arXiv2019
Classic concepts of genetic (gene) diversity (heterozygosity) such as Nei (1973: PNAS) and Nei and Li (1979: PNAS) nucleotide diversity were defined within the context of populations. Although variations are often measured in population context, the basic carriers of variation are individuals. Hence, measuring variations such as SNP of individual against a reference genome, which has been ignored currently, is certainly of its own right. Indeed, similar practice has been a tradition in ecology, where the basic framework of diversity measure is individual community sample. We propose to use Renyi-entropy-derived Hill numbers to define SNP (single nucleotide polymorphism) diversity (including alpha-, beta-, and gamma-diversities) and similarity profiles. Hill numbers are derived from Renyi entropy, of which Shannon entropy is a special case and which have found widely applications including measuring the quantum information entanglement, wealth distribution in economics and ecological diversity. The newly proposed SNP diversity not only complements the existing genetic diversity concepts by offering individual-level metrics, but also offers building blocks for comparative genetic analysis at higher levels. The profile concept also helps to resolve a dilemma in measuring diversity: the choice from various diversity indexes, because diversity profile unifies some of the most commonly used indexes (as special cases) with different diversity orders (along the rareness-commonness spectrum of gene mutations). Finally, the profiles can be estimated with rarefaction approach, which may help to relieve some effect of insufficient sequencing coverage.