Journal of Nonlinear Mathematical Physics

Volume 18, Issue Supplement 2, December 2011, Pages 321 - 338

Nonlinear Deterministic Equations in Biological Evolution

Authors
Kavita Jain*, , Sarada Seetharaman
Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore, India

Also at Evolutionary and Organismal Biology Unit.

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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
18 - Supplement 2
Pages
321 - 338
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925111001556How to use a DOI?
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  -