Computational protocol: Functional Morphometric Analysis of the Furcula in Mesozoic Birds

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[…] It is widely recognised that the interrelatedness of data points in biological datasets violates assumptions of traditional statistical methods – and can lead to elevated Type I errors . For this reason, phylogenetic comparative methods were favoured over ahistorical tests. All statistical analyses were conducted in R 2.13.1 (CRAN Project, . R FAQ. Available: http://cran.r-project.org/doc/FAQ/R-FAQ.html. Accessed 13 April 2012) using the ape , geiger (CRAN - Package geiger. Available: http://cran.r-project.org/web/packages/geiger/index.html. Accessed 13 April 2012), picante , phytools (CRAN - Package phytools. Available: http://CRAN.R-project.org/package=phytools. Accessed 13 April 2012) and adephylo packages. [...] A composite phylogenetic tree () for use with PCMs was constructed in Mesquite 2.75 (Mesquite. Available: http://mesquiteproject.org. Accessed 13 April 2012). The topology was based at an ordinal level on the mitochondrial study of Hackett et al. , which has recently received support from the retroposon analysis of Suh et al. . Additional phylogenetic studies were consulted to resolve the intra-ordinal relationships not sampled by : Barker et al. for Passeriformes, Livezey for Charadriiformes, and Lerner and Mindell for Falconiformes and Accipitriformes. The topology for our Mesozoic bird dataset was derived from the recent cladistic analysis of O'Connor et al. , while non-avian theropod relationships follow Turner et al. .Because of the composite nature of the phylogeny, branch lengths could not be obtained directly from the aforementioned studies. Several scaling methods were evaluated, including arbitrary methods such as Grafen's (performed using Manabu Sakamoto's unpublished rho.branch() function) and that of Pagel , accomplished using Mesquite 2.54; Blomberg et al.'s Ornstein-Uhlenbeck transform (using the ouTree() function in geiger); and the semi-arbitrary approach of Brusatte et al. that is based on Ruta et al. ; applied using Graeme T. LloydÕs R script for dating phylogenetic trees containing fossil taxa: http://graemetlloyd.com/methdpf.html. Accessed 2011 October 26]. In the latter method, branch lengths are shared equally between dates specified for the root and all terminal nodes; internal node ages are not directly derived from phylogenetic analyses.Ultimately, however, we adopted the more ‘realistic’ approach advocated by Schmitz and Motani , in which internal node ages were assigned using a combination of molecular divergence estimates from TimeTree.org for crown-group birds, and dates estimated by O'Connor et al. for Mesozoic lineages. Divergence dates for non-avian theropods were obtained from . Terminal taxon ages for extinct taxa were defined using fossil ranges, and set to 0 Ma for extant taxa. Where divergence dates were not available (e.g., for splits within families or genera), branch-lengths were shared equally. Assignment of node ages and scaling of branches was performed in R using Gene Hunt's scalePhylo() function using a vector of all node and tip ages (available at https://stat.ethz.ch/pipermail/r-sig-phylo/attachments/20110311/5c0c7568/attachment.obj. Accessed 2011 October 26.)Transformation of branch lengths to conform to Brownian Motion (BM) assumptions was not necessary for either the Phylogenetic Eigenvector Regression, the estimation of Blomberg et al's K (which seek to estimate departure from BM) or the pFDA routine (which corrects for phylogenetic bias). However, as the phylogenetic (M)ANOVA assumes BM character-state evolution, the fitContinuous() function in geiger was used to infer the suitability of this evolutionary model by comparing the second order, or bias-corrected, Akaike Information Criterion (AICc) for a range of fitted models including BM, Ornstein-Uhlenbeck (OU), Early Burst (EB) and white-noise. Because the shape variables were found to depart from BM evolution, branch lengths were transformed using the power.branch() function written by Manabu Sakamoto (pers. comm.) prior to the latter analysis. [...] Several methods were used to detect phylogenetic signal in the morphometric data. Blomberg's K statistic, a measure of phylogenetic autocorrelation developed by Blomberg et al. , was implemented via the multiPhylosignal() function in the package ‘picante’ ; a value of K>1 corresponds to stronger phylogenetic signal than would be expected for a BM model of character-state evolution, while K<1 indicates a weaker signal. Abouheif's test for serial independence (TFSI), a test for phylogenetic signal equivalent to Moran's I statistic was performed using the abouheif.moran() function in the package ‘adephylo’ . Phylogenetic Eigenvector Regression (PVR; ) was also performed with R using the ape and picante packages , . Additionally, the phylogenetic flexible discriminant analysis (pFDA) R script provided by Schmitz and Motani estimates Pagel's , another measure of phylogenetic signal that varies between a value of 0 (no phylogenetic signal) and 1 (strong phylogenetic bias; trait evolution is perfectly described by a BM model). […]

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