Maternal Cytoplasmic Inheritance

We explicitly solve and analyze a series of deterministic continent-island models to delimit the effects of pollen and seed migration on cytonuclear frequencies and disequilibria in random-mating, mixed-mating and self-fertilized populations. Given the critical assumption of maternal cytoplasmic inheritance, five major findings are (i) nonzero cytonuclear disequilibria will be maintained in the island population if and only if at least some migration occurs each generation through seeds with nonrandom cytonuclear associations; (ii) immigrant seeds with no cytonuclear disequilibria can strongly affect the genetic structure of the island population by generating significant and long-lasting transient associations; (iii) with all else being equal, substantially greater admixture disequilibria are generally found with higher rates of seed migration into, or higher levels of self-fertilization within, the island population (with the possible exception of the heterozygote disequilibrium); (iv) pollen migration can either enhance or reduce the cytonuclear disequilibria caused by seed migration, or that due to mixedmating in the absence of seed migration, but the effect is usually small and appears primarily to make a noticeable difference in predominantly outcrossing populations; and (v) pollen migration alone cannot generate even transient disequilibria de novo in populations with completely random associations. This same basic behavior is exhibited as long as there is some random outcrossing in the island population. Self-fertilized populations represent a special case, however, in that they are necessarily closed to pollen migration, and nonzero disequilibria can be maintained even in the absence of seed migration. All of these general results hold whether the population is censused as adults or as seeds, but the ability to detect nonrandom cytonuclear associations can depend strongly on the life stage censused in populations with a significant level of random outcrossing. We suggest how these models might be used for the estimation of seed and pollen migration. J O I N T nuclear-cytoplasmic frequencies and the statistical associations (disequilibria) between the corresponding single-locus frequencies represent a new and extremely useful tool for the study of natural populations. T h e special utility of cytonuclear systems stems from the juxtaposition of the uniparental inheritance of haploid, cytoplasmic genes against the biparental inheritance of diploid, nuclear genes. This is perhaps most obvious in the delineation of certain nonrandom mating patterns, where it has been shown both empirically and theoretically that joint nuclearcytoplasmic data allow biological inferences and mating parameter estimates that are unobtainable from surveys of nuclear loci alone (LAMB and AVISE 1986; ASMUSSEN, ARNOLD and AVISE 1987; ARNOLD, AsMUSSEN and AVISE 1988). An important practical by-product of the underlying mating system models is that the sign pattern of observed cytonuclear disequilibria may itself convey much information concerning the mating system in a population. This is because of the critical discovery that substantial nonrandom cytonuclear associations Genetics 148: 639-654 (July, 1991) can be generated by nonrandom mating even in the absence of natural selection, migration and genetic drift. The resulting disequilibria will be transient in the case of partial self-fertilization, partial assortative mating based on nuclear genotype, or partial assortative mating in hybrid zones based on an interaction between the cytotype and the multilocus nuclear genotype characteristic of the pure parental species (AsMUSSEN, ARNOLD and AVISE 1987; SCHNABEL and ASMUSSEN 1989). Permanent cytonuclear disequilibria can be produced, however, under an assortative mating pattern based on an interaction between cytotype and genotype at a single nuclear locus (ARNOLD, AsMUSSEN and AVISE 1988). Recent theoretical studies indicate that cytonuclear data also offer a novel perspective on the study of gene flow into a hybrid zone and other zones of admixture (ASMUSSEN, ARNOLD and AVISE 1989; AsMUSSEN and ARNOLD 1991). T h e first of these investigations demonstrated how joint cytonuclear frequencies allow particularly sensitive estimates of the migration rates from the two parental species into a 640 M. A. Asmussen and A. Schnabel hybrid zone, as well as of the rate at which pure species females preferentially mate with conspecific males in the zone (ASMUSSEN, ARNOLD and AVISE 1989). An important concurrent finding was that continued immigration from two genetically distinct parental species will generate permanent cytonuclear disequilibria in a hybrid zone, whether or not pure parental females mate assortatively. This theoretical framework has recently been extended beyond the context of hybrid zones to show how cytonuclear frequencies and disequilibria can help identify zones of admixture as well as provide estimates of gene flow between one or more random-mating populations (AsMUSSEN and ARNOLD 1991). The latter investigation also revealed how cytonuclear disequilibria can be generated by population subdivision, admixture, and continued migration into or between random-mating populations. Here we expand the study of the cytonuclear effects of migration to the special case of seed plants, where not only may there be complete or partial self-fertilization, but gene flow has both diploid (seed) and haploid (pollen) components. The latter distinction is noteworthy for two major biological reasons. First, although several cases of biparental and paternal organelle inheritance are known (SEARS 1980; BOBLENZ, NOTHNAGEL and METZLAFF 1990; SMITH 1988; ~ C H U MANN and HANCOCK 1989; NEALE, MARSHALL and SEDEROFF 1989), the majority of plant species appear to exhibit strictly maternal inheritance of mitochondria and chloroplasts, in which case their pollen does not transmit cytoplasmic genes. The two forms of gene flow would therefore be expected to have different effects on the cytonuclear structure of most species. Second, for partially or fully outcrossing species, gene flow via pollen is generally believed to occur at much greater rates than gene flow via seed (LEVIN and KERSTER 1974; HANDEL 1983). The two forms of gene flow would, however, be expected to be more comparable in highly selfing species and in species with seeds that are dispersed long distances by water or highly mobile animals (BULLOCK and PRIMACK 1977; LANNER and VANDER WALL 1980; DARLEYHILL and JOHNSON 198 1 ; SCHNEIDER and SHARITZ 1988). The present paper examines and contrasts the separate and joint effects of these two types of gene flow on the cytonuclear dynamics within single randommating, mixed-mating, and self-fertilized populations, based on a continent-island formulation. Paralleling previous migration studies (ASMUSSEN, ARNOLD and AVISE 1989; ASMUSSEN and ARNOLD 1991), we also examine the extent to which the two standard census times for plants (adults us. seeds) affect the ability to detect and utilize nonrandom cytonuclear associations. TABLE 1 Joint nuclear-cytoplasmic genotype frequencies