Generalized Urn Models of Evolutionary Processes

Details Generalized Urn Models of Evolutionary Processes Generalized Urn Models of Evolutionary Processes

2004-07-08

arxiv.org/abs/math/0407129v1

Annals of Probability 2004, Vol. 14, No. 3, 1455-1478

Mathematics

Probability

Scientific paper

10.1214/105051604000000422

Generalized Polya urn models can describe the dynamics of finite populations of interacting genotypes. Three basic questions these models can address are: Under what conditions does a population exhibit growth? On the event of growth, at what rate does the population increase? What is the long-term behavior of the distribution of genotypes? To address these questions, we associate a mean limit ordinary differential equation (ODE) with the urn model. Previously, it has been shown that on the event of population growth, the limiting distribution of genotypes is a connected internally chain recurrent set for the mean limit ODE. To determine when growth and convergence occurs with positive probability, we prove two results. First, if the mean limit ODE has an ``attainable'' attractor at which growth is expected, then growth and convergence toward this attractor occurs with positive probability. Second, the population distribution almost surely does not converge to sets where growth is not expected

Affiliated with

Also associated with

No associations

Rating

Generalized Urn Models of Evolutionary Processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized Urn Models of Evolutionary Processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Urn Models of Evolutionary Processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-222477