The meaning of genetic variation within and between subpopulations

Argumentation is presented which indicates that the additive decomposition of the total genetic variation of a population into variation within and between (among) its subpopulations suffers from conceptual inconsistency. While the measurement of variation between subpopulations can be shown to be identical to the measurement of subpopulation differentiation, the notion of variation within subpopulations, when viewed as a single measurement, cannot be derived as an independent and cogent concept. Rather, it appears to be merely technically defined as the arithmetic difference between the total variation and the variation between subpopulations, and this difference happens to be non-negative for concave measures of variation such as the (statistical) variance or certain measures of genetic diversity. In order to overcome the conceptual inconsistency, "variation between subpopulations" could be regarded as subpopulation differentiation and the notion of "variation within subpopulations" could be replaced by measurements of the degree to which the variation in the total population is represented within the subpopulations. A complementary situation with respect to total variation is thus realized once more, and appropriate measures can be directly derived from existing ones.