Evolutionary stability of ideal free nonlocal dispersal

Journal of Biological Dynamics

Volumn 6, Issue 2, 2012, Pages 395-405

  Cosner, Chris ^a   Dávila, Juan ^b   Martínez, Salomé ^b  

^a Department of Biology   (United States)

^b UNIVERSITY OF CHILE   (Chile)

Author keywords

evolution of dispersal; evolutionarily stable strategy; ideal free distribution; intergrodifferential equations; nonlocal dispersal

Indexed keywords

ANIMAL; ANIMAL DISPERSAL; ARTICLE; BIOLOGICAL MODEL; EVOLUTION; PHYSIOLOGY;

ANIMAL DISTRIBUTION; ANIMALS; BIOLOGICAL EVOLUTION; MODELS, BIOLOGICAL;

EID: 84868307946     PISSN: 17513758     EISSN: 17513766     Source Type: Journal    
DOI: 10.1080/17513758.2011.588341     Document Type: Article

References (27)

1. Amarasekare, P. 2007. Spatial dynamics of communities with intraguild predation: the role of dispersal strategies. Am. Nat., 170: 819-831.
2. Bates, P. and Zhao, G. 2007. Existence, uniqueness, and stability of the stationary solution to a nonlocal equation arising in population dispersal. J. Math. Anal. Appl., 332: 428-440.
3. Cantrell, R. S. and Cosner, C. 2003. Spatial Ecology via Reaction--Diffusion Equations, Chichester: Wiley.
4. Cantrell, R. S., Cosner, C., DeAngelis, D. L. and Padrón, V. 2007. The ideal free distribution as an evolutionarily stable strategy. J. Biol. Dyn., 1: 249-271.
5. Cantrell, R. S., Cosner, C. and Lou, Y. 2009. "Evolution of dispersal in heterogeneous landscapes". Edited by: Cantrell, R. S., Cosner, C. and Ruan, S. Boca Raton, FL: Chapman Hall/CRC. in Spatial Ecology
6. Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and the ideal free distribution. Math. Biosci. Eng., 7: 17-36.
7. Clobert, J., Danchin, E., Dhondt, A. and Nichols, J. 2001. Oxford: Oxford University Press. Dispersal
8. Cortázar, C., Coville, J., Elgueta, M. and Martínez, S. 2007. A nonlocal inhomogeneous dispersal process. J. Differential Equations, 241: 332-358.
9. Cosner, C. 2005. A dynamic model for the ideal free distribution as a partial differential equation. Theoret. Popul. Biol., 67: 101-108.
10. Cosner, C. 2008. "Reaction--diffusion equations and ecological modeling". Edited by: Friedman, A. 77-116. New York: Springer. in Tutorials in Mathematical Biosciences IV, Lecture Notes in Mathematics Vol. 1922
11. Coville, J. 2008. Remarks on the strong maximum principle for nonlocal operators. Electron. J. Differential Equations, 66: 1-10.
12. Coville, J. 2010. On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators. J. Differential Equations, 249: 2921-2953.
13. Coville, J., Dávila, J. and Martíinez, S. 2008. Existence and uniqueness of solutions to a nonlocal equation with monostable nonlinearity. SIAM J. Math. Anal., 39: 1693-1709.
14. Cressman, R. and Krivan, V. 2006. Migration dynamics for the ideal free distribution. Am. Nat., 168: 384-397.
15. Cressman, R., Krivan, V. and Garay, J. 2004. Ideal free distributions, evolutionary games, and population dynamics in multiple-species environments. Am. Nat., 164: 473-489.
16. Dockery, J., Hutson, V., Mischaikow, K. and Pernarowski, M. 1998. The evolution of slow dispersal rates: a reaction diffusion model. J. Math. Biol., 37: 61-83.
17. Fretwell, S. D. and Hucas, H.L. Jr. 1970. On territorial behavior and other factors influencing habitat selection in birds. Theoretical development. Acta Biotheoretica, 19: 16-36.
18. Hadeler, K. P. 1999. "Reaction-transport systems in biological modelling". Edited by: Capasso, V. and Diekmann, O. 95-150. New York: Springer. in Mathematics Inspired by Biology, Lecture Notes Mathematics Vol. 1714
19. Hastings, A. 1983. Can spatial variation alone lead to selection for dispersal?. Theoret. Popul. Biol., 24: 244-251.
20. Hutson, V., Martínez, S., Mischaikow, K. and Vickers, G. T. 2003. The evolution of dispersal. J. Math. Biol., 47: 483-517.
21. Jin, Y. and Lewis, M. A. Seasonal influences on population spread and persistence in streams II:critical domain size. SIAM J. Appl. Math., in press
22. Kao, C.-Y., Lou, Y. and Shen, W. 2010. Random dispersal vs. non-local dispersal. Discrete and Continuous Dynamical Systems-A, 26: 551-596.
23. Kot, M., Lewis, M. and Driessche, P. van. 1996. Dispersal data and the spread of invading organisms. Ecology, 77: 2027-2042.
24. Krivan, V., Cressman, R. and Schneider, C. 2008. The ideal free distribution: a review and synthesis of the game theoretic perspective. Theoret. Popul. Biol., 73: 403-425.
25. Meysman, F. J.R., Boudreau, B. P. and Middelburg, J. J. 2003. Relations between local, nonlocal, discrete and continuous models of bioturbation. J. Mar. Res., 61: 391-410.
26. Okubo, A. 1980. Diffusion and Ecological Problems: Mathematical Models, Berlin: Springer.
27. Othmer, H. G., Dunbar, S. R. and Alt, W. 1988. Models of dispersal in biological systems. J. Math. Biol., 26: 263-298.