The relationship between the concepts of genetic diversity and differentiation

Diversity as a measure of individual variation within a population is widely agreed to reflect the number of different types in the population, taking into account their frequencies. In contrast, differentiation measures variation between two or more populations, demes or subpopulations. As such, it is based on the relative frequencies of types within these subpopulations and, ideally, measures the average distance of subpopulations from their respective lumped remainders. This concept of subpopulation differentiation can be applied consistently to a single population by regarding each individual as a deme (subpopulation) of its own, and it results in a measure of population differentiation δ T which depends on the relative frequencies of the types and the population size. δ T corresponds to several indices of variation frequently applied in population genetics and ecology, and it verifies these indices as measures of differentiation rather than diversity. For any particular frequency distribution of types, the diversity ν is then shown to be the size of a hypothetical population in which each type is represented exactly once, i. e. for which δ T =1. Hence, the diversity of a population is its differentiation effective number of types. This uniquely specifies the link between the two concepts. Moreover, ν again corresponds to known measures of diversity applied in population genetics and ecology. While population differentiation can always be estimated from samples, the diversity of a population, particularly if it is large, may not be. In such cases, it is recommended that population differentiation is estimated and the corresponding sample diversity merely computed. Finally, a solution to the problem of measuring multi-locus diversities is provided.