The Moran coalescent in a discrete one-dimensional spatial model

Abstract

Among many organisms, offspring are constrained to occur at sites adjacent to their parents. This applies to plants and animals with limited dispersal ability, to colonies of microbes in biofilms, and to other genetically heterogeneous aggregates of cells, such as cancerous tumors. The spatial structure of such populations leads to greater relatedness among proximate individuals while increasing the genetic divergence between distant individuals. In this study, we analyze a Moran coa-lescent in a one-dimensional spatial model where a randomly selected individual dies and is replaced by the progeny of an adjacent neighbor in every generation. We derive a recursive system of equations using the spatial distance among haplotypes as a state variable to compute coalescent probabilities and coalescent times. The coalescent probabilities near the branch termini are smaller than in the unstructured Moran model (except for t = 1, where they are equal), corresponding to longer branch lengths and greater expected pairwise coalescent times. The lower terminal coalescent probabilities result from a spatial separation of lineages, i.e. a coalescent event between a haplotype and its neighbor in one spatial direction at time t cannot co-occur with a coalescent event with a haplotype in the opposite direction at t + 1. The concomitant increased pairwise genetic distance among randomly sampled haplotypes in spatially constrained populations could lead to incorrect inferences of recent diversifying selection or of population bottlenecks when analyzed using an unconstrained coalescent model as a null hypothesis.