A. Polanski et al., APPLICATION OF A TIME-DEPENDENT COALESCENCE PROCESS FOR INFERRING THEHISTORY OF POPULATION-SIZE CHANGES FROM DNA-SEQUENCE DATA, Proceedings of the National Academy of Sciences of the United Statesof America, 95(10), 1998, pp. 5456-5461
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.