Frank, S. A. 1986. Dispersal polymorphisms in subdivided populations. Journal of Theoretical Biology 122:303-309.
Price's method for analyzing natural selection in subdivided populations is applied to the problem of dispersal polymorphism strategies in a stable habitat. The results agree with the more traditional Mendelian models for this same problem that have recently been published. Further, by using Price's method, the results obtained are simpler and more general, and the causal evolutionary mechanisms underlying the predicted patterns are more easily recognized. The most interesting new result is that the equilibrium proportion of dispersed individuals is a simple function of the risk of dispersing and the regression coefficient of relatedness among individuals who, in the absence of dispersal, would compete for a limited, local resource. This regression coefficient refers to the genotypes that control the dispersal phenotype. For example, when mothers control the phenotype of their progeny, then the regression is from the mother onto an offspring chosen randomly from the local group before dispersal; while when offspring control their own phenotype, the regression is taken directly from offspring onto a randomly chosen cohort member before dispersal. This use of controlling genotypes to calculate regressions explains the form of the parent-offspring conflict over dispersal noted by previous authors. The simplicity and generality of these results suggests that Price's method is a useful approach for studying the class of phenomena known as games among relatives.