Are populations like a circuit? Comparing isolation by resistance to a new coalescent‐based method

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 modelled 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 implemented a Bayesian method to infer effective movement rates and population sizes under both these models, and found that inference using commute times could produce misleading results in the presence of biased gene flow. We then used 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.

Isolation by Distance in Populations with Power-law Dispersal

“…Standard methods for dispersal inference typically assume either short-range, diffusive motion [Rousset, 1997, 2000, Robledo-Arnuncio and Rousset, 2010, Ringbauer et al, 2017, Bradburd et al, 2018 (perhaps with recent long-range admixture [Bradburd et al, 2016]) or a small number of discrete demes [Slatkin, 1991, Whitlock and McCauley, 1999, Rousset and Leblois, 2011, Petkova et al, 2016, Al-Asadi et al, 2019, Lundgren and Ralph, 2019. Our results open the way to methods for inferring more general, realistic dispersal patterns.…”

Space is the Place: Effects of Continuous Spatial Structure on Analysis of Population Genetic Data

“…This pattern of "isolation by distance" (Wright 1943) is one of the most widely replicated empirical findings in population genetics (Sharbel et al 2000;Jay et al 2012;Aguillon et al 2017). Despite a long history of analytical work describing the genetics of populations distributed across continuous geography (e.g., Wright 1943;Rousset 1997;Barton et al 2002Barton et al , 2010Wilkins and Wakeley 2002;Wilkins 2004;Ringbauer et al 2017;Robledo-Arnuncio and Rousset 2010), much modern work still describes geographic structure as a set of discrete populations connected by migration (e.g., Wright 1931;Epperson 2003;Rousset and Leblois 2011;Shirk and Cushman 2014;Lundgren and Ralph 2019) or as an average over such discrete models (Petkova et al 2015;Al-Asadi et al 2019). For this reason, most population genetics statistics are interpreted with reference to discrete, well-mixed populations, and most empirical papers analyze variation within clusters of genetic variation inferred by programs like STRUCTURE (Pritchard et al 2000) with methods that assume these are randomly mating units.…”

Fast and flexible estimation of effective migration surfaces

“…Notably, one major difference between EEMS and FEEMS is that in FEEMS each edge weight is assigned its own parameter to be estimated, whereas in EEMS each node is assigned a parameter and each edge is constrained to be the average effective migration between the nodes it connects (see Materials and methods and Appendix 1 ‘ Edge versus node parameterization ’ for details). The node-based parameterization in EEMS makes it difficult to incorporate anisotropy and asymmeteric migration ( Lundgren and Ralph, 2019 ). As we have shown here, FEEMS’s simple and novel parameterization already has potential to fit anisotropic migration (as shown in coalescent simulations) and may be extendable to other more complex migration processes (such as long-range migration, see below).…”

“…Another interesting extension would be to incorporate asymmetric migration into the framework of resistance distance and Gaussian Markov Random Field based models. FEEMS, like EEMS, used a likelihood that is based on resistance distances, which are limited in their ability to model asymmetric migration ( Lundgren and Ralph, 2019 ). Recently, Hanks, 2015 developed a promising new framework for deriving the stationary distribution of a continuous time stochastic process with asymmetric migration on a spatial graph.…”

“…This distance metric is inspired by concepts of effective resistance in circuit theory models, or alternatively understood as the commute time of a random walk on a weighted graph or as a Gaussian graphical model (specifically a conditional auto-regressive process) ( Chandra et al, 1996 ; Hanks and Hooten, 2013 ; Rue and Held, 2005 ). Additionally, the resistance distance approach is a computationally convenient and accurate approximation to spatial coalescent models ( McRae, 2006 ), although it has limitations in asymmetric migration settings ( Lundgren and Ralph, 2019 ).…”