If substitutions in DNA sequences follow a Poisson process, the ratio of the variance in the number of substitutions to the mean number of substitutions (the index of dispersion) should equal 1. In this paper, the robustness of the commonly applied estimator of the index of dispersion in replacement sites and silent sites to various assumptions regarding DNA evolution is explored using simulation methods. The estimate of the index of dispersion may be strongly biased if the assumptions of the model of substitution are violated. However, the results of this study support the conclusions of studies by Gillespie and Ohta that the process of substitution in replacement sites is overdispersed. This result contradicts those of a recent study and shows that the high index of dispersion for replacement sites is not an artifact caused by the method of estimation.