MODELING BRAIN EVOLUTION FROM BEHAVIOR - A PERMUTATIONAL REGRESSION APPROACH

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 understan d the computation method, consider that the dependent matrix is unfold ed as a vector y; similarly, consider X to be a table containing the i ndependent matrices, also unfolded as vectors. A multiple regression i s computed to express y as a function of X. The parameters of this reg ression (R(2) and partial regression coefficients) are tested by permu tations, as follows. When the dependent matrix variable y represents a simple distance or similarity matrix, permutations are performed in t he same manner as the Mantel permutational test. When it is an ultrame tric matrix representing a dendrogram, we use the double-permutation m ethod (Lapointe and legendre 1990, 1991). When it is a path-length mat rix representing an additive tree (cladogram), we use the triple-permu tation method (Lapointe and Legendre 1992). The independent matrix var iables in X are kept fixed with respect to one another during the perm utations. Selection of predictors can be accomplished by forward selec tion, backward elimination, or a stepwise procedure. A phylogenetic tr ee, derived from marsupial brain morphology data (28 species), is comp ared to trees depicting the evolution of diet, sociability, locomotion , and habitat in these animals, as well as their taxonomy and geograph ical relationships. A model is derived in which brain evolution can be predicted from taxonomy, diet, sociability and locomotion (R(2) = 0.7 5). A new tree, derived from the ''predicted'' data, shows a lot of si milarity to the brain evolution tree. The meaning of the taxonomy, die t, sociability, and locomotion predictors are discussed and conclusion s are drawn about the evolution of brain and behavior in marsupials.