Many of the traits that we care about, as evolutionary biologists, human geneticists, or simply as human beings, are genetically complex. This means that genetic differences at many genes (as well as differences in environment exposure and developmental trajectory) contribute to differences in the trait among individuals. Traits of this kind include height and other anthropometric measurements, skin pigmentation, life history traits, as well as many medically defined diseases and disorders (e.g. heart disease, diabetes, schizophrenia, and autism). The genetic differences arise as the result of accidental mutations in a single individual, which are then passed down through Mendelian inheritance, reshuffled through genetic recombination, amplified or removed by natural selection, and moved around by migration/gene flow.
Over the last hundred years or so, mathematical geneticists have developed a body of theory to describe how genetically complex traits evolve in response to these fundamental population genetic forces. For most of this period, data was scarce. In the last decade, this script has flipped. We are now swimming in genetic data from genome-wide association studies and other resources, but we lack the theoretical and statistical tools to deal with it's messy reality.
Much of my work is aimed at developing theoretical models and statistical tools that will allow us to learn about the evolution and genetics of complex traits. I am interested in questions such as:
-- How has adaptation impacted variation in complex traits among populations?
-- What forces maintain genetic variation for complex traits within populations?
-- Are human complex traits at or close to mutation-selection balance and what is the relative role of stabilizing vs. directional selection?
-- At how many positions in the genome will a newly arising mutation affect a given trait, and what is the distribution of effect sizes for these newly arising mutations?
-- What role, if any, does linked selection play in determining the genetic architecture of complex traits.
In general, I try to approach problems with a blend of theory and data analysis. Ideally, theoretical modeling will suggest new approaches for analyzing data, and the results of data analysis can suggest new directions for theoretical exploration.
While the main thrust of my work is currently on the evolution of complex traits, I find interest in a broad array of problems in population genetics, including linked selection (e.g. selective sweeps and background selection) and its consequences, pedigree reconstruction and demographic inference, coalescent theory and ARG inference, and the evolution of mutation and recombination rates, to name a few.