EVOLUTION OF SEX RATIO IN STRUCTURED DEMES

In 1930 R. A. Fisher proposed an evolutionary model to explain why so many species produce roughly equal numbers of male and female offspring at birth. Very simply, since each offspring has a male and female parent (or grandparent, for haplodiploids), whichever sex is in short supply has the greater fecundity. A genotype that produces an excess of the minority sex among its own offspring is favored by natural selection, until an equilibrium is reached at a 1:1 population sex ratio (assuming male and female offspring cost the same to produce). Charnov (1979) and Maynard Smith (1978) have recently reviewed the subject. As with many other traits for which fitness is frequency dependent, the evolution of sex ratio is influenced by the spatial structure of the population. To see this, consider an organism that depends upon some patchy resource. The patches themselves are temporary, but last long enough for the organism to complete one or more generations before dispersal to new patches becomes necessary. Many small arthropods, parasites, and successional species fit this pattern well, and vertebrates that undergo extreme periodic fluctuations in density approximate it. Now suppose that the genotype of each female determines the sex ratio of her progeny: one allele codes for a female-biased sex ratio, and another for equal numbers of sons and daughters, with total fecundity the same for both alleles. If mating is random within each patch, the local frequency of the biased sex ratio allele will decline in every generation in every patch. This is simply a case of Fisher's principle, which operates with equal force regardless of the size of the breeding group (Colwell, 1981). However, patches will vary by chance in the frequency of the two alleles among the initial colonists. Defining the occupants of a single patch as a "group," those groups that have a higher initial frequency of the female-biasing allele will produce more grandprogeny, simply because a greater number of the founders' progeny are females. If the local groups continue to grow in size, the effect will persist through successive generations of local mating, so that a group initiated with a higher than average frequency of the biased sex ratio allele eventually produces a higher than average number of dispersers. Moreover, the dispersers from such a patch still carry a higher than average frequency of the allele, in spite of its local decline within every group during each generation of local mating. Consequently, the frequency of the biased sex ratio allele can nonetheless increase in the global population, to the degree that the differential productivity of groups (group selection) counters the effect of Fisher's principle (individual selection). This process is shown diagrammatically in Figure 1. It is an example of the structured deme model of population genetics (Uyenoyama and Feldman, 1980; Wilson, 1980), in which the dispersal pool represents the deme as a whole, and the breeding group in each resource patch is a "trait group." In general, the structured deme model explains the evolution of altruism by the differential productivity of trait groups. In the present case, any female