I am interested in why some clades diversify really rapidly while other go through long periods of stasis, both in terms of species and in traits. To get at one aspect of this question, I am working on theory that address when speciation is limited by various processes, particularly mutation rate and geographic range expansion. In collaboration with Matt Hahn, we have shown that even when reproductive isolation evolves by neutral mutations (no selection), ecological factors (range expansion) are often still the main driver of variation in speciation rates. I would like to extend this theory to incorporate selected mutations and more realistic assumptions about geographic range evolution. Our paper was recently accepted at The American NaturalistI've copied the abstract for now, but I'll provide a link to the pdf once it's ready.

The limited contribution of reciprocal gene loss to increased speciation rates following whole genome duplication

Hybrid incompatibilities contribute to reproductive isolation between species, allowing them to follow independent evolutionary trajectories. Since hybrid incompatibilities are by definition deleterious, they cannot be selected for directly and must arise as a byproduct of evolutionary divergence. Divergent resolution of duplicate genes, a special case of Dobzhansky-Muller incompatibilities, is one mechanism by which hybrid incompatibility can evolve. Following whole genome duplication, loss of gene copies could possibly increase the opportunity for divergent resolution and, hence, the evolution of hybrid incompatibilities.  However, divergent resolution can only take place when populations are isolated in allopatry; genes lost within a species cannot contribute to future speciation.  Furthermore, nearly complete allopatry is necessary for passive divergent resolution.  Using mathematical models, we demonstrate that these two factors severely impede the ability of divergent resolution alone to increase speciation rates, except under very particular conditions. Instead, we find that the population dynamics of diverging lineages dominate this process, leading to a larger role for ecology relative to genetics in the origin of new species, even by passive mechanisms. Divergent resolution of duplicate genes might increase speciation rates in some clades at some times, but our results indicate that it alone is unlikely to account for the macroevolutionary success of polyploid clades.