Expansions of population size leave characteristic signatures in mitoc
hondrial ''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 gene
rations before the present, a population grows (or shrinks) suddenly f
rom female size N-0 to female size N-1. Although this model is simple,
it often provides an accurate description of data generated by comple
x population histories. I develop statistical methods that estimate th
eta(0) = 2uN(0), theta(1) = 2uN(1), and tau = 2ut (where u is the muta
tion rate), and place a confidence region around these estimates. Thes
e estimators are well behaved, and insensitive to simplifying assumpti
ons. Finally, I apply these methods to published mitochondrial data, a
nd infer that a major expansion of the human population occurred durin
g the late Pleistocene.