A mathematical model of a biological arms race with a dangerous prey

Journal of Theoretical Biology

Volumn 218, Issue 1, 2002, Pages 55-70

  Waltman, Paul ^a   Braselton, James ^b   Braselton, Lorraine ^b  

^a EMORY UNIVERSITY   (United States)

^b GEORGIA SOUTHERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARMS RACE; COEVOLUTION; NUMERICAL MODEL; PREDATOR-PREY INTERACTION;

ARTICLE; BIOLOGY; GENETICS; MATHEMATICAL MODEL; NONHUMAN; PREDATOR; PREY; PRIORITY JOURNAL; SIMULATION; SNAKE; THEORY;

SALAMANDRIDAE; SERPENTES; THAMNOPHIS;

EID: 0036403854     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.2002.3057     Document Type: Article

References (25)

1. Abell, M. L. & Braselton, J. P. (2000). Modern Differential Equations, 2nd Edn, Fort Worth, TX: Harcourt College Publishers.
2. Abrams, P. A. (2000). The evolution of predator-prey interactions: theory and evidence. Ann. Rev. Ecol. Syst. 31, 79-105.
3. Beck, K. (1982). A model of population genetics of cystic fibrosis in the United States. Math. Biosci. 58, 243-257.
4. Beck, K. (1984). Coevolution: mathematical analysis of host-parasite interactions. J. Math. Biol. 19, 63-67.
5. Beck, K., Keener, J. P. & Ricciardi, P. (1982). Influence of infectious disease on the growth of a population with three genotypes. In: Lecture Notes in Biomathematics, Vol. 52. New York: Springer.
6. Beck, K., Keener, J. P. & Ricciardi, P. (1984). The effect of epidemics on genetic evolution. J. Math. Biol. 19, 79-94.
7. Brodie, E. D. III & Brodie, E. D. Jr (1999). Predator prey arms races: asymmetrical selection on predators and prey may be reduced when prey are dangerous. BioScience 49, 557-568.
8. Butler, G. J., Freedman, H. I. & Waltman, P. (1981). Global dynamics of a selection model for the growth of a population with genotypic fertility differences. J. Math. Biol. 12, 25-35.
9. Dawkins, R. & Krebs J. R. (1979). Arms race between and within species. Proceedings of the Royal Society of London. Series, Biological Sciences. 205, 489-511.
10. Doebeli, M. (1997). Genetic variation and the persistence of predator-prey interactions in the Nicholson-Bailey model. J. theor. Biol. 188, 109-120.
11. Doebeli, M. & de Jong, G. (1998). A simple genetic model with non-equilibrium dynamics. J. Math. Biol. 36, 550-536.
12. Epstein, J. M. (1997). Nonlinear Dynamics: Mathematical Biology and Social Sciences, Santa Fe Institute Studies in the Sciences of Complexity. Reading, MA: Addison-Wesley.
13. Freedman, H. I. (1980). Deterministic Mathematical Models in Population Ecology. New York: Marcel Dekker.
14. Freedman, H. I. & Waltman, P. (1978). Predator influence on the growth of a population with three genotypes. J. Math. Biol. 6, 367-374.
15. Freedman, H. I., So, J. W.-H. & Waltman, P. (1987). Predator influence on the growth of a population with three genotypes III. J. Math. Anal. Appl. 128, 287-304.
16. Hadeler, K. P. & Glas, D. (1983). Quasimonotone systems and convergence to equilibrium in a population genetic model. J. Math. Anal. Appl. 95, 297-303.
17. Hadeler, K. P. & Lieberman, V. (1975). Selection models with fertility differences. J. Math. Biol. 2, 19-32.
18. Hutchinson, G. E. (1978). An Introduction to Population Ecology. New Haven, CT: Yale University Press.
19. Josic, K. (1997). Local bifurcations in the symmetric model of selection with fertility differences. J. theor. Biol. 189, 291-295.
20. Nagylaki, T. & Crow, J. F. (1974). Continuous selection models. J. Theor. Popul. Biol. 5, 267-283.
21. PBS video (2001). Nature: Triumph of Life: The Eternal Arms Race (video). Available at: http://www.shoppbs.com.
22. So, J. W.-H. (1986). Analysis of a continuous one-locus, two-allele genetic model with genotypic fertility differences. Math. Biosci. 82, 221-233.
23. So, J. W.-H. (1990). Persistence and extinction in a predator prey model consisting of nine prey genotypes. J. Austr. Math. Soc. 31, 347-365.
24. So, J. W.-H. & Freedman, H. I. (1986). Persistence and global stability in a predator prey model consisting of three prey genotypes with fertility differences. Bull. Math. Biol. 48, 469-484.
25. Wolfram, S. (1999). The Mathematica Book, 2nd Edn. Cambridge: Cambridge University Press.