Molecular evolution modeled as a fractal Poisson process in agreement with mammalian sequence comparisons

The fractal doubly stochastic Poisson process (FDSPP) model of molecular evolution, like other doubly stochastic Poisson models, agrees with the high estimates for the index of dispersion found from sequence comparisons. Unlike certain previous models, the FDSPP also predicts a positive geometric correlation between the index of dispersion and the mean number of substitutions. Such a relationship is statistically proven herein using comparisons between 49 mammalian genes. There is no characteristic rate associated with molecular evolution according to this model, but there is a scaling relationship in rates according to a fractal dimension of evolution. The FDSPP is a suitable replacement for the homogeneous Poisson process in tests of the lineage dependence of rates and in estimating confidence intervals for divergence times. As opposed to other fractal models, this model can be interpreted in terms of Darwinian selection and drift.