DOI: 10.5061/dryad.9kd51c5ct
title: A Bayesian extension of phylogenetic generalized least squares (PGLS): incorporating uncertainty in the comparative study of trait relationships and evolutionary rates

description: Phylogenetic comparative methods use tree topology, branch lengths, and
 models of phenotypic change to take into account non-independence in
 statistical analysis. However, these methods normally assume that trees
 and models are known without error. Approaches relying on evolutionary
 regimes also assume specific distributions of character states across a
 tree, which often result from ancestral state reconstructions that are
 subject to uncertainty. Several methods have been proposed to deal with
 some of these sources of uncertainty, but approaches accounting for all of
 them are less common. Here we show how Bayesian statistics facilitates
 this task while relaxing the homogeneous rate assumption of the well-known
 phylogenetic generalized least squares (PGLS) framework.  This
 Bayesian formulation allows uncertainty about phylogeny, evolutionary
 regimes, or other statistical parameters to be taken into account for
 studies as simple as testing for coevolution in two traits or as complex
 as testing whether bursts of phenotypic change are associated with
 evolutionary shifts in inter-trait correlations. A mixture of validation
 approaches indicate that the approach has good inferential properties and
 predictive performance. We provide suggestions for implementation and show
 its usefulness by exploring the coevolution of ankle posture and forefoot
 proportions in Carnivora.
description: There are two sets of data, one corresponds to the worked example
 and the other one to toy simulated data to test the scripts implementing
 the method described in the paper, which are also provided. Below we
 provide further details on the three sets: worked example, toy data, and R
 scripts. <strong>Worked
 example</strong> The worked example explores limb
 coevolution in the order Carnivora. Both phenotypic data (CarnData.cvs)
 and phylogenetic trees (CarnTrees.nex) are provided.
 The phenotypic data inlcudes three variables for 102 carnivoran
 species: lengths for the third metacarpal (MC3L) and third proximal
 phalanx (fph3p), and posture codification (Digitigrady). The continuous
 variables (lengths) were obtained from Samuels et al. (2013; J Morphol),
 and the categorical variable (posture) from Polly (2010; Carnivoran
 evolution: New views on phylogeny, form, and function). See paper for full
 references. Polly (2010) proposed the posture variable based on the use of
 the heel during normal resting stance and during walking locomotion,
 recognizing three categories: plantigrade (heel in contact with the
 ground), semidigitigrade (heel may or may not be in contact with the
 ground during walking locomotion), and digitigrade (heel does not come in
 contact with the ground). This three-state categorization offers the
 advantage of recognizing a continuum in posture (with an intermediate
 state between plantigrady and digitigrady), which partially captures the
 continuous nature of ankle morphology. However, the intermediate state is
 ambiguous regarding the use of the heel during walking locomotion, making
 it little informative for our purposes (which link the coevolutionary
 pattern of limb morphology with locomotor performance). Therefore, our
 categorization reduced posture to two character states, clearly
 differentiating those carnivorans that keep the heel elevated during
 walking locomotion (digitigrady: 1) from the rest (plantigrady:
 0). The phylogenies correspond to a posterior
 distribution of 1000 dated trees pruned from the
 <em>10kTrees</em> project (Arnold et al. 2010; Evol
 Anthropol). See paper for reference and further details about the
 phylogeny.  <strong>Toy
 data</strong> The files of the toy dataset allow
 testing the scripts provided in this package (see below). The toy
 simulated data (Data.csv) emulates the variable system of the worked
 example (CarnData.csv) and was generated with the R packages phytools and
 geiger. It is accompanied by a sample of 10 trees with 5 stochastic
 character mappings reconstructed for each of them (Maps.tre), which can be
 generated with programs such as SIMMAP or phytools.
 <strong>R scripts</strong> The
 main script implements the mixed model described in the paper (MM.R), but
 scripts implementing specific models of phylogenetic relatedness are also
 provided: Lambda model (LM.R), Brownian motion (BM.R), and
 non-phylogenetic analysis (IID.R). Each file allows accounting for both
 equal and unequal rates, and currently calls the toy data files (Data.csv
 and Maps.tre) as inputs (thus, the toy data files can be used as templates
 to prepare new files to be analyzed with the scripts). 
 The scripts modify codes from de Villemereuil et al. (2012: BMC
 Evol Biol) and Kruschke (2011; Doing Bayesian Data Analysis: A Tutorial
 with R and BUGS), and require prior installation of the program JAGS as
 well as the R packages rjags, ape, and phytools (See paper for full
 references). Detailed instructions on installing JAGS can be found at
 the website of Kruschke (2011). This resource also offers detailed explanations (with codes) on processing the MCMC outputs, which can be helpful as the scripts provided here incorporate very basic descriptions of the posterior distributions (based on posterior means, medians, and credible intervals).