Genetic drift should encompass all random forces that change gene frequency stochastically. However, the conventional model such as the WF (Wright-Fisher) or Moran model is limited to sampling errors between generations. The Haldane model based on the branching process is more intuitive, versatile and powerful and has been proposed as an alternative to the conventions. Indeed, genetic systems that have multiple copies within individuals such as mitochondrial DNAs, transposons, viruses and multi-copy genes cannot be analyzed by the WF model. For example, rRNA genes, with a median of C ~ 150 copies per haploid in humans, appear to evolve rapidly. Without the means to determine genetic drift, positive selection has been invoked even in DNA segments of no apparent functions. By using the Haldane model, we determine the strength of genetic drift in rRNA genes to be ~ 20 times higher than single-copy genes in human and mouse polymorphisms. The large increases in drift, likely due to the homogenizing forces (such as unbiased gene conversion) within individuals, reduce Ne* to < 10Ne, despite C ~ 150 (Ne* and Ne being the effective population sizes of rRNA genes and single-copy genes respectively). Significantly, when the divergence between species is analyzed, some variants appear to experience extremely strong drift such that Ne* becomes smaller than Ne, as if C < 1. By these analyses, positive selection is detected in the great apes but not evident in mice. To account for random evolutionary forces, the results provide further support for the Haldane model as a powerful alternative to the conventional models.
The Haldane model of genetic drift as an alternative to the conventions - II. Drift in multi-copy genetic systems