Reduction of supercritical multiregional stochastic models with fast migration

Acta Biotheoretica

Volumn 57, Issue 4, 2009, Pages 479-500

  Rincón, Ángeles ^a   Alonso, Juan Antonio ^a   Sanz, Luis ^a  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

Approximate aggregation; Multiregional models; Multitype Bienaym Galton Watson branching processes; Time scales

Indexed keywords

AGE CLASS; DEMOGRAPHY; MIGRATION; NUMERICAL MODEL; POPULATION DYNAMICS; POPULATION MODELING; POPULATION SIZE; REPRODUCTION; STOCHASTICITY; TIMESCALE;

AGE; ANIMAL; ARTICLE; BIOLOGICAL MODEL; POPULATION DYNAMICS; POPULATION MIGRATION; STATISTICS;

AGE FACTORS; ANIMAL MIGRATION; ANIMALS; MODELS, BIOLOGICAL; POPULATION DYNAMICS; STOCHASTIC PROCESSES;

EID: 77949905800     PISSN: 00015342     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10441-009-9084-y     Document Type: Article

References (22)

1. Auger P, Bravo de la Parra R (2000) Methods of aggregation of variables in population dynamics. C R Acad Sci Paris Life Sci 323: 665-674.
2. Arino O, Sánchez E, Bravo de la Parra R, Auger P (1999) A singular perturbation in an age-structured population model. SIAM J Appl Math 60: 408-436.
3. Blasco A, Sanz L, Auger P, Bravo de la Parra R (2001) Linear discrete population models with two time scales in fast changing environments I: autonomous case. Acta Biotheor 49(4): 261-276.
4. Blasco A, Sanz L, Bravo de la Parra R (2002) Approximate reduction of multiregional birth-death models with fast migration. Math Comput Model 36: 47-65.
5. Biggins JD, Cohn H, Nerman O (1999) Multi-type branching in varying environment. Stoch Process Appl 83: 357-400.
6. Caswell H (2001) Matrix population models, 2nd edn. Sinauer Associates Inc., Sunderland.
7. Charles S, Bravo de la Parra R, Mallet JP, Persat H, Auger P (1998) Population dynamics modelling in an hierarchical arborescent river network: an attempt with Salmo trutta. Acta Biotheor 46(3): 223-234.
8. Billingsley P (1986) Probability and measure, 2nd edn. Wiley, New York.
9. Block GL, Allen LJS (2000) Population extinction and quasi-stationary behavior in stochastic density-dependent structured models. Bull Math Biol 62: 199-228.
10. Harris T (1963) The theory of branching processes. Springer-Verlag, Berlin.
11. Holsinger KE (2000) Demography and extinction in small populations. In: Young A, Clarke G (eds) Genetics, demography and the viability of fragmented populations. Cambridge University Press, London.
12. Kimmel M, Axelrod DE (2002) Branching processes in biology. Springer, New York.
13. Mode CJ (1971) Multitype branching processes. American Elsevier, New York.
14. Pichancourt JB, Burel F, Auger P (2006) Assessing the effect of habitat fragmentation on population dynamics: an implicit modelling approach. Ecol Modell 192: 543-556.
15. Rogers A (1995) Multiregional demography. Chichester, New York.
16. Sánchez E, Bravo de la Parra R, Auger P, Gómez Mourelo P (2006) Time scales in linear delayed differential equations. J Math Anal Appl 323: 680-699.
17. Sanz L, Bravo de la Parra R (1999) Variables aggregation in a time discrete linear model. Math Biosci 157: 111-146.
18. Sanz L, Bravo de la Parra R (2000) Time scales in stochastic multiregional models. Nonlinear Anal Real World Appl 1: 89-122.
19. Sanz L, Bravo de la Parra R (2001) Time scales in a non autonomous linear discrete model. Math Models Methods Appl Sci 11(7): 1-33.
20. Sanz L, Blasco A, Bravo de la Parra R (2003) Approximate reduction of Galton-Watson processes with two time scales. Math Models Methods Appl Sci 13: 491-525.
21. Sanz L, Bravo de la Parra R (2007) Approximate reduction of multiregional models with environmental stochasticity. Math Biosci 206: 134-154.
22. Sanz L, Bravo de la Parra R, Sánchez E (2008) Approximate reduction of non-linear discrete models with two time scales. J Differ Equ Appl 14: 607-627.