Predictions of single-nucleotide polymorphism differentiation between two populations in terms of mutual information RODERICK C. DEWAR,* WILLIAM B. SHERWIN,*† EMMA THOMAS,* CLARE E. HOLLELEY† and RICHARD A. NICHOLS†‡ *Division of Plant Sciences, Research School of Biology, The Australian National University, Canberra, ACT 0200, Australia, †Evolution and Ecology Research Centre, School of Biological Earth and Environmental Science, University of New South Wales, Sydney, NSW 2052, Australia, ‡School of Biological Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK Abstract Mutual information (I) provides a robust measure of genetic differentiation for the purposes of estimating dispersal between populations. At present, however, there is little predictive theory for I. The growing importance in population biology of analyses of single-nucleotide and other single-feature polymorphisms (SFPs) is a potent reason for developing an analytic theory for I with respect to a single locus. This study represents a first step towards such a theory. We present theoretical predictions of I between two populations with respect to a single haploid biallelic locus. Dynamical and steady-state forecasts of I are derived from a Wright–Fisher model with symmetrical mutation between alleles and symmetrical dispersal between populations. Analytical predictions of a simple Taylor approximation to I are in good agreement with numerical simulations of I and with data on I from SFP analyses of dispersal experiments on Drosophila fly populations. The theory presented here also provides a basis for the future inclusion of selection effects and extension to multiallelic loci. Keywords: biodiversity, drift–mutation–dispersal, migration, population genetics, single-nucleo- tide polymorphism, SNP Received 20 January 2011; revision accepted 10 May 2011 Introduction Mutual information as a measure of genetic differentiation between populations Debate continues about the most appropriate measure of biological diversity for various purposes (Jost 2006, 2007, 2009; Sherwin et al. 2006; Heller & Siegismund 2009; Ryman & Leimar 2009; Sherwin 2010). Several cri- teria for a useful measure of diversity have been pro- posed, including: (A) ability to partition diversity in a way that makes intuitive sense, (e.g. when pooling K equally diverse areas with no shared species or alleles, pooled diversity is K times the diversity of each area), (B) no undue sensitivity to rare or common species or alleles and (C) reasonable sensitivity to key processes (e.g. mutation, speciation, dispersal and selection). In genetics, much work has focused on heterozygosity and related measures such as nucleotide diversity. The predictive theory of heterozygosity for isolated popula- tions has proven useful for detecting departures from neutrality in genetics and also in ecology (Hubbell 2001). When populations are partially subdivided with some dispersal between subpopulations, it is useful to have a diversity measure that works universally across all hier- archical levels (cf. criterion A). Wright (1951) defined F ST , which has since been calculated in many ways, but for a pair of populations is a function of the average het- erozygosity in the two populations (H S ) and the hetero- zygosity in the metapopulation (H T ) (Halliburton 2004). This measure of F ST , often denoted by G ST , is Correspondence: Roderick C. Dewar, Fax: +61 2 6125 4919; E-mail: roderick.dewar@anu.edu.au Ó 2011 Blackwell Publishing Ltd Molecular Ecology (2011) 20, 3156–3166 doi: 10.1111/j.1365-294X.2011.05171.x