An Eigenvector Method for Estimating Phylogenetic Inertia

Abstract

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.

Bird species in Mediterranean pine plantations exhibit different characteristics to those in natural reforested woodlands

“…Therefore, the effect of common ancestry among taxa can lead to an overestimation of degrees of freedom if phylogenetic relationships are not taken into account. We used phylogenetic eigenvector regression (PVR) to quantify the amount of phylogenetic signal and to correct for it in the analysis of the relationship between bird density and ecological, morphological and life-history traits (Diniz-Filho et al 1998). Diniz-Filho and Torres (2002) and Martins et al (2002) tested several comparative methods (Felsenstein's independent contrasts, autoregressive method, PVR, and phylogenetic generalised least squares) and found that PVR yields good statistical performance regardless of the details of the evolutionary mode used to generate the data, and provides similar results to other methods, with very good (i.e., low) type I and II errors.…”

“…In a second step we selected the first ten eigenvectors to account parsimoniously for the phylogenetic signal. Eigenvectors extracted from double-centred phylogenetic distance matrices are able to detect the main topological features of the cladogram under different sample sizes or numbers of taxa used in the analyses (Diniz-Filho et al 1998). We found that the original matrix of phylogenetic distances between the 44 bird species and the reproduced matrix of distances estimated based on the first ten eigenvectors were very similar (Mantel test with 999 randomised matrices to estimate significance: r = 0.920, P \ 0.001; test carried out using PopTools 3.1; Hood 2009).…”

A Comparative Analysis of Viral Richness and Viral Sharing in Cave-Roosting Bats

“…From the IUCN spatial shapefiles, we calculated geographic range size (log 10 km 2 ) and sympatric viral host species (i.e., count of bat species in both main and stringent virus databases that have overlapping spatial ranges) with the rgeos package in R. Species body mass was extracted from PanTHERIA [45]. As more closely related species will have similar body mass due to shared evolutionary history, we controlled for this by calculating the residuals from a phylogenetic eigenvector regression (PVR) on body mass [46,47]. As described in Olival et al [11], we calculated PVR for body mass using the R package PVR and a pruned mammalian supertree that only included bat species in our viral database [48,49].…”

Bird population declines due to radiation exposure at Chernobyl are stronger in species with pheomelanin-based coloration

“…In a second step, we selected the first nine eigenvectors obtained by the broken-stick rule as the most parsimonious accounting of the phylogenetic signal. Eigenvectors extracted from double-centred phylogenetic distance matrices are able to detect the main topological features of the cladogram under different sample sizes or number of taxa used in the analyses (Diniz-Filho et al 1998). We found that the original matrix of phylogenetic distances between the 97 bird species and the reproduced matrix of distances estimated based on the first nine eigenvectors were very similar (Mantel test with 999 randomised matrices to estimate significance: r = 0.840, P \ 0.0001; test carried out using PopTools 3.2.3; Hood 2010).…”

“…Thus, the effect of common ancestry among taxa can lead to an overestimation of degrees of freedom if phylogenetic relationships are not taken into account. We used phylogenetic eigenvector regression (PVR) to quantify the amount of phylogenetic signal and to correct for it in the analysis of the relationship between the expression of melanin-based coloration and bird responses to radiation levels (Diniz-Filho et al 1998). Diniz-Filho and Torres (2002) and Martins et al (2002) have tested several comparative methods (Felsenstein's independent contrasts, autoregressive method, PVR, and phylogenetic generalised least squares) and have found that PVR yields good statistical performance regardless of the details of the evolutionary mode used to generate the data and provides similar results to other methods, with very good (i.e.…”