Quantitative matrix comparisons in ecological and evolutionary investigations

The pair-wise statistical comparison of data matrices is a methodological problem which must be dealt with in a variety of disciplines. In this report we demonstrate an innovative approach using the Mantel test (a nonparametric, multivariate evaluation of test matrices) to quantitatively contrast observed color polymorphisms in male Poecilia reticulata collected from 41 samples sites in Trinidad against four evolutionary models: (1) response to an environmental gradient, (2) localized environmental patches, (3) isolation by distance, and (4) historical factors. To represent these models we derived pair-wise distances between study sites for the following data: (1) altitude, (2) density of predators, and (3) kilometric distances. To represent model four above, we generated an imposed asymptotic distance matrix for geographically contiguous sites, and a Gabriel connectivity matrix for stream-connected sites (e.g. those within the same watershed). We found that differences in color polymorphisms covary significantly with differences in predator densities and in altitudes, suggesting that male color polymorphisms track clinally distributed communities of visually hunting predators. These data substantiate previously published results from field and laboratory experiments. The utility of the Mantel procedure is that it permits a quantitative evaluation of ecological and evolutionary problems which have previously been difficult to approach statistically. © 1982.