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Complex population dynamics as a competition between multiple-time-scale phenomena

Ioana Bena* and Michel Droz†

Janusz Szwabiński‡

Andrzej Pȩkalski§

  • Theoretical Physics Department, University of Geneva, Quai E. Ansermet no. 24, 1211 Geneva 4, Switzerland

  • Theoretical Physics Department, University of Geneva, Quai E. Ansermet no. 24, 1211 Geneva 4, Switzerland and Institute of Theoretical Physics, University of Wrocław, Pl. M. Borna 9, 50-204 Wrocław, Poland

  • Institute of Theoretical Physics, University of Wrocław, Pl. M. Borna 9, 50-204 Wrocław, Poland

  • *Electronic address: ioana.bena@physics.unige.ch
  • †Electronic address: michel.droz@physics.unige.ch
  • ‡Electronic address: janusz.szwabinski@physics.unige.ch
  • §Electronic address: apekal@ift.uni.wroc.pl
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Phys. Rev. E 76, 011908 – Published 16 July, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.011908

Abstract

The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The mean-field level of description allows one to highlight the delicate interplay between the different time-scale processes in the resulting complex dynamics of the system. We clarify the influence of the amplitude and period of the environmental changes on the critical value of the selection pressure corresponding to a phase-transition “extinct-alive” of the population. However, the intrinsic stochasticity and the dynamically-built in correlations among the individuals, as well as the role of the mutation-induced variety in population’s evolution are not appropriately accounted for. A more refined level of description, which is an individual-based one, has to be considered. The inherent fluctuations do not destroy the phase transition “extinct-alive,” and the mutation amplitude is strongly influencing the value of the critical selection pressure. The phase diagram in the plane of the population’s parameters—selection and mutation are discussed as a function of the environmental variation characteristics. The differences between a smooth variation of the environment and an abrupt, catastrophic change are also addressed.

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Phys. Rev. E 76, 011908– Published 16 July, 2007
  • Received 14 March 2007

© 2007 American Physical Society

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