Counting genes in models of biparental inbreeding

It is generally recognized that biparental reproduction experiences a "cost" in comparison with uniparental reproduction by either asexual means or self-fertilization. However, less agreement exists on the nature and size of the cost. The cost of cross-fertilization (or less formally, the cost of sex) may arise from two different sources. Williams (1971) proposed that crossfertilizing individuals are at a disadvantage because they contribute only one set of genes to each offspring, whereas uniparentally reproducing individuals contribute two sets. If the genetic cost is measured as the relative loss of fitness from cross-fertilization compared with uniparental reproduction, the gene halving constitutes a 50% loss of fitness, the "cost of meiosis. " In the same publication, Maynard Smith (1971a) postulated that biparental organisms are disadvantaged because they spend resources on producing males that do not contribute towards raising young. This allocation cost, the "cost of males," is also precisely 50% if parents invest equally in male and female offspring. The alternative costs of sex apply in different circumstances, depending on the order in which decisions are made on investing in male and female offspring (or gametes) and on reproducing uniparentally or biparentally (Lively and Lloyd 1990). When the decision on how much to invest in the sexes is made first, the subsequent mode of reproduction does not affect the previous sex allocations, and there is no cost of males. A 50% cost of meiosis is then experienced. The cost of meiosis applies to asexual reproduction via embryos in cosexes (parthenogenesis in animals, agamospermy in seed plants), and to open flower (chasmogamous) self-fertilization in plants. However, when the decision to reproduce uniparentally is made first, the cost of meiosis is fully retrieved because the double contribution to the offspring is exactly canceled by the loss of the outcrossing male contribution. The cost of males is experienced unless males contribute to parental care (Maynard Smith 197 lb). The cost of males applies to somatic asexuality (vegetative reproduction in plants, budding in animals), embryonic asexuality by females of dioecious populations, and cleistogamous self-fertilization in plants. The cross-fertilizing components of reproduction may not occur randomly among all members of a population. One source of nonrandom mating is biparental inbreeding through the mating of relatives. In many flowering plants, for example, both seeds and pollen are dispersed very locally so that adjacent relatives mate disproportionately (Handel 1983; Levin 1988). A proportion, r, of the genes of cross-fertilizing relatives are identical by descent from a common ancestor. Several authors therefore have suggested that a gene in an individual that crosses with a relative obtains an indirect contribution to its inclusive fitness in addition to the direct contribution to offspring. Hence, the cost of meiosis is reduced in proportion to the relatedness of the inbreeding relatives, from 1/2 to 1/2(1 r) (Barash 1976; Maynard Smith 1978; Solbrig 1979; Lloyd 1980; Williams 1980; Uyenoyama 1986, 1987; Yahara 1992). It is this conclusion that is reexamined here. We concentrate our attention on self-fertilization within open flowers, which Yahara (1992) considered, with some changes to the symbols. Consider a population in which individuals with