Computational protocol: Inferring ancestral states without assuming neutrality or gradualism using a stable model of continuous character evolution

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Protocol publication

[…] In order to assess the improvement (if any) in quality of ancestral state reconstruction and the ability of statistical tests to identify biological characters that have evolved under a stable rather than Brownian stochastic process, data were simulated under a variety of conditions. Evolutionary increments were generated randomly from a stable model with unit scale and index of stability ranging from 1.0 to 2.0 in steps of 0.2, on random phylogenetic trees with 25, 40, 60, 90, 130, 175, 235, 325, 440 and 600 tips generated under the Yule model in Mesquite []. This procedure gave rise to 60 experimental conditions, each consisting of 250 trees and simulated datasets, and varying in tree size and index of stability of simulated trait values. Based on data at the tips, ancestral states were reconstructed using the modal posterior density estimate from MCMC, first with α fixed at 2.0 (representing a Brownian motion model) and second with a free α (representing a general symmetric stable model). Ancestral states were also estimated using the homogenous Ornstein-Uhlenbeck model for comparison. Estimates of Type I and Type II error rates under the BPIC criterion were made for each tree size/stability condition. Accuracy was assessed for Brownian, Stable and OU models by calculating variance of the inferred ancestral states from the true simulated states for each simulated dataset under each condition. We report here the median variance ratio of stable/Brownian and stable/Ornstein-Uhlenbeck reconstructions within each experimental condition.To provide a demonstration of the model’s application to real biological datasets, we made use of a supertree of mammalian species [] and fitted the stable model of character evolution to data on the log adult body mass of 1,679 eutherian mammals [combined data from [,]]. For purposes of comparison we also estimated ancestral states under two homogenous evolutionary models, the Brownian motion model and the Ornstein-Uhlenbeck model, the latter estimates obtained by maximum likelihood search from parameter estimates generated by the SLOUCH package in R []. Finally we also inferred ancestral states using two heterogenous models, the time-heterogenous Early Burst model [,] in which the rate of a Brownian process increases or decreases exponentially in time, and the clade-heterogenous model of Eastman et al. [] in which the rate of a Brownian process is “inherited” within clades but allowed to occasionally shift in value on probabilistically selected branches of a phylogeny. The former ancestral state estimates were made by maximum likelihood search based on parameter estimates and scaled phylogenies derived from the GEIGER package in R [] while the latter ancestral state estimates were made by Brownian motion maximum likelihood reconstruction on a tree with branch lengths scaled by the maximum posterior probability estimates of rates reported by the Auteur package in R []. Connections between these various models and the stable model are discussed below. […]

Pipeline specifications

Software tools Mesquite, GEIGER
Application Phylogenetics
Organisms Homo sapiens