Spatial pattern and genetic diversity estimates are linked in stochastic models of population differentiation

In the present study, we used both simulations and real data set analyses to show that, under stochastic processes of population differentiation, the concepts of spatial heterogeneity and spatial pattern overlap. In these processes, the proportion of variation among and within a population (measured by GST and 1 GST, respectively) is correlated with the slope and intercept of a Mantel’s test relating genetic and geographic distances. Beyond the conceptual interest, the inspection of the relationship between population heterogeneity and spatial pattern can be used to test departures from stochasticity in the study of population differentiation. Departamento de Biologia Geral, ICB, Universidade Federal de Goiás. Caixa Postal 131, 74001-970 Goiânia, GO, Brasil. Send correspondence to J.A.F.D.-F. E-mail: [email protected] Mestrado em Agronomia, Genética e Melhoramento de Plantas, Escola de Agronomia, Universidade Federal de Goiás, Goiânia, GO, Brasil. 542 Diniz-Filho and Telles the GSTRUN program. For each data set, we also performed a Mantel’s test (Smouse et al., 1986; Manly, 1991) comparing Nei’s (1972) pairwise genetic distances between populations with their geographic distances. Since we assume here that genetic divergence is a function of geographic distances, we also estimated the regression parameters of the linear model Nij = a + b Dij + ε where Nij is the Nei’s (1972) genetic distance between populations i and j, Dij is the geographic distance between the same pair of populations and ε is the residual term. The intercept of this matrix regression (a) can be interpreted as the estimated genetic distance when the geographic distance is zero, which should be then related to the proportion of genetic variation within local populations (1 GST). Its slope (b), in turn, must indicate the rate at which genetic divergence increases with geographic distance. We used both model I and II regression estimates of a and b (Sokal and Rohlf, 1995) in the analyses, calculated by the MATREG program. The empirical results for model II regression parameters (assuming that X is also defined with error) are much clearer, and only these will be shown here. This occurred probably because both genetic and geographic distances are estimated with an error related to the definition of patches of genetic similarity caused by the stochastic variation in the simulations. Both programs (GSTRUN and MATREG) were written in Basic language by one of us (J.A.F.D.-F.) especially for the simulation analyses and are available upon request. As predicted, slopes and intercepts of Mantel’s regressions are significantly correlated with the proportion of variation among (GST) and within (1 GST) local populations, respectively (Figure 1). These linear patterns are indeed coherent with simple stochastic processes of geFigure 1 Relationship between slope (A) and intercept (B) of the matrix regression of Nei’s (1972) genetic distances against geographic distances with the estimated proportion of variation among (GST) and within (1 GST) local populations, for 50 simulated data matrices. A