We will study global properties of evolutional Lotka-Volterra system. We assume that the predatory efficiency is a function ofa character of species whose evolution obeys a quantitative genetic model. We will show that the structure ofa solution is rather different from that of a non-evolutional system.We will analytically show new ecological features of the dynamics.
References
[1]
R. Lande, “Quantitative Genetic Analysis of Multivariate Evolution Applied to Brain: Body Allometry,” Evolution, Vol. 33, No. 1, 1979, pp. 402-416. http://dx.doi.org/10.2307/2407630
[2]
R. Lande and S. J. Arnold, “The Measurement of Selection on Correlated Characters,” Evolution, Vol. 37, No. 6, 1983, pp.1210-1226. http://dx.doi.org/10.2307/2408842
[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. http://dx.doi.org/10.2307/2410997
[4]
P. A. Abrams, “Evolutionay Responses Offoraging-Related traits in Unstable Predator-Prey Systems,” Evolutionary Ecology, Vol. 11, No. 6, 1997, pp. 673-686. http://dx.doi.org/10.1023/A:1018482218068
[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. http://dx.doi.org/10.1023/A:1018445517101
[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.