Volume 18, Issue Supplement 2, December 2011, Pages 321 - 338
Nonlinear Deterministic Equations in Biological Evolution
Received 24 November 2010, Accepted 18 March 2011, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925111001556How to use a DOI?
- Keywords
- Deterministic equations; biological evolution; multiple equilibria; phase transitions
- Abstract
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise in many complex situations. For sexual populations, even in the simplest setting, the equations are necessarily nonlinear due to the mixing of the parental genetic material. The solutions of such nonlinear equations display interesting features such as multiple equilibria and phase transitions. We mainly discuss those models for which an analytical understanding of such nonlinear equations is available.
- Copyright
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Kavita Jain AU - Sarada Seetharaman PY - 2021 DA - 2021/01/07 TI - Nonlinear Deterministic Equations in Biological Evolution JO - Journal of Nonlinear Mathematical Physics SP - 321 EP - 338 VL - 18 IS - Supplement 2 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001556 DO - 10.1142/S1402925111001556 ID - Jain2021 ER -