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Nucleotide diversity

Nucleotide diversity is a concept in molecular genetics which is used to measure the degree of polymorphism within a population. It was first introduced by Nei and Li in 1979.

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It is defined as the average number of nucleotide differences per site between any two DNA sequences chosen randomly from the sample population, and is denoted by Π.

It is given by the formula:

Π =	∑	x_ix_jπ_ij
	ij

in which π_ij is the proportion of different nucleotides between the ith and jth types of DNA sequences, and x_i andx_j are the respective frequencies of these sequences.

The summation is taken over all distinct pairs i,j, without repetition. That is:

$\Pi = \sum_{ij} x_i x_j \pi_{ij} = \sum_{i=1}^n \sum_{j=1}^i x_i x_j \pi_{ij}$