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Choosing an ancestral state reconstruction method among the alternatives available for quantitative characters may be puzzling. We present here a comparison of seven of them, namely the maximum likelihood, restricted maximum likelihood, generalized least squares under Brownian, Brownian-with-trend and Ornstein-Uhlenbeck models, phylogenetic independent contrasts and squared parsimony methods. A review of the relations between these methods shows that the maximum likelihood, the restricted maximum likelihood and the generalized least squares under Brownian model infer the same ancestral states and can only be distinguished by the distributions accounting for the reconstruction uncertainty which they provide. The respective accuracy of the methods is assessed over character evolution simulated under a Brownian motion with (and without) directional or stabilizing selection. We give the general form of ancestral state distributions conditioned on leaf states under the simulation models. Ancestral distributions are used first, to give a theoretical lower bound of the expected reconstruction error, and second, to develop an original evaluation scheme which is more efficient than comparing the reconstructed and the simulated states. Our simulations show that: (i) the distributions of the reconstruction uncertainty provided by the methods generally make sense (some more than others); (ii) it is essential to detect the presence of an evolutionary trend and to choose a reconstruction method accordingly; (iii) all the methods show good performances on characters under stabilizing selection; (iv) without trend or stabilizing selection, the maximum likelihood method is generally the most accurate., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Abstract: Using the fossil record yields more detailed reconstructions of the evolutionary process than what is obtained from contemporary lineages only. In this work, we present a stochastic process modeling not only speciation and extinction, but also fossil finds. Next, we derive an explicit formula for the likelihood of a reconstructed phylogeny with fossils, which can be used to estimate the speciation and extinction rates. Finally, we provide a comparative simulation-based evaluation of the accuracy of estimations of these rates from complete phylogenies (including extinct lineages), from reconstructions with contemporary lineages only and from reconstructions with contemporary lineages and the fossil record. Results show that taking the fossil record into account yields more accurate estimates of speciation and extinction rates than considering only contemporary lineages. [Copyright &y& Elsevier]