Abstract
Barriers to gene flow play an important role in structuring populations, especially in human-modified landscapes, and several methods have been proposed to detect such barriers. However, most applications of these methods require a relative large number of individuals or populations distributed in space, connected by vertices from Delaunay or Gabriel networks. Here we show, using both simulated and empirical data, a new application of geographically weighted regression (GWR) to detect such barriers, modeling the genetic variation as a “local” linear function of geographic coordinates (latitude and longitude). In the GWR, standard regression statistics, such as R2 and slopes, are estimated for each sampling unit and thus are mapped. Peaks in these local statistics are then expected close to the barriers if genetic discontinuities exist, capturing a higher rate of population differentiation among neighboring populations. Isolation-by-Distance simulations on a longitudinally warped lattice revealed that higher local slopes from GWR coincide with the barrier detected with Monmonier algorithm. Even with a relatively small effect of the barrier, the power of local GWR in detecting the east–west barriers was higher than 95 %. We also analyzed empirical data of genetic differentiation among tree populations of Dipteryx alata and Eugenia dysenterica Brazilian Cerrado. GWR was applied to the principal coordinate of the pairwise FST matrix based on microsatellite loci. In both simulated and empirical data, the GWR results were consistent with discontinuities detected by Monmonier algorithm, as well as with previous explanations for the spatial patterns of genetic differentiation for the two species. Our analyses reveal how this new application of GWR can viewed as a generalized Wombling in a continuous space and be a useful approach to detect barriers and discontinuities to gene flow.
References
Balkenhol N, Waits LP, Dezzani RJ (2009) Statistical approaches in landscape genetics: an evaluation of methods for linking landscape and genetic data. Ecography 32:818–830
Barbosa ACOF, Collevatti RG, Chaves LJ, Guedes LBS, Diniz-Filho JAF, Telles MPC (2015) Range-wide genetic differentiation of E. dysenterica (Myrtaceae) populations in Brazilian Cerrado. Biochem Syst Ecol 59:288–296
Barbujani G (1987) Autocorrelation of gene frequencies under isolation-by-distance. Genetics 177:772–782
Bocquet-Appel JP, Sokal RR (1989) Spatial autocorrelation analysis of trend residuals in biological data. Syst Zool 38:331–341
Burnham KP, Anderson DR (2002) Model selection and multimodel inference. A practical information—theoretical approach. Springer, New York, p 528
Collevatti RG, Telles MPC, Nabout JC, Chaves LJ, Soares TN (2013) Demographic history and the low genetic diversity in Dipteryx alata (Fabaceae) from Brazilian Neotropical savannas. Heredity 111:97–105
Crida A, Manel S (2007) Wombsoft: an r package that implements the Wombling method to identify genetic boundary. Mol Ecol Notes 7:588–591
Diniz-Filho JAF, Nabout JC, Telles MPC, Soares TN, Rangel TFLVB (2009) A review of techniques for spatial modeling in geographical, conservation and landscape genetics. Genet Mol Biol 32:203–211
Diniz-Filho JAF, Melo DB, Oliveira G, Collevatti RG, Soares TN, Nabout JC, Lima JS, Dobrovolski R, Chaves LJ, Naves RV, Telles MPC (2012a) Planning for optimal conservation of geographical genetic variability within species. Conserv Genet 13:1085–1093
Diniz-Filho JAF, Collevatti RG, Soares TN, Telles MPC (2012b) Geographical patterns of turnover and nestedness-resultant components of allelic diversity among populations. Genetica 140:189–195
Diniz-Filho JAF, Diniz JVBPL, Rangel TF, Soares TN, Telles MPC, Collevatti RG, Bini LM (2012c) A new eigenfunction spatial analysis describing population genetic structure. Genetica 141:479–489
Diniz-Filho JAF, Soares TN, Telles MPC (2014) Pattern-oriented modeling of population genetic struture. Biol J Linn Soc 113:1152–1161
Diniz-Filho JAF, Rodrigues H, Telles MPC, Oliveira G, Terribile LC, Soares TN, Nabout JC (2015) Correlation between genetic diversity and environmental suitability: taking uncertainty from ecological niche models into account. Mol Ecol Resour 15:1059–1066
Diniz-Filho JAF, Barbosa ACOF, Collevatti RG, Chaves LJ, Terribile, LC, Lima-Ribeiro MS, Telles MPC (2016) Spatial autocorrelation analysis and ecological niche modelling allows inference of range dynamics driving the population genetic structure of a Neotropical savanna tree. J Biogeogr 43:167–177
Fortin M-J, Dale MRT (2005) Spatial analysis: a guide for ecologists. Cambridge University Press, Cambridge, p 382
Fotheringham AS, Brunsdon C, Charlton M (2002) Geographically weighted regression: the analysis of spatially varying relationships. Wiley, Chichester, p 288
Guillot G, Leblois R, Coulon A, Frantz AC (2009) Statistical methods in spatial genetics. Mol Ecol 18:4734–4756
Holderegger R, Wagner HH (2008) Landscape genetics. Bioscience 58:199–208
Hortal J, Diniz-Filho JAF, Bini LM, Rodriguez MA, Baselga A, Nogués-Bravo D, Rangel TF, Hawkins BA, Lobo JM (2011) Ice age climate, evolutionary constraints and diversity patterns of European dung beetles. Ecol Lett 14:741–748
Legendre P (1993) Spatial autocorrelation: trouble or new paradigm? Ecology 74:1659–1673
Legendre P, Legendre L (2012) Numerical ecology, 3rd edn. Elsevier, Amsterdam 990 pp
Manel S, Holderegger R (2013) Ten years of landscape genetics. Trends Ecol Evol 28:614–621
Manel S, Schwartz MK, Luikart G, Taberlet P (2003) Landscape genetics: combining landscape ecology and population genetics. Trends Ecol Evol 15:189–197
Philibert MD, Fortin M-J, Csillag F (2008) Spatial structure effects on the detection of patches boundaries using local operators. Env Ecol Stat 15:447–467
R Development Core Team (2015) R: a language and environment for statistical computing, reference index version 2.15. R Foundation for statistical computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org
Soares TN, Melo DB, Resende LV, Vianello RP, Chaves LJ, Collevatti RG, Telles MPC (2012) Development of microsatellite markers for the Neotropical tree species Dipteryx alata (Fabacea). Am J Bot 99:72–73
Soares TN, Diniz-Filho JAF, Nabout JC, Telles MPC, Terribile LC, Chaves LJ (2015) Patterns of genetic variability in central and peripheral populations of Dipteryx alata (Fabaceae) in the Brazilian Cerrado. Plant Syst Evol 301:1315–1324
Sokal RR, Oden NL (1978) Spatial autocorrelation in biology. 1. Methodology. Biol J Linn Soc 10:199–228
Storfer A, Murphy MA, Evans JS, Goldberg CS, Robinson S, Spear SF, Dezzani R, Delmelle E, Vierling L, Waits LP (2007) Putting the ‘landscape’ in landscape genetics. Heredity 98:128–142
Telles MPC, Coelho ASG, Chaves LJ, Diniz-Filho JAF, Valva FD (2003) Genetic diversity and population structure of Eugenia dysenterica DC. (“cagaiteira”–Myrtaceae) in Central Brazil: Spatial analysis and implications for conservation and management. Conserv Genet 4:685–695
Wagner HH, Fortin MJ (2013) A conceptual framework for the spatial analysis of landscape genetic data. Conserv Genet 14:253–261
Acknowledgments
We thank Thiago F. Rangel and the students in the Geographical Genetics 2015 graduate course for discussions that allowed me to propose this new approach. Our research program integrating macroecology and molecular ecology of plants has been continuously supported by several grants and fellowships to the research network GENPAC (Geographical Genetics and Regional Planning for natural resources in Brazilian Cerrado) from CNPq/MCT/CAPES (projects # 564717/2010-0 and 563624/2010-8) and by the “Núcleo de Excelência em Genética e Conservação de Espécies do Cerrado” (GECER) and the Núcleo de excelência em recursos genéticos vegetais do Cerrado (CERGEN) (PRONEX/FAPEG/CNPq CP 07-2009 and 07-2012). Field work has been supported by Systema Naturae Consultoria Ambiental LTDA. Work by the three authors have been continuously supported by productivity fellowships from CNPq.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Diniz-Filho, J.A.F., Soares, T.N. & de Campos Telles, M.P. Geographically weighted regression as a generalized Wombling to detect barriers to gene flow. Genetica 144, 425–433 (2016). https://doi.org/10.1007/s10709-016-9911-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10709-016-9911-4