Recent advances in sequencing allow population-genomic data to be generated for virtually any species. However, approaches to analyse such data lag behind the ability to generate it, particularly in nonmodel species. Linkage disequilibrium (LD, the nonrandom association of alleles from different loci) is a highly sensitive indicator of many evolutionary phenomena including chromosomal inversions, local adaptation and geographical structure. Here, we present linkage disequilibrium network analysis (LDna), which accesses information on LD shared between multiple loci genomewide. In LD networks, vertices represent loci, and connections between vertices represent the LD between them. We analysed such networks in two test cases: a new restriction-site-associated DNA sequence (RAD-seq) data set for Anopheles baimaii, a Southeast Asian malaria vector; and a well-characterized single nucleotide polymorphism (SNP) data set from 21 three-spined stickleback individuals. In each case, we readily identified five distinct LD network clusters (single-outlier clusters, SOCs), each comprising many loci connected by high LD. In A. baimaii, further population-genetic analyses supported the inference that each SOC corresponds to a large inversion, consistent with previous cytological studies. For sticklebacks, we inferred that each SOC was associated with a distinct evolutionary phenomenon: two chromosomal inversions, local adaptation, population-demographic history and geographic structure. LDna is thus a useful exploratory tool, able to give a global overview of LD associated with diverse evolutionary phenomena and identify loci potentially involved. LDna does not require a linkage map or reference genome, so it is applicable to any population-genomic data set, making it especially valuable for nonmodel species.

Computational and Evolutionary Biology Faculty of Life Sciences University of Manchester Manchester UK

Department of Medical Research Medical Entomology Research Division 5 Ziwaka Road Dagon P O Yangon 11191 Myanmar

Department of Parasitology Faculty of Medicine Chiang Mai University Chiang Mai 50200 Thailand

Institute of Vertebrate Biology Academy of Sciences of the Czech Republic Brno Czech Republic

Regional Medical Research Centre NE Dibrugarh 786 001 India

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Andrew RL, Bernatchez L, Bonin A, et al. A road map for molecular ecology. Molecular Ecology. 2013;22:2605–2626. PubMed

Ardlie KG, Kruglyak L, Seielstad M. Patterns of linkage disequilibrium in the human genome. Nature Reviews Genetics. 2002;3:299–309. PubMed

Baimai V, Poopittayasataporn A, Kijchalao U. Cytological differences and chromosomal rearrangements in four members of the Anopheles dirus complex (Diptera: Culicidae) Genome. 1988a;30:372–379. PubMed

Baimai V, Thu MM, Paing M. Distribution and chromosomal polymorphism of the malaria vector Anopheles dirus species D. The Southeast Asian Journal of Tropical Medicine and Public Health. 1988b;19:661–665. PubMed

Barton NH. Estimating linkage disequilibria. Heredity. 2011;106:205–206. PubMed PMC

Barton NH, Briggs D, Eisen JA, Goldstein DB. Evolution. Cold Spring Harbor, New York: Cold spring harbor laboratory press; 2007.

Bolshakov VN. A comparative genomic analysis of two distant Diptera, the fruit fly, Drosophila melanogaster, and the Malaria Mosquito, Anopheles gambiae. Genome Research. 2002;12:57–66. PubMed PMC

Colosimo PF, Hosemann KE, Balabhadra S, et al. Widespread parallel evolution in sticklebacks by repeated fixation of Ectodysplasin alleles. Science. 2005;307:1928–1933. PubMed

Conrad DF, Jakobsson M, Coop G, et al. A worldwide survey of haplotype variation and linkage disequilibrium in the human genome. Nature Genetics. 2006;38:1251–1260. PubMed

Corbett-Detig RB, Cardeno C, Langley CH. Sequence-based detection and breakpoint assembly of polymorphic inversions. Genetics. 2012;192:131–137. PubMed PMC

Csardi G, Nepusz T. The igraph software package for complex network research. InterJournal, Complex Systems. 2006;1695 http://cran.r-project.org/web/packages/igraph/citation.html.

Davey JW, Hohenlohe PA, Etter PD, et al. Genome-wide genetic marker discovery and genotyping using next-generation sequencing. Nature Reviews Genetics. 2011;12:499–510. PubMed

Davey JW, Cezard T, Fuentes-Utrilla P, et al. Special features of RAD Sequencing data: implications for genotyping. Molecular Ecology. 2013;22:3151–3164. PubMed PMC

Excoffier L, Foll M. fastsimcoal: a continuous-time coalescent simulator of genomic diversity under arbitrarily complex evolutionary scenarios. Bioinformatics (Oxford, England) 2011;27:1332–1334. PubMed

Excoffier L, Dupanloup I, Huerta-Sánchez E, Sousa VC, Foll M. Robust demographic inference from genomic and SNP data. PLoS Genetics. 2013;9:e1003905. PubMed PMC

Falush D, Stephens M, Pritchard JK. Inference of population structure using multilocus genotype data: linked loci and correlated allele frequencies. Genetics. 2003;164:1567–1587. PubMed PMC

Falush D, Stephens M, Pritchard JK. Inference of population structure using multilocus genotype data: dominant markers and null alleles. Molecular Ecology Notes. 2007;7:574–578. PubMed PMC

Fisher CM, Foll M, Excoffier L, Heckel G. Enhanced AFLP genome scans detect local adaptation in high-altitude populations of a small rodent (Microtus arvalis. Molecular Ecology. 2011;20:1450–1462. PubMed

Foote AD, Similä T, Víkingsson GA, Stevick PT. Movement, site fidelity and connectivity in a top marine predator, the killer whale. Evolutionary Ecology. 2009;24:803–814.

Gaggiotti OE, Bekkevold D, Jørgensen HBH, et al. Disentangling the effects of evolutionary, demographic, and environmental factors influencing genetic structure of natural populations: Atlantic herring as a case study. Evolution. 2009;63:2939–2951. PubMed

Gray MM, Granka JM, Bustamante CD, et al. Linkage disequilibrium and demographic history of wild and domestic canids. Genetics. 2009;181:1493–1505. PubMed PMC

Hill WG, Robertson A. Linkage disequilibrium in finite populations. TAG. Theoretical and Applied Genetics. Theoretische und angewandte Genetik. 1968;38:226–231. PubMed

Hoffmann AA, Rieseberg LH. Revisiting the impact of inversions in evolution: from population genetic markers to drivers of adaptive shifts and speciation? Annual Review of Ecology, Evolution, and Systematics. 2008;39:21–42. PubMed PMC

Hohenlohe PA, Bassham S, Currey M, Cresko WA. Extensive linkage disequilibrium and parallel adaptive divergence across threespine stickleback genomes. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences. 2012;367:395–408. PubMed PMC

International HapMap Consortium. A haplotype map of the human genome. Nature. 2005;437:1299–1320. PubMed PMC

Jombart T, Ahmed I. adegenet 1.3-1: new tools for the analysis of genome-wide SNP data. Bioinformatics (Oxford, England) 2011;27:3070–3071. PubMed PMC

Jones FC, Grabherr MG, Chan YF, et al. The genomic basis of adaptive evolution in threespine sticklebacks. Nature. 2012;484:55–61. PubMed PMC

Kent WJ. BLAT–the BLAST-like alignment tool. Genome Research. 2002;12:656–664. PubMed PMC

Kim S, Plagnol V, Hu TT, et al. Recombination and linkage disequilibrium in Arabidopsis thaliana. Nature Genetics. 2007;39:1151–1155. PubMed

Kim Y, Feng S, Zeng Z-B. Measuring and partitioning the high-order linkage disequilibrium by multiple order Markov chains. Genetic Epidemiology. 2008;32:301–312. PubMed

Kirkpatrick M, Barton N. Chromosome inversions, local adaptation and speciation. Genetics. 2006;173:419–434. PubMed PMC

Knight CG, Pinney JW. Making the right connections: biological networks in the light of evolution. BioEssays: News and Reviews in Molecular, Cellular and Developmental Biology. 2009;31:1080–1090. PubMed PMC

Koch E, Ristroph M, Kirkpatrick M. Long range linkage disequilibrium across the human genome. PLoS One. 2013;8:e80754. PubMed PMC

Kumasaka N, Nakamura Y, Kamatani N. The textile plot: a new linkage disequilibrium display of multiple-single nucleotide polymorphism genotype data. PLoS One. 2010;5:e10207. PubMed PMC

Lawson DJ, Hellenthal G, Myers S, Falush D. Inference of population structure using dense haplotype data. PLoS Genetics. 2012;8:e1002453. PubMed PMC

Leskovec J, Lang KJ, Dasgupta A, Mahoney MW. Community structure in large networks: natural cluster sizes and the absence of large well-defined clusters. Internet Mathematics. 2009;6:29–123.

Lowry DB, Willis JH. A widespread chromosomal inversion polymorphism contributes to a major life-history transition, local adaptation, and reproductive isolation. PLoS Biology. 2010;8:e1000500. PubMed PMC

Maniatis N. The first linkage disequilibrium (LD) maps: delineation of hot and cold blocks by diplotype analysis. Proceedings of the National Academy of Sciences of the USA. 2002;99:2228–2233. PubMed PMC

Marbach D, Prill RJ, Schaffter T, et al. Revealing strengths and weaknesses of methods for gene network inference. Proceedings of the National Academy of Sciences of the USA. 2010;107:6286–6291. PubMed PMC

Mason O, Verwoerd M. Graph theory and networks in Biology. IET Systems Biology. 2007;1:89–119. PubMed

Morgan K, Linton Y-M, Somboon P, et al. Inter-specific gene flow dynamics during the Pleistocene-dated speciation of forest-dependent mosquitoes in Southeast Asia. Molecular Ecology. 2010;19:2269–2285. PubMed

Narum SR, Buerkle CA, Davey JW, Miller MR, Hohenlohe PA. Genotyping-by-sequencing in ecological and conservation genomics. Molecular Ecology. 2013;22:2841–2847. PubMed PMC

Newman MEJ, Girvan M. Finding and evaluating community structure in networks. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics. 2004;69:026113. PubMed

Noor MAF, Bennett SM. Islands of speciation or mirages in the desert? Examining the role of restricted recombination in maintaining species. Heredity. 2009;103:439–444. PubMed PMC

Obsomer V, Defourny P, Coosemans M. Predicted distribution of major malaria vectors belonging to the Anopheles dirus complex in Asia: ecological niche and environmental influences. PLoS One. 2012;7:e50475. PubMed PMC

Poopittayasataporn A, Baimai V. Polytene chromosome relationships of five species of the Anopheles dirus complex in Thailand. Genome. 1995;38:426–434. PubMed

R Core Team. A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing; 2014.

Ralph P, Coop G. The geography of recent genetic ancestry across Europe. PLoS Biology. 2013;11:e1001555. PubMed PMC

Rieseberg LH. Chromosomal rearrangements and speciation. Trends in Ecology & Evolution. 2001;16:351–358. PubMed

Sabeti PC, Varilly P, Fry B, et al. Genome-wide detection and characterization of positive selection in human populations. Nature. 2007;449:913–918. PubMed PMC

Sarma DK, Prakash A, O'Loughlin SM, et al. Genetic population structure of the malaria vector Anopheles baimaii in north-east India using mitochondrial DNA. Malaria Journal. 2012;11:76. PubMed PMC

Schumer M, Cui R, Powell D, et al. High-resolution mapping reveals hundreds of genetic incompatibilities in hybridizing fish species. eLife. 2014 doi: 10.7554/eLife.02535. PubMed DOI PMC

Seeb JE, Carvalho G, Hauser L, et al. Single-nucleotide polymorphism (SNP) discovery and applications of SNP genotyping in nonmodel organisms. Molecular Ecology Resources. 2011;11:1–8. PubMed

Sinka ME, Bangs MJ, Manguin S, et al. The dominant Anopheles vectors of human malaria in the Asia-Pacific region: occurrence data, distribution maps and bionomic précis. Parasites & Vectors. 2011;4:89. PubMed PMC

Slate J, Pemberton JM. Admixture and patterns of linkage disequilibrium in a free-living vertebrate population. Journal of Evolutionary Biology. 2007;20:1415–1427. PubMed

Slatkin M. Linkage disequilibrium—understanding the evolutionary past and mapping the medical future. Nature Reviews Genetics. 2008;9:477–485. PubMed PMC

Tang X, Szinay D, Lang C, et al. Cross-species bacterial artificial chromosome-fluorescence in situ hybridization painting of the tomato and potato chromosome 6 reveals undescribed chromosomal rearrangements. Genetics. 2008;180:1319–1328. PubMed PMC

Via S. Divergence hitchhiking and the spread of genomic isolation during ecological speciation-with-gene-flow. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences. 2011;367:451–460. PubMed PMC

Voight BF, Kudaravalli S, Wen X, Pritchard JK. A map of recent positive selection in the human genome. PLoS Biology. 2006;4:e72. PubMed PMC

Warnes G, Gorjanc WCFG, Leisch F, Man M. 2013. The genetics package. R package version 1.3.8.1. Available from http://CRAN.R-project.org/package=genetics.

Wilson JF, Goldstein DB. Consistent long-range linkage disequilibrium generated by admixture in a Bantu-Semitic hybrid population. American Journal of Human Genetics. 2000;67:926–935. PubMed PMC