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Geographically weighted regression as a generalized Wombling to detect barriers to gene flow

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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.

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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.

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Correspondence to José Alexandre Felizola Diniz-Filho.

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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

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  • DOI: https://doi.org/10.1007/s10709-016-9911-4

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