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A Diffusion Approximation of a Three Species Fitness-Dependent Population Model

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A Diffusion Approximation of a Three Species Fitness-Dependent Population Model

Peuckert, Liam (2015) A Diffusion Approximation of a Three Species Fitness-Dependent Population Model. Masters thesis, Concordia University.

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Abstract

We introduce a continuous time Markov chain to model the ecological competition in the population of 3 species with fitness governed by a modified Moran process based on environmental resources in a limited niche of constant total population N. We run simulations to observe population behavior under different N and initial conditions. We then propose a model approximation which for large N converges to an ODE over most of the population space, with the population following a deterministic trajectory until it reaches an asymptotically stable line. We then prove that the approximation converges to a one dimensional diffusion forced onto the stable line until the first extinction occurs. We use the drift and diffusion coefficients of the diffusion to calculate the expected probability of first extinction for specific species, as well as the expected time until first extinction. Finally, we compare these with data obtained via simulations to show that the approximation is a good fit.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Peuckert, Liam
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:22 November 2015
Thesis Supervisor(s):Popovic, Lea
ID Code:980699
Deposited By: LIAM PEUCKERT
Deposited On:17 Jun 2016 14:56
Last Modified:18 Jan 2018 17:51
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