Resolving Paradoxes in Molecular Evolution: The Integrated WF-Haldane (WFH) Model of Genetic Drift

Genetic drift, the random changes in frequencies of neutral variants, is the fundamental force of molecular evolution. Under-estimation of genetic drift is a major cause of mis-conclusions on 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/Ne (Ne being a function of varying N's). In parallel, JBS Haldane proposed the branching process for genetic drift (Haldane 1927), whereby each gene copy is transmitted to K descendants with the mean and variance of E(K) and V(K). Genetic drift in its essence is V(K), i.e., the variance in transmission success, or V(K)/N when averaged over the population. Under the general WF models (i.e., the standard model as well as the many modifications), paradoxes have emerged. They include: i) Most curiously, genetic drift may often become stronger as N becomes larger at the ecological time scale, opposite to the model; ii) Sex chromosomes experience drift differently even with the same normalized N; iii) Genetic drift operates on advantageous mutations depends on V(K) but not on N; iv) Irresolution and paradoxes emerge in multi-copy gene systems, including diploidy, viruses and others, whereby evolution progresses both within and between individuals (Wang, et al. 2024). We now show that the integration of the WF and Haldane (i.e., WFH) model can resolve these paradoxes. Most important, the WFH model can fully define genetic drift in molecular evolution.