Journal of Probability and Statistics
Volume 2011 (2011), Article ID 867493, 39 pages
Research Article

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

1Department of Mathematics, Drexel University, Philadelphia, PA 19104, USA
2Division of Genetics, Department of Medicine, Brigham and Women's Hospital/Harvard Medical School, Boston, MA 02115, USA
3NAVTEQ Corporation, Malvern, PA 19335, USA

Received 18 May 2011; Revised 19 August 2011; Accepted 24 August 2011

Academic Editor: Shein-chung Chow

Copyright © 2011 Charles J. Mode et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.