I have been working lately on models and inference methods for quantitative characters varying between species and within-species, allowing us to infer correlated evolution of different characters. One important case is discrete 0/1 phenotypes, which can be caused by an underlying polygenic quantitative character. Years ago Sewall Wright made such a model, called the threshold model. I have adapted this to inference of covariation between characters in their evolution, by assuming that the underlying characters evolve in a correlated fashion, but that the 0/1 characters just show which of the underlying characters exceed the threshold that separates the two states. Making inferences about the covariation requires Markov chain Monte Carlo methods. I have also been working on inferring whether characters measured in different populations of a single species are under natural selection which is affected by some measured environments. There the problem is to correct for the similarities of populations that are connected by gene flow.

Before that I was working on methods for estimating population parameters (such as effective population size, mutation rate, and so on) from population samples of molecular sequences. The genes at one locus in a population are related by a "gene tree" that depicts which ones are descended from recent common ancestors.

We have been using a computationally intensive method known as Markov Chain Monte Carlo Integration to make approximate calculations of the statistical likelihoods for different values of the population parameters. We are now distributing a free package of computer programs, LAMARC, to do these calculations. We think that these methods will become the standard way of analyzing population samples of sequences. My colleagues in this work have been Mary Kuhner, Jon Yamato, and Peter Beerli.