Spread of new mutations through space

Abstract

The terms population size and population density are often used interchangeably, when in fact they are quite different. When viewed in a spatial landscape, density is defined as the number of individuals within a square unit of distance, while population size is simply the total count of a population. In discrete population genetics models, the effective population size is known to influence the interaction between selection and random drift with selection playing a larger role in large populations while random drift has more influence in smaller populations. Using a spatially explicit simulation software we investigate how population density affects the flow of new mutations through a geographical space. Using population density, selectional advantage, and dispersal distributions, a model is developed to predict the speed at which the new allele will travel, obtaining more accurate results than current diffusion approximations provide. We note that the rate at which a neutral mutation spreads begins to decay over time while the rate of spread of an advantageous allele remains constant. We also show that new advantageous mutations spread faster in dense populations.