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A new eigenfunction spatial analysis describing population genetic structure

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Abstract

Several methods of spatial analyses have been proposed to infer the relative importance of evolutionary processes on genetic population structure. Here we show how a new eigenfunction spatial analysis can be used to model spatial patterns in genetic data. Considering a sample of n local populations, the method starts by modeling the response variable (allele frequencies or phenotypic variation) against the eigenvectors sequentially extracted from a geographic distance matrix (n × n). The relationship between the coefficient of determination (R 2) of the models and the cumulative eigenvalues, which we named the spatial signal-representation (SSR) curve, can be more efficient than Moran’s I correlograms in describing different patterns. The SSR curve was also applied to simulated data (under distinct scenarios of population differentiation) and to analyze spatial patterns in alleles from microsatellite data for 25 local populations of Dipteryx alata, a tree species endemic to the Brazilian Cerrado. The SSR curves are consistent with previous phylogeographical patterns of the species, revealing combined effects of isolation-by-distance and range expansion. Our analyses demonstrate that the SSR curve is a useful exploratory tool for describing spatial patterns of genetic variability and for selecting spatial eigenvectors for models aiming to explain spatial responses to environmental variables and landscape features.

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Acknowledgments

We thank Pedro Peres-Neto for several discussions about PSR/SSR curve and Guillaume Guénard for many suggestions that improved early versions of this manuscript. We also thank Thiago Santos for preparing the R-code that is available for analysis. This work was 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 (PRONEX/FAPEG/CNPq CP 07-2009). Field work has been supported by Systema Naturae Consultoria Ambiental LTDA. Work by J.A.F.D.-F., L. M. B., T. F. R., M.P.C.T. and R.G.C. has been continuously supported by productivity fellowships from CNPq.

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Authors and Affiliations

  1. Laboratório de Ecologia Teórica e Síntese, Departamento de Ecologia, Instituto de Ciências Biológica (ICB), Universidade Federal de Goiás (UFG), C.P. 131, Goiânia, GO, 74001-970, Brazil

    José Alexandre Felizola Diniz-Filho, Thiago Fernando Rangel & Luis Mauricio Bini

  2. Graduação em Engenharia da Computação, Universidade Federal de Goiás (UFG), Goiânia, Brazil

    João Vitor Barnez P. L. Diniz

  3. Laboratório de Genética e Biodiversidade, Departamento de Biologia Geral, Instituto de Ciências Biológica (ICB), Universidade Federal de Goiás (UFG), Goiânia, Brazil

    Thannya Nascimento Soares, Mariana Pires de Campos Telles & Rosane Garcia Collevatti

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  1. José Alexandre Felizola Diniz-Filho
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Correspondence to José Alexandre Felizola Diniz-Filho.

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Diniz-Filho, J.A.F., Diniz, J.V.B.P.L., Rangel, T.F. et al. A new eigenfunction spatial analysis describing population genetic structure. Genetica 141, 479–489 (2013). https://doi.org/10.1007/s10709-013-9747-0

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