Defining Individual-Level Genetic Diversity and Similarity Profiles

Classic concepts of genetic (gene) diversity (heterozygosity) such as Nei & Li's nucleotide diversity were defined within a population context. Although variations are often measured in population context, the basic carriers of variation are individuals. Hence, measuring variations such as SNP of an individual against a reference genome, which has been ignored previously, is certainly in its own right. Indeed, similar practice has been a tradition in community ecology, where the basic unit of diversity measure is individual community sample. We propose to use Renyi's-entropy-based Hill numbers to define individual-level genetic diversity and similarity and demonstrate the definitions with the SNP (single nucleotide polymorphism) datasets from the 1000-Genomes Project. Hill numbers, derived from Renyi's entropy (of which Shannon's entropy is a special case), have found widely applications including measuring the quantum information entanglement and ecological diversity. The demonstrated individual-level SNP diversity not only complements the existing population-level genetic diversity concepts, but also offers building blocks for comparative genetic analysis at higher levels. The concept of individual covers, but is not limited to, individual chromosome, region of chromosome, gene cluster(s), or whole genome. Similarly, the SNP can be replaced by other structural variants or mutation types such as indels.