Pairwise comparisons of mitochondrial DNA sequences in stable and exponentially growing populations.

TLDR

The study investigates how pairwise mitochondrial DNA differences are distributed in populations of constant size versus those that have grown exponentially over time. The authors analytically and via simulation derive that, given a known mutation rate μ and current size N₀, the growth rate r can be estimated from the average pairwise difference i by solving r/μ = ln(N₀r) – γ, where γ≈0.577. They find that in constant‑size populations the pairwise differences deviate from the expected geometric distribution, rendering simple goodness‑of‑fit tests invalid, whereas in exponentially growing populations with large N₀r the coalescent events cluster early, yielding a star‑like gene tree and a pairwise difference distribution that is nearly Poisson.

Abstract

We consider the distribution of pairwise sequence differences of mitochondrial DNA or of other nonrecombining portions of the genome in a population that has been of constant size and in a population that has been growing in size exponentially for a long time. We show that, in a population of constant size, the sample distribution of pairwise differences will typically deviate substantially from the geometric distribution expected, because the history of coalescent events in a single sample of genes imposes a substantial correlation on pairwise differences. Consequently, a goodness-of-fit test of observed pairwise differences to the geometric distribution, which assumes that each pairwise comparison is independent, is not a valid test of the hypothesis that the genes were sampled from a panmictic population of constant size. In an exponentially growing population in which the product of the current population size and the growth rate is substantially larger than one, our analytical and simulation results show that most coalescent events occur relatively early and in a restricted range of times. Hence, the "gene tree" will be nearly a "star phylogeny" and the distribution of pairwise differences will be nearly a Poisson distribution. In that case, it is possible to estimate r, the population growth rate, if the mutation rate, mu, and current population size, N0, are assumed known. The estimate of r is the solution to ri/mu = ln(N0r) - gamma, where i is the average pairwise difference and gamma approximately 0.577 is Euler's constant.