The Theory of Fitness in a Heterogeneous Environment. IV. The Adaptive Significance of Gene Flow

Gene flow has generally been regarded as detrimental to a population, its principal effect being to swamp a local population and prevent its adaptation to local conditions. The swamping effect has been considered so strong that prior isolation was thought to be a necessary first step in speciation. More recently it has been recognized that strong selection can produce divergence even in the face of a high rate of migration (Thoday and Gibson, 1962; Streams and Pimentel, 1961), while the experiments of Koopman (1950) show that sexual isolation can arise in populations in contact. This has raised the opposite question: why do we not have local speciation on a much greater scale, why are there any widespread species at all, why is not each local ecotype a distinct species? The obvious first answer refers to population size. As the environment becomes infinitely subdivided, local population size decreases, and the probability of random extinction increases. Suppose that the average number of offspring per pair is r, and each has a probability 1/r of survival. Then the probability that a population of size 2n becomes extinct by chance is [ 1 (1/r) ] rn which approaches el-n for large r. However, this probability decreases rapidly with n, and would not be an important factor for populations greater than several hundred. A second disadvantage to small population size is the loss of genetic variance through random drift, which might be important in very small populations, but the same objection applies as in the previous argument. Drift cannot account for the paucity of abundant but local species. It will be argued below that gene flow among populations is part of the adaptive system of a species, that there are optimum values for gene flow that depend on the statistical structure of the environment, and that natural selection can establish these optimal levels (or more precisely, that the actual levels of gene flow among populations of different species differ in the same direction as their optimal values). The model used here is a continuation of that used in the previous papers of this series (Levins, 1962, 1963, 1964). It is assumed that corresponding to each environment there is an optimum phenotype S, which may vary in time and space; that when the actual phenotype is the optimum, the adaptive value is maximized; and that fitness declines toward zero as the deviation of actual from optimum phenotype increases. (The phenotype is genetically determined. Any developmental or physiological modification of phenotype by the environment has the effect of reducing the environmental variance, as explained in the second paper of this series.) We further specialize the model by assuming that the fitness of each phenotype declines with the square of the deviation of that phenotype from the optimum, so that