The Generalized Haldane (GH) model of genetic drift resolving the many paradoxes of molecular evolution

Genetic drift, the random changes in frequencies of neutral variants, is the fundamental force of molecular evolution. However, the standard Wright-Fisher (WF) model of random sampling in population of size N only partially defines genetic drift with 1/ N or 1/ N _e ( N _e being a function of varying N’ s). In parallel, JBS Haldane (1927) proposed the branching process for genetic drift, whereby each gene copy is transmitted to K descendants with the mean and variance of E ( K ) and V ( K ). Whereas N is externally imposed on the standard and modified WF models, the Haldane model can be generalized (hence, the GH model) for regulating N ’s internally as a function of E ( K ). The determination of N , as well as the broader definition of genetic drift based on V ( K ), enables the GH model to account for many paradoxes of molecular evolution. They include: i) Genetic drift may often become stronger as N becomes larger; ii) The two sexes experience drift differently; iii) Genetic drift operates on advantageous mutations is independent of N ; iv) Irresolution and paradoxes emerge in multi-copy gene systems (viruses, mitochondria, etc.) whereby genetic drift happens within and between individuals. We show how a GH model can resolve these paradoxes that elude the WF models. By integrating their results, GH models may supplant the WF models of genetic drift for the ever more complex biological systems.