Commun. Comput. Phys., 2 (2007), pp. 1174-1183.


Lotka-Volterra Population Model of Genetic Evolution

Miros{\l}aw R. Dudek 1*

1 Institute of Physics, Zielona G\'ora University, 65-069 Zielona G\'ora, Poland.

Received 3 January 2007; Accepted (in revised version) 30 January 2007
Communicated by Dietrich Stauffer
Available online 15 June 2007

Abstract

A deterministic model of an age-structured population with genetics analogous to the discrete time Penna model \cite{Penna1,Penna2} of genetic evolution is constructed on the basis of the Lotka-Volterra scheme. It is shown that if, as in the Penna model, genetic information is represented by the fraction of defective genes in the population, the population numbers for each specific individual's age are represented by exactly the same functions of age in both models. This gives us a new possibility to consider multi-species evolution without using detailed microscopic Penna model. We discuss a particular case of the predator-prey system representing an ecosystem consisting of a limited amount of energy resources consumed by the age-structured species living in this ecosystem. Then, the increase in number of the individuals in the population under consideration depends on the available energy resources, the shape of the distribution function of defective genes in the population and the fertility age. We show that these parameters determine the trend toward equilibrium of the whole ecosystem.

AMS subject classifications: 92D15, 92D25, 92D40, 34C23
PACS: 87.23.-n, 87.53.Wz,02.30.Hq
Key words: Lotka-Volterra equations, Penna model, evolution.

*Corresponding author.
Email: mdudek@proton.if.uz.zgora.pl (M. R. Dudek)
 

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