Anisogamy, Expenditure of Reproductive Effort, and the Optimality of Having Two Sexes

The precise origins of sexual reproduction itself remain unclear (Bell 1982, Michod and Levin 1988), but the potential advantages of the genetic variation produced by sexual reproduction have been noted for almost half a century (Fisher 1958, Charnov 1982). Prime among these are the advantages to individuals, subject to changing environments, of being able to produce variable offspring through mechanisms such as recombination (e.g., Williams 1966; Ghiselin 1974, 1988) so that individuals can overcome the loss of genetic representation that accompanies sex. The mechanics of sexual reproduction can vary greatly across taxa. When only nuclear genetic information is exchanged, as in slime molds, for example, there can be more than two mating types (Hoekstra 1987, Hurst and Hamilton 1992); but when information is exchanged through the production of haploid gametes, the mating types reduce to two sexes. Furthermore, the gametes are typically (Parker et al. 1972, review by Low 2000, pp. 37–44) anisogamous (i.e., of unequal size). As we note in §2, anisogamy has implications for life history and behavioral ecology. There are several main nonalternative current hypotheses for explaining the origins of anisogamy in gametic-sex species. Parker et al. (1972) (see also Charlesworth 1978; Maynard Smith 1978, 1982; Bell 1982; Charnov 1982) noted that two antithetical processes are required to create a successful zygote: traveling to “meet” another gamete, and saving energy to become large and therefore produce a well-invested zygote. These processes generate disruptive selection on the production of a successful zygote, favoring either very small or very large gametes at the expense of middle-sized gametes. Hurst and Hamilton (1992) and Hurst (1995, 1996) noted that because genetic information is carried in the cytoplasm as well as in the nucleus, damaging conflicts of interest can exist, and one set of gametes might become small in response, divesting themselves of cytoplasm to avoid these conflicts. Randerson and Hurst’s (2001) recent analysis, relating zygote and gamete sizes to fertilization probabilities and other fitness measures has re-ignited interest in the evolution of anisogamy in gametic-sex species. Bulmer and Parker (2002) have explored the implications of anisogamy versus isogamy in a game-theoretic context. In this paper, we present a mathematical model that relies on concepts in Maynard Smith (1978). Our model, although quite simple, takes advantage of heretofore unutilized tools of mathematical optimization to show how the existence and degree of anisogamy depends on (among other factors) the shape of the zygote fitness function.