M.A. Ball

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 (σ) 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 females inter-clutch interval is assumed to be independent of s or M, we show that σ is directly proportional to the mean E for a species; across species σ 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∝E/M; both E and M increase with sperm competition, but E increases differently with sperm competition in its two ranges.

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 males 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.

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.

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.

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.

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 hosts 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 hosts 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 hosts 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 hosts 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.

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.