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Mirosław Dudek (Institute of Physics, University of Zielona Góra)
On Lotka-Volterra models of population growth.
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Abstract:
After a short review of the deterministic growth models which are used in modelling the population dynamics ([Wangersky]) we discuss how to model the growth of age-structured population with genetics ([Dudek]). In the latter case, a deterministic model of an age structured population has been constructed which shares many features common with the discrete time Penna model
([Penna],[Moss de Oliveira et al]) of genetic evolution. Similarly, as in the Penna model, genetic information is represented by the fraction of defective genes in the population under consideration. We discuss some extentions of the model ([Dudek]) including methods of self-adaptive stochastic processes.
References:
1. V. Volterra, Théorie mathématique de la lutte
pour la vie, Gauthier-Villars, Paris, 1931
2. D. C. Gazis, E. W. Montroll and J. E. Ryniker, Age-specific, deterministic model of predator-prey populations: application to Isle Royale, IBM J. Res. Develop., 17 (1973), 47-53.198
3. P. J. Wangersky, Lotka-Volterra population models, Annu. Rev. Ecol. Syst., 9 (1978), 189-218
4. T.J. P. Penna, A bit-string model for biological aging, J. Stat. Phys., 78 (1995), 1629-1633.
5. S. Moss de Oliveira, P. M. C. de Oliveira and D. Stauffer,
Evolution, Money, War, and Computers, Teubner, Stuttgart-Leipzig, 1999.
6. M.R. Dudek Lotka-Volterra population model of genetic evolution, Commun. Comput. Phys. 2, 1174-1183 (2007)
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