Stochastic processes in the adiabatic limit: applications to biochemistry and population genetics

Ilya Nemenman (October 25, 2011)

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Abstract

Stochastic biochemical systems and population genetics models are described by similar mathematical equations, and hence similar phenomena should be observed in both systems. Here we focus on stochastic kinetics with time scale separation. We show how to integrate out the fast degrees of freedom, while rigorously preserving their effects on the fluctuations of slower variables. This procedure allows to speed up simulation of kinetic networks and reveals a number of interesting phenomena, previously unobserved in the context of classical stochastic kinetics. One of the most interesting is the emergence of geometric phases, which we show may have substantial effects on, in particular, the frequency of fixation of new mutations in slowly variable environments.