A COMMENT ON THE ROLE OF ENVIRONMENTAL VARIATION IN MAINTAINING POLYMORPHISMS IN NATURAL POPULATIONS.

The discovery of high levels of genetic variability in natural populations by electrophoresis has renewed interest in the theory of genetic polymorphism in heterogeneous environments. A plethora of recent investigations have verified that both spatial and temporal variation in the environment can maintain genetic variability in diploid populations, although the conditions for stability in temporally varying environments appear more stringent than those for spatial variation (e.g., Haldane and Jayakar, 1963; Gillespie and Langley, 1974) and coarse-grained environments are more conducive to polymorphism than fine-grained ones (e.g., Levins, 1968; Gillespie, 1974b). By implication then, the fluctuations always present in natural environments could provide an answer to observed cosmopolitan polymorphism. In spite of the unquestionable success of these theoretical inquiries, however, many of their conclusions are set forth in rather dogmatic terms, detracting from their heuristic value and leaving the reader with the impression that there are few alternative interpretations. I would like here to review briefly a few of the current theoretical conclusions on environmental heterogeneity, offer possible alternative interpretations to these and thereby suggest they may not offer a realistic basis for experimentally investigating the causes of genetic variability in natural populations. Because of mathematical simplicity, the majority of theoretical conclusions on environmental variation stem from the influence of this variation on infinite populations, while fewer studies have concentrated on the consequences of finite population size. Recently, Cook and Hartl (1975) implied that stable equilibria for infinite populations also retarded fixation in smaller ones, although the force was not particularly satisfying for most of the parameter combinations they used and did not hold for all models. They did conclude, however, that "the meaning of polymorphism in stochastic selection models will have to be more rigorously defined, particularly in finite populations." Indeed, Hedrick (1974), utilizing a slightly different model, concluded that temporal variation could not effectively retard fixation in finite populations unless successive environments were opposite and equal in selection intensity. Since the effective size of most natural populations must be small, allowing such constraints as mating systems and small winter numbers in temperate localities, most theoretical results can only be applied with caution to natural organisms. This is not to say, however, that organisms would not have to adapt (genetically) to unavoidable vicissitudes of environment, but that the mechanisms may not be those suggested by the models. Without much loss in exactness, conditions for polymorphic stability in temporally varying environments reduce to a greater geometric mean fitness of the heterozygote than both homozygotes (Gillespie, 1973; Cook and Hartl, 1975) in an environment sufficiently variable to overcome any systematic pressures (Bryant, 1973; Gillespie and Langley, 1974). This conclusion, however, depends upon characterizing fitness linearly upon environment (i.e., Wrightian) so that under fluctuating conditions the geometric mean fitness, which determines the eventual contribution of each genotype to the population, is no longer equal to the arithmetic mean fitness. Since the difference between these means is a function of variance and an intermediate hererozygote will vary less by greater smoothing of environmental fluctuations, environment can mediate heterozygote superiority even though the Wrightian fitness of all genotypes may be equal. It is the geometric mean fitness therefore, that is the statistic of interest and it would seem intuitively more valid and operationally more useful to define fitness on a geometric scale, such as the intrinsic rate of increase of ecology. In doing so, genetic polymorphism can only be maintained by historically recognized pressures such as heterosis (on a geometric scale), obviating the appealing interaction of fitness and environmental variance (see also Hartl and Cook, 1973). Hence, while the "general model" for enzyme polymorphisms of Gillespie and Langley (1974) seemingly depends only upon the pervasive law of large numbers, it also hinges upon a particular formulation of fitness. In attempting to extrapolate their conclusions to natural populations it becomes critical to determine which formulation is more nearly correct. If the geometric formulation is correct, polymorphism is not due to the statistical homeostasis of Gillespie and Langley, but more likely to a true biochemical homeostasis provided