Divergence Time and Evolutionary Rate Estimation with Multilocus Data

—Bayesian methods for estimating evolutionary divergence times are extended to multigene data sets, and a technique is described for detecting correlated changes in evolutionary rates among genes. Simulations are employed to explore the effect of multigene data on divergence time estimation, and the methodology is illustrated with a previously published data set representing diverse plant taxa. The fact that evolutionary rates and times are confounded when sequence data are compared is emphasized and the importance of fossil information for disentangling rates and times is stressed. [Markov chain Monte Carlo; Metropolis–Hastings algorithm; molecular clock; phylogeny. ] Because of improved technology, molecular sequence data are becoming increasingly easy to collect. As a result, the pattern and process of evolution are being characterized in ever ner detail. In the past, it was typical to infer evolutionary divergence times by selecting a single gene and then sequencing that gene in the taxa of interest. In the future, these single–gene data sets will give way to multigene data sets. The advantage of multigene over single–gene data sets is clear— bigger data sets contain more information. How to properly combine evolutionary information from multiple genes is less clear. Because of recombination, the genealogy relating the sequences of one gene can differ from the genealogies of other genes. Hence, divergence times can vary among genes. However, this variation should be negligible when the number of generations between speciation events on a tree is large relative to effective population size. Even when variation of divergence times among genes can be safely neglected, the question of how to properly extract and combine evolutionary information from multiple genes is not trivial. Evolutionary rates differ over time and among genes. Although variation of rates among genes and over time is problematic for estimating divergence times, understanding this variation is one of the central goals of evolutionary biology. Unfortunately, this variation cannot be directly studied. Comparisons between DNA or protein sequences yield estimates of amounts of molecular evolution, but evolutionary rates and times are confounded when molecular sequences are compared. Without information external to the molecular sequence data, these rates and times cannot be separated. This confounding of rates and times has hampered the study of evolution. For example, effective population size and substitution rate per generation are two of the most important quantities in population genetics. Because rates and times are confounded when molecular sequence data are compared, population geneticists generally resort to estimating the product of effective population size and substitution rate per generation (e.g., Watterson, 1975) rather than the more desirable option of estimating each of these factors separately. Similarly, the confounding of rates and times has affected the study of macroevolution by preventing the estimation of absolute rates of evolution and fostering the less desirable alternative of estimating the ratio of evolutionary rates of different genes. For macroevolutionary studies, it has long been recognized that fossil data permit some disentangling of times and absolute rates of evolution (Zuckerkandl and Pauling, 1962). Although serially sampled sequence data can be exploited for quickly evolving organisms (Leitner and Albert, 1999; Drummond and Rodrigo, 2000; Korber et al., 2000; Rambaut, 2000), the usual approach to estimating absolute rates of molecular evolution is to assume both that rates are constant over time and that fossil data allow estimation without error of the time since a common ancestral sequence. Both of these assumptions may be seriously awed. Fossil data are imperfect and have associated uncertainty. A specic fossil specimen is unlikely to represent the specic organism that harbored the