Distributed predator-prey co-evolution

Evolutionary Ecology Research

Volumn 5, Issue 6, 2003, Pages 819-834

  Cohen, Yosef ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Evolutionary distributions; Evolutionary games; Predator prey co evolution; Reaction diffusion equations

Indexed keywords

EID: 2542419450     PISSN: 15220613     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. Abrams, P.A. and Ginzburg, L.R. 2000. The nature of predation: prey dependent, ratio dependent or neither? Trends Ecol. Evol., 15: 337-341.
2. Alonso, D., Bartumeus, F. and Catalan, J. 2002. Mutual interference between predators can give rise to Turing spatial patterns. Ecology, 83: 28-34.
3. Arditi, R., Tyutyunov, Y., Morgulis, A., Govorukhin, V. and Senina, I. 2001. Directed movement of predators and the emergence of density-dependence in predator-prey models. Theor. Pop. Biol., 59: 207-221.
4. Britton, N.F. 1986. Reaction-Diffusion Equations and Their Applications to Biology. New York: Academic Press.
5. Brown, J. 1987. Predator-prey co-evolution as an evolutionary game. In Applications of Control Theory in Ecology (Y. Cohen, ed.), pp. 83-101. Berlin: Springer-Verlag.
6. Cohen, Y. 2003. Distributed evolutionary games. Evol. Ecol. Res., 5: 1-14.
7. Cohen, Y., Vincent, T.L. and Brown, J.S. 2000. A G-function approach to fitness minima, fitness maxima, evolutionarily stable strategies and adaptive landscapes. Evol. Ecol. Res., 1: 923-942.
8. Cohen, Y., Vincent, T.L. and Brown, J.S. 2001. Does the G-function deserve an F? Evol. Ecol. Res., 3: 375-377.
9. Conway, E.D. 1984. Partial Differential Equations and Dynamical Systems. Berlin: Springer-Verlag.
10. Dieckmann, U., Law, R. and Metz, J., eds. 2000. The Geometry of Ecological Interactions: Simplifying Spatial Complexity. Cambridge: Cambridge University Press.
11. Elton, C.S. and Nicholson, M. 1942. The ten-year cycle in numbers of lynx in Canada. J. Anim. Ecol., 191: 215-244.
12. Huisman, G. and de Boer, R.J. 1997. A formal derivation of Beddington functional response. J. Theor. Biol., 185: 389-400.
13. Keshet, Y. and Segel, L.A. 1984. Pattern formation in aspect. In Modelling of Patterns in Space and Time (W. Jager, ed.), pp. 188-197. Berlin: Springer-Verlag.
14. Leung, A.W. 2001. Positive solutions for systems of PDE and optimal control. Nonlinear Anal., 47: 1345-1356.
15. Levin, S.A. and Segel, L.A. 1976. Hypothesis for origin of planktonic patchiness. Nature, 259: 659.
16. Levin, S.A. and Segel, L.A. 1985. Pattern generation in space and aspect. SIAM Rev., 27: 45-67.
17. Lotka, A.J. 1920. Updated oscillations derived from the law of mass actions. J. Am. Chem. Soc., 42: 1595-1599.
18. Lotka, A.J. 1925. Elements of Physical Biology. Baltimore, MD: Williams & Wilkins.
19. Mimura, M. and Murray, J.D. 1978, On a diffusive prey-predator model which exhibits patchiness. J. Theor. Biol., 75: 249-262.
20. Mimura, M., Nishiura, Y. and Yamaguti, M. 1979. Some diffusive prey and predator systems and their bifurcation problems. Ann. NY Acad. Sci., 316, 490-510.
21. Murray, J.D. 1989. Mathematical Biology. New York: Springer-Verlag.
22. Okubo, A. 1980. Diffusion and Ecological Problems: Mathematical Models. Berlin: Springer-Verlag.
23. Rosen, G. 1977. Effects of diffusion on the stability of the equilibrium in multispecies communities. Bull. Math. Biol., 39: 373-383.
24. Ruxton, G.D., Gurney, WS.C. and de Roos, A.M. 1992. Interference and generation cycles. Theor. Pop. Biol., 42: 235-254.
25. Segel, L.A. and Jackson. J.L. 1972. Dissipative structure: an explanation of an ecological example. J. Theor. Biol., 37: 545-559.
26. Smoller, J. 1982. Shock Waves and Reaction-Diffusion Equations. New York: Springer-Verlag.
27. Turing, A.M. 1952. On the chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B, 237: 37-72.
28. Vincent, T.L., Cohen, Y. and Brown, J.S. 1993. Evolution via strategy dynamics. Theor. Pop. Biol., 44: 149-176.
29. Volterra, V. 1926. Variations and Fluctuations of a Number of Individuals in Animal Species Living Together, pp. 409-448. Translation in R.N. Chapman, 1931, Animal Ecology. New York: McGraw Hill.
30. Volterra, V. 1926. Variations and Fluctuations of a Number of Individuals in Animal Species Living Together, pp. 409-448. Translation in R.N. Chapman, 1931, Animal Ecology. New York: McGraw Hill.