Disease in prey population and body size of intermediate predator reduce the prevalence of chaos-conclusion drawn from Hastings-Powell model

Ecological Complexity

Volumn 6, Issue 3, 2009, Pages 363-374

  Das, Krishna pada ^a   Chatterjee, Samrat ^a   Chattopadhyay, J ^a  

^a INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Body size; Chaos; Disease in prey; Impermanence; Intermediate predator; Permanence; Stable

Indexed keywords

EID: 67651091609     PISSN: 1476945X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ecocom.2009.03.003     Document Type: Article

References (39)

1. Anderson R.M., and May R.M. The invasion, persistence and spread of infectious diseases within animal and plant communities. Philos. Trans. R. Soc. Lond. B 314 (1986) 533-570
2. Arino O., Abdllaoui A., Mikram J., and Chattopadhyay J. Infection on prey population may act as a biological control in ratio-dependent predator-prey model. Nonlinearity 17 (2004) 1101-1116
3. Blueweiss L., Fox H., Kudzma V., Nakashima D., and Peters R.H.S. Relationships between some body size and some life history parameters. Oecologia (Berl.) 37 (1978) 257-272
4. Butler G.J., Freedman H., and Waltman P. Uniformly persistent systems. Proc. Am. Math. Soc. 96 (1986) 425-429
5. Chatterjee S., Bandyopadhyay M., and Chattopadhyay J. Proper predation makes the system disease free- conclusion drawn from an eco-epidemiological model. J. Biol. Syst. 14 4 (2006) 599-616
6. Chattopadhyay J., and Sarkar R.R. Chaos to order: preliminary experiments with a population dynamics models of three trophic levels. Ecol. Model. 163 1-2 (2003) 45-50
7. Chattopadhyay J., and Arino O. A predator-prey model with disease in the prey. Nonlinear Anal. 36 (1999) 747-766
8. Dobson A.P. The population biology of parasite induced changes in host behaviour. Q. Rev. Biol. 63 (1988) 139-165
9. Eisenberg J.N., and Maszle D.R. The structural stability o f a three-species food chain model. J. Theor. Biol. 176 (1995) 501-510
10. Freedman H.I. A model of predator-prey dynamics modified by the action of parasite. Math. Biosci. 99 (1990) 143-155
11. Hadeler K.P., and Freedman H.I. Predator-prey populations with parasitic infection. J. Math. Biol. 27 (1989) 609-631
12. Hastings A., and Powell T. Chaos in three-species food chain. Ecology 72 3 (1991) 896-903
13. Hethcote H.W., Ma Z., and Lio S. Effects of quarantine in six endemic models for infectious diseases. Math. Biosci. 180 (2002) 141-160
14. Hethcote H.W., Han W.W.L., and Zhien Ma. A predator-prey model with infected prey. Theor. Pop. Biol. 66 (2004) 259-268
15. Hofbauer, J., 1986. Saturated equilibria, permanence and stability for ecological systems. In: Groos, L., Hallam, T., Levin, S. (Eds.), Mathematical Ecology, Proc. Trieste. World Scientific, Singapore.
16. Hrbacek J. Species composition and amount of the zooplankton in relation to fish stock. Rozpr. Cesk. Akad. Ved., Rada. Mat. Prir. Ved. 10 (1962) 1-116
17. Hutson V., and Law R. Permanent coexistence in general models of three interacting species. J. Math. Biol. 21 (1985) 289-298
18. Jogensen S.E., Ray S., Berec L., and Straskraba M. Improved calibration of a eutrophication model by use of the size variation due to succession. Ecol. Model. 153 (2002) 269-277
19. Kumar R., and Freedman H. A mathematical model of facultative mutualism with populations interacting in a food chain. Math. Biosci. 97 (1989) 235-261
20. La Barbera M. The evolution and ecology of body size. In: Ranp M., and Jablonsky D. (Eds). Patterns and Process in the History of Life (1986), Springer-Verlag, Berlin, Heidelberg 69-98
21. Lehman J. The filter feeder as an optimal forager and the predicted shapes of feeding curves. Limnol. Oceanogr. 21 (1976) 501-516
22. Lonngren K.E., Bai E.W., and Ucar A. Dynamics and synchronization of the Hastings-Powell model of the food chain. Chaos Solitons Fract. 20 (2004) 387-393
23. Maionchi, D.O., Reis, S.F.d., Aguiar, M.A.M.d., 2005. Chaos and pattern formation in a spatial tritrophic food chain. Ecol. Model., doi:10.1016/j.ecolmodel.2005.04.028.
24. Mandal S., Ray S., Roy S., and Jorgensen S.E. Investigation of thermodynamic properties in an ecological model developing from ordered to chaotic states. Ecol. Model. 204 (2007) 40-46
25. McCann K., and Hastings A. Re-evaluating the omnivory-stability relationship in food webs. Proc. R. Soc. Lond. B 264 (1997) 1249-1254
26. McMahon T.A. Size and shape in biology. science 179 (1973) 1201-1204
27. Nagumo M. Uber die Lage der Integralkurven gew onlicher Differentialgleichungen. Proc. Phys. Math. Soc. Japan 24 (1942) 551
28. Rai V., and Sreenivasan R. Period-doubling bifurcations leading to chaos in a model food chain. Ecol. Model. 69 1-2 (1993) 63-77
29. Ray S., Berec L., Straskraba M., and Jogensen S.E. Optimization of exergy and the implications of body sizes of phytoplankton and zooplankton in an aquatic ecosystem model. Ecol. Model. 140 (2001) 219-234
30. Ray S., Berec L., Straskraba M., and Ulanowicz R.E. Evaluation of system performance through optimizing ascendancy in an aquatic ecosystem model. J. Biol. Syst. 9 (2001) 1-22
31. Rosenzweig M.L. Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171 (1971) 385-387
32. Ruxton G.D. Low levels of immigration between chaotic populations can reduce system extinctions by inducing asynchronous cycles. Proc. R. Soc. Lond. B 256 (1994) 189-193
33. Ruxton G.D. Chaos in a three-species food chain with a lower bound on the bottom population. Ecology 77 1 (1996) 317-319
34. Tag E.P.Y. The allometry of algal growth rates. J. Plank. Res. 17 (1995) 1325-1335
35. Turchin P. Complex Population Dynamics. A Theoretical empirical Synthesis (2003), Princeton University Press, Princeton, NJ
36. Varriale M.C., and Gomes A.A. A study of a three species food chain. Ecol. Model. 110 2 (1998) 119-133
37. Venturino E. Epidemics in predator-prey model: disease in the predators. IMA J. Math. Appl. Med. Biol. 19 (2002) 185-205
38. Xiao Y., and Chen L. Modelling and analysis of a predator-prey model with disease in the prey. Math. Biosci. 171 (2001) 59-82
39. Xu C., and Li Z. Influence of intraspecific density dependence on a three-species food chain with and without external stochastic disturbances. Ecol. Model. 155 (2002) 71-83