Molecular Biology and Evolution, Vol 9, 552-569, Copyright © 1992 by Society for Molecular Biology and Evolution
AR Rogers and H Harpending
Episodes of population growth and decline leave characteristic signatures
in the distribution of nucleotide (or restriction) site differences between
pairs of individuals. These signatures appear in histograms showing the
relative frequencies of pairs of individuals who differ by i sites, where i
= 0, 1, .... In this distribution an episode of growth generates a wave
that travels to the right, traversing 1 unit of the horizontal axis in each
1/2u generations, where u is the mutation rate. The smaller the initial
population, the steeper will be the leading face of the wave. The larger
the increase in population size, the smaller will be the distribution's
vertical intercept. The implications of continued exponential growth are
indistinguishable from those of a sudden burst of population growth
Bottlenecks in population size also generate waves similar to those
produced by a sudden expansion, but with elevated uppertail probabilities.
Reductions in population size initially generate L-shaped distributions
with high probability of identity, but these converge rapidly to a new
equilibrium. In equilibrium populations the theoretical curves are free of
waves. However, computer simulations of such populations generate empirical
distributions with many peaks and little resemblance to the theory. On the
other hand, agreement is better in the transient (nonequilibrium) case,
where simulated empirical distributions typically exhibit waves very
similar to those predicted by theory. Thus, waves in empirical
distributions may be rich in information about the history of population
dynamics.
ORIGINAL ARTICLE
Population growth makes waves in the distribution of pairwise genetic differences
Department of Anthropology, University of Utah, Salt Lake City 84112.
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