Methods for approximating stochastic evolutionary dynamics on graphs

Overton, Christopher E, Broom, Mark, Hadjichrysanthou, Christoforos and Sharkey, Kieran J ORCID: 0000-0002-7210-9246 (2019) Methods for approximating stochastic evolutionary dynamics on graphs. JOURNAL OF THEORETICAL BIOLOGY, 468. pp. 45-59.

Access the full-text of this item by clicking on the Open Access link.

Official URL: http://dx.doi.org/10.1016/j.jtbi.2019.02.009

Abstract

Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the evolutionary process. However, for more complicated heterogeneous structures, computationally intensive methods are required such as individual-based stochastic simulations. By adapting methods from statistical physics, including moment closure techniques, we first show how to derive existing homogenised pair approximation models and the exact neutral drift model. We then develop node-level approximations to stochastic evolutionary processes on arbitrarily complex structured populations represented by finite graphs, which can capture the different dynamics for individual nodes in the population. Using these approximations, we evaluate the fixation probability of invading mutants for given initial conditions, where the dynamics follow standard evolutionary processes such as the invasion process. Comparisons with the output of stochastic simulations reveal the effectiveness of our approximations in describing the stochastic processes and in predicting the probability of fixation of mutants on a wide range of graphs. Construction of these models facilitates a systematic analysis and is valuable for a greater understanding of the influence of population structure on evolutionary processes.

Item Type:	Article
Uncontrolled Keywords:	Evolutionary graph theory, Moment closure, Fixation probability, Network, Markov process
Depositing User:	Symplectic Admin
Date Deposited:	08 Mar 2019 14:24
Last Modified:	19 Jan 2023 00:57
DOI:	10.1016/j.jtbi.2019.02.009
Open Access URL:	https://doi.org/10.1016/j.jtbi.2019.02.009
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3033940