Abstract.-We investigate mate availability in different models of multiallelic self-incompatibility systems in mutationselection-drift balance in finite populations. Substantial differences among self-incompatibility systems occur in average mate availability, and in variances of mate availability among individual plants. These differences are most pronounced in small populations in which low mate availability may reduce seed set in some types of sporophytic self-incompatibility. In cases where the pollination system causes a restriction in the number of pollen genotypes available to an individual plant, the fecundity of that plant depends on the availability of compatible pollen, which is determined by its genotype at the incompatibility locus. This leads to an additional component of selection acting on selfincompatibility systems, which we term "fecundity selection." Fecundity selection increases the number of alleles maintained in finite populations and increases mate availability in small populations. The strength of fecundity selection is dependent on the type of self-incompatibility. In some cases, fecundity selection markedly alters the equilibrium dynamics of self-incompatibility alleles. We discuss the population genetic consequences of mate availability and fecundity selection in the contexts of conservation management of self-incompatible plant species and experimental investigations on self-incompatibility in natural populations.Key words.-Fecundity selection, mate availability, plant mating systems, self-incompatibility.Received May 21, 1997. Accepted September 29, 1997.A key feature of self-incompatibility (SI) systems in plants is the mate availability or proportion of compatible matings in a population (Bateman 1952;de Nettancourt 1977). A mating is the transfer of pollen from a paternally acting individual to the stigma of a maternally acting individual, and the mating is incompatible if pollen and stigma share the same phenotype with respect to SL Mate availability of an individual can therefore be defined as the likelihood that a randomly chosen mate is compatible. Darwin (1877) first noted that SI in distylous species causes each plant to be cross-sterile with "half its brethren," that is, reduces mate availability to 50%. The consequences of limited mate availability for the evolution of SI systems were discussed by Charlesworth (1988) and Lloyd and Webb (1992), and limited mate availability has been invoked in comparisons of reproductive efficiency in dioecy versus gametophytic SI (Anderson andStebbins 1984, 1994;Karoly 1994). Conservation management in endangered plant species with SI systems also involves the consideration of mate availability (e.g. Byers and Meagher 1992;DeMauro 1993;Godt and Hamrick 1995). The number of alleles maintained in small populations with multiallelic SI systems is expected to be low (Wright 1939;Imrie et al. 1972), and therefore mate availability is expected to be generally low. Low mate availability may add to a crisis by causing low seed set (Les et al. 199...

The stationary frequency distribution and allelic dynamics in finite populations are analyzed through stochastic simulations in three models of single-locus, multi-allelic sporophytic self-incompatibility. The models differ in the dominance relationships among alleles. In one model, alleles act codominantly in both pollen and style (SSIcod), in the second, alleles form a dominance hierarchy in pollen and style (SSIdom). In the third model, alleles interact codominantly in the style and form a dominance hierarchy in the pollen (SSIdomcod). The SSIcod model behaves similarly to the model of gametophytic self-incompatibility, but the selection intensity is stronger. With dominance, dominant alleles invade the population more easily than recessive alleles and have a lower frequency at equilibrium. In the SSIdom model, recessive alleles have both a higher allele frequency and higher expected life span. In the SSIdomcod model, however, loss due to drift occurs more easily for pollen-recessive than for pollen-dominant alleles, and therefore, dominant alleles have a higher expected life span than the more recessive alleles. The process of allelic turnover in the SSIdomcod and SSIdom models is closely approximated by a random walk on a dominance ladder. Implications of the results for experimental studies of sporophytic self-incompatibility in natural populations are discussed.

Expectations for the time scale and structure of allelic genealogies in finite populations are formed under three models of sporophytic self-incompatibility. The models differ in the dominance interactions among the alleles that determine the self-incompatibility phenotype: In the SSIcod model, alleles act codominantly in both pollen and style, in the SSIdom model, alleles form a dominance hierarchy, and in SSIdomcod, alleles are codominant in the style and show a dominance hierarchy in the pollen. Coalescence times of alleles rarely differ more than threefold from those under gametophytic self-incompatibility, and transspecific polymorphism is therefore expected to be equally common. The previously reported directional turnover process of alleles in the SSIdomcod model results in coalescence times lower and substitution rates higher than those in the other models. The SSIdom model assumes strong asymmetries in allelic action, and the most recessive extant allele is likely to be the most recent common ancestor. Despite these asymmetries, the expected shape of the allele genealogies does not deviate markedly from the shape of a neutral gene genealogy. The application of the results to sequence surveys of alleles, including interspecific comparisons, is discussed.