On the Inclusion of Self Regulating Branching Processes in the Working Paradigm of Evolutionary and Population Genetics

Frontiers in Genetics

Charles J Mode¹  Towfique eRaj²  Candace K Sleeman³ 

[1] Drexel University;Harvard Medical School and Brigham Women’s Hospital;Nokia;

关键词: mutations;    branching processes;    Embedded deterministic model;    Monte Carlo simulation experiments;    Self regulating branching processes;    Stochastic population dynamics;   

DOI  :  10.3389/fgene.2013.00011

来源: DOAJ

【 摘 要 】

The principal goal of this methodological paper is to suggest to a generalaudience in the genetics community that the consideration of recentdevelopments of self regulating branching processes may lead to thepossibility of including this class of stochastic processes as part ofworking paradigm of evolutionary and population genetics. This class ofbranching processes is self regulating in the sense that an evolvingpopulation will grow only to a total population size that can be sustainedby the environment. From the mathematical point of view the class processesunder consideration belongs to a subfield of probability and statisticssometimes referred to as computational applied probability and stochasticprocesses. Computer intensive methods based on Monte Carlo simulationprocedures have been used to empirically work out the predictions of aformulation by assigning numerical values to some point in the parameterspace and computing replications of realizations of the process overthousands of generations of evolution. Statistical methods are then used onsuch samples of simulated data to produce informative summarizations of thedata that provide insights into the evolutionary implications of computerexperiments. Briefly, it is also possible to embed deterministic non-lineardifference equations in the stochastic process by using a statisticalprocedure to estimate the sample functions of the process, which hasinteresting methodological implications as to whether stochastic ordeterministic formulations may be applied separately or in combination inthe study of evolution. It is recognized that the literature on populationgenetics contains a substantial number of papers in which Monte Carlosimulation methods have been used. But, this extensive literature is beyondthe scope of this paper, which is focused on potential applications of selfregulating branching processes in evolutionary and population genetics.

【 授权许可】

Unknown