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Birds are one of the most speciose (over 10,000 recognized species) and ecological diverse living vertebrates (Gill 2007). It has been held that birds underwent two large-scale radiations during their 160 million years evolution, one for the stem groups in the Cretaceous, and the other for the crown groups in the Paleogene (Mayr 2009; Prum et al. 2015; Wang and Zhonghe 2017). Over the last few years, numerous well-preserved Mesozoic bird fossils have been described (Chiappe and Meng 2016; Wang and Zhonghe 2017), and consensus has been approached regarding their systematic relationships (O'Connor and Zhou 2013; Wang et al. 2017, 2018). These wealthy data have significantly bridged the large morphological gap between birds and their non-avian theropod predecessors (O'Connor and Zhou 2015; Wang and Zhonghe 2017), and demonstrated their evolutionary success related to novel traits. Expanded morphological characters that cover the major Mesozoic avian groups with chronological data become accessibly recently (Wang and Lloyd 2016), making it possible to trace the early avian evolution more quantitively by addressing important questions such as the divergence times of the major clades and comparative study of the pattern of morphological character changes in and between lineages (Brusatte et al. 2014; Lloyd 2016). In this study, we reinvestigate the dataset which has been analyzed previously to explore evolutionary rate heterogeneity under maximum parsimony (Wang and Lloyd 2016). The approach was stepwise: first to infer the most parsimonious trees, then to inform the internal node ages using certain ad hoc measures, and last to obtain the rates from dividing the number of parsimonious changes by the time durations. It did not account for the uncertainties of tree topology, times and rates statistically, and was unable to model the evolutionary process explicitly. Furthermore, we expand the original data with 18 morphological characters and ten Mesozoic birds (Wang and Zhou, in press, see also Supplementary Information). The dataset now consists of 280 morphological characters and 68 operational taxonomic units (Dromaeosauridae as the outgroup, 65 Mesozoic and 2 extant birds Anas and Gallus). Here, we exploit the advantage of tip dating to infer both the divergence times and evolutionary rates while accounting for their uncertainties in a coherent Bayesian statistical framework. The inference is based on the posterior probability distribution of the model parameters, which combines the information from the data (morphological characters) and the priors (including the distributions of the fossil ages and the other parameters in the tree model and clock model). We further investigate the evolutionary rate heterogeneity across different parts of bird body by subdividing the characters into six categories.
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