A logistic branching process for population genetics

A logistic (regulated population size) branching process population genetic model is presented. It is a modification of both the Wright–Fisher and (unconstrained) branching process models, and shares several properties including the coalescent time and shape, and structure of the coalescent process with those models. An important feature of the model is that population size fluctuation and regulation are intrinsic to the model rather than externally imposed. A consequence of this model is that the fluctuation in population size enhances the prospects for fixation of a beneficial mutation with constant relative viability, which is contrary to a result for the Wright–Fisher model with fluctuating population size. Explanation of this result follows from distinguishing between expected and realized viabilities, in addition to the contrast between absolute and relative viabilities.