MAINTENANCE OF POLYGENIC VARIATION VIA A MIGRATION-SELECTION BALANCE UNDER UNIFORM SELECTION.

Population subdivision is often invoked to explain the large amount of heterozygosity found at single loci in natural populations (Felsenstein 1976; Hedrick et al., 1976; Karlin 1982; Hedrick 1986). Surprisingly, relatively few studies describe the effects of population structure on the maintenance of genetic variance for polygenic (quantitative) traits. Felsenstein (1977) and Slatkin (1978) presented models in which additive genetic variance can be maintained via migration along a cline (see also Barton and Turelli 1989). Goldstein and Holsinger (1992) used simulations to show that variance for quantitative traits could be maintained under uniform selection in a population subject to isolation by distance (see also Lande [1991]), and Slatkin and Lande (1994) demonstrated that the segregation variance generated by betweenpopulation crosses depends on how variance is generated within each population. Here I analyze the amount of genetic variance that can be maintained deterministically via a migration-selection balance under uniform selection and conclude that a potentially large amount of variance can be generated in this way. This is true only when migration is very weak, so as not to overcome the influence of selection. When variance is maintained, it is maximal at the critical balance between migration and selection. The deterministic interaction between migration and selection has been the subject of a great deal of analysis in the context of Wright's shifting-balance theory (Crow et al. 1990; Barton 1992; Kondrashov 1992; Phillips 1993). These studies have shown that migration can be very effective at overcoming the effects of selection and driving populations to uniformity. For the shifting-balance process, this means that once a population has undergone a peak shift, it might be expected to drive peak shifts in neighboring populations, depending on the details of the genetic system and population structure (Barton 1992; Phillips 1993). The purpose here is to explore regions of the parametric space in which this does not happen, but instead both populations remain polymorphic. Results from this deterministic approach will be contrasted with models that include stochastic effects and make somewhat different predictions (Lande 1991; Goldstein and Holsinger 1992; Barton and Rouhani 1993). Uniform stabilizing selection on an additive character generates disruptive selection at the genetic level because various combinations of alleles can yield the same optimal phenotype, but the marginal fitness of any allele depends on the genetic background in which it is found (Wright 1935). This is called "genetic redundancy" by Goldstein and Holsinger [1992]). Two populations can thus display the same phenotype but be fixed for different genotypes. If these populations were to exchange migrants, the mixing of the different genotypes would generate variance within each population. This would be a somewhat cryptic source of genetic variation because there would be no obvious differentiation between the populations. Depending on the strength of migration, most of the variance generated by migration would then be quickly eliminated by selection, creating a migration-selection balance. This is the multilocus equivalent of a migration-selection polymorphism generated by underdominance at a single locus (Karlin and McGregor 1972). Because many characters are assumed to be under stabilizing selection, and because population structure is undoubtedly an important feature of natural populations, the interaction of migration and selection could obviously be an important influence on the maintenance of genetic variance.