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Abstract. There has been wide disagreement as to whether sperm competition among animals can produce a soldier class of sperm to fight against other males. Utilizing mathematical models, we analyze the appropriate conditions for the evolution and maintenance of a soldier sperm class. We conclude that: (1) soldier sperm evolve even if one soldier sperm can kill or block less than one competing sperm; (2) soldier sperm evolve faster when there is a large variance in the number of competing sperm; (3) soldier ratio increases until reproductive sperm are too scarce to fertilize all ova or a sperm intensely refuses to become a soldier; and (4) soldier sperm are more likely to be smaller than reproductive sperm. Our models suggest that the conditions for the evolution of a soldier sperm class are not stringent.

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In many species that have internal fertilization, seminal flow includes various elements and materials in addition to the fertilizing sperm. The roles of these components are unknown. One hypothesis is that they are nutritional gifts to the female as a paternal investment. We made game theoretical models from the point of view of sperm competition among males and examined this hypothesis. The evolutionary stable strategy (ESS) of the models showed that (1) when multiple mating in the female is relatively low, gifts in seminal flow or other types of gift may evolve, at least, a male does not resist a female digesting his sperm; and (2) the ratio of nutritional gift rapidly decreases to zero with the probability or frequency of multiple mating in the female. Hence, we concluded that nutritional gifts in seminal flow can exist only in species in which sperm competition among males is rare. Furthermore, we concluded that if an element or material eminently decreases when sperm competition becomes intense, it may be a gift as a paternal investment; if not, other hypotheses concerned with more agonistic roles are more feasible.

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