Evolution of complex life cycles in trophically transmitted helminths. II. How do life-history stages adapt to their hosts?

We review how trophically transmitted helminths adapt to the special problems associated with successive hosts in complex cycles. In intermediate hosts, larvae typically show growth arrest at larval maturity (GALM). Theoretical models indicate that optimization of size at GALM requires larval mortality rate to increase with time between infection and GALM: low larval growth or paratenicity (no growth) arises from unfavourable growth and mortality rates in the intermediate host and low transmission rates to the definitive host. Reverse conditions favour high GALM size or continuous growth. Some support is found for these predictions. Intermediate host manipulation involves predation suppression (which decreases host vulnerability before the larva can establish in its next host) and predation enhancement (which increases host vulnerability after the larva can establish in its next host). Switches between suppression and enhancement suggest adaptive manipulation. Manipulation conflicts can occur between larvae of different ages/species a host individual. Larvae must usually develop to GALM before becoming infective to the next host, possibly due to trade-offs, e.g. between growth/survival in the present host and infection ability for the next host. In definitive hosts, if mortality rate is constant, optimal growth before switching to reproduction is set by the growth/morality rate ratio. Rarely, no growth occurs in definitive hosts, predicted (with empirical support) when larval size on infection exceeds growth/mortality rate. Tissue migration patterns and residence sites may be explained by variations in growth/mortality rates between host gut and soma, migration costs and benefits of releasing eggs in the gut.

Evolution of complex life cycles in trophically transmitted helminths. I. Host incorporation and trophic ascent.

Links between parasites and food webs are evolutionarily ancient but dynamic: life history theory provides insights into helminth complex life cycle origins. Most adult helminths benefit by sexual reproduction in vertebrates, often high up food chains, but direct infection is commonly constrained by a trophic vacuum between free-living propagules and definitive hosts. Intermediate hosts fill this vacuum, facilitating transmission to definitive hosts. The central question concerns why sexual reproduction, and sometimes even larval growth, is suppressed in intermediate hosts, favouring growth arrest at larval maturity in intermediate hosts and reproductive suppression until transmission to definitive hosts? Increased longevity and higher growth in definitive hosts can generate selection for larger parasite body size and higher fecundity at sexual maturity. Life cycle length is increased by two evolutionary mechanisms, upward and downward incorporation, allowing simple (one-host) cycles to become complex (multihost). In downward incorporation, an intermediate host is added below the definitive host: models suggest that downward incorporation probably evolves only after ecological or evolutionary perturbations create a trophic vacuum. In upward incorporation, a new definitive host is added above the original definitive host, which subsequently becomes an intermediate host, again maintained by the trophic vacuum: theory suggests that this is plausible even under constant ecological/evolutionary conditions. The final cycle is similar irrespective of its origin (upward or downward). Insights about host incorporation are best gained by linking comparative phylogenetic analyses (describing evolutionary history) with evolutionary models (examining selective forces). Ascent of host trophic levels and evolution of optimal host taxa ranges are discussed.

Sperm competition games: sperm size (mass) and number under raffle and displacement, and the evolution of P2.

We examine models for evolution of sperm size (i.e. mass m) and number (s) under three mechanisms of sperm competition at low 'risk' levels: (i) raffle with no constraint on space available for competing sperm, (ii) direct displacement mainly by seminal fluid, and (iii) direct displacement mainly by sperm mass. Increasing sperm mass increases a sperm's 'competitive weight' against rival sperm through a diminishing returns function, r(m). ESS total ejaculate expenditure (the product m(*)s(*)) increases in all three models with sperm competition risk, q. If r(m), or ratio r'(m)/r(m), is independent of ESS sperm numbers, ESS sperm mass remains constant, and the sperm mass/number ratio (m(*)/s(*)) therefore decreases with risk. Dependency of sperm mass on risk can arise if r(m) depends on competing sperm density (sperm number / space available for sperm competition). Such dependencies generate complex relationships between sperm mass and number with risk, depending both on the mechanism and how sperm density affects r(m). While numbers always increase with risk, mass can either increase or decrease, but m(*)/s(*) typically decreases with risk unless sperm density strongly influences r(m). Where there is no extrinsic loading due to mating order, ESS paternity of the second (i.e. last) male to mate (P(2)) under displacement always exceeds 0.5, and increases with risk (in the raffle P(2)=0.5). Caution is needed when seeking evidence for a sperm size-number trade off. Although size and number trade-off independently against effort spent on acquiring matings, their product, m(*)s(*), is invariant or fixed at a given risk level, effectively generating a size-number trade off. However, unless controlled for the effects of risk, the relation between m(*) and s(*) can be either positive or negative (a positive relation is usually taken as evidence against a size-number trade off).

Why do larval helminths avoid the gut of intermediate hosts?

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.

To grow or not to grow? Intermediate and paratenic hosts as helminth life cycle strategies.

Larval helminths in intermediate hosts often stop growing long before their growth is limited by host resources, and do not grow at all in paratenic hosts. We develop our model [Ball, M.A., Parker, G.A., Chubb, J.C., 2008. The evolution of complex life cycles when parasite mortality is size- or time-dependent. J. Theor. Biol. 253, 202-214] for optimal growth arrest at larval maturity (GALM) in trophically transmitted helminths. This model assumes that on entering an intermediate host, larval death rate initially has both time- (or size-) dependent and time-constant components, the former increasing as the larva grows. At GALM, mortality changes to a new and constant rate in which the size-dependent component is proportional to that immediately before GALM. Mortality then remains constant until death or transmission to the definitive host. We analyse linear increasing and accelerating forms for time-dependent mortality to deduce why there is sometimes growth (intermediate hosts) and sometimes no growth (paratenic hosts). Calling i the intermediate or paratenic host, and j the definitive host, conditions favouring paratenicity are: (i) high values in host i for size at establishment, size-related mortality, expected intensity, (ii) low values in host i for size-independent mortality rate, potential growth rate, transmission rate to j, and ratio of death rate in j/growth rate in j. Opposite conditions favour growth in the (intermediate) host, either to GALM or until death without GALM. We offer circumstantial evidence from the literature supporting some of these predictions. In certain conditions, two of the three possible growth strategies (no growth; growth to an optimal size then growth arrest (GALM); unlimited growth until larval death) can exist as local optima. The effect of the discontinuity in death rate after GALM is complex and depends on mortality and growth parameters in the two hosts, and on the mortality functions before and after GALM.

The evolution of complex life cycles when parasite mortality is size- or time-dependent.

In complex cycles, helminth larvae in their intermediate hosts typically grow to a fixed size. We define this cessation of growth before transmission to the next host as growth arrest at larval maturity (GALM). Where the larval parasite controls its own growth in the intermediate host, in order that growth eventually arrests, some form of size- or time-dependent increase in its death rate must apply. In contrast, the switch from growth to sexual reproduction in the definitive host can be regulated by constant (time-independent) mortality as in standard life history theory. We here develop a step-wise model for the evolution of complex helminth life cycles through trophic transmission, based on the approach of Parker et al. [2003a. Evolution of complex life cycles in helminth parasites. Nature London 425, 480-484], but which includes size- or time-dependent increase in mortality rate. We assume that the growing larval parasite has two components to its death rate: (i) a constant, size- or time-independent component, and (ii) a component that increases with size or time in the intermediate host. When growth stops at larval maturity, there is a discontinuous change in mortality to a constant (time-independent) rate. This model generates the same optimal size for the parasite larva at GALM in the intermediate host whether the evolutionary approach to the complex life cycle is by adding a new host above the original definitive host (upward incorporation), or below the original definitive host (downward incorporation). We discuss some unexplored problems for cases where complex life cycles evolve through trophic transmission.

Sperm competition games: the risk model can generate higher sperm allocation to virgin females.

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 over mating and fertilization: an overview.

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.

Male "mixed" reproductive strategies in biparental species: Trivers was probably right, but why?

Trivers proposed that, if parental care by both sexes is advantageous, males should practice a "mixed" strategy of seeking extrapair copulations, while restricting their parental investment to offspring of social mates. We explore circumstances under which males should limit their parental care in the predicted manner. We find that Trivers's "mixed" strategy will generally be evolutionarily stable so long as either socially monogamous or polygynous males usually sire more offspring per brood from a social mate than they typically sire in broods of extrapair mates. Polygynous males should spread investment across their home nests unless the expected number of chicks sired in them differs widely. Whether polygynous males should restrict paternal care to social mates' offspring hinges additionally on resident male investment in broods containing extrapair young: if resident males contribute minimally, some investment by a polygynous extrapair male becomes more advantageous. Recently reviewed data on extrapair fertilization distributions within monogamous and polygynous passerines suggest that extrapair offspring often predominate numerically within their broods, consistent with sperm expenditure theory. Nevertheless, most species conform to the model's criterion regarding relative parentage levels in broods of social versus extrapair mates. Patterns of extrapair parentage thus appear sufficient to stabilize biparental care systems.

Sperm competition, mating rate and the evolution of testis and ejaculate sizes: a population model.

There are various ways to estimate ejaculate expenditure. Ejaculate size or sperm number (s) is an absolute number of units of ejaculate. Relative ejaculate expenditure (E) is the expenditure on the ejaculate as the proportion of the total expenditure on all aspects of the mating, including finding and acquiring a female, and so on. Relative testis size or gonadosomatic index (sigma) is testes mass divided by body mass; it is assumed to reflect the product of mating rate (M) and ejaculate mass (s). In a new model, where mating rate, sperm competition and sperm allocation interact, and where the female's inter-clutch interval is assumed to be independent of s or M, we show that sigma is directly proportional to the mean E for a species; across species sigma and E increase monotonically with sperm competition. However, the relation between s and sperm competition across species depends on the range of sperm competition (low risk or high intensity): s increases with sperm competition at low risk levels, but decreases with sperm competition at high intensity levels. This situation arises because s alpha E/M; both E and M increase with sperm competition, but E increases differently with sperm competition in its two ranges.

Optimal growth strategies of larval helminths in their intermediate hosts.

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 <1/intensity, thus increasing the parasite burden on the host. We discuss whether body size of competing parasites is an evolved LHS or simply reflects resource constraints (RC) on growth fixed by the host, leading to a constant total burden with intensity. Growth under competition appears comparable with "the tragedy of the commons", much analysed in social sciences. Our LHS prediction suggests that evolution generates a solution that seems cooperative but is actually selfish.

Sperm competition games: sperm selection by females.

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 evolution of anisogamy: a game-theoretic approach.

A popular theory has proposed that anisogamy originated through disruptive selection acting on an ancestral isogamous population, though recent work has emphasized the importance of other factors in its evolution. We re-examine the disruptive selection theory, starting from an isogamous population with two mating types and taking into account the functional relationship, g(m), between the fitness of a gamete and its size, m, as well as the relationship, f(S), between the fitness of a zygote and its size, S. Evolutionary game theory is used to determine the existence and continuous stability of isogamous and anisogamous strategies for the two mating types under various models for the two functions g(m) and f(S). In the ancestral unicellular state, these two functions are likely to have been similar; this leads to isogamy whether they are sigmoidal or concave, though in the latter case allowance must be made for a minimal gamete size. The development of multicellularity may leave g(m) relatively unchanged while f(S) moves to the right, leading to the evolution of anisogamy. Thus, the disruptive selection theory provides a powerful explanation of the origin of anisogamy, though other selective forces may have been involved in the subsequent specialization of micro- and macrogametes.

Life history consequences of mammal sibling rivalry.

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.

Rhinosporidiosis in a domestic cat.

Rhinosporidiosis was diagnosed in a domestic shorthair cat from a suburb of Washington DC, USA. The clinical presentation of protracted sneezing and epistaxis was associated with a polypoid lesion in the right nostril. Light microscopic examination revealed a polypoid lesion with numerous sporangia containing maturing endospores. Free endospores were present in the stroma of the polyp and lumen of the nasal cavity. Transmission electron microscopy revealed ultrastructural features typical of Rhinosporidium seeberi. The case was followed clinically for a total of 70 months and there were five attempts at surgical excision. This is the first reported case of rhinosporidiosis in a domestic cat.

Activators of the Epstein-Barr virus lytic program concomitantly induce apoptosis, but lytic gene expression protects from cell death.

Expression of the lytic cycle genes of Epstain-Barr virus (EBV) is induced in type I Burkitt's lymphoma-derived cells by treatment with phorbol esters (e.g., phorbol myristate acetate [PMA]), anti-immunoglobulin, or the cytokine transforming growth factor beta (TGF-beta). Concomitantly, all these agents induce apoptosis as judged by a sub-G1 fluorescence-activated cell sorter (FACS) profile, proteolytic cleavage of poly(ADP-ribose) polymerase (PARP) and terminal deoxynucleotidyltransferase-mediated dUTP-biotin nick end labeling (TUNEL) staining. However, caspase activation is not required for induction of the lytic cycle since the latter is not blocked by the caspase inhibitor ZVAD. Furthermore, not all agents that induce apoptosis in these cultures (for example, cisplatin and ceramide) induce the EBV lytic programme. Although it is closely associated with the lytic cycle, apoptosis is neither necessary nor sufficient for its activation. Multiparameter FACS analysis of cultures treated with PMA, anti-Ig, or TGF-beta revealed BZLF1-expressing cells distributed in different phases of the cell cycle according to which inducer was used. However, BZLF1-positive cells did not appear to undergo apoptosis and accumulate with a sub-G1 DNA content, irrespective of the inducer used. This result, which suggests that lytic gene expression is protective, was confirmed and extended by immunofluorescence staining doubled with TUNEL analysis. BZLF1- and also gp350-expressing cells were almost always shown to be negative for TUNEL staining. Similar experiments using EBV-positive and -negative subclones of Akata BL cells carrying an episomal BZLF1 reporter plasmid confirmed that protection from apoptosis was associated with the presence of the EBV genome. Finally, treatment with phosphonoacetic acid or acyclovir prior to induction with PMA, anti-Ig, or TGF-beta blocked the protective effect in Mutu-I cells. These data suggest that a late gene product(s) may be particularly important for protection against caspase activity and cell death.

Scramble in behaviour and ecology.

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)/n2). 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 ideal-free 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.

Sperm competition games: a comparison of loaded raffle models and their biological implications.

Our main aim is to compare the additive model, due to Mesterton-Gibbons, and the multiplicative model, due to Parker, of sperm allocation under sperm competition, when other influences are treated in the same way. We first review these (and other) models and their foundations, leading to a generalization of the multiplicative model. Sperm is assumed to cost energy, and this constraint is incorporated differently in the two models. These give the same results in the random-roles situation when the males occupy roles (of first and second to mate) randomly: the number of sperm ejaculated in the favoured role is greater than that in the disfavoured role by an amount that depends on the effect of sperm limitation (i.e. the probability that there is insufficient sperm to ensure full fertility). If the latter is negligible, or the fertilization raffle fair, this difference is zero, as Parker found originally. In the constant roles situation (where males of a particular type always occupy the same role) the predictions differ: the additive model has the same predictions as in the random roles case, but the multiplicative model predicts that males of the type occupying the favoured role ejaculate less than males of the type occupying the disfavoured role, in accord with Parker's original conclusion. The fitnesses of the two types of male can be calculated in the multiplicative model: the fitness of the favoured male is usually higher, even if he has to expend more energy in "finding" a female, e.g. through fighting, etc. These conclusions relate to inter-male behaviour (i.e. of different male types), as distinct from intra-male behaviour (i.e. of a given male when in different roles). We analyse situations in which one male type has some probability of acting in its less usual role: calculations with varying amounts of sperm limitation are presented. It is found that the presence of a male of a different type has an effect on intra-male ejaculate behaviour, which also depends critically on the role usually occupied. We conclude that the multiplicative model is the more accurate model and provides more information. Some experimental data on sperm numbers are used to find the effects of sperm limitation. For species which conform to the loaded raffle model, sperm limitation typically has small or negligible effects: in this case, we argue that empiricists should look for equal ejaculates in the two roles when studying random role situations; when roles are occupied non-randomly average sperm expenditure should be greater by male types typically occupying the disfavoured role, but within a male type, expenditure should be greater in the role it typically occupies.

Optimal copula duration in yellow dung flies: ejaculatory duct dimensions and size-dependent sperm displacement.

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 a male size-dependent decrease in this species. We apply the indirect model of sperm displacement, in conjunction with parameters obtained from field and laboratory data, to predict size-dependent changes in optimal copula duration from the male perspective. This model concurs with the observations by predicting a size-dependent decline in optimal copula duration, as did an earlier model in which displacement was direct (new sperm displace previously stored sperm directly from the sperm stores). Our new approach gives a better fit than the earlier direct model. Thus, both results (displacement rates and copula duration) can be explained by size-dependent changes in the ejaculatory apparatus of the male with the female's exchange rate of sperm (from bursa to spermathecae) remaining constant with respect to male size, although we discuss the possibility that this female process may accelerate with increased male size. In general, where the sperm input rate is around the same magnitude as the exchange rate, indirect displacement will be dependent on the size of the male, as in dung flies, but this dependency is lost if the input rate is very high relative to the exchange rate across the entire range of male size. Size-dependent displacement should always apply for males with direct displacement.

Sperm competition games between related males.

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.