A new eigenfunction spatial analysis describing population genetic structure.

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.