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. 2016 Jan;48(1):94-100.
doi: 10.1038/ng.3464. Epub 2015 Dec 7.

Visualizing Spatial Population Structure With Estimated Effective Migration Surfaces

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Free PMC article

Visualizing Spatial Population Structure With Estimated Effective Migration Surfaces

Desislava Petkova et al. Nat Genet. .
Free PMC article

Abstract

Genetic data often exhibit patterns broadly consistent with 'isolation by distance'-a phenomenon where genetic similarity decays with geographic distance. In a heterogeneous habitat, this may occur more quickly in some regions than in others: for example, barriers to gene flow can accelerate differentiation between neighboring groups. We use the concept of 'effective migration' to model the relationship between genetics and geography. In this paradigm, effective migration is low in regions where genetic similarity decays quickly. We present a method to visualize variation in effective migration across a habitat from geographically indexed genetic data. Our approach uses a population genetic model to relate effective migration rates to expected genetic dissimilarities. We illustrate its potential and limitations using simulations and data from elephant, human and Arabidopsis thaliana populations. The resulting visualizations highlight important spatial features of population structure that are difficult to discern using existing methods for summarizing genetic variation.

Conflict of interest statement

The authors declare no competing financial intersts.

Figures

Figure 1
Figure 1
A schematic overview of EEMS, using African elephant data for illustration. (a–c) Setting up the population grid: (a) Samples are collected at known locations across a two-dimensional habitat; green and orange colors represent two subspecies – forest and savanna elephants. (b) A dense triangular grid is chosen to span the habitat. (c) Each sample is assigned to the closest deme on the grid. (d–f) Estimated Effective Migration Surface (EEMS) analysis: (d) Migration rates vary according to a Voronoi tessellation which partitions the habitat into “cells” with constant migration rate; colors represent relative rates of migration, ranging from low (orange) to high (blue). (e) Each edge has the same migration rate as the cell it falls into. The cell locations and migration rates are adjusted, using Bayesian inference, so that the expected genetic dissimilarities under the EEMS model matches the observed genetic dissimilarities. (f) The EEMS is a color contour plot produced by averaging draws from the posterior distribution of the migration rates, interpolating between grid points. Here, and in all other figures, log(m) denotes the effective migration rate on the log10 scale, relative to the overall migration rate across the habitat. (Thus log(m) = 1 corresponds to effective migration that is 10-fold faster than the average.) The main feature of the elephant EEMS is a “barrier” of low effective migration that separates the habitats of the two subspecies: forest elephants to the west, and savanna elephants to the north, south and east.
Figure 2
Figure 2
Simulation comparing EEMS and PCA analysis. For each method, we show results for two migration scenarios, representing “uniform” migration and a “barrier” to migration, and three different sampling schemes. (a,b) The true underlying migration rates under the two scenarios; colors represent relative migration rates. (c) The three sampling schemes used; the size of the circle at each node is proportional to the number of individuals sampled at that location, and locations are color-coded to facilitate cross-referencing the EEMS and PCA results. (d) PCA results. (e) EEMS results. In contrast to PCA, EEMS is robust to the sampling scheme and shows clear qualitative differences between the estimated effective migration rates under the two scenarios, which reflect the underlying simulation truth.
Figure 3
Figure 3
Simulations illustrate that EEMS infers effective migration rates, rather than actual steady-state migration rates. (a) Individuals have uniform migration rates but the central area has lower population density (those demes have fewer individuals, which is represented by smaller circles in gray). Thus fewer migrants are exchanged per generation in the central area, producing an effective barrier to gene flow that is reflected in the EEMS. (b) A simple “population split” scenario: migration is initially uniform, but at some time in the past a complete barrier to migration arises in the central area (represented by dashed edges). Under this scenario the groups on either side of the central region diverge, which creates a barrier in the EEMS.
Figure 4
Figure 4
EEMS analysis of African elephant data . (a) African elephant samples are collected from two subspecies in five biogeographic regions: the forest elephant subspecies (in green) inhabits the west and central regions; the savanna elephant subspecies (in orange) inhabits the north, east and south regions. (b) Estimated effective migration rates for forest and savanna samples analyzed jointly. (c,d) Estimated effective migration rates for savanna and forest, respectively.
Figure 5
Figure 5
EEMS analysis of human population structure in Western Europe and in Sub-Saharan Africa. (a) Effective migration rates in Western Europe, estimated using geo-referenced data from the POPRES project . (b) Effective migration rates in Sub-Saharan Africa, estimated using geo-referenced data from two previously published studies , .
Figure 6
Figure 6
EEMS analysis of Arabidopsis thaliana data from the RegMap project : (a) Estimated effective migration rates in North America, Europe and across the Atlantic Ocean; (b) Estimated effective migration rates in North America; (c) Estimated effective migration rates in Europe.

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