MODELING BRAIN EVOLUTION FROM BEHAVIOR: A PERMUTATIONAL REGRESSION APPROACH

Abstract

This paper has two complementary purposes: first, to present a method to perform multiple regression on distance matrices, with permutation testing appropriate for path‐length matrices representing evolutionary trees, and then, to apply this method to study the joint evolution of brain, behavior and other characteristics in marsupials. To understand the computation method, consider that the dependent matrix is unfolded as a vector y; similarly, consider X to be a table containing the independent matrices, also unfolded as vectors. A multiple regression is computed to express y as a function of X. The parameters of this regression (R2 and partial regression coefficients) are tested by permutations, as follows. When the dependent matrix variable y represents a simple distance or similarity matrix, permutations are performed in the same manner as the Mantel permutational test. When it is an ultrametric matrix representing a dendrogram, we use the double‐permutation method (Lapointe and Legendre 1990, 1991). When it is a path‐length matrix representing an additive tree (cladogram), we use the triple‐permutation method (Lapointe and Legendre 1992). The independent matrix variables in X are kept fixed with respect to one another during the permutations. Selection of predictors can be accomplished by forward selection, backward elimination, or a stepwise procedure. A phylogenetic tree, derived from marsupial brain morphology data (28 species), is compared to trees depicting the evolution of diet, sociability, locomotion, and habitat in these animals, as well as their taxonomy and geographical relationships. A model is derived in which brain evolution can be predicted from taxonomy, diet, sociability and locomotion (R2 = 0.75). A new tree, derived from the “predicted” data, shows a lot of similarity to the brain evolution tree. The meaning of the taxonomy, diet, sociability, and locomotion predictors are discussed and conclusions are drawn about the evolution of brain and behavior in marsupials.