*Understanding variation in rates of molecular evolution*

I am currently working on developing models for estimating branch lengths in units proportional to time without assuming a strict, global molecular clock. Our understanding of how substitution rate changes over time is still underdeveloped. My research in this field is aimed at identifying models that can accommodate rate change resulting from different processes. Such flexible models can provide more accurate estimates of species divergence times. I have developed and implemented a model for estimating lineage-specific substitution rates that employs a Dirichlet process prior (DPP) model. The DPP is a type of distribution for modeling mixtures of data. Under this model, branches of a phylogenetic tree are clustered into specific rate classes and the values associated with each class are drawn from a separate parametric distribution. The number of different rate classes and the rate values are treated as random variables under this model. Thus, a strict molecular clock and a model where each lineage evolves under a different rate are special cases of the DPP model.

*Combining paleontological and molecular data for calibrating phylogenetic trees*

Because there is a great deal of uncertainty associated with calibration points, it is necessary to accommodate this in methods for inferring species divergence times. In a Bayesian framework, additional prior distributions can be placed on fossil age estimates and the parameters associated with those priors. A prior distribution on a parameter of a prior distribution is called a hyperprior. I have developed novel approaches for applying hyperpriors to node calibration priors. These hyperpriors can provide additional information about the minimum age estimates and the fossils and nodes associated with them. Additionally, in collaboration with Matt Davis (The Field Museum) and Charles Linkem (KU) I am working on applying novel methods for incorporating fossil data in phylogenetic inference using a data set of ray-finned fishes.

Heath, T.A. 2012. A hierarchical Bayesian model for calibrating estimates of species
divergence times. *Systematic Biology,* in press.

Heath, T.A., M.T. Holder, and J.P. Huelsenbeck. 2011. A Dirichlet process prior for
estimating lineage-specific substitution rates. *Molecular Biology and Evolution,* doi: 10.1093/molbev/msr255.

Heath, T.A., S.M. Hedtke, and D.M. Hillis. 2008. Taxon sampling and the accuracy of
phylogenetic analyses. *Journal of Systematics and Evolution* 46:239-257.

Heath, T.A., D.J. Zwickl, J. Kim, and D.M. Hillis. 2008. Taxon sampling affects inferences
of macroevolutionary processes from phylogenetic trees. *Systematic Biology* 57:160-166.