Orthonormal transform to decompose the variance of a life-history trait across a phylogenetic tree

In recent years, there has been an increased interest in studying the variability of a quantitative life-history trait across a set of species sharing a common phylogeny. However, such studies have suffered from an insufficient development of statistical methods aimed at decomposing the trait variance with respect to the topological structure of the tree. Here we propose a new and generic approach that expresses the topological properties of the phylogenetic tree via an orthonormal basis, which is further used to decompose the trait variance. Such a decomposition provides a structure function, referred to as an "orthogram," which is relevant to characterize in both graphical and statistical aspects the dependence of trait values on the topology of the tree ("phylogenetic dependence"). We also propose four complementary test statistics to be computed from orthogram values that help to diagnose both the intensity and the nature of phylogenetic dependence. The relevance of the method is illustrated by the analysis of three phylogenetic data sets, drawn from the literature and typifying contrasted levels and aspects of phylogenetic dependence. Freely available routines which have been programmed in the R framework are also proposed.     

Assessing phylogenetic dependence of morphological traits using co-inertia prior to investigate character evolution in Loricariinae catfishes

With the increase of laboratory facilities, molecular phylogenies are playing a predominant role in evolutionary analyses. However, understanding the evolution of morphological traits remains essential for a comprehensive view of the evolution of a group. Here we present a new approach based on co-inertia analysis for identifying characters which variations are dependent to the phylogeny, a prerequisite for analyzing the evolution of characters. Our approach has the advantage of treating the full data set at once, including qualitative and quantitative variables. It provides a graphical output giving the contribution of each variable to the co-structure, allowing a direct discrimination among phylogenetically dependent and independent variables. We have implemented this approach in deciphering the evolution of morphological traits in a highly specialized group of Neotropical catfishes: the Loricariinae. We have first inferred a molecular phylogeny of this group based on the 12S and 16S mitochondrial genes. The resulting phylogeny indicated that the subtribe Harttiini was restricted to the single genus Harttia, and within the subtribe Loricariini, two sister subtribes were distinguished, Sturisomina (new subtribe), and Loricariina. Among Loricariina, the morphological groups Loricariichthys and Loricaria+Pseudohemiodon were confirmed. The co-inertia analysis highlighted a strong relationship between the morphological and the genetic data sets, and identified three quantitative and eight qualitative variables linked to the phylogeny. The evolution of quantitative variables was assessed using the orthogram method and showed a major punctual event in the evolution of the number of caudal-fin rays, and a more gradual pattern of evolution of the number of teeth along the phylogeny. The evolution of qualitative variables was inferred using ancestral states reconstructions and highlighted parallel patterns of evolution in characters linked to the mouth, suggesting co-evolution of the traits for adapting to divergent substrates.