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Life history strategy models in which female size depends on fecundity and male size on male-male competition, are used to predict male and female size. Sperm competition alone—without any form of contest competition—cannot readily generate size ratios (male weight/female weight) greater than 1·0, and if sperm competition is very weak, small or even dwarf males are predicted. Increasing sperm competition increases male size, but only with high numbers of competing males can male size approach that of females. Size dimorphism is also affected by the ratio: growth rate/mortality rate in each sex. If this is higher in one sex, its size increases. Two trade-offs in fish could affect this ratio but neither appears likely to yield size ratios above unity under sperm competition. Male-male combat is capable of pushing male size beyond that of females, but male size seems never to exceed female size by more than one order of ten, whilst the reverse can proceed to many orders of ten (dwarf males), a pattern which applies generally in animals. Reasons for this asymmetry in size ratio include buffering effects of reducing growth rate (‘von Bertalanffy buffering’), and an asymmetry in the homeostatic effect of operational sex ratio (‘OSR buffering’). High adult male mortality and weak male-male competition can generate dwarf males. A fundamental problem concerns why the sexes are often so similar in size: this may relate to sperm competition, size buffering effects, and many other features not considered in the present models.

SEXUAL dimorphism in body size is widespread in the animal kingdom. Whereas male giantism has been studied and explained extensively1,2, male dwarfism has not. Yet it is neither rare3–7 nor without theoretical interest8,9. Here we provide experimental and comparative data on spiders to support the theory that dwarf males are associated with high differential adult mortality, with males at much greater risk. Species with sedentary (low-risk) females have dwarf, roving (high-risk) males. Life-history theory could readily explain dwarfing if juvenile, but not adult, male mortality were large. We present a new model in which high mortality of searching mature males reduces the adult sex ratio (males: females), relaxing male–male competition and reducing the importance of male body size to favour dwarfing by early maturation. Early maturity also reduces male juvenile mortality and thus opposes adult mortality. This provides a mechanism that buffers skews in adult sex ratio and which is quite distinct from Fisher's principle10 and allied mechanisms9,11 for the primary sex ratio.

Fretwell's (1972, Populations in a Seasonal Environment, Princeton University Press) ideal tree model predicts the ideal distribution when individuals in a habitat are free to move between patches. In this paper, the relationship between the ‘continuous input’ and ‘interference’ ideal free models of Sutherland & Parker (1985, In: Behavioural Ecology: Ecological Consequences of Adaptive Behaviour, ed. by R. M. Sibly & R. H. Smith, pp. 255–274, Blackwell) and Parker & Sutherland (1986, Anim. Behav., 34, 1222–1242) are examined. Continuous input describes cases where resource items arrive at patches containing groups of waiting competitors. Increasing their density in a patch reduces individual gain rates because the resource items arrive at a fixed rate, and are shared between competitors. Interference describes cases where foragers search for prey items hidden within the patches. Increasing competitor density in a patch can reduce individual gain rates due to interference between individuals. Both can be modelled using the form: individual gain rate = Q i n i − m , in which Qi is the input rate or prey density in patch i, ni is the number of competitors, and m is a constant which increases with the strength of interference. A previous formulation of the above model in which individuals have unequal competitive abilities is extended to cover the case where phenotypic differences are reflected by a scaling of Qi (rather than by a scaling of the level of m). Here, many different mixed distributions of phenotypes can exist as ideal free equilibria, provided that relative competitive abilities stay constant across patches. Many different phenotypes can occur across several patch types. However, where phenotypic differences are best reflected by a scaling of m, then these mixed distributions of phenotypes are not possible, and no more than one phenotype can play a mixed strategy across the same pair of patch types. Typically, a truncated distribution of phenotypes between the patches can be expected, with the best phenotypes in the best patches. Some general conditions are proposed for ideal free distributions of unequal competitors.

The classical version of marginal value theorem (MVT) assumes constant costs of time spent in different activities (searching; resource uptake). This article investigates the logic of MVT when these have different costs. Models are developed specifically to offer a plausible adaptive explanation for results obtained by P. I. Ward and L. W. Simmons on the copula duration of the yellow dung fly: (1) copula duration does not alter during successive matings in a sequence, (2) copula duration declines with dietary restriction, and (3) the number of copulations in a sequence declines with dietary restriction. In dung flies, mate searching is energetically expensive, and copulation expends sperm. Both energy losses and sperm losses must be paid for by food foraging (for nectar and prey items, respectively). Two models are examined. In model 1, sperm reserves increase linearly during food foraging, and the organization of time between mate searching and foraging is unstated. It predicts that low prey densities du...

Intraspecific variation in the proportion of offspring sired by the second male to mate with a female (P2) is an aspect of sperm competition that has received little attention. We examined variation in the sperm competition success of individual male dung flies, Scatophaga stercoraria. In unmanipulated matings, copula duration was dependent on male size with smaller males cop- ulating for longer. A principal component analysis was used to generate uncorrelated scores based on a male's size and copula duration. Using these scores demonstrated that P2 values were dependent both on the relative size and copula durations of competing males. When copula duration was held constant, the success of an individual male increased as his body size, relative to the first male, increased. We interrupted copulations of "large" and "small" second males and fitted the resultant P2 values to a linear model of sperm competition with unequal ejaculates. The data fit well to a model of sperm displacement in which sperm mix quickly on introduction to the sperm stores. Furthermore, they show that "large" males have a greater rate of sperm displacement than "small" males. The levels of prey availability during testis maturation may influence a male's success in sperm competition although his immediate mating history does not. We show why an understanding of variation in sperm competition success is important for understanding the mech- anisms and evolutionary significance of sperm competition.

Population genetic models have shown that exploitation competition for resources between siblings can often lead to severe reductions in offspring fitness. As the parental optimum is normally the absence of competition, the presence of sibling competition is an aspect of parent-offspring conflict. Phenotypic techniques are developed for modelling sibling competition in broods where all members have equal competitive ability. Two forms of sibling competition are modelled, one suggested by competition between nestling birds, and the second suggested by competition between the larvae of gregarious insects. The phenotypic models confirm the genetic analysis and allow the study of the relationship between sibling competition and clutch size (the genetic models assumed infinite clutch size). Conflict may either increase or decrease with clutch size depending on how the costs of competition are spread among the members of the brood. It is also shown that in the presence of sibling competition, parents may be selected to produce smaller clutches than those that would be optimum in the absence of sibling competition.

In complex life cycles, larval helminths typically migrate from the gut to exploit the tissues of their intermediate hosts. Yet the definitive host's gut is overwhelmingly the most favoured site for adult helminths to release eggs. Vertebrate nematodes with one-host cycles commonly migrate to a site in the host away from the gut before returning to the gut for reproduction; those with complex cycles occupy sites exclusively in the intermediate host's tissues or body spaces, and may or may not show tissue migration before (typically) returning to the gut in the definitive host. We develop models to explain the patterns of exploitation of different host sites, and in particular why larval helminths avoid the intermediate host's gut, and adult helminths favour it. Our models include the survival costs of migration between sites, and maximise fitness (=expected lifetime number of eggs produced by a given helminth propagule) in seeking the optimal strategy (host gut versus host tissue exploitation) under different growth, mortality, transmission and reproductive rates in the gut and tissues (i.e. sites away from the gut). We consider the relative merits of the gut and tissues, and conclude that (i) growth rates are likely to be higher in the tissues, (ii) mortality rates possibly higher in the gut (despite the immunological inertness of the gut lumen), and (iii) that there are very high benefits to egg release in the gut. The models show that these growth and mortality relativities would account for the common life history pattern of avoidance of the intermediate host's gut because the tissues offer a higher growth rate/mortality rate ratio (discounted by the costs of migration), and make a number of testable predictions. Though nematode larvae in paratenic hosts usually migrate to the tissues, unlike larvae in intermediates, they sometimes remain in the gut, which is predicted since in paratenics mortality rate and migration costs alone determine the site to be exploited.

Publisher Summary Sperm competition is the competition between the ejaculates of different males for the fertilization of a given set of ova. Charles Darwin (1871) proposed sexual selection as a process that operates on variation in male ability to compete with other males for access to reproductive opportunities, and which promotes traits that confer an advantage in reproductive competition. In most taxa individual females may copulate (or spawn) with multiple males (i.e., are polyandrous). As a consequence, the ejaculates of different males may co-occur around a set of ova at the time of fertilization, resulting in sperm competition. Sperm competition introduces variation in male reproductive success determined by the relative competitive fertilizing efficiency of the ejaculates of different males, and generates postcopulatory, intrasexual selection, which promotes traits that increase the fertilization success of an ejaculate under competitive conditions. A second consequence of polyandry is the potential for intersexual selection to continue after copulation through mechanisms that enable females (or ova) to bias the outcome of sperm competition in favor of the sperm of certain males, a process known as sperm selection or cryptic female choice. The past three decades have seen an explosion of interest in postcopulatory sexual selection that has highlighted the importance of sperm competition and cryptic female choice as engines of evolutionary change. This chapter reviews recent empirical and theoretical advances to discuss various ways in which sperm competition may shape the evolution of sperm and ejaculate traits.

We examine the risk model in sperm competition games for cases where female fertility increases significantly with sperm numbers (sperm limitation). Without sperm competition, sperm allocation increases with sperm limitation. We define ‘average risk’ as the probability q that females in the population mate twice, and ‘perceived risk’ as the information males gain about the sperm competition probability with individual females. If males obtain no information from individual females, sperm numbers increase with q unless sperm limitation is high and one of the two competing ejaculates is strongly disfavoured. If males can distinguish between virgin and mated females, greater sperm allocation to virgins is favoured by high sperm limitation, high q, and by the second male's ejaculate being disfavoured. With high sperm limitation, sperm allocation to virgins increases and to mated females decreases with q at high q levels. With perfect information about female mating pattern, sperm allocation (i) to virgins that will mate again exceeds that to mated females and to virgins that will mate only once, (ii) to virgins that mate only once exceeds that for mated females if q is high and there is high second male disadvantage and (iii) to each type of female can decrease with q if sperm limitation is high, although the average allocation increases at least across low q levels. In general, higher sperm allocation to virgins is favoured by: strong disadvantage to the second ejaculate, high sperm limitation, high average risk and increased information (perceived risk). These conditions may apply in a few species, especially spiders.

Sexual conflict is a conflict between the evolutionary interests of individuals of the two sexes. The sexes can have different trait optima but this need not imply conflict if their optima can be attained simultaneously. Conflict requires an interaction between males and females (e.g. mating or parental care), such that the optimal outcomes for each sex cannot be achieved simultaneously. It is important to distinguish between battleground models, which define the parameter space for conflict and resolution models, which seek solutions for how conflicts are resolved. Overt behavioural conflict may or may not be manifest at resolution. Following Fisherian principles, an immediate (i.e. direct) benefit to a male that has a direct cost to his female partner can have an indirect benefit to the female via her male progeny. Female resistance to mating has been claimed to represent concurrence rather than conflict, due to female benefits via sons (males with low mating advantage are screened out by resistance). However, the weight of current evidence (both theoretical and empirical) supports sexual conflict for many cases. I review (i) conflicts over mate quality, encounters between males and females of genetically diverged subpopulations, mating rate and inbreeding, (ii) the special features of postcopulatory sexual conflict and (iii) some general features of importance for conflict resolution.

We consider optimal growth of larval stages in complex parasite life cycles where there is no constraint because of host immune responses. Our model predicts an individual’s asymptotic size in its intermediate host, with and without competition from conspecific larvae. We match observed variations in larval growth patterns in pseudophyllid cestodes with theoretical predictions of our model. If survival of the host is vital for transmission, larvae should reduce asymptotic size as intensity increases, to avoid killing the host. The life history strategy (LHS) model predicts a size reduction

We analyse a co-evolutionary sexual conflict game, in which males compete for fertilizations (sperm competition) and females operate sperm selection against unfavourable ejaculates (cryptic female choice). For simplicity, each female mates with two males per reproductive event, and the competing ejaculates are of two types, favourable (having high viability or success) or unfavourable (where progeny are less successful). Over evolutionary time, females can increase their level of sperm selection (measured as the proportion of unfavourable sperm eliminated) by paying a fecundity cost. Males can regulate sperm allocations depending on whether they will be favoured or disfavoured, but increasing sperm allocation reduces their mating rate. The resolution of this game depends on whether males are equal, or unequal. Males could be equal: each is favoured with probability, p , reflecting the proportion of females in the population that favour his ejaculate (the ‘random-roles’ model); different males are favoured by different sets of females. Alternatively, males could be unequal: given males are perceived consistently by all females as two distinct types, favoured and disfavoured, where p is now the frequency of the favoured male type in the population (the ‘constant-types’ model). In both cases, the evolutionarily stable strategy (ESS) is for females initially to increase sperm selection from zero as the viability of offspring from unfavourable ejaculates falls below that of favourable ejaculates. But in the random-roles model, sperm selection decreases again towards zero as the unfavourable ejaculates become disastrous (i.e. as their progeny viability decreases towards zero). This occurs because males avoid expenditure in unfavourable matings, to conserve sperm for matings in the favoured role where their offspring have high viability, thus allowing females to relax sperm selection. If sperm selection is costly to females, ESS sperm selection is high across a region of intermediate viabilities. If it is uncostly, there is no ESS in this region unless sperm limitation (i.e. some eggs fail to be fertilized because sperm numbers are too low) is included into the model. In the constant-types model, no relaxation of sperm selection occurs at very low viabilities of disfavoured male progeny. If sperm selection is sufficiently costly, ESS sperm selection increases as progeny viability decreases down towards zero; but if it is uncostly, there is no ESS at the lowest viabilities, and unlike the random-roles model, this cannot be stabilized by including sperm limitation. Sperm allocations in the ESS regions differ between the two models. With random roles, males always allocate more sperm in the favoured role. With constant types, the male type that is favoured allocates less sperm than the disfavoured type. These results suggests that empiricists studying cryptic female choice and sperm allocation patterns need to determine whether sperm selection is applied differently, or consistently, on given males by different females in the same population.

The fundamental question of how complex life cycles--where there is typically more than one host-evolve in host--parasite systems remains largely unexplored. We suggest that complex cycles in helminths without penetrative infective stages evolve by two essentially different processes, depending on where in the cycle a new host is inserted. In 'upward incorporation', a new definitive host, typically higher up a food web and which preys on the original definitive host, is added. Advantages to the parasite are avoidance of mortality due to the predator, greater body size at maturity and higher fecundity. The original host typically becomes an intermediate host, in which reproduction is suppressed. In 'downward incorporation', a new intermediate host is added at a lower trophic level; this reduces mortality and facilitates transmission to the original definitive host. These two processes should also apply in helminths with penetrative infective stages, although the mathematical conditions differ.

Mammal life history traits relating to growth and reproduction are extremely diverse. Sibling rivalry may contribute to selection pressures influencing this diversity, because individuals that are relatively large at birth typically have an advantage in competition for milk. However, selection for increased growth rate is likely to be constrained by kin selection and physiological costs. Here, we present and test a model examining the ESS (evolutionarily stable strategy) balance between these constraints and advantages associated with increased prenatal growth in mammal sibling rivalry. Predictions of the model are supported by results of comparative analyses for the Carnivora and Insectivora, which demonstrate an increase in prenatal growth rate with increasing intensity of postnatal scramble competition, and a decrease in postnatal growth rate relative to size at birth. Because increased prenatal growth rates are predicted to select for reduced gestation length under certain conditions, our study also indicates that sibling rivalry may contribute to selection pressures influencing variation in altriciality and precociality among mammals.

We outline and develop current theory on how inherent genetic conflicts of interest between the various family members can affect the flow of parental investment from parents to offspring, and discuss the problems for empirical testing that this generates. The parental investment pattern realized in nature reflects the simultaneous resolution of all the conflicts between the family players. This depends on the genetic mechanism, the mating system and reproductive constraints, on whether extra demand by progeny affects current or future sibs, and particularly on the behavioural mechanisms underlying demand (begging or solicitation) and supply (provision of parental investment by parents). The direction of deviation from the optimal parental investment for the parent(s) depends on the slope of what we term the ‘effect of supply on demand’, the mechanism that determines how changes in food supply affect begging levels. If increasing food increases begging (positive slope), less parental investment is supplied than the parental optimum and if increasing food decreases begging (negative slope), more parental investment is supplied. The magnitude of deviation depends on both the ‘effect of supply on demand’ and on the ‘effect of demand on supply’ (the mechanism determining how changes in begging affect food supply, which always has a positive slope). We conclude that it will often be impossible to deduce the extent of underlying conflict by establishing the amount of parental investment given relative to the ideal optimum for the parent. Some possible directions for future research are discussed.

Parasitic worms (helminths) frequently have complex life cycles in which they are transmitted trophically between two or more successive hosts. Sexual reproduction often takes place in high trophic-level (TL) vertebrates, where parasites can grow to large sizes with high fecundity. Direct infection of high TL hosts, while advantageous, may be unachievable for parasites constrained to transmit trophically, because helminth propagules are unlikely to be ingested by large predators. Lack of niche overlap between propagule and definitive host (the trophic transmission vacuum) may explain the origin and/or maintenance of intermediate hosts, which overcome this transmission barrier. We show that nematodes infecting high TL definitive hosts tend to have more successive hosts in their life cycles. This relationship was modest, though, driven mainly by the minimum TL of hosts, suggesting that the shortest trophic chains leading to a host define the boundaries of the transmission vacuum. We also show that alternative modes of transmission, like host penetration, allow nematodes to reach high TLs without intermediate hosts. We suggest that widespread omnivory as well as parasite adaptations to increase transmission probably reduce, but do not eliminate, the barriers to the transmission of helminths through the food web.

Both gamete competition and gamete limitation can generate anisogamy from ancestral isogamy, and both sperm competition (SC) and sperm limitation (SL) can increase sperm numbers. Here, we compare the marginal benefits due to these two components at any given population level of sperm production using the risk and intensity models in sperm economics. We show quite generally for the intensity model (where N males compete for each set of eggs) that however severe the degree of SL, if there is at least one competitor for fertilization ( N − 1 ≥ 1), the marginal gains through SC exceed those for SL, provided that the relationship between the probability of fertilization ( F ) and increasing sperm numbers ( x ) is a concave function. In the risk model, as fertility F increases from 0 to 1.0, the threshold SC risk (the probability q that two males compete for fertilization) for SC to be the dominant force drops from 1.0 to 0. The gamete competition and gamete limitation theories for the evolution of anisogamy rely on very similar considerations: our results imply that gamete limitation could dominate only if ancestral reproduction took place in highly isolated, small spawning groups.

Sperm precedence patterns are typically highly variable within (and between) species. Intraspecific variation in sperm precedence (measured as P2, the proportion of progeny fathered by the last male to mate' is frequently seen as a candidate for adaptive interpretation through either male effects (e.g. body size), female effects (e.g. cryptic female choice) or an interaction between the two. Here we show, using computer simulation, that if ejaculates divide into a number of 'packets' and packets from two males mix randomly, then a variety of patterns of sperm precedence may result. We term this process 'sloppy' mixing. If ejaculates break into a small number of packets, bimodal P2 distributions are predicted. As the number of packets is increased, then a complex series of changes through multimodal and flat to unimodal distributions results. Sloppy mixing can thus result in many of the observed P2 distributions. Sloppy mixing is unlikely to change the predictions of adaptive models of sperm competition.

Nicholson's distinction between ‘scramble’ and ‘contest’ modes of competition has received widespread attention in ecology and in behaviour, though the emphasis has been different between the two disciplines. In ecology the focus has been on the effects on population; in behavioural ecology the focus has been on the consequences at the individual level. This paper reviews and develops a theory of scramble competition at the individual level, deriving a general evolutionarily stable strategy (ESS) for individual scramble expenditure in a patchy habitat in which individuals compete in local groups for available resources, and examines two population consequences. The critical parameter determining the relationship between individual scramble expenditure and the number of competitors in a patch is the expected resource per capita. If resource input, R , to a patch is constant and independent of the number of competitors, n , then as the number of competitors increases, the per–capita resources declines as R / n , and the ESS scramble level declines (in proportion to ( n −1)/ n 2 ). However, if the resource input to a patch is positively related to the number of competitors in the patch, scramble expenditure may increase with the number of competitors. In the case where the per–capita resource input stays constant (i.e. R ( n ) = Rn ), the scramble level increases with competitor number (in proportion to ( n −1)/ n ). There are plausible ecological reasons why either of these extreme limits may be approached in nature, making it important to ascertain the relationship between R and n before predicting individual scramble expenditure. For example, resource input may be constant when groups of competitors are constrained to remain together in given patches, and constant per–capita resources may be approached when ideal–free foraging rules apply. However, in the latter case, scramble expenditure must be accounted for in determining the idealfree distribution. An analysis shows that this leads to ‘undermatching’, i.e. the ratio of numbers of competitors for good/bad patches becomes progressively less than the ratio of input rates for good/bad patches as the difference between the good and bad patches increases. A second population consequence of the scramble ESS relates to the fact that scrambles may dramatically affect fitness. The per–capita gain in energy can be reduced by a factor of up to 1/ n as a result of scramble expenditure, potentially reducing realized population size to as little as the square root of the maximum potential carrying capacity, though reasons are given why such large reductions are unlikely.

The female reproductive tract can be particularly aggressive towards ejaculates, often leading to the death of large numbers of sperm. It has been suggested that males can respond to these actions by investing more in sperm and donating larger ejaculates. Such counteractions may lead to arms races, which can have significant implications for the mating system. In a series of simple models we first show that arms races are not necessarily supported: in fact, sperm killing may even favour no change or reductions in sperm allocation. Second, we identify a simple mechanistic rule for sperm killing that determines whether an arms race or sperm reduction will be favoured. Which of these responses is favoured by selection depends on whether a certain number, or proportion, of sperm are killed. When a specific number is killed, larger investment in sperm is favoured and when a specific proportion is killed, no change or lower investment in sperm is favoured. Both of these mechanisms are biologically plausible.

Three sperm competition games against relatives are examined. In the first, a male has no information at the time of mating as to whether or not his ejaculate will face sperm competition from a related or unrelated male. Sperm expenditure increases with overall sperm competition risk q and declines with the probability rho that the competitor shares the same allele for sperm expenditure. In the second game, males have almost perfect information: they 'know' whether there will be sperm competition and, if so, whether this involves a related or unrelated male. Sperm expenditure is reduced by a factor rho when competing with a relative. In the third game, males 'know' when they compete with relatives, but have no information for other matings whether they will face sperm competition from unrelated males. A male without information expends less on his ejaculate than a male competing with a close relative if the overall risk of sperm competition is low, but more if the overall risk is high. The average relative ejaculate expenditure is the same in all three games so that, if this determines testis size, data is required only on the overall sperm competition risk, the probability of competing with a relative and the average rho in order to perform comparative analyses.

MALE mate choice is predicted to occur when males transfer nutrients to females during copulation, provide paternal care, or are otherwise limited in mating capacity1–7. Most commonly, field studies have revealed male choice to be focused on females offering high fecundity8–10. Here we describe male mating selectivity that appears to be driven by sperm competition: male thirteen-lined ground squirrels (Spermophilus tridecemlineatus) avoid copulating with previously mated females once the fertilization gain rate drops below the average obtainable from alternative matings. Although this behaviour seems advantageous to males, it limits the duration of female sexual activity.

We investigate game theory models of ejaculate expenditure by males in a species where there is a risk probability, q, that females will mate twice before laying a given set of eggs. With frequency 1-q females mate just once; then males optimally ejaculate an arbitrary minimum amount of sperm. The paper extends the analysis of Parker et al. (1997) in which males have limited information about the three risk states of the female: 0 (virgins which will mate now but not again), 1 (virgins which will mate now and then once more), and 2 (once-mated females who will mate now but not again). We derive a general structure for finding ESSs under imperfect information about states, and examine two special cases in which males know the overall risk probability q, but have imperfect knowledge of the states (0, 1, 2). In Case 1, males cannot distinguish between states 0 and 1 but have limited information about state 2. As their information increases, so does the difference in sperm allocation, with more going to females assessed as mated (state 2) than to females assessed as virgins (0, 1). This difference decreases with q in a species, but the average ejaculate expenditure increases with q. Even for small amounts of information, the behaviour as q--0 is different from that predicted for zero information. In Case 2, males have perfect information about state 2, but limited information about states 0, 1. This has a major effect if q is small: males effectively behave as if they had perfect information by giving equal amounts of sperm to females assessed as 1 as those assessed to be 2, while giving a minimum amount to females assessed as 0. Ejaculate expenditures generally increase with the overall species-level risk q. A result common to both cases is that even a small amount of information allows more strategic choice than the zero information case and hence qualitatively different behaviour.

We review the significance of two forms of sexual conflict (different evolutionary interests of the two sexes) for genetic differentiation of populations and the evolution of reproductive isolation. Conflicting selection on the alleles at a single locus can occur in males and females if the sexes have different optima for a trait, and there are pleiotropic genetic correlations between the sexes for it. There will then be selection for sex limitation and hence sexual dimorphism. This sex limitation could break down in hybrids and reduce their fitness. Pleiotropic genetic correlations between the sexes could also affect the likelihood of mating in interpopulation encounters. Conflict can also occur between (sex–limited) loci that determine behaviour in males and those that determine behaviour in females. Reproductive isolation may occur by rapid coevolution of male trait and female mating preference. This would tend to generate assortative mating on secondary contact, hence promoting speciation. Sexual conflict resulting from sensory exploitation, polyspermy and the cost of mating could result in high levels of interpopulation mating. If females evolve resistance to male pre– and postmating manipulation, males from one population could be more successful with females from the other, because females would have evolved resistance to their own (but not to the allopatric) males. Between–locus sexual conflict could also occur as a result of confict between males and females of different populations over the production of unfit hybrids. We develop models which show that females are in general selected to resist such matings and males to persist, and this could have a bearing on both the initial level of interpopulation matings and the likelihood that reinforcement will occur. In effect, selection on males usually acts to promote gene flow and to restrict premating isolation, whereas selection on females usually acts in the reverse direction. We review theoretical models relevant to resolution of this conflict. The winning role depends on a balance between the ‘value of winning’ and ‘power’ (relating to contest or armament costs): the winning role is likely to correlate with high value of winning and low costs. Sperm–ovum (or sperm–female tract) conflicts (and their plant parallels) are likely to obey the same principles. Males may typically have higher values of winning, but it is difficult to quantify ‘power’, and females may often be able to resist mating more cheaply than males can force it. We tentatively predict that sexual conflict will typically result in a higher rate of speciation in ‘female–win’ clades, that females will be responsible for premating isolation through reinforcement, and that ‘female–win’ populations will be less genetically diverse.

We develop the logic of assessment of sperm competition risk by individual males where the mechanism of sperm competition follows a 'loaded raffle' (first and second inseminates of a female have unequal prospects). Male roles (first or second to mate) are determined randomly. In model 1, males have no information about the risk associated with individual females and ejaculation strategy depends only on the probability, q, that females mate twice. Evolutionarily stable strategy (ESS) ejaculate expenditure increases linearly from zero with q, and reduces with increasing inequality between ejaculates, though the direction of the loading (which role is favoured) is unimportant. In model 2, males have perfect information and can identify each of three risk states: females that will (1) mate just once ('no risk'), (2) mate twice but have not yet mated ('future risk'), and (3) mate twice and have already mated ('past risk'). The ESS is to ejaculate minimally with 'no risk' females, and to expand equally with 'past' and 'future' risk females; the direction of the competitive loading is again unimportant. Expenditure again increases with risk, but is now non-zero at extremely low risk. Model 3 examines three cases of partial information where males can identify only one of the three risk states and cannot distinguish between the other two: they therefore have just two information sets or 'contexts'. Expenditure in both contexts typically rises non-linearly from zero with q, but (whatever the loading direction) expenditure is higher in the context with higher risk (e.g. if contexts are 'mated' and 'virgin', males spend more with mated females). However, in highly loaded raffles, sperm expenditure can decrease over part of the range of risk. Also, the direction of the loading now affects expenditure. Biological evidence for the predictions of the models is summarized and discussed.

Fishes show one of the widest ranges of sperm competition intensity of any animal group. Here we present a comparative study whose aim is to investigate the effect of relative intensity of sperm competition on investment in spermatogenesis and the number and size of sperm produced. We find that both the gonadosomatic index (GSI5 (gonad weight/body weight) 3 100) and sperm numbers increase with intensity of sperm competition across species but that sperm length decreases. These new findings are consistent with a raffle-based mode of sperm competition in fishes. Most of these results (positive correlation of the GSI and sperm number with sperm competition intensity) concur with the predictions of current sperm competition the- ory. However, we also find that sperm longevity decreases with sperm length across species. Cur- rent models for continuous fertilization suggest that if length increases a sperm's speed but de- creases its longevity, sperm length should increase with sperm competition intensity, whereas models for instant fertilization suggest that sperm length should remain constant. The negative relationship found between sperm competition and sperm length therefore does not fit predictions of either model.

We give a historic overview and critical perspective of polyandry in the context of sexual selection. Early approaches tended to obfuscate the fact that the total matings (copulations) by the two sexes is equal, neglecting female interests and that females often mate with (or receive ejaculates from) more than one male (polyandry). In recent years, we have gained much more insight into adaptive reasons for polyandry, particularly from the female perspective. However, costs and benefits of multiple mating are unlikely to be equal for males and females. These must be assessed for each partner at each potential mating between male i and female j , and will often be highly asymmetric. Interests of i and j may be in conflict, with (typically, ultimately because of primordial sex differences) i benefitting and j losing from mating, although theoretically the reverse can also obtain. Polyandry reduces the sex difference in Bateman gradients, and the probability of sexual conflict over mating by: (i) reducing the potential expected value of each mating to males in inverse proportion to the number of mates per female per clutch, and also often by (ii) increasing ejaculate costs through increased sperm allocation. It can nevertheless create conflict over fertilization and increase conflict over parental investment. The observed mean mating frequency for the population (and hence the degree of polyandry) is likely, at least in part, to reflect a resolution of sexual conflict. Immense diversity exists across and within taxa in the extent of polyandry, and views on its significance have changed radically, as we illustrate using avian polyandry as a case study. Despite recent criticisms, the contribution of the early pioneers of sexual selection, Darwin and Bateman, remains generally valid, and should not, therefore, be negated; as with much in science, pioneering advances are more often amplified and refined, rather than replaced with entirely new paradigms.

We develop a model of a continuous fertilization process in which eggs and sperm are shed simultaneously, and in which the eggs are fertilized at a rate proportional to sperm density surrounding the egg mass. The model derives the ESS size and number of sperm in an ejaculate of an externally-fertilizing animal such as a fish species, in which the probability or intensity of sperm competition varies. It also predicts the ESS level of infertility (eggs remaining unfertilized after all sperm have died). Sperm size is assumed to increase sperm competitive ability (e.g. by increasing speed) and is also assumed to affect sperm longevity (either positively or negatively). Ejaculate expenditure is traded off against expenditure on obtaining further spawnings, and size and number of sperm can vary independently. The model predicts that the ESS ejaculate expenditure (product of sperm size and number) should increase, and that the ESS infertility should decrease with sperm competition intensity measured across species. Other results depend on the way that sperm size affects longevity. The available biological evidence suggests that longevity decreases with sperm size, probably because the main increase is in tail length which increases sperm energy expenditure. In this case, sperm size should increase with sperm competition intensity from an optimum at zero competition which maximizes the total distance travelled by the entire ejaculate in its lifetime, to an optimum for maximum sperm competition which maximizes the product of speed and sperm number. However, if longevity increases with sperm size, then the non-competitive optimal sperm size is greater than that for maximum competition, so that sperm size decreases with sperm competition intensity. Sperm numbers typically increase with sperm competition intensity, and always so if sperm competition is high enough, though decreases are possible over a range of low sperm competition intensity if (i) sperm longevity decreases with sperm size, and (ii) infertility is high enough.

The addition of frequency dependence to the marginal value theorem (MVT) model of the dung fly (Scatophaga stercoraria) male's optimal copula duration makes virtually no difference to the predicted competitive optimum (ESS). However, this evolutionarily stable strategy (ESS) version allows an explicit solution for the optimum. In a general sense, MVT optima will be close to their ESS equivalent when the cycle duration (expected time between the starts of two successive patch exploitations) is long relative to the plausible patch exploitation times. The optimal copula duration for male dung flies will depend on the ratio of virgin to mated females arriving at the droppings and on whether a male can discriminate between the two sorts of female. In nature, we found only an average of 3% of the total females arriving at the droppings to be virgins, rather less than had been estimated. This means that matings away from droppings (“extra-dung matings”) must be much commoner than previously suspected. Cumulative gains through copulation time rise much more steeply with virgins than with mated females, and so if males are able to discriminate, on the present model, we calculate that the ESS copula durations (at 20° C) would be around 42 min for non-virgins and 11 min for virgins. If they do not discriminate, the ESS is to copulate for a fixed duration of 41.5 min, i.e. very close to the optimum for mated females. The data indicate that copula duration does not differ for the two types of mating (mated females; virgins), suggesting that males cannot discriminate (or that the copula duration with virgins is not optimised to male interests). ESS copula durations with discrimination are almost entirely independent of the frequency of virgins in the population of females arriving at the droppings; without discrimination the optimal copula duration shifts between the ESS for mated females and that for virgins as the virgin frequency increases from 0 to 1. But at their naturally occurring frequency of only 3%, virgins can be ignored from calculations of optimal copula duration without significant loss of precision.

Prospective models are developed for analysing sperm competition data so as to predict the underlying mechanisms determining paternity in multiply mated females. The models require: 1) estimations of proportion of offspring sired by the last male to mate (P 2), 2) knowledge of the number of sperm transferred by each male, and 3) knowledge of the sperm storage capacity of the female, should this be limited. They will distinguish between “raffles” (sperm mixing without displacement) and sperm displacement mechanisms. The sensitivity of the techniques can be increased by manipulating the number of sperm transferred by each male. Typically, this can be done by manipulating copula duration or number of ejaculations, given a knowledge of the rate of sperm transfer. Data from two contrasting insect species are fitted to the models to demonstrate the techniques. These models are prospective only, and their limitations are discussed. The principal limitation is that we assume that sperm used for fertilization mix randomly in a “fertilization set” immediately prior to fertilization; in reality this may be difficult to identify. When sperm mixing is very rapid, the fertilization set will often be equivalent to the sperm stores, but with slow mixing, the fertilization set may be equivalent to a much more restricted zone and may change with time.

Correction for ‘The evolution of anisogamy: a game-theoretic approach’ by M. G. Bulmer and G. A. Parker (Proc. R. Soc. Lond. B 269 , 2381–2388. (doi: [10.1098/rspb.2002.2161][1])). On page 2383, below equation (2.8), the first sentence of the new paragraph should read: [1]: /lookup/doi/10.1098/rspb.2002.2161

We aim to interpret sperm displacement in relation to male size in the yellow dung fly, Scatophaga stercoraria, and to compare the general properties of indirect and direct size-dependent sperm displacement in insects. We examine the hypothesis that male size-dependent sperm displacement in dung flies can be explained by size-dependent increases in the ejaculatory apparatus, allowing greater sperm flow rates in larger males. We expect sperm flow rates to be proportional to the diameter of the aedeagus duct to the power x, where x lies between 2 and 3. We test this hypothesis using a simulation model of indirect sperm displacement that has been developed to accommodate recent observations on sperm transfer, in which sperm flow from the male into the female bursa and are then transferred to the spermathecae by movements of the female tract. The indirect model approximates to the pattern of size-related sperm displacement, with scaling power 3 giving a better fit than power 2. Copula duration shows ...

We admire the fine primatological research1xSee all References1 to which Harcourt rightly draws our attention, and which shows the relationships between rank, group size and feeding behaviour. There does, however, seem to be a difference in terminology between this work and our own. We considered interference in terms of a quantified relationship between population density and mean or individual intake rate2xHassell, M.P. and Varley, G.C. Nature. 1969; 223: 1133–1136CrossRef | PubMed | Scopus (378)See all References2 as used in innumerable entomological and some ornithological studies. Many primate studies, for sensible reasons, consider interference as a change in foraging efficiency, activity budgets, or feeding-bout durations with group size; however, these measures may have a complex relationship with intake rate. Some studies do relate intake to rank (e.g. 2xHassell, M.P. and Varley, G.C. Nature. 1969; 223: 1133–1136CrossRef | PubMed | Scopus (378)See all References, 3xvan Schaik, C.P. and van Noordwijk, M.A. Behaviour. 1988; 105: 77–98CrossRefSee all References, 4xJanson, C.H. Behav. Ecol. Sociobiol. 1985; 18: 125–138CrossRef | Scopus (174)See all References, 5xBarton, R.A. and Whiten, A. Anim. Behav. 1993; 46: 777–789CrossRef | Scopus (92)See all References) and group size (e.g. Ref. 5xBarton, R.A. and Whiten, A. Anim. Behav. 1993; 46: 777–789CrossRef | Scopus (92)See all ReferencesRef. 5).Although in such examples the data are not presented in a manner that can be used to calculate the strength of interference, we suggest it would be extremely useful, and probably reasonably straightforward, to use such data to do so – both to incorporate within theoretical models and provide comparisons with other taxa.

It was formerly argued that alternative evolutionarily stable strategies (ESSs) are possible for animal contests characterized by some asymmetry that can be perceived with perfect accuracy. Where roles A and B refer to the asymmetry between opponents, ESSs are: ‘fight when A, retreat when B’, and vice versa. Either can be an ESS, but only if the ‘reserve strategy’ (=what an animal does when it fights) is sufficiently damaging. We examine the ‘war of attrition’ (winner = opponent that persists longer). In a population at either ESS, reserve strategy is never normally shown; it is therefore subject to drift unless the selective action of rare individuals which break the convention is considered. These could arise either by mutation or by mistakes in role assessment. When mutations and mistakes simply specify that occasionally an animal fights when it ‘should’ retreat, selection adjusts reserve strategy to a level where only one ESS (the ‘commonsense’ ESS) is possible, if the asymmetry is relevant to payoff. Thus for asymmetries in fighting ability or resource value, the individual with the lower score will retreat. However, we are particularly concerned with cases where both payoff-relevant aspects (fighting ability and resource value) are asymmetric. If opponents sustain contest costs at rates KA and KB, and their resource values are VA and VB, an ‘optimal assessor’ strategy defined by the interaction between the two asymmetries, is a unique ESS. It obeys the rule ‘fight on estimating role A, where VA/KA>VB/KB; retreat in B’. If mistakes can occur in both roles, but are very rate, the ESS is not fundamentally altered though there will be infinitesimal tendencies for persisting in role B. Selection to improve assessment abilities intensifies as abilities improve, but is weak if roles A and B are rather similar. Over a range of similarity between roles, an ‘owner wins’ convention may be adopted if ownership correlates positively with role A and an individual cannot tell when it would otherwise pay him to break the convention. We also examine a contest in which information about roles can be acquired only during a contest itself, and at a cost. Much depends on the rate at which information is acquired relative to the rate at which costs are expended, and on whether contests normally escalate in intensity, remain at the same level, or de-escalate. Selection favours short contests when costs are high relative to resource value, where the outcome of a round contains much information about fighting ability, and where the actual disparity in fighting ability is large.

When two male thirteen-lined ground squirrels pursue an oestrous female simultaneously, whichever of the males had been the first to locate the female has priority in copulating with her. Copulation by the later-arriving male is typically deferred until the departure of the earlier male, as if males ‘queue’ for the opportunity to mate. In this study earlier males were often heavier than later-arriving males; perhaps more importantly, they were more competent in tracking the movements of the female than were later-arriving males. Order of arrival thus corresponds with the abilities of the males to maintain access to the female, and the convention of settling contests in favour of earlier-arriving males is consistent with predictions based on evolutionarily stable strategy analyses of contests where costs can be regulated continuously. Two simple models were developed to explore the evolutionary stability of the behaviour of early-and late-arriving males. In the first, later-arriving males' toleration of the delay in mating was found to be highly advantageous relative to their alternative option of searching for an unaccompanied oestrous female. The second model indicates that the advantage to early-arriving males of resuming search after mating depends on either the effectiveness of their post-copulatory mate-guarding alternative or an advantage in sperm competition.

A genetic model of parent-offspring conflict is developed for the situation where conflictors cause the parent to redirect resources from contemporaneous siblings to themselves, by increased solicitation. It is shown that there is no restriction on the spread of genes causing such conflict if there is no direct cost associated with it. We examine the effect of imposing on the conflictors a cost of the extra solicitation when the cost is felt (a) by the individual conflictor only, and (b) by all members of the brood equally. It is shown that the Evolutionarily Stable Strategies for the two situations allow a greater degree of solicitation when its cost is borne by the whole brood. Multipaternity of broods also increases the degree of conflict.

We present a model for sexually-reproducing diploids in which a female can produce a variable (generally large) clutch size, where the sibs then compete over some fixed resource, and where certain offspring use siblicide to reduce the primary clutch/brood size created by the mother. Where siblicide involves neither direct energy loss (e.g. fighting cost) nor gain (e.g. cannibalism) to an offspring, the optimal clutch size for an offspring can differ from the optimum for the mother, i.e. there can be parent-offspring conflict over clutch size. The magnitude of this evolutionary conflict (measured in terms of difference between clutch size optima) increases with multipaternity of the brood and with the steepness of the initial decline in offspring survivorship (through sib-competition as further offspring are added to the brood). However, the disparity in clutch size optima may not be great. Where the integer clutch size optima are the same, there will clearly be no conflict. Where this differs, resolution of the evolutionary conflict could involve much apparent behavioral conflict, commonly manifest as siblicidal aggression. The ESS (evolutionarily stable strategy) for such a game will depend upon the direct costs and benefits of siblicide, as well as on the indirect costs to sibs via relatedness. If the only costs of siblicide arise through relatedness, then offspring will ‘win’ in the sense that the eventual clutch size will match the offspring optimum. Whether or not the mother will produce this clutch size depends on the mechanism controlling siblicide. A siblicidal ESS will occur when offspring are programmed to kill a fixed number/proportion of a brood (‘victim-based siblicide’), but not if programmed to reduce the sibship to the offspring optimum (‘survivor-based siblicide’). With survivor-based siblicide, the mother can do no better than to lay the offsprings' optimal clutch size.

We have earlier analysed ESSs for the amount of parental investment (PI) that offspring are expected to solicit from their parents, given that parents acquiesce to offspring demands. The present paper considers evolutionary retaliation by the parent for species where only one parent provides PI. Two genetic loci are envisaged: one (the ‘conflictor’ locus) determines the extent of offspring solicitation; the other (the ‘suppressor’ locus) determines how parents retaliate. Solicitation is assumed to carry a cost which may affect a particular offspring uniquely if time and energy are the major costs, or may affect all offspring in a brood equally if the main cost is predation risk. Two kinds of parental retaliation are possible. Parents may supply PI in proportion to offspring demands, or may ignore solicitation altogether and give a fixed PI. Analytical models of conflict in which the parent supplies PI in proportion to solicitation yield pure ESSs with PI at a compromise level between parent and offspring interests. These are termed ‘pro rata’ ESSs. Where solicitation costs are high, an ‘offspring wins’ ESS (offspring get all they ‘want’) is possible especially for forms of conflict that affect future sibs, and a ‘parent wins’ ESS (parent supplies its optimum) is possible especially for conflict that affects contemporary sibs. When parental retaliation takes the form of ignoring offspring solicitation, this can lead to a ‘parent wins’ ESS if costs of ignoring solicitation are negligible, but where parental insensitivity carries costs, the result is an unresolvable evolutionary chase with cycling frequencies of alleles coding for parent and offspring strategies. ‘Pro rata’ ESSs cannot be invaded by ‘ignore solicitation’ mutants but ‘pro rata’ mutants can often invade at certain stages in ‘ignore solicitation’ limit cycles. We therefore conclude that the probable evolutionary end product for most species will be the ‘pro rata’ ESS in which the parent supplies more PI than would be optimal in the absence of conflict, but less PI than would be an ESS for the offspring in the absence of parental retaliation. Such ESSs will be characterized by solicitation costs; offspring will ‘ask’ for more PI than they get. In nature, under similar conditions, highest conflict will occur when both parents sustain equally the effects of conflict, or when conflict affects contemporary rather than future sibs.

Females of the tiger blue butterfly (Tarucus theophrastus) fly upwind in search of the larval hostplant. Males perch or patrol the downwind edges, searching for incoming females or those already on the bush. A model of competitive mate-searching is developed for the case where not all receptive females are contacted by searching males: the model differs from the earlier ones of Parker (1970, 1974), particularly when few males are involved. Observed distributions of males upon bushes of different sizes agree better with the predictions of the game theory model than with a random distribution of males. The described model may be widely applicable to populations where females remate, but frequently evade detection by searching males.

The opponent-independent cost game is an animal contest in which the bigger and more heavily-armed opponent wins a disputed resource without significant fighting costs. A strategy is a choice of investment level in armament. Increasing armament is assumed to have fitness costs that are unrelated to contests; i.e. the cost of an individual's investment in arms is independent of the strategy played by an opponent. Previous work with this model showed that no ESS exists if a strategy prescribes an arms level exactly. This is equivalent to the notion that there is no environmental variation in the arms level attained by a given strategy. If environmental variation is introduced, a pure ESS can generally exist. A strategy is assumed to prescribe an exact investment cost, but this is translated into a probability distribution of arms levels attained, rather than an exact arms level. Increasing investment increases the mean of the arms level distribution. The ESS investment level depends both on how environmental factors distribute arms levels, and on the shape of the cost function (i.e. on the way that costs increase with investment); in some instances there is no ESS. Two types of model are investigated; in one fitness is additive (benefit-cost), in the other it is multiplicative (benefit × survivorship). The multiplicative model is likely to apply to the case where contests are between males for access to females. Here the ESS investment level (an ESS degree of risk that a male sustains as a result of armament) increases as fewer individuals guard the available resources. Thus sexual size dimorphism (male/female size) and relative male armament should increase as harem size increases. The ESS investment level will also be highest if most individuals are small and poorly armed, as would often be the case where size increases throughout life. The model can be applied to coevolutionary arms races between two classes of opponent, such as prey and predator, or parent and offspring. Here the ESS is likely to be a pair of ESS arms levels, one for each class of opponent.

Models are proposed which examine emigration thresholds from resource patches encountered within a given search strategy. With one patch type and no competition during utilization, there is a single optimal investment duration (Iopt) which depends on the gain accumulated during investment in the patch, G(I), and on the mean search cost between patches. Solutions for Iopt depend on the form of G(I); various models are considered which offer diminishing returns with investment. With variation in the value of the patch type encountered, the animal should leave a patch when dG/dI becomes equal to SLmax, the average gain rate for the overall search strategy when the investment in each patch is optimal. For some resources, Iopt may equal 0. Selection should here favor more and more efficient "resource assessment" strategies which ensure the most efficient monitoring of cues correlating with G(I). These are all pure stratengies in relation to particular circumstances. Where there is resource sharing and systems ...