Intrafamilial conflict and parental investment: a synthesis

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.

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.

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.

'Sloppy' sperm mixing and intraspecific variation in sperm precedence (P2) patterns

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.

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.

Spermicide by females: what should males do?

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.

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.

Rydberg electron interferometry

A recent quantum mechanical study [W. Isaacs and M. A. Morrison, Phys. Rev. A 57, R9 (1998)] discovered pronounced oscillations in cross sections for near-resonant energy transfer collisions of rare-gas atoms with initially aligned Rydberg atoms. We analyze such collisions for 17d(m)-->18p(m(')) transitions in the Ca-He system semiclassically and show that the oscillations arise from a phase interference process unique to Rydberg target states. In addition to explaining the origin of these structures, this analysis explains their disappearance when the relative Ca-He velocity goes to infinity and/or the energy defect vanishes and their dependence on the initial and final magnetic quantum numbers of the transition.

Epstein-Barr virus EBNA3C can disrupt multiple cell cycle checkpoints and induce nuclear division divorced from cytokinesis

Expression of EBNA3C is essential for the immortalization of B cells by EBV in vitro and, in co-operation with activated ras, EBNA3C has oncogenic activity in primary rodent fibroblasts. This suggested that this viral oncoprotein might disrupt the cyclin/CDK-pRb-E2F pathway, which regulates cell cycle progression at the restriction point (R-point) in G1 of the proliferation cycle. An assay was established in which transfected EBNA3C-positive cells could be sorted and simultaneously analysed for their distribution in the cell cycle. This revealed that in NIH3T3 fibroblasts compelled to arrest by serum-withdrawal, EBNA3C induces nuclear division that is often divorced from cytokinesis and so produces bi- and multinucleated cells. This was confirmed using the ecdysone-inducible system for expression of EBNA3C in human U2OS cells and by microinjection of expression vectors into NIH3T3 and U2OS. Further analysis revealed that in the inducible system, EBNA3C expression inhibits the accumulation of p27(K1P1) but not the dephosphorylation of pRb. Experiments using the microtubule destabilizing drug nocodazole, showed that EBNA3C could abrogate the mitotic spindle checkpoint.

Optimal copula duration in yellow dung flies: effects of female size and egg content

We examine data on copula duration in dung flies, Scatophaga stercoraria, in relation to female phenotype. We use a marginal value theorem approach based on the plausible mechanisms of sperm competition to predict the effect of female variation on optimal copula duration, t *, from the male perspective. Future fertilizations are expected to have a trivial effect on t * with fully gravid females, but an increasing relative effect on t * towards completion of oviposition. t * is expected to be affected by female size because of variation in (1) a female's egg content, which increases the maximum egg gain available from a mating, and (2) the female reproductive tract, which affects the rate at which sperm are displaced. In fully gravid females, t * was not dependent on egg number variation, but showed a positive relation with egg content in females that had laid a varying proportion of their mature egg load at the time of mating, and were therefore not fully gravid. Our models predict that if a male can estimate egg content only by the distension of a female's abdomen, t * should increase in a similar way to that seen with 'take-over' females. We predict t * for fully gravid females by assuming that males can monitor female size. The data showed that sperm displacement rate decreased, and average egg content increased, with female size. Under two models for a sperm displacement mechanism, one (which assumes indirect displacement at a rate proportional to the increase in spermathecal volume) predicts the observed relation between t * and female size almost exactly. Small males copulated for longer than large males (as predicted and reported previously). Copyright 1999 The Association for the Study of Animal Behaviour.

Sperm Displacement in the Yellow Dung Fly, Scatophaga stercoraria: An Investigation of Male and Female Processes

Despite the ubiquity with which patterns of sperm utilization have been studied, the mechanisms underlying fertilization in insects are far from clear. One well-studied system is the yellow dung fly, in which the last male's ejaculate is thought to displace rival sperm from the female's sperm stores. Here we follow the movement of the copulating male's ejaculate through the female's reproductive tract using males labeled with different radioisotopes. We find that males ejaculate into the bursa copulatrix and that male-1 sperm are displaced from the spermathecae during copulation. The increase in male-2 ejaculate in the spermathecae matches the pattern of male-2 fertilization gain, indicating that only spermathecal sperm are utilized at fertilization. Previously we have analyzed this system with a direct model of sperm displacement in which the male displaces rival sperm from the spermathecae. The data, and morphology of the female, clearly preclude such a mechanism. Here we contrast this model with a new indirect model, in which the female facilitates displacement by exchange of sperm from the bursa copulatrix to the spermathecae. The two models give equivalent fits to the observed sperm utilization patterns because the rate of sperm transfer into the bursa copulatrix greatly exceeds the rate of sperm exchange with the spermathecae so that the concentration of the first male's sperm in the bursa remains considerably lower than that of the second male. These analyses provide a quantitative attempt to incorporate female processes into the analysis of sperm utilization patterns in insects.

Information asymmetries among males: implications for fertilization success in the thirteen-lined ground squirrel

The classical view of mammalian mating competition focuses on combat and threat. By contrast, field studies have revealed that male mating success in some species is more strongly determined by mate location ability than by physical dominance. In thirteen-lined ground squirrels, competition in locating oestrous females is exacerbated by sperm competition that favours the first male to mate with a female. We used a female-removal experiment to identify the distinguishing characteristics of males that were the first at finding and mating with females. Each focal female was observed the day before she entered oestrus; the identities of males that made contact with her and the locations of their interactions were recorded. The following morning the females were temporarily removed, and we monitored male search behaviour in their absence. Males that arrived first were those that had spent more time with the female the previous day relative to their rivals. Time invested the day before, in turn, was highly correlated with male search persistence and familiarity with the female's likely whereabouts. These results demonstrate that differential fertilization success can arise from information asymmetries among males: the advantaged individuals are those that have greater a priori knowledge of the reproductive state and spatial locations of prospective mates than rivals.

Sperm competition games: a general approach to risk assessment

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.

Siblicide, family conflict and the evolutionary limits of selfishness

In animal and plant taxa where parents deposit an oversupply of eggs/neonates into a spatially restricted 'nursery', intense sibling competition commonly results. An inversion of Hamilton's rule identifies the theoretical lower limit for how an individual in a sexual species ought to favour its own welfare over that of its close kin in such an ecological squeeze. A broad array of behavioural and life-history phenotypes appears to have evolved, at least in part, for dealing with close kin as serious competitors. We have recently summarized the theory and empirical data addressing both sibling competition and parent-offspring conflict (Mock & Parker 1997, The Evolution of Sibling Rivalry), and here present a précis that aims both to give a quick overview of that fuller treatment while allowing us to update the book's literature review with a few late-breaking findings. Copyright 1998 The Association for the Study of Animal Behaviour

A transforming p53 mutant, which binds DNA, transactivates and induces apoptosis reveals a nuclear:cytoplasmic shuttling defect

The DG75 Burkitt lymphoma-derived human B cell line is heterozygous for p53, carrying wild type (WT) and mutant (Arg283His) alleles. The cells constitutively express high levels of both p53 proteins and also Mdm2. Arg283His transactivates the p21Waf1, Mdm2, bax, cyclin G and IGF-BP3 promoters in transient transfection assays equally as well as, if not better than WT p53. It also suppresses the outgrowth of SAOS-2 cells and specifically binds DNA like wild type protein. However, in primary rodent fibroblasts Arg283His fails to suppress transformation by HPV16-E7 and (Ha-)ras and even has modest transforming activity when transfected alone with (Ha-)ras. When Arg283His is transiently transfected into SAOS-2 cells it efficiently induces apoptosis, so - unlike mutants such as Arg175Pro - its behaviour in transformation assays does not clearly correlate with loss of the apoptosis function. Immunofluorescence staining of both REF transformants and transiently transfected SAOS-2 revealed that this unusual mutant becomes excluded from the nucleus and produces striking cytoplasmic fluorescence. The best correlation with transformation, therefore, appears to be the lack of nuclear retention of Arg283His. Since this mutation does not map to any known nuclear localization signal and its presence seems to result in aberrant exclusion from the nucleus, then it may prove very useful in exploring mechanisms involved in the nuclear:cytoplasmic shuttling of p53.

Sexual conflict and speciation

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 make 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 conflict 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.

Sperm competition games: a prospective analysis of risk assessment

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.

Sperm competition games: inter- and intra-species results of a continuous external fertilization model

We investigate the relationship between sperm competition intensity and sperm expenditure, both across species and within a species, using a two sperm competition models. In model 1, the males cannot assess the number of competitors, and their ejaculate effort is shaped by the average number <N> of competitors. In model 2, males can assess the number Ni of competitors at each spawning exactly. Males can vary the mass m of their sperm and the number si at a spawning. The aim is to find the evolutionarily stable strategies and hence the way that m and si vary with Ni. A continuous fertilization model in which the sperm have to swim in order to fertilize an egg is described. This is used to find simultaneous equations describing m and si. These are solved numerically.