Santa Fe Institute

Seminar

April 02, 2013
12:15 PM
Collins Conference Room

Burton Voorhees (Athabasca University)

Abstract.  Given a finite, genetically homogeneous population, suppose that a single mutant in introduced.  What is the probability this mutant will become fixed in the population? In 1958 the Australian statistician Patrick Moran answered this question for birth-death processes in unstructured populations.  Whether and how the introduction of structure in the population alters the Moran result, however, has been extensively studied for only a few years.  This talk presents an adaptation of the Moran birth-death model of evolutionary processes on graphs.  The model makes use of the full population state space, consisting of 2^N binary valued vectors, and a Markov process on this space with transition matrix defined by the edge weight matrix of the given graph.  Simple graphs that suppress or enhance selection with respect to the Moran process are analyzed and new analytic results presented.  One interesting result is that in some cases a graph may enhance selection relative to a complete graph for only limited values of fitness.  The model used, and related models, have a large variety of potential applications outside of population genetics, including models of: biological defenses against cancer; neural network information processing; the spread of innovations and rumors; tracing sources of computer viruses and epidemics, as well as more sinister possibilities.

Purpose: Research Collaboration

SFI Host: Cris Moore

More Info

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