We introduce an approach to revealing the likelihood of different population histories that utilizes an explicit model of sequence evolution for the DNA segment under study. Based on a phylogenetic tree reconstruction method we show that a Tamura-Nei model with heterogeneous mutation rates is a fair description of the evolutionary process of the hypervariable region I of the mitochondrial DNA from humans. Assuming this complex model still allows the estimation of population history parameters, we suggest a likelihood approach to conducting statistical inference within a class of expansion models. More precisely, the likelihood of the data is based on the mean pairwise differences between DNA sequences and the number of variable sites in a sample. The use of likelihood ratios enables comparison of different hypotheses about population history, such as constant population size during the past or an increase or decrease of population size starting at some point back in time. This method was applied to show that the population of the Basques has expanded, whereas that of the Biaka pygmies is most likely decreasing. The Nuu-Chah-Nulth data are consistent with a model of constant population.