Are populations like a circuit? The relationship between isolation by distance and isolation by resistance

Abstract

A number of methods commonly used in landscape genetics use an analogy to electrical resistance on a network to describe and fit barriers to movement across the landscape using genetic distance data. These are motivated by a mathematical equivalence between electrical resistance between two nodes of a network and the \"commute time\", which is the mean time for a random walk on that network to leave one node, visit the other, and return. However, genetic data are more accurately modeled by a different quantity, the coalescence time. Here, we describe the differences between resistance distance and coalescence time, and explore the consequences for inference. We implement a Bayesian method to infer effective movement rates and population sizes under both these models, and find that inference using commute times can produce misleading results in the presence of biased gene flow. We then use forwards-time simulation with continuous geography to demonstrate that coalescence-based inference remains more accurate than resistance-based methods on realistic data, but difficulties highlight the need for methods that explicitly model continuous, heterogeneous geography.