Between discrete and continuous: Consumer-resource dynamics with synchronized reproduction

Ecology

Volumn 89, Issue 1, 2008, Pages 280-288

  Pachepsky, E ^a,b   Nisbet, R M ^a   Murdoch, W W ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b MICROSOFT RESEARCH   (United Kingdom)

Author keywords

Consumer resource cycles; Consumer resource dynamics; Impulsive differential equations; Overcompensation; Pulsed differential equations; Semi discrete models

Indexed keywords

COMPENSATION; FECUNDITY; MODELING; REPRODUCTION; SYNCHRONY;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; CATERING SERVICE; ECOSYSTEM; FEEDING BEHAVIOR; PHYSIOLOGY; POPULATION DENSITY; POPULATION DYNAMICS; POPULATION GROWTH; REPRODUCTION; TIME;

ANIMALS; ECOSYSTEM; FEEDING BEHAVIOR; FOOD SUPPLY; MODELS, BIOLOGICAL; POPULATION DENSITY; POPULATION DYNAMICS; POPULATION GROWTH; REPRODUCTION; TIME FACTORS;

EID: 40449083104     PISSN: 00129658     EISSN: None     Source Type: Journal    
DOI: 10.1890/07-0641.1     Document Type: Article

References (20)

1. Bonsall, M. B., H. C. J. Godfray, C. J. Briggs, and M. P. Hassell. 1999. Does host self-regulation increase the likelihood of insect-pathogen population cycles? American Naturalist 153:228-235.
2. Briggs, C. J., and H. C. J. Godfray. 1996. The dynamics of insect-pathogen interactions in seasonal environments. Theoretical Population Biology 50:149-177.
3. Dugaw, C. J., A. Hastings, E. L. Preisser, and D. R. Strong. 2004. Seasonally limited host supply generates microparasite population cycles. Bulletin of Mathematical Biology 66:583-594.
4. Funasaki, E., and M. Kot. 1993. Invasion and chaos in a periodically pulsed mass-action chemostat. Theoretical Population Biology 44:203-224.
5. Geritz, S. A. H., and E. Kisdi. 2004. On the mechanistic underpinning of discrete-time population models with complex dynamics. Journal of Theoretical Biology 228:261-269.
6. Hui, J., and L. Chen. 2004. Implusive vaccination of SIR epidemic models with nonlinear incidence rates. Discrete and Continuous Dynamical Systems-Series B 4:595-605.
7. Kot, M. 2001. Elements of mathematical ecology. Cambridge University Press, New York, New York, USA.
8. Lakshmikantham, V., D. D. Bainov, and P. S. Simeonov. 1989. Theory of impulsive differential equations. World Scientific, Singapore.
9. Liu, B., and L. Chen. 2004. The periodic competing Lotka-Volterra model with impulsive effect. Mathematical Medicine and Biology 21:129-145.
10. Liu, B., Y. Zhang, and L. Chen. 2004. Dynamic complexities of a Holling I predator-prey model concerning periodic biological and chemical control. Chaos, Solitons and Fractals 22:123-134.
11. May, R. M. 1976. Simple mathematical models with very complicated dynamics. Nature 261:459-467.
12. Murdoch, W. W., C. J. Briggs, and R. M. Nisbet. 2003. Consumer-resource dynamics. Princeton University Press, Princeton, New Jersey, USA.
13. Murdoch, W. W., B. E. Kendall, R. M. Nisbet, C. J. Briggs, E. McCauley, and R. Bolser. 2002. Single-species models for many-species food webs. Nature 417:541-543.
14. Neubert, M. G., and M. Kot. 1992. The subcritical collapse of predator populations in discrete-time predator-prey models. Mathematical Biosciences 110:45-66.
15. Nielsen, S. L., S. Enriquez, C. M. Duarte, and K. Sand-Jensen. 1996. Scaling maximum growth rates across photosynthetic organisms. Functional Ecology 10:167-175.
16. Nisbet, R. M., and W. S. C. Gurney. 1982. Modelling fluctuating populations. John Wiley and Sons, Chichester, UK.
17. Singh, A., and R. M. Nisbet. 2007. Semi-discrete host-parasitoid models. Journal of Theoretical Biology 247:733-742.
18. Thieme, H. R. 2003. Mathematics in population biology. Princeton University Press, Princeton, New Jersey, USA.
19. Turchin, P., and I. Hanski. 1997. An empirically based model for latitudinal gradient in vole population dynamics. American Naturalist 149:842-874.
20. Zhang, S., and L. Chen. 2005. A Holling II functional response food chain model with impulsive perturbations. Chaos, Solitons and Fractals 24:1269-1278.