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.
At a glance
- Worldwide human relationships inferred from genome-wide patterns of variation. Science 319, 1100–1104 (2008). et al.
- Reconstructing Indian population history. Nature 461, 489–494 (2009). , , , &
- Identifying adaptive genetic divergence among populations from genome scans. Mol. Ecol. 13, 969–980 (2004). &
- A new approach to estimate parameters of speciation models with application to apes. Genome Res. 17, 1505–1519 (2007). &
- Genome-wide patterns of gene flow across a house mouse hybrid zone. Genome Res. 18, 67–76 (2008). et al.
- Multilocus analyses of admixture and introgression among hybridizing Heliconius butterflies. Evolution 60, 1254–1268 (2006). , , &
- The landscape of recombination in African Americans. Nature 476, 170–175 (2011). et al.
- Evidence from Cameroon reveals differences in the genetic structure and histories of chimpanzee populations. Proc. Natl. Acad. Sci. USA 108, 4766–4771 (2011). et al.
- Assigning African elephant DNA to geographic region of origin: applications to the ivory trade. Proc. Natl. Acad. Sci. USA 101, 14847–14852 (2004). et al.
- A model-based approach for analysis of spatial structure in genetic data. Nat. Genet. 44, 725–731 (2012). , , &
- Demonstrating stratification in a European American population. Nat. Genet. 37, 868–872 (2005). et al.
- New approaches to population stratification in genome-wide association studies. Nat. Rev. Genet. 11, 459–463 (2010). , , &
- Inference of population structure using multilocus genotype data. Genetics 155, 945–959 (2000). , &
- A spatial statistical model for landscape genetics. Genetics 170, 1261–1280 (2005). , , &
- Principal components analysis corrects for stratification in genome-wide association studies. Nat. Genet. 38, 904–909 (2006). et al.
- Population structure and eigenanalysis. PLoS Genet. 2, e190 (2006). , &
- Genetic differentiation and estimation of gene flow from F-statistics under isolation by distance. Genetics 145, 1219–1228 (1997).
- Genes mirror geography within Europe. Nature 456, 98–101 (2008). et al.
- Interpreting principal component analyses of spatial population genetic variation. Nat. Genet. 40, 646–649 (2008). &
- A genealogical interpretation of principal components analysis. PLoS Genet. 5, e1000686 (2009).
- Geographic sampling scheme as a determinant of the major axis of genetic variation in principal components analysis. Mol. Biol. Evol. 30, 480–488 (2013). &
- Geographic patterns of (genetic, morphologic, linguistic) variation: how barriers can be detected by using Monmonier's algorithm. Hum. Biol. 76, 173–190 (2004). , &
- A new individual-based spatial approach for identifying genetic discontinuities in natural populations. Mol. Ecol. 16, 2031–2043 (2007). et al.
- Nonstationary patterns of isolation-by-distance: inferring measures of local genetic differentiation with Bayesian kriging. Evolution 68, 1110–1123 (2014). &
- Maximum likelihood estimation of a migration matrix and effective population sizes in n subpopulations by using a coalescent approach. Proc. Natl. Acad. Sci. USA 98, 4563–4568 (2001). &
- Isolation by resistance. Evolution 60, 1551–1561 (2006).
- Circuit theory and model-based inference for landscape connectivity. J. Am. Stat. Assoc. 108, 22–33 (2013). &
- The stepping stone model of population structure and the decrease of genetic correlation with distance. Genetics 49, 561–576 (1964). &
- Generating samples under a Wright-Fisher neutral model of genetic variation. Bioinformatics 18, 337–338 (2002).
- Genetic assignment of large seizures of elephant ivory reveals Africa's major poaching hotspots. Science 349, 84–87 (2015). et al.
- Evaluating loci for use in the genetic analysis of population structure. Proc. R. Soc. Lond. B 263, 1619–1626 (1996). &
- Structure and history of African elephant populations: I. eastern and southern Africa. J. Hered. 85, 100–104 (1994). et al.
- Patterns of molecular genetic variation among African elephant populations. Mol. Ecol. 11, 2489–2498 (2002). et al.
- The Population Reference Sample, POPRES: a resource for population, disease, and pharmacological genetics research. Am. J. Hum. Genet. 83, 347–358 (2008). et al.
- Toward a more uniform sampling of human genetic diversity: a survey of worldwide populations by high-density genotyping. Genomics 96, 199–210 (2010). et al.
- Hunter-gatherer genomic diversity suggests a southern African origin for modern humans. Proc. Natl. Acad. Sci. USA 108, 5154–5162 (2011). et al.
- A quantitative comparison of the similarity between genes and geography in worldwide human populations. PLoS Genet. 8, e1002886 (2012). , &
- Correlation between genetic and geographic structure in Europe. Curr. Biol. 18, 1241–1248 (2008). et al.
- Analysis and application of European genetic substructure using 300 K SNP information. PLoS Genet. 4, e4 (2008). et al.
- The pattern of polymorphism in Arabidopsis thaliana. PLoS Biol. 3, e196 (2005). et al.
- The scale of population structure in Arabidopsis thaliana. PLoS Genet. 6, e1000843 (2010). et al.
- Genome-wide patterns of genetic variation in worldwide Arabidopsis thaliana accessions from the RegMap panel. Nat. Genet. 44, 212–216 (2012). et al.
- A synopsis of Arabidopsis (Brassicaceae). Novon 7, 323–327 (1997). &
- Using circuit theory to model connectivity in ecology, evolution, and conservation. Ecology 89, 2712–2724 (2008). , , &
- A pain in the torus: some difficulties with models of isolation by distance. Am. Nat. 109, 359–368 (1975).
- Inference of population structure using dense haplotype data. PLoS Genet. 8, e1002453 (2012). , , &
- Differential confounding of rare and common variants in spatially structured populations. Nat. Genet. 44, 243–246 (2012). &
- Phylogenetic analysis. Models and estimation procedures. Am. J. Hum. Genet. 19, 233–257 (1967). &
- Maximum-likelihood estimation of evolutionary trees from continuous characters. Am. J. Hum. Genet. 25, 471–492 (1973).
- The neighbor-joining method: a new method for reconstructing phylogenetic trees. Mol. Biol. Evol. 4, 406–425 (1987). &
- Inference of population splits and mixtures from genome-wide allele frequency data. PLoS Genet. 8, e1002967 (2012). &
- Marginal likelihood for distance matrices. Stat. Sin. 19, 631–649 (2009).
- Coalescence time for two genes from a subdivided population. J. Math. Biol. 43, 397–410 (2001). &
- A multi-dimensional coalescent process applied to multi-allelic selection models and migration models. Theor. Popul. Biol. 39, 30–48 (1991).
- Resistance distance. J. Math. Chem. 12, 81–95 (1993). &
- Resistance-distance matrix: a computational algorithm and its application. Int. J. Quantum Chem. 90, 166–176 (2002). , , , &
- The end of the rainbow? Color schemes for improved data graphics. Eos 85, 385 (2004). &
- Supplementary Text and Figures (11,060 KB)
Supplementary Figures 1–17 and Supplementary Note.