Simulating the Emergence and Survival of Mutations Using a Self Regulating Multitype Branching Processes

Abstract

It is difficult for an experimenter to study the emergence and survival of mutations, because mutations are rare events so that large experimental population must be maintained to ensure a reasonable chance that a mutation will be observed. In his famous book, The Genetical Theory of Natural Selection, Sir R. A. Fisher introduced branching processes into evolutionary genetics as a framework for studying the emergence and survival of mutations in an evolving population. During the lifespan of Fisher, computer technology had not advanced to a point at which it became an effective tool for simulating the phenomenon of the emergence and survival of mutations, but given the wide availability of personal desktop and laptop computers, it is now possible and financially feasible for investigators to perform Monte Carlo Simulation experiments. In this paper all computer simulation experiments were carried out within a framework of self regulating multitype branching processes, which are part of a stochastic working paradigm. Emergence and survival of mutations could also be studied within a deterministic paradigm, which raises the issue as to what sense are predictions based on the stochastic and deterministic models are consistent. To come to grips with this issue, a technique was used such that a deterministic model could be embedded in a branching process so that the predictions of both the stochastic and deterministic compared based on the same assigned values of parameters.