Statistical inference of correlated evolution between macroecological variables using phylogenetic eigenvector regression

Abstract

In this paper, a recently developed method for comparative data analysis, called phylogenetic eigenvector regression (PVR), was applied to macroecological data of five groups of mammals and birds from South America. In these data sets, the relationship between geographic range size and body length was functional or generated a constraint envelope in the bivariate space, in which minimum geographic range size increased with body length. Using the PVR, eigenvectors were extracted from the double-centered phylogenetic distance matrix, derived from phylogenies based on different sources. These eigenvectors were used as predictors in a multiple regression in which the response variables were body length and geographic range size. Body size usually displayed significant phylogenetic inertia, measured by the coefficient of determination (R2) of the PVR regression model. The partial correlation between these two variables, after controlling for phylogenetic eigenvectors, varied in the different groups. Only for the primate data set, with 50 species, the correlation disappeared after controlling phylogenetic inertia in both variables. For the owl data set (29 species), the constraint envelope was transformed in a significant functional relationship after using the PVR. One thousand simulations assuming a Brownian motion pattern of phenotypic evolution, with a parametric correlation of input equal to zero, permitted to calculate the true Type I error of the method at 5% as being around 10% for most data sets. This was considered to be satisfactory in comparison with other methods, specially with the non phylogenetic standard correlation (TIPS). Power curves of PVR were also estimated for all data sets, using 5000 simulations with input correlations ranging from 0.20 to 0.95, and indicated a relatively low statistical power when samples sizes are smaller than 25 species. In general, the PVR method works fine with macroecological data and the results supported the importance of controlling for phylogenetic patterns before using ecological or evolutionary mechanisms to explain geographic range size - body size relationships.