10Discrete morphological data have been widely used to study species evolution, but the use of 11 quantitative (or continuous) morphological characters is less common. Here, we implement a 12 Bayesian method to estimate species divergence times using quantitative characters. Quantitative 13 character evolution is modelled using Brownian diffusion with character correlation and 14 character variation within populations. Through simulations, we demonstrate that ignoring the 15 population variation (or population "noise") and the correlation among characters leads to biased 16 estimates of divergence times and rate, especially if the correlation and population noise are 17 high. We apply our new method to the analysis of quantitative characters (cranium landmarks) 18 and molecular data from carnivoran mammals. Our results show that time estimates are affected 19 by whether the correlations and population noise are accounted for or ignored in the analysis.
20The estimates are also affected by the type of data analysed, with analyses of morphological 21 characters only, molecular data only, or a combination of both; showing noticeable differences 22 among the time estimates. Rate variation of morphological characters among the carnivoran 23 1 species appears to be very high, with Bayesian model selection indicating that the 24 independent-rates model fits the morphological data better than the autocorrelated-rates model. 25 We suggest that using morphological continuous characters, together with molecular data, can 26 bring a new perspective to the study of species evolution. Our new model is implemented in the 27 MCMCtree computer program for Bayesian inference of divergence times. [Bayesian inference, 28 continuous morphological characters, geometric morphometrics, Procrustes alignment, 29 molecular clock, divergence times, phylogeny] 30Molecular sequences are informative about the relative ages of nodes on a phylogeny, but not about 31 the geological times of divergence or the absolute molecular evolutionary rate. The Bayesian method 32 offers a way to use fossil information to construct a prior on divergence times, which can then be 33 integrated with the molecular data to produce posterior estimates of absolute divergence times 34 (e.g., Thorne et al., 1998; Drummond et al., 2006; Rannala and Yang, 2007). However, modelling 35 clade ages with statistical distributions based on the fossil evidence is challenging. Fossils may 36 provide estimates of minimum clade ages, but maximum clade ages are typically based on the 37 absence of fossil evidence, and are thus hard to justify (Benton and Donoghue, 2007).
38The problem is illustrated in Figure 1. Imagine we wish to estimate the age of the last common 39 ancestor of species A and B, t AB . The oldest fossil in the A-B ingroup is F, which has known age t F .
40If we measure time towards the past (so that present time is zero), we can immediately see that 41 t AB > t F , so that the age of the fossil, t F , imposes a minimum constraint on t AB . However, we do not ...