Recent studies of RNA folding have led to a renewed interest in the genotype/phenotype relation. In particular, there has been much debate as to how silent mutations - mutations that leave the phenotype unchanged - affect the rate of evolution and the capacity to evolve in populations. I will discuss how such questions may be posed in the framework of branching random walks on random graphs and reduced to a simple mathematical models abstracting the genotype/phenotype map. I will show how this approach provides a partial resolution to the debate, provides a potential explanation observed levels of genetic diversity, and suggests some interesting implications for the molecular clock.

This is based upon an on-going collaboration with Jeremy Draghi, Alexander Stewart, Günter Wagner, and Joshua Plotkin.

Keywords: Population genetics; Random graphs; Branching processes; First passage time

Biography: Todd Parsons is a research associate in the Mathematical Biology group at the University of Pennsylvania. After obtaining a B.Sc. in pure mathematics at the University of Waterloo and an M.Sc. in algebraic number theory at the University of Toronto, he saw the light and did doctoral studies in applied probability. In his research, he seeks to develop new mathematical tools that will allow insights from ecology and molecular genetics to be incorporated into the modern synthesis of population genetics.