The potential importance of group or interdemic selection as an evolutionary force depends on the potential for local genetic differentiation. If there are significant genetic differences among local populations, there can be little doubt that selection based on those differences can lead to genetic change. Theoretical studies should examine carefully the mechanisms that can establish and maintain local genetic differences, since group selection, no matter how intense, cannot act in the absence of those differences.The purpose of this study is to examine how between-population genetic differences in the average value of a quantitative character are established and maintained in local populations. I will show that this process can be easily understood in terms of the partitioning of variance among lines in a subdivided population. The analysis of a populational characteristic leads to the definition of the "populational heritability," which is analogous to the heritability used in quantitative genetics. The idea of populational heritability is well known in quantitative genetics and is similar to the "heritability of the family mean" (Falconer, 1960, Ch. 13). But it has not been related to the evolutionary problem of group selection.This paper is partly motivated by general considerations of group selection and partly by a set of experiments by Wade and McCauley (1980) on the establishment of between-population genetic differences in Tribolium castaneum. These experiments provide a particular context in which to discuss the more general problem and data with which to compare the predictions of the simple theory developed in this paper. Wade and McCauley used as a populational characteristic the numbers of adults obtained after 45 days from pop-ulations that were started from specified numbers of adults. This is obviously a complex property, which is related to the intrinsic rate of increase and which is determined by the interactions among all the individuals in each population. Wade (1979) and McCauley and Wade (1980) have shown that this property cannot be attributed to a single phenotypic change in individuals. Nevertheless, I will show that many of the qualitative and quantitative features of the results of the Wade-McCauley experiments can be predicted using an additive model of a quantitative character.
The ModelThe model is developed using a combination of standard methods in quantitative genetics and methods for the determination of probabilities of identity by descent of alleles in a subdivided population. The model consists of two distinct parts. The first part determines the partitioning of the variance of the average value of a quantitative character among local populations as a function of the covariance between alleles in those populations. The second part determines how those covariances are affected by the population structure.Part 1.-The model will be formulated to facilitate comparison with the Wade-McCauley results. Consider a monecious, diploid species which is divided into n local populations....