A New Formulation of Random Genetic Drift and Its Application to the Evolution of Cell Populations

Random genetic drift, or stochastic change in gene frequency, is a fundamental evolutionary force that is usually defined within the ideal Wright-Fisher (WF) population. However, as the theory is increasingly applied to populations that deviate strongly from the ideal model, a paradox of random drift has emerged. When drift is defined by the WF model, it becomes stronger as the population size, N, decreases. However, the intensity of competition decreases when N decreases and, hence, drift might become weaker. To resolve the paradox, we propose that random drift be defined by the variance of "individual output", V(k) [k being the progeny number of each individual with the mean of E(k)], rather than by the WF sampling. If the distribution of k is known for any population, its strength of drift relative to a WF population of the same size, N, can be calculated. Generally, E(k) and V(k) should be density dependent but their relationships are different with or without competition, leading to opposite predictions on the efficiency of random drift as N changes. We apply the "individual output" model to asexual cell populations that are either unregulated (such as tumors) or negatively density-dependent (e.g., bacteria). In such populations, the efficiency of drift could be as low as <10% of that in WF populations. Interestingly, when N is below the carrying capacity, random drift could in fact increase as N increases. Growing asexual populations, especially tumors, may therefore be genetically even more heterogeneous than the high diversity estimated by some conventional models.