Narrow Results

Many multi-cellular organisms exhibit remarkably similar patterns of aging and mortality. Because this phenomenon appears to arise from the complex interaction of many genes, it has been a challenge to explain it quantitatively as a response to natural selection. We survey attempts by the author and his collaborators to build a framework for understanding how mutation, selection and recombination acting on many genes combine to shape the distribution of genotypes in a large population. A genotype drawn at random from the population at a given time is described by a Poisson random measure on the space of loci and its distribution is characterized by the associated intensity measure. The intensity measures evolve according to a continuous-time measure-valued dynamical system. We present general results on the existence and uniqueness of this dynamical system and how it arises as a limit of discrete generation systems. We also discuss existence of equilibria.