APM  Vol.3 No.9 , December 2013
Global Properties of Evolutional Lotka-Volterra System

We will study global properties of evolutional Lotka-Volterra system. We assume that the predatory efficiency is a function of a character of species whose evolution obeys a quantitative genetic model. We will show that the structure of a solution is rather different from that of a non-evolutional system. We will analytically show new ecological features of the dynamics.

Cite this paper: M. Yoshino and Y. Tanaka, "Global Properties of Evolutional Lotka-Volterra System," Advances in Pure Mathematics, Vol. 3 No. 9, 2013, pp. 709-718. doi: 10.4236/apm.2013.39097.

[1]   R. Lande, “Quantitative Genetic Analysis of Multivariate Evolution Applied to Brain: Body Allometry,” Evolution, Vol. 33, No. 1, 1979, pp. 402-416.

[2]   R. Lande and S. J. Arnold, “The Measurement of Selection on Correlated Characters,” Evolution, Vol. 37, No. 6, 1983, pp.1210-1226.

[3]   P. A. Abrams and H. Matsuda, “Prey Adaptation as a Cause of Predator-Prey Cycles,” Evolution, Vol. 51, No. 6, 1997, pp. 1742-1750.

[4]   P. A. Abrams, “Evolutionay Responses Offoraging-Related traits in Unstable Predator-Prey Systems,” Evolutionary Ecology, Vol. 11, No. 6, 1997, pp. 673-686.

[5]   P. A. Abrams and H. Matsuda, “Fitness Minimization and Dynamic Instability as a Consequence of Predator-Prey Coevolution,” Evolutionary Ecology, Vol. 11, No. 1, 1997, pp. 1-20.

[6]   Y. Takeuchi, “Global Dynamical Properties of Lotka-Volterra Systems,” World Scientific, Singapore, 1996.

[7]   R. A. Fisher, “The Genetical Theory of Natural Selection,” Claredon Press, Oxford, 1930.