A Model for the Evolution of Dioecy and Gynodioecy
A model for the evolution of gynodioecy from the hermaphrodite or monoecious condition is described, taking into account the effects of partial selfing and inbreeding depression. It is shown that a mutant causing male-sterility can be selected even if the female plants have the same ovule output as the hermaphrodites, but that the conditions for this are very stringent: The product of the selfing rate and the inbreeding depression must exceed one-half. If the females have an increased ovule output, gynodioecy can evolve with lower values of the selfing and inbreeding depression parameters. Expressions for the equilibrium frequency of females and of the male-sterility gene in both the dominant and the recessive case are given. By a similar technique, conditions for the evolution of androdioecy are derived. In a selfing population, these conditions are much less easily satisfied than those for gynodioecy, though in a randomly mating population the conditions are similar: If ovule production is abolished, pollen production must be more than doubled, or vice versa. Since androdioecy is known to be a very rare condition, it seems likely that avoidance of selfing has played a role in the evolution of gynodioecy. Using the equilibria derived for gynodioecy, the conditions for the evolution of subdioecy or dioecy, by means of a partial or total female-sterility mutation, are studied. In contrast to the situation in a hermaphrodite population, a female-sterility gene can be selected in a gynodioecious population if it confers a moderate increase in pollen output; some increase in pollen output is essential. The fate of such a female-sterility gene also depends on its linkage with the male-sterility gene. If this is recessive, and the female-sterility gene is dominant and has an effect in the females as well as the hermaphrodite individuals, then the second mutation will usually be eliminated unless it occurs at a locus tightly linked to the first gene. In other cases there is no such "linkage constraint," though in all situations there may be selection for tighter linkage between the loci; this will result in an initially subdioecious population becoming more fully dioecious. These results agree with some of the facts known about the evolution of dioecy in plants. First, since gynodioecy is more often controlled by a recessive than a dominant gene, male heterogamety should be commoner than female, as is observed. Second, subdioecy should be common, since full dioecy requires not only the correct phenotypic effects of the two genes but also complementary dominance relations and tight linkage; subdioecy is indeed known in many species. The equilibria reached by our model have only one type of female in appreciable frequency, whereas the polleniferous individuals may fall into several genotypic classes; it is often observed that in subdioecious species the males are more variable than the females, regardless of which is the heterogametic sex. Finally, the equilibria generated by our model agree closely with the results of genetical studies of those dioecious species with male-determining Y chromosomes that have been investigated, in which both male-and female-sterility factors have been found, showing complementary dominance relations and no crossing-over between the loci, so that just two gamete types exist. Such a situation can be explained by the operation of the linkage constraint, which ensures that only linked mutations become established and does not require that unlinked genes have been brought together. This is consistent with the fact that dioecious species often have the same chromosome numbers as their bisexual relatives.