The amount of DNA polymorphism when population size changes linearly

Abstract

Population size is one of the main factors that determine the amount of DNA polymorphism. We examined a model under which the population size changed linearly. Because of the simplicity of this model, we could analytically obtain the expectation of nucleotide diversity, E(π), and the expectation of the amount of DNA polymorphism, E(θ), based on the number of segregating sites. The results suggest that E(π) is larger than E(θ) when the population size decreased and that E(π) is smaller than E(θ) when the population size increased. The expected time to the most recent common ancestor could also be obtained under this model.