Genetic drift on networks: ploidy and the time to fixation

Genetic drift in finite populations ultimately leads to the loss of genetic variation. This paper examines the rate of neutral gene loss for a range of population structures defined by a graph. We show that, where individuals reside at fixed points on an undirected graph with equal degree nodes, the mean time to loss differs from the panmictic value by a positive additive term that depends on the number of individuals (not genes) in the population. The effect of these spatial structures is to slow the time to fixation by an amount that depends on the way individuals are distributed, rather than changing the apparent number of genes available to be sampled. This relationship breaks down, however, for a broad class of spatial structures such as random, small-world and scale-free networks. For the latter structures there is a counter-intuitive acceleration of fixation proportional to the level of ploidy.