Sperm competition games: individual assessment of sperm competition intensity by group spawners

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Abstract
A distinction is made between sperm competition risk (where there is typically a low probability of competition between two ejaculates) and sperm competition intensity (where typically two or more ejaculates compete). The relation between sperm competition intensity and sperm expenditure can be radically different across species from that within a species. Across species, the average ejaculate expenditure will increase with the average intensity of sperm competition. But within a species, the reverse trend is generally predicted for greater than two males competing for the same set of eggs. These effects are demonstrated with three sperm competition game models. They are devised mainly for externally fertilizing group-spawning species such as many fish, in which males group around a female and ejaculate when the female sheds her eggs. Fertilization is assumed to be instantaneous and each male gains a proportion of the eggs equal to his sperm number divided by the total sperm. In the first model, males cannot assess the number of competitors, and their ejaculate effort is shaped by the average number of males for the species or locally isolated deme. The proportion of reproductive effort expended on the ejaculate is predicted to increase as (N-1)/N, where N = the mean number of competing males present at a spawning. Thus if N is large, ejaculate expenditure dominates reproductive effort. In the second model, males can estimate whether there are more or less than average numbers of competitors present at a spawning, and in the third model, males can assess the number of competitors exactly. As in the first model, these models confirm that the mean ejaculate effort should increase with the mean number of competitors for the species. However, they predict that males should decrease their sperm expenditure as the estimated number of competitors present at a given spawning increases above two. These conclusions do not apply to sperm competition risk: there is thus no conflict with earlier models based on risk.

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