A generalized approach to genetic drift and its applications -- I. An example of the evolution of ribosomal RNA genes

Multi-copy gene systems that evolve within, as well as between, individuals are common. They include viruses, mitochondrial DNAs, multi-gene families etc. The paradox is that neutral evolution in two stages should be slower than single-copy systems but the opposite is often true. We now apply the Haldane model, recently generalized as the GH model (1), to quantify genetic drift in mammalian ribosomal RNA genes (rDNAs). On average, the copy number (C) is 150 - 300 per haploid. A neutral mutation in rDNA should take 4NC* generations to become fixed (N, the population size; C *, the effective copy number within individuals). While C > C* >> 1 is expected, the observed fixation time in mouse is < 4N, leading to the paradox of C* < 1. Genetic drift of rRNA genes thus appears 10-100 times stronger than in single-copy genes. The large increases are driven by a host of molecular mechanisms such as gene conversion and unequal crossover. Although each mechanism of drift is very difficult to quantify, the GH model permits the estimation of their total effects that constitute the aggregate "evolutionary noises". In humans, the fixation rate of rRNA genes is higher than the theoretical maximum of drift, hence, justifying the inference of adaptive evolution. In conclusion, the stochastic evolution in multi-copy gene systems, including viruses and others, can be effectively tracked by GH model.