ABSTRACT
Department of Integrative Biology, University of California, Berkeley, California, USA
Brian R. Moore
Department of Evolution and Ecology, University of California, Davis, California, USA
CONTENTS
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 13.2 Priors on branch rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
13.2.1 Autocorrelated-rate models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 13.2.2 Independent-rate models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 13.2.3 Local molecular clock models . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 13.2.4 Mixture models on branch rates . . . . . . . . . . . . . . . . . . . . . . . . . 291
13.3 Priors on node times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 13.3.1 Generic priors on node ages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 13.3.2 Branching-process priors on node ages . . . . . . . . . . . . . . . . . . 296
13.4 Priors for calibrating divergence times . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 13.4.1 Hierarchical models for calibrating node ages . . . . . . . . . . . 303
13.4.1.1 Evaluating hierarchical calibration priors . . . . 304 13.5 Practical issues for estimating divergence times . . . . . . . . . . . . . . . . . 308
13.5.1 Model selection and model uncertainty . . . . . . . . . . . . . . . . . 308 13.5.2 (Hyper)prior sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 13.5.3 Limitations and challenges of fossil calibration . . . . . . . . . 312
13.6 Summary and prospectus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Phylogenies provide an explicit historical perspective that critically informs biological research in a vast and growing number of scientific disciplines. For
Algorithms, and
many inference problems, the tree topology and/or branch lengths-rendered as the expected amount of character change-provide sufficient information. Many other inference problems, however, require an ultrametric tree that confers temporal information: i.e., where branch durations and node heights are proportional to absolute or relative time. The study of continuous and discrete traits, for example, relies on stochastic models in which the probability of change is proportional to relative time; the study of lineage diversification relies upon stochastic branching process models that leverage information on the relative waiting times between events, etc. For such inference problems, a relative time scale is often sufficient. Other evolutionary questions require an absolute time scale. The study of biogeographic history, for instance, may use models that incorporate information on the changing proximity of areas through time, studies that seek to assess the correlation between shifts in rates of lineage diversification and events in earth history require branch lengths proportional to geological time, etc.
