EVOLUTIONARY LANDSCAPES FOR COMPLEX SELECTION

Wright's (1932, 1969) "surface of selective value" is one of the most influential concepts in evolutionary genetics. The surface, also known as an "adaptive topography" or "evolutionary landscape," is an n-dimensional picture of the way that natural selection changes the genetic composition of a population. For one-locus models, the surface is defined by n -1 independent allele frequency axes and one dimension for population "fitness." At any given time, a population can be represented as a point on the surface. Through time, the point moves on the surface in such a way that population "fitness" is always increasing, until equilibrium is attained at a maximal state of adaptation. For the well known deterministic model of viability selection at one locus, the notion of increasing population "fitness" until equilibrium is an exact mathematical theorem (Kingman, 196 1), provided that certain assumptions are satisfied: mating occurs at random, mutation and immigration are negligible, genotypespecific viabilities are constant, segregation follows Mendelian ratios, and selection is independent of sex. The appropriate measure of population "fitness" under these circumstances is the average zygote viability, usually called "mean fitness." However, for many models that depart from the assumptions of the classical viability selection model, mean fitness is not necessarily an increasing quantity that is maximized at equilibrium. Following is a representative list of biologically significant situations in which the principle of increasing population fitness is known to be violated. Multiple Loci. -If an individual's viability depends on the genotype at two loci, then the population mean viability is not generally maximized at equilibrium (Moran, 1964). Mean viability can decrease from generation to generation, even though selection coefficients are constant (Karlin and Carmelli, 1975). The mean viability is nondecreasing if fitness is determined by additive interactions between loci (Ewens, 1969), but epistasis is often found when the appropriate experimental design is employed (e.g., Clark and Feldman, 1981a; see Barker, 1979, for a review). Wright (1969 p. 475) was aware of this limitation, noting that "Selection formulas for single loci can never be more than momentary approximations because of the practical universality of interactions with the other loci, ...." Meiotic Drive. -If heterozygotes produce a non-Mendelian ratio of gamete types, then mean viability at the polymorphic equilibrium is always less than maximal (Hiraizumi et al., 1960). There can exist a stable fixation equilibrium that is a minimum of the mean viability. Naturally occurring major meiotic drive elements have been documented in the rodents Myopus schisticolor (Fredga et al., 1976) and Mus musculus (Dunn, 1956), two lepidopteran species (Chanter and Owen, 1972; Smith, 1975), at least 12 species of Drosophila (Sturtevant and Dobzhansky, 1936; Stalker, 1961; Faulhaber, 1967; Hartl and Hiraizumi, 1976), two other dipterans (Hiroyoshi, 1964; Hickey and Craig, 1966), two species of Neurospora (Turner and Perkins, 1976), and several higher plants (Cameron and Moav, 1957; Loegering and Sears, 1963; Redei, 1965; Carlson, 1969; Muintzing, 1968). Further, there is evidence that populations of Drosophila carry minor elements that modify segregation (Hanks,