An Eigenvector Method for Estimating Phylogenetic Inertia

Abstract

We propose a new method to estimate and correct for phylogenetic inertia in comparative data analysis. The method, called phylogenetic eigenvector regression (PVR) starts by performing a principal coordinate analysis on a pairwise phylogenetic distance matrix between species. Traits under analysis are regressed on eigenvectors retained by a broken-stick model in such a way that estimated values express phylogenetic trends in data and residuals express independent evolution of each species. This partitioning is similar to that realized by the spatial autoregressive method, but the method proposed here overcomes the problem of low statistical performance that occurs with autoregressive method when phylogenetic correlation is low or when sample size is too small to detect it. Also, PVR is easier to perform with large samples because it is based on well-known techniques of multivariate and regression analyses. We evaluated the performance of PVR and compared it with the autoregressive method using real datasets and simulations. A detailed worked example using body size evolution of Carnivora mammals indicated that phylogenetic inertia in this trait is elevated and similarly estimated by both methods. In this example, Type I error at a = 0.05 of PVR was equal to 0.048, but an increase in the number of eigenvectors used in the regression increases the error. Also, similarity between PVR and the autoregressive method, defined by correlation between their residuals, decreased by overestimating the number of eigenvalues necessary to express the phylogenetic distance matrix. To evaluate the influence of c1adogram topology on the distribution of eigenvalues extracted from the double-centered phylogenetic distance matrix, we analyzed 100 randomly generated c1adograms (up to 100 species). Multiple linear regression of log transformed variables indicated that the number of eigenvalues extracted by the broken-stick model can be fully explained by c1adogram topology. Therefore, the broken-stick model is an adequate criterion for determining the correct number of eigenvectors to be used by PVR. We also simulated distinct levels of phylogenetic inertia by producing a trend across 10, 25, and 50 species arranged in "comblike" c1adograms and then adding random vectors with increased residual variances around this trend. In doing so, we provide an evaluation of the performance of both methods with data generated under different evolutionary models than tested previously. The results showed that both PVR and autoregressive method are efficient in detecting inertia in data when sample size is relatively high (more than 25 species) and when phylogenetic inertia is high. However, PVR is more efficient at smaller sample sizes and when level of phylogenetic inertia is low. These conclusions were also supported by the analysis of 10 real datasets regarding body size evolution in different animal clades. We concluded that PVR can be a useful alternative to an autoregressive method in comparative data analysis.

Refugia and Speciation in North American Scarlet Snakes (Cemophora)

“…This data set describes the phylogeny of carnivora as reported by Diniz-Filho et al (1998). It also gives the body mass of these 19 species.…”

Phylogenetic signal and major ecological shifts in the ecomorphological structure of stream fish in two river basins in Brazil

“…Nonetheless, until recently, most studies did not account for the influence of phylogeny on the ecological similarities among assemblages (Lauder, 1981;Strauss, 1987;Emerson & Gillespie, 2008), most likely because analytical methods were used that assumed the similarity in a given characteristic was due to its independent appearance in each species (Dobson, 1985). Considerable advances in analytical techniques have enabled phylogenetic information to be incorporated into such studies, making it possible to partition the variance into at least two components: (i) the contribution of the phylogenetic history of a species, measured by phylogenetic signal (Losos, 2008); and (ii) the contribution that is unique to each species and reflects adaptation or modification in a structure (Diniz-Filho et al, 1998).Quantifying phylogenetic signal (i.e., the 'tendency for related species to resemble each other more than they resemble species drawn at random from the tree', sensu Blomberg & Garland, 2002) indicates the relationship between the degree of phylogenetic relatedness and the ecological similarity (Losos, 2008). In the context of ecomorphological analysis, the distinction between phylogenetic constraint and local adaptation may be a nonissue, because the phenotype of a species limits the type of environment in which it can survive regardless of its evolutionary conservatism (Ricklefs & Miles, 1994).…”

“…The Phylogenetic Eigenvector Regression (PVR) method (Diniz-Filho et al, 1998) was used to test the effect of phylogeny on the ecomorphological structure of the fish in the two basins. With this approach, the ecomorphological variation explained by the significant PCs is divided into two components: phylogenetic (P), which is the variation inherited from ancestors, and specific (S), which represents the independent variations of each lineage and the independent evolution of each species after speciation events; the correlation between P and S can be interpreted as phylogenetic niche conservatism (Desdevises et al, 2003;Diniz-Filho et al, 2009).The PVR method first uses a Principal Coordinate Analysis (PCoA, see Legendre & Legendre, 1998) to calculate eigenvectors from the species phylogenetic distance matrix (Diniz-Filho et al, 1998). These eigenvectors can be used as predictors in a multiple regression, in which the dependent variable is the species traits (Diniz-Filho et al, 1998).…”

“…The Phylogenetic Eigenvector Regression (PVR) method (Diniz-Filho et al, 1998) was used to test the effect of phylogeny on the ecomorphological structure of the fish in the two basins. With this approach, the ecomorphological variation explained by the significant PCs is divided into two components: phylogenetic (P), which is the variation inherited from ancestors, and specific (S), which represents the independent variations of each lineage and the independent evolution of each species after speciation events; the correlation between P and S can be interpreted as phylogenetic niche conservatism (Desdevises et al, 2003;Diniz-Filho et al, 2009).…”

“…The PVR method first uses a Principal Coordinate Analysis (PCoA, see Legendre & Legendre, 1998) to calculate eigenvectors from the species phylogenetic distance matrix (Diniz-Filho et al, 1998). These eigenvectors can be used as predictors in a multiple regression, in which the dependent variable is the species traits (Diniz-Filho et al, 1998).…”