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.

Expansions of population size leave characteristic signatures in mitochondrial "mismatch distributions." Consequently, these distributions can inform us about the history of changes in population size. Here, I study a simple model of population history that assumes that, t generations before the present, a population grows (or shrinks) suddenly from female size N to female size N . Although this model is simple, it often provides an accurate description of data generated by complex population histories. I develop statistical methods that estimate θ = 2uN , θ = 2uN , and τ = 2ut (where u is the mutation rate), and place a confidence region around these estimates. These estimators are well behaved, and insensitive to simplifying assumptions. Finally, I apply these methods to published mitochondrial data, and infer that a major expansion of the human population occurred during the late Pleistocene.

Most social scientists would agree that the capacity for human culture was probably fashioned by natural selection, but they disagree about the implications of this supposition. Some believe that natural selection imposes important constraints on the ways in which culture can vary, while others believe that any such constraints must be negligible. This paper employs a "thought experiment" to demonstrate that neither of these positions can be justified by appeal to general properties of culture or of evolution. Natural selection can produce mechanisms of cultural transmission that are neither adaptive nor consistent with the predictions of acultural evolutionary models (those ignoring cultural evolution). On the other hand, natural selection can also produce mechanisms of cultural transmission that are highly consistent with acultural models. Thus, neither side of the sociobiology debate is justified in dismissing the arguments of the other. Natural selection may impose significant constraints on some human behaviors, but negligible constraints on others. Models of simultaneous genetic/cultural evolution will be useful in identifying domains in which acultural evolutionary models are, and are not, likely to be useful.

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