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

Abstract

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).

Resolving variation in the reproductive tradeoff between sperm size and number

“…For this scenario, our models predict sperm size to increase more than sperm number with increasing risk of sperm competition (m*/s* increasing; Box 1 and Fig. 1D) only under special circumstances, most easily met in displacement systems, when sperm size has special and strong competitive advantages in skewing fertilization, notably if the minimum successful sperm size escalates as sperm density increases (7,13). The propensity for increasingly escalating competitive benefits of sperm size with sperm density in systems such as Drosophila is considerable, and some of the largest sperm described to date are found in small-bodied invertebrate taxa (33,34).…”

“…Under an indirect tradeoff (6), a fixed resource budget, R, is allocated between the ejaculate and effort spent acquiring a mating, C, where the number of matings, n, obtained by a male is given by R/(C + Dsm) and where Dsm defines the amount of energy invested into the ejaculate. Thus, a male can effectively now vary three strategic parameters: n, s, and m. Our recent theoretical model (7) shows that at a given level of R and sperm competition risk q (i.e., at a given level β; Box 1), a direct tradeoff between sperm size and number effectively still operates even under the indirect tradeoff model. However, empirical evidence for such a tradeoff has been equivocal (8)(9)(10)(11).…”

“…To clarify the logic, we give an overview of our recent theoretical model of sperm size-number tradeoffs and its main predictions in Box 1; the full account is complex and is presented elsewhere (7). It differs from previous models (6) in predicting how absolute and relative expenditure on sperm size and number should vary in relation to sperm competition risk, q, in both sperm mixing and sperm displacement systems, under varying sperm density: (i) sperm number, s, should always increase with q, but sperm size (defined here as mass), m, may be constant, increasing, or decreasing with q, (ii) total ejaculate investment, ms, should always increase with q, and (iii) the ratio m/s (which indicates how allocation within ms is skewed toward size or number as q increases) can increase or decrease with q depending on the influence of sperm density (the density of sperm in the set from which fertilizations are drawn) on sperm competition; specifically, (iv) if sperm size has no effect (or only a moderate effect) on sperm competitive ability with increasing sperm density (e.g., in systems with a raffle mechanism, such as external fertilizers and internally fertilizing vertebrates), then sperm number is favored over sperm size with increasing risk of sperm competition (thus as ms increases with q, the ratio m/s decreases), or (v) if sperm competitive ability is strongly affected by increases in sperm density, (e.g., where sperm displacement is an important mechanism), then sperm size is favored over sperm number with increasing risk of sperm competition (thus as ms increases with q, m/s may also increase).…”

Female reproductive tract form drives the evolution of complex sperm morphology

“…44). On the basis of these observations, we propose that conjugation in diving beetles is an adaptation for positional advantage in the displacement-based system of sperm competition observed in many insects (47,48). Such interpretation, however, will remain highly speculative until detailed investigations of postcopulatory sexual selection, including the relationships between variation in sperm form, female tract form, and competitive fertilization success, are conducted in diving beetles and other taxa with diverse sperm and female reproductive tract morphology.…”

Sperm wars and the evolution of male fertility

“…Over a slightly longer time frame (w1 month), following experimental manipulation of adult densities in the broadcast spawning ascidian Styela plicata, males experimentally allocated to high-density treatment groups, where sperm competition is more likely, produced longer and more motile sperm that swam for longer periods of time than did males in low-density treatment groups (Crean & Marshall 2008). Finally, in the Gouldian finch, Erythrura gouldiae, changes in social environment that reflect changes in the levels of sperm competition led to changes in sperm midpiece and flagellum lengths (Immler et al 2010).…”