APPLICATION OF A TIME-DEPENDENT COALESCENCE PROCESS FOR INFERRING THEHISTORY OF POPULATION-SIZE CHANGES FROM DNA-SEQUENCE DATA

Distribution of pairwise differences of nucleotides from data on a sam ple of DNA sequences from a given segment of the genome has been used in the past to draw inferences about the past history of population si ze changes. However, all earlier methods assume a given model of popul ation size changes (such as sudden expansion), parameters of which (e. g., time and amplitude of expansion) are fitted to the observed distri butions of nucleotide differences among pairwise comparisons of all DN A sequences in the sample. Our theory indicates that for any time-depe ndent population size, N(tau) (in which time tau is counted backward f rom present), a time-dependent coalescence process yields the distribu tion, p(tau), of the time of coalescence between two DNA sequences ran domly drawn from the population. prediction of p(tau) and N(tau) requi res the use of a reverse Laplace transform known to be unstable. Never theless, simulated data obtained from three models of monotone populat ion change (stepwise, exponential, and logistic) indicate that the pat tern of a past population size change leaves its signature on the patt ern of DNA polymorphism. Application of the theory to the published mt DNA sequences indicates that the current mtDNA sequence variation is n ot inconsistent with a logistic growth of the human population.