The discovery of high levels of genetic variability in natural populations by electrophoresis has renewed interest in theory of genetic polymorphism in heterogeneous environments. A plethora of recent investigations have verified that both spatial and temporal variation in environment can maintain genetic variability in diploid populations, although 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, fluctuations always present in natural environments could provide an answer to observed cosmopolitan polymorphism. In spite of 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 reader with impression that there are few alternative interpretations. I would like here to review briefly a few of 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 causes of genetic variability in natural Because of mathematical simplicity, majority of theoretical conclusions on environmental variation stem from influence of this variation on infinite populations, while fewer studies have concentrated on consequences of finite population size. Recently, Cook and Hartl (1975) implied that stable equilibria for infinite populations also retarded fixation in smaller ones, although force was not particularly satisfying for most of 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 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 mechanisms may not be those suggested by models. Without much loss in exactness, conditions for polymorphic stability in temporally varying environments reduce to a greater geometric mean fitness of 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 geometric mean fitness, which determines eventual contribution of each genotype to population, is no longer equal to arithmetic mean fitness. Since 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 Wrightian fitness of all genotypes may be equal. It is geometric mean fitness therefore, that is statistic of interest and it would seem intuitively more valid and operationally more useful to define fitness on a geometric scale, such as 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 appealing interaction of fitness and environmental variance (see also Hartl and Cook, 1973). Hence, while general model for enzyme polymorphisms of Gillespie and Langley (1974) seemingly depends only upon 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 geometric formulation is correct, polymorphism is not due to statistical homeostasis of Gillespie and Langley, but more likely to a true biochemical homeostasis provided
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Jul 1, 1987
Sotos Raptis + 6
Open Access