A stochastic metapopulation model accounting for habitat dynamics

Journal of Mathematical Biology

Volumn 52, Issue 6, 2006, Pages 788-806

  Ross, J V ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Diffusion approximations; Habitat dynamics; Markov chains; Metapopulations; Stochastic logistic model; Stochastic models

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; ENVIRONMENT; POPULATION DYNAMICS; STATISTICS;

ANIMALS; COMPUTER SIMULATION; ENVIRONMENT; MODELS, BIOLOGICAL; POPULATION DYNAMICS; STOCHASTIC PROCESSES;

EID: 33646676997     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-006-0372-8     Document Type: Article

References (20)

1. Amarasekare, P., Possingham, H.: Patch dynamics and metapopulation theory: The case of successional species. J. Theoret. Biol. 209, 333-344 (2001)
2. Barbour, A.D.: On a functional central limit theorem for Markov population processes. Adv. Appl. Probab. 6, 21-39 (1974)
3. Barbour, A.D.: Quasi-stationary distributions in Markov population processes. Adv. Appl. Probab. 8, 296-314 (1976)
4. Barbour, A.D.: Equilibrium distributions Markov population processes. Adv. Appl. Probab. 12, 591-614 (1980)
5. Barbour, A.D.: Density dependent Markov population processes. In Biological growth and spread, W. Jäger, H. Rost, P. Tautu (eds.), Lecture Notes in Biomathematics 38, Springer, Berlin, pp 36-49 1980
6. Brachet, S., Olivieri, I., Godelle, B., Klein, E., Frascaria-Lacoste, N., Gouyon, P.H.: Dispersal and metapopulation viability in a heterogeneous landscape. J. Theoret. Biol. 198, 479-495 (1999)
7. Clancy, D., O'Neill, P.D., Pollett, P.K.: Approximations for the long-term behaviour of an open-population epidemic model. Methodol. Comput. Appl. Probab. 3, 75-95 (2001)
8. 0 in models for infectious diseases in heterogenous populations. J. Math. Biol. 28 (4), 365-382 (1990)
9. Ellner, S.P., Fussmann, G.: Effects of successional dynamics on metapopulation persistence. Ecology 84, 882-889 (2003)
10. Hanski, I.A., Gaggiotti, O.E. (Eds.), Ecology Genetics and Evolution of Metapopulations. Academic Press, London (2004)
11. Hastings, A.: Metapopulation persistence with age-dependent disturbance or succession. Science 301, 1525-1526 (2003)
12. Hess, G.R.: Linking extinction to connectivity and habitat destruction in metapopulation models. Am. Nat. 148, 226-236 (1996)
13. Johnson, M.P.: The influence of patch demographics on metapopulations, with particular reference to successional landscapes. Oikos 88, 67-74 (2000)
14. Keymer, J.E., Marquet, P.A., Velasco-Hernandez, J.X., Levin, S.A.: Extinction thresholds and metapopulation persistence in dynamic landscapes. Amer. Natur. 156, 478-494 (2000)
15. Kurtz, T.: Solutions of ordinary differential equations as limits of pure jump Markov processes. J. Appl. Probab. 7, 49-58 (1970)
16. Kurtz, T.: Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Probab. 8, 344-356 (1971)
17. Levins, R.: Some demographic and genetic consequences of environmental heterogeneity for biological control. Bull. Entom. Soc. Amer. 15, 237-240 (1969)
18. Parsons, R.W., Pollett, P.K.: Quasistationary distributions for some autocatalytic reactions. J. Statist. Phys. 46, 249-254 (1987)
19. Pollett, P.K.: On a model for interference between searching insect parasites. J. Austral. Math. Soc. Ser. B 32, 133-150 (1990)
20. Pollett, P.K., Vassallo, A.: Diffusion approximations for some simple chemical reaction schemes. Adv. in Appl. Probab. 24, 875-893 (1992)