On Genetic Information, Diversity and Distance

OBJECTIVES: General information-theoretic concepts such as f-divergence, f-information and f-entropy are applied to the genetic models where genes are characterized by randomly distributed alleles. The paper thus presents an information-theoretic background for measuring genetic distances between populations, genetic information in various observations on individuals about their alleles and, finally, genetic diversities in various populations. METHODS: Genetic distances were derived as divergences between frequencies of alleles representing a gene in two different populations. Genetic information was derived as a measure of statistical association between the observations taken on individuals and the alleles of these individuals. Genetic diversities were derived from divergences and information. RESULTS: The concept of genetic f-information introduced in the paper seems to be new. We show that the measures of genetic distance and diversity used in the previous literature are special cases of the genetic f-divergence and f-diversity introduced in the paper and illustrated by examples. We also display intimate connections between the genetic f-information and the genetic f-divergence on one side and genetic f-diversity on the other side. The examples at the same time also illustrate practical computations and applications of the important concepts of quantitative genetics introduced in the paper. CONCLUSIONS: We discussed a general class of f- divergence measures that are suitable measures of genetic distance between populations characterized by concrete frequencies of alleles. We have shown that a wide class of genetic information, called f-information, can be obtained from f-divergences and that a wide class of measures of genetic diversity, called f-diversities, can be obtained from the f-divergences and f-information.