIXREFERENCES |
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We investigate under which conditions we can expect the evolution of costly male care for unrelated offspring, when the benefit of such care is in the form of increased mating success. This applies to male helping behavior that cannot be explained as paternal care because the male's own offspring does not benefit from his behavior. Our model shows that caring for others' offspring can be a stable strategy for males, if a male that does not "help" loses mating opportunities, for example if females discriminate against non-helping males as mating partners. This is possible when females are polyandrous. Increasing population density decreases the parameter region where male care is stable. Male care is also more likely to be stable when male mortality rate is higher than that of females. We discuss the results with special reference to the golden egg bug Phyllomorpha laciniata, where females lay eggs on conspecifics, often on males before mating. Males therefore carry mostly unrelated eggs. We investigate how oviposition rate and female mating rate influences when egg carrying is an evolutionary stable strategy. We conclude that in the golden egg bug, male egg carrying could be explained as a form of mating investment.
Key words: mating investment, paternal care, P. laciniata, sexual conflict.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTSDISCUSSIONAPPENDIXREFERENCES |
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If variation in reproductive success is higher in the male sex than in the female, this will for very basic theoretical reasons often be a result of higher variation among males in the number of reproductive events (Wade, 1979
). Therefore, males in such cases are expected to compete over mates and to evolve traits that aid them in the competition.
Costly male behavior with the purpose of achieving a mating is not unusual. It includes, for example, sexual display as well as all cases in which males increase the probability of mating by providing the female with resources (Andersson, 1994). These resources could benefit the female directly, as in the case of nuptial gifts, or be for the benefit of her offspring. We find many examples of this in insects, such as butterflies and Orthopterans (Boggs and Gilbert, 1979; Simmons and Parker, 1989; Wedell, 1991; for review see Arnqvist and Nilsson, 2000; Jennions and Petrie, 2000).
In most of these cases when males attract females by offering resources, male mating investment is at least partly an investment in his offspring as well (Simmons and Parker, 1989). This is because a female offers a mating in return for the gift, and a part of the male nutrient gift is later incorporated into his eggs. Thus, it is usually not easy to separate when a male makes a costly investment to obtain matings and when he mainly invests in his own offspring.
A paternity assurance mechanism is often a precondition for male care of young (Smith, 1979, 1997). In general, male care of young has evolved and been maintained as a form of paternal investment, because by helping, the male increases the survival of his offspring (Tallamy, 2000, 2001). This may not always be the case, though; male "care" is not always beneficial—that is, presence of a male in a nest may not increase offspring survival. This occurs in some burying and bark beetles (Lissemore, 1997; Scott, 1990). In the golden egg bug Phyllomorpha laciniata (Heteroptera, Coreidae), a male may care mostly for unrelated offspring (Tay et al., 2003). In these cases it is important to make clear who is helping whom, and whether the help is directed to the male's or the female's offspring. Parental care is defined by Clutton-Brock (1991) as "any form of parental behavior that appears likely to increase the fitness of a parent's offspring" (our italics). A female may increase fitness of her offspring by having an unrelated individual caring for them. Then, the mother is caring for her young, but the individual that helps to rear her offspring does not increase its own offspring's survival by doing so, and thus it is by definition not performing parental care (Kaitala and Kaitala, 2001).
Tallamy (2000, 2001) has suggested that paternal care in arthropods has arisen more as a sexually selected means of attracting mates than as a naturally selected mechanism for improving offspring survival. However, can male care evolve without paternity or without kin selection? This would represent a case in which male care is purely sexually selected. Here we study the evolution of costly male premating behavior by using a simple model, in which the cost is in the form of increased mortality and could involve "helping" to care for a female's offspring. If the males' own offspring does not gain from his behavior, there must be some other male benefit. In our model, we investigate the potential benefit of increased probability of mating, and we ask how large such a benefit must be to offset a given increase in mortality. While we are interested in the general problem, we have formulated the model with special reference to the golden egg bug, because of our familiarity with this system. However, we expect many of our principles to carry over to other systems. Female golden egg bugs oviposit on conspecific males and on mating pairs without discrimination (Kaitala and Miettinen, 1997; Miettinen and Kaitala, 2000) such that most eggs carried by any male are not his own (Tay et al., 2003), and this provides a good example of the kind of male behavior in which we are interested.
The golden egg bug
Females may lay eggs on the host plant Paronychia or on the bodies of conspecifics (Kaitala, 1996), but they strongly prefer other bugs as hosts for eggs, because they soon stop laying eggs if deprived of conspecifics (Kaitala and Smith, 2002). Eggs survive fairly well when carried (Kaitala, 1996; Katvala and Kaitala, 2001a), but survival is poor if eggs are laid on a host plant (Kaitala, 1996; Reguera and Gomendio, 2002). Females lay eggs on any conspecifics regardless of the host's sex, but males carry twice as many eggs as females and seem to receive eggs especially during mating activities (Katvala and Kaitala, 2001b). Females do not prefer to mate with a male who carries eggs; thus, male-carried eggs are not functioning as male ornaments (Kaitala, 1998). Nor do females trade eggs for matings by mating only with males who first accept eggs (Miettinen and Kaitala, 2000). Males do receive most eggs when they court a female, and females do not generally lay eggs directly after mating. Rather, some females seem reluctant to mate before they have oviposited (Kaitala and Miettinen, 1997). In general, most matings occur after oviposition (Katvala and Kaitala, 2001b). Because of sperm precedence, 43% of a non-virgin female's eggs are sired by the last male to mate (Garcia-Gonzalez et al., 2003). Bugs can easily avoid receiving eggs by avoiding conspecifics (Katvala, 2003). We do not know how voluntarily males receive eggs during courtship in nature; however, while mating they are unable to avoid receiving eggs from other females (Kaitala and Miettinen, 1997). Finding a host back is a problem for females, and there is a clear indication that availability of conspecifics as egg hosts limits female reproduction in the field (Kaitala and Smith, 2002). The conspicuous appearance of the eggs destroys the male camouflage and makes bugs more vulnerable to ant (Kaitala and Axén, 2000; Kaitala et al., 2000) and bird predation (Kaitala et al., 2003; Reguera and Gomendio, 1999); thus, egg carrying is costly.
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THE MODEL |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTSDISCUSSIONAPPENDIXREFERENCES |
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The probability of mating
Males that accept to carry eggs may have a mating advantage if females do not mate until after having oviposited, because of the behavior of both sexes: When a male courts a female, the female may first attempt to oviposit on the males' back. Whether she does this depends on if she has produced an egg, and we assume that a fraction, p, of the females will attempt to oviposit on a courting male. The probability that a randomly picked female will attempt to oviposit is thus p. We assume that males have some possible means of avoiding being oviposited upon, for example by resisting or by avoiding to court gravid females. Let us assume that the probability that a randomly chosen female wants to mate is f. If a male does not perform the avoidance behavior, his mating probability will then be f in an encounter with a female. A male that avoids all females that want to oviposit mates with the lower probability f(1 – p), if female mating and oviposition are independent events. If oviposition and mating are correlated, the probability is lowered to f(1 – p) – a, where a is a convenient measure of the association between mating and oviposition. We can define the association as a =
, where is the correlation between the two events. Technically, a is analogous to linkage disequilibrium, D, in genetic models (Hartl and Clark 1997). Written this way, a ranges between –0.25 and 0.25. If a = 0.25, mating and oviposition always occur together, and if a = –0.25, they never occur in the same encounter. For the argument, it is not necessary that the male avoidance behavior is perfect, the important thing is that resistance, whether active or passive, and even with low efficiency, will have the general effect of decreasing the average mating rate. Will this disadvantage be outweighed by the advantage of not having to pay the mortality cost of carrying eggs? Because the cost directly affects a life-history parameter, we cannot investigate this question without modeling the life-history dynamics of males and females and then finding the evolutionary stable strategy (ESS) for males under different female behavior. This is done in the next section.
Population dynamics
First, we will construct a simple dynamic model of the mating system and solve for the stable number of single males, single females, and pairs that result from any given behavior of the animals. We will then focus on the male helping behavior and calculate the fitness of mutant males with behavior that differs from the prevailing population strategy. We use this mutant fitness expression to find the evolutionarily stable male behavior, i.e. to find out when caring is evolutionarily stable to invasion by the alternative strategy "not care" and vice versa. Technically, the model is a version of the life-history models developed by Hanna Kokko and Rufus Johnstone (e.g., Kokko and Johnstone, 2002).
We assume that the population is composed of nB single males and nS single females, and that at any one time there are nP mating pairs. This population structure is determined by the life history and behavior of the animals, and, in this section, we will use a dynamic approach to model the population structure in terms of the prevailing strategies (Figure 1).
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The probability that a female mates when courted may differ for males that accept, and do not accept, to provide care. We will consider two alternative pure male strategies, r, called "Always care," for which r = 1, and "Never care," with r = 0. Let the mating probability be q1 for males that provide care and q2 for males that don't. We will investigate the full strategy space for females, (0 < q1 < 1) and (0 < q2 < 1). We assume that males are unable to force copulation (Miettinen and Kaitala, 2000
). The rate by which the male mates with females (m) can then be described by the function:
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We assume that male mortality rate depends on whether or not the male provides care, and also on whether he is single (i.e., in state "in") or mating (in state "out"). With respect to the golden egg bug, if the male does not carry eggs, the mortality rate is assumed to be µIO for mating males and µIIM for single males (Table 1). If the male accepts eggs when courting, the increased number of eggs on his back increases his mortality rate by C. Thus, the cost C is only experienced by the caring strategy.
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The mortality rate of single females is µSF, and while mating the female mortality rate is µO or µO + C, depending on whether or not the male in the pair carries eggs (see Kaitala and Axén, 2000
; Kaitala et al., 2003). The mortality rates are summarized in Table 1. The mating duration is assumed to be exponentially distributed with the expected value T. The probability that a male, entering the population at time 0, is alive and mating at time t, pOM(t), or for single males, pIM(t), can be solved from the initial value problem:
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The solution to Equation 2 is given in the Appendix. We assume that a constant number, 2R, of new individuals with sex ratio 1:1 is recruited into the population every time unit, so the population does not change in size over time, given a male strategy. Thus, the male care is assumed not to have any ultimate effect on population recruitment. In the golden egg bug, this may be true if factors other than egg survival, such as adult predation or number of overwintering sites, determine population density.
The density of bachelors, nB, is proportional to the probability that a male is alive and single at any one time of its potential lifespan. Similarly, the number of pairs, nP, is proportional to the probability that the male is alive and mating, integrated over time. Mathematically,
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The female mating rate depends on the strategy of the population in the same way as in Equation 1, but when we calculate female mating rate, nS should be changed to the number of bachelors (nB) (cf. Equation 1). The female dynamics are dictated by a set of equations equivalent to Equation 2, and the number of spinsters at equilibrium can be calculated in the same way as for males (see Appendix).
Because the male and female dynamics are interdependent, we used a numerical procedure to calculate the solution to the dynamics for each strategy (see Appendix). In each step of the iteration we calculated new values for nS, nP, and nB. These values were then used as input for the next iteration step, until we reached a stable population structure.
The fitness of mutants
Let us say that the prevailing strategy for males is "Never care". If a mutant male who does provide care has higher fitness than other males, this strategy will invade the population and increase in frequency. An evolutionarily stable strategy is stable against such invasions by mutants. To find the male evolutionarily stable strategy, we must find an expression for male fitness in a population following some strategy r. Then we calculate the fitness of mutant males that differ from the population strategy by using r' instead of r. This is what is done in this section.
In a constant population of males that follow the strategy r, a male's lifetime fitness is his offspring production. This can be calculated as the probability pO(t) that the male is mating at time t, multiplied by the rate of termination of mating, 1/T, multiplied by the fitness gain, G(r), resulting from one mating, and this whole expression is integrated over time (see Appendix). We let the fitness gain, G(r), depend on the prevailing strategy because eggs have higher survival prospects when males generally provide care. When we calculate the fitness of mutant males, we assume that the female population has a fixed mating strategy, represented by values of q1 and q2, and that the prevailing strategy among males is r. We also assume that the population has reached the stable population structure that is connected with the prevailing population strategies, and that the fitness gain, G(r), of a mating is unaffected by the decision of the mutant male.
The mutants' success compared with that of the other males is determined by his own strategy (i.e., his r'-value), and the strategy of the female population (q1 and q2). The value of r' that maximizes mutant fitness is called the best reply to the population strategy. We simplify the analysis by limiting the male strategy set to the pure strategies "Always care" and "Never care" only, ignoring all mixed strategies for which 0 < r < 1. This way we avoid making assumptions about how G(r) changes with mixed strategies. The best reply for mutant males is to provide care (r' = 1) if this results in a higher number of offspring than the alternative, r' = 0, and vice versa. The best reply is given by
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We assume that males never provide care for their own offspring, so that there are no inclusive fitness benefits. Because the male strategy was assumed to take only two values, we used best-reply dynamics (Hofbauer and Sigmund, 1998) to find the stable state, i.e., the ESS. When we had calculated the best reply using (4), we changed population r to the best reply value, and calculated a new stable population state. We calculated new best replies until the system stabilised. The stable male strategy was said to be an ESS, denoted r *. With our assumptions, we only found solutions where either "Always care" or "Never care" was an ESS. We did not find any parameter region where both strategies could be invaded by the alternative, which would have indicated a mixed ESS. Nor did we find any region where both strategies were alternative ESS solutions.
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RESULTS |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTSDISCUSSIONAPPENDIXREFERENCES |
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The female strategy has a strong influence on the stability of the male behavior. Male acceptance of eggs (r * = 1) requires that q1 is sufficiently larger than q2, i.e., that males that accept eggs have a higher probability of mating with a female (Figure 2). The results are influenced by the cost of helping (C). The higher the cost, the higher q1 has to be in relation to q2 for male care to be stable (Figure 2). The solutions are also influenced by the relation between mortality rate of single males without eggs on the back (µIM) and mortality rate of single females (µIF)(Figure 3). If µIM = µIF , the parameter region of q1 and q2 in which egg acceptance is an ESS is smaller, compared to when single males have higher mortality than single females (Figure 3). A relation µIM > µIF could be the result of higher exposure to predators of males in a natural situation, for example if males are more mobile in order to search for females.
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We investigated the importance of population density by altering the value of R, i.e., the number of individuals recruited into the population each time unit. Increasing R from 10 to 100 decreases the parameter region in which r * = 1 is an ESS (Figure 4). Thus, increasing population density could change a situation in which accepting eggs is an ESS into the opposite, one in which males are not expected to carry eggs.
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With respect to male egg carrying in the golden egg bug we make the following general observations. When q1 equals the overall mating probability, f, increasing oviposition rate (higher p) leads to decreasing q2 = f(1 – p), which always moves the solution closer to the region where males accept to carry eggs (see arrow 1 in Figure 5). Increased rate of oviposition can thus make egg acceptance stable. If oviposition and mating are correlated events, this will move q2 even further towards the region where r * = 1, because an association, a, between f and p yields q2 = f(1 – p) – a (arrow 2, Figure 5). Conversely, for given oviposition rate, increased mating rate can potentially move a solution where egg acceptance is an ESS into the region where it is not. This is shown by arrow 3 in Figure 5, where increasing mating probability from f to f' moves the solution upwards and to the right, into the region where r * = 0.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTSDISCUSSIONAPPENDIXREFERENCES |
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We present evolutionary stability conditions for when male care of unrelated offspring can evolve and be maintained as a mechanism by which males improve their chances of obtaining mates (Tallamy, 2000
, 2001). Female behavior dictates this solution to the underlying sexual conflict, because although females always benefit if a male provides care for her offspring, males should accept the cost connected with helping only if the probability of mating is increased enough when the behavior is performed, i.e., if q1 is sufficiently larger than q2(Figure 2). Females may therefore be able to bend the rules so that males benefit from providing care. Males, then, are not expected to evolve resistance to female attempts to exploit them. The result is quantitatively affected by the cost of providing care, which in our model is caused by increased mortality of care-giving males (Figure 2). There is also an effect of population density, such that with increasing density, the region where helping is an ESS, becomes smaller (Figure 4). The reason for this result is that all else equal, males will meet females more frequently in dense populations. The decreased lifespan caused by helping indicates that a helping male will court fewer females during his life. Fitness is therefore lowered. In less dense populations, males do not meet females as often. Males with higher probability of acquiring a mating with a female, then, have an advantage. For this reason alone, males are predicted to provide care more readily in low-density populations. It should be remembered that this is purely a result of changing the density, as the sex ratio is equal, because of identical mortality rates of males and females (Figure 4).
Higher predation on single males than on single females (µIM > µIF) could result if males suffer higher predation pressure while mobile and searching for females (e.g., Jormalainen et al., 1995). Such increased mortality of single males has the effect of enlarging the region where helping is an ESS (Figure 3). This partly has to do with the expected lifespan of males. The increase in predation pressure caused by egg carrying is less important when male mortality is already high, because the expected lifespan is already short. As the cost is smaller, it can be outweighed by a smaller benefit, so that helping may become a more easily attained solution.
We have not investigated the effect of interference during intra-sexual competition over mates, which could influence the result in male-biased populations. For example, increased density of males could lead to competition resulting in lowered mating probabilities (Vepsäläinen and Savolainen, 1995). Competition could also affect males' propensity to offer help (Tallamy, 2000). As a first step, however, it is interesting to investigate the situation without such interference. We have limited our analysis to cases with equal or female-biased sex ratio, where male interference competition should be low.
Female mating behavior is important when considering the evolution of male care. Polyandry is a necessary precondition for the evolution of costly male care for unrelated offspring (Kaitala and Katvala, 2001). Polyandry has recently gained a lot of attention among ecologists (for review see Arnqvist and Nilsson, 2000; Jennions and Petrie, 2000) and theoretical ecologists (e.g., Ihara, 2002; Yasui, 1998). In most insects, females mate much more often than is necessary to fertilize eggs (Thornhill and Alcock, 1983), and very often females benefit directly by mating multiple times (Arnqvist and Nilsson, 2000). Tallamy (2000, 2001) has reviewed the arthropod lineages where male care occurs and argues that male care in arthropods often has evolved because of female mating preference for males that provide care. Under this "enhanced fecundity hypothesis," male care is a parallel to other resources that males may provide, such as nuptial gifts that increase fecundity. In our model we have isolated the benefit of increased attractiveness to females, to investigate whether and when this is sufficient to make male care beneficial.
Because male golden egg bugs care for offspring they have not sired, it has been discussed whether males are simply the victims of parasitism by females or if they in fact benefit from cooperating with the female (e.g., Kaitala and Kaitala 2001; Tallamy 2001). We investigate how female mating rate and oviposition rate together might determine the outcome in the golden egg bug, given the assumption that females that want to oviposit do not mate until after oviposition. Katvala and Kaitala (2001b) showed that males might frequently receive eggs before the female mates, although after the mating it may take several hours until the next oviposition (Kaitala and Miettinen, 1997; Katvala and Kaitala, 2001b). We show that both the relation between the two rates and their absolute values influence the solution. Male acceptance of eggs is favored if oviposition rate is high in comparison with mating rate. A high rate of oviposition always makes male acceptance of eggs a more probable strategy, because it decreases the mating probability for a male that does not accept eggs. For a given oviposition rate, an increasing mating rate may change the evolutionarily stable outcome from "Always care" to "Never care" (Figure 5). Males should also accept eggs more readily if oviposition and mating are correlated events.
Katvala and Kaitala (2001b) observed courting by Phyllomorpha males under laboratory conditions. Of 39 observed courtings, 23 resulted in copulation. Out of these, 14 were preceded by oviposition (of unrelated eggs). This experiment thus gives an estimate of (q1= 0.47) for female mating probability and q2= 0.18 for the probability of mating without ovipositing. Here we assume that the female would not have copulated unless the male had accepted the eggs. Furthermore, 14 males received eggs, but no mating, when they courted. Thus, egg reception and mating were not associated events in this experiment.
We have assumed that the helping behavior of males has no effect on population density. This could be unrealistic for Phyllomorpha, because carrying increases egg survival dramatically (Kaitala, 1996; Reguera and Gomendio, 2002) and could therefore lead to higher equilibrium population density. However, even if egg carrying affects population density, female behavior still dictates when males benefit from carrying. This will still be at a point where q2 is much smaller than q1 (Figure 2), so the main conclusion remains unchanged; male care of young may evolve as a competition strategy for males, where the mortality cost of caring for unrelated offspring is traded against the increase in mating frequency.
In most insect species with paternal care of offspring, male care has evolved as a means of offering increased reproductive success to females, either by releasing females from the need for offspring care or by identifying males with good genes (Tallamy, 2000, 2001). Typically, though, the male help is directed to the male's own offspring. For example, in Belastomidae, a male carries the eggs on his back until they hatch. The mating behavior of this species ensures that the male is the father of the carried eggs, because when united, they alternate between oviposition and mating until the clutch is completed (e.g., Smith, 1979, 1997). In the golden egg bug most eggs are carried non-paternally (Tay et al., 2003), and males receive most eggs before they mate (Katvala and Kaitala, 2001b). Therefore, the fitness benefits received by the male cannot be very strongly related to the increased fitness of the female's offspring. With the present model we wanted to stress that paternity is not a necessary condition for egg carrying to evolve. If males that do not accept eggs get fewer matings, egg carrying could evolve as part of the male mating strategy. Alternative explanations include that the male ESS is actually "Never care," but that males have not yet evolved efficient defenses against a purely parasitic exploitation by females (Kaitala and Kaitala, 2001). Egg carrying behavior is, of course, more likely to evolve if some of the eggs are the male's own. While such benefits for own or related offspring are part of the definition of parental care, and generally expected in systems with care of young, kin selection is not in principle needed to explain the helping of other's offspring.
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APPENDIX |
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Population dynamics
A male gains fitness every time he finishes breeding. Fitness can be calculated as the probability that the male is mating at t, pOM(t), multiplied by the rate of termination of breeding, 1/T, and multiplied by the average fitness gain from one mating, G(r). G(r) depends on the prevailing male strategy because the male behavior is assumed to influence the survival of the helped young. When integrated over time, this yields the lifetime fitness of males, W(r):
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To find pOM(t), we solve the dynamic system in Equation 2. The total time an average male spends mating during his life is the probability, pOM(t), that he is mating at time t, and integrated over time. With the notation a11 = –µSM – m(r, q1, q2); a12 = 1/T; a21 = m(r, q1, q2); a22 = –µP – 1/T, this can be written:
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To calculate Equation A2, we need to know the number of single females at the stable population state. This is determined by the joint dynamics of males and females and can be calculated iteratively. The number of single males at any one time is proportional to the average time during which a male is alive and single, that is:
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Here R is a constant that scales population density, and which can be interpreted as the constant number of new males recruited into the population each time unit. The female mating rate depends on the strategy of the population in the same way as in Equation 1, but nS should be changed to the number of bachelors (nB) for the female case (cf. Equation 1). The female dynamics are dictated by a set of equations equivalent to Equations 1 and 2, and the number of spinsters at equilibrium can accordingly be calculated as
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The condition for ESS stability
Assume that the strategy set for the male population is r = {0, 1}. The fitness of a mutant individual with strategy r' in a population following strategy r, i.e., W(r', r), is given by Equation 4. For r * to be an ESS, the following must hold (Maynard Smith, 1982), either
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ACKNOWLEDGEMENTS |
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Mari Katvala, Lotta Kvarnemo, and Juha Tuomi provided helpful comments. The study was supported by the Academy of Finland (projects #53899 and #80322 to A.K.).
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REFERENCES |
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