Population size changes and extinction risk of populations driven by mutant interactors

Hye Jin Park, Yuriy Pichugin, Weini Huang, and Arne Traulsen
Phys. Rev. E 99, 022305 – Published 6 February 2019

Abstract

Spontaneous random mutations are an important source of variation in populations. Many evolutionary models consider mutants with a fixed fitness, chosen from a fitness distribution without considering microscopic interactions among the residents and mutants. Here, we go beyond this and consider “mutant interactors,” which lead to new interactions between the residents and invading mutants that can affect the population size and the extinction risk of populations. We model microscopic interactions between individuals by using a dynamic interaction matrix, the dimension of which increases with the emergence of a new mutant and decreases with extinction. The new interaction parameters of the mutant follow a probability distribution around the payoff entries of its ancestor. These new interactions can drive the population away from the previous equilibrium and lead to changes in the population size. Thus, the population size is an evolving property rather than an externally controlled variable. We calculate the average population size of our stochastic system over time and quantify the extinction risk of the population by the mean time to extinction.

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  • Received 17 August 2018

DOI:https://doi.org/10.1103/PhysRevE.99.022305

©2019 American Physical Society

Physics Subject Headings (PhySH)

Interdisciplinary Physics

Authors & Affiliations

Hye Jin Park1, Yuriy Pichugin1, Weini Huang2,3, and Arne Traulsen1

  • 1Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, 24306 Plön, Germany
  • 2Complex Systems and Networks Research Group, School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
  • 3Group of Theoretical Biology, The State Key Laboratory of Biocontrol, School of Life Science, Sun Yat-sen University, Guangzhou 510060, China

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Issue

Vol. 99, Iss. 2 — February 2019

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