Establishment success and extinction risk in autocorrelated environments

Theoretical Population Biology

Volumn 64, Issue 3, 2003, Pages 303-314

  Haccou, Patsy ^a   Vatutin, Vladimir ^b  

^a LEIDEN UNIVERSITY   (Netherlands)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

Branching process model; Establishment success; Extinction; Small population; Temporal correlation; Temporal variation

Indexed keywords

AUTOCORRELATION; BIOLOGICAL INVASION; COLONIZATION; ENVIRONMENTAL CONDITIONS; EXTINCTION RISK; POPULATION MODELING; REPRODUCTION;

EID: 0347599026     PISSN: 00405809     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0040-5809(03)00092-3     Document Type: Article

References (23)

1. Athreya K.B., Karlin S. On branching processes with random environments I. extinction probabilities Ann. Math. Stat. 42:1971;1499-1520.
2. Athreya K.B., Karlin S. Branching processes with random environments, II. limit theorems Ann. Math. Stat. 42:1971;1843-1858.
3. Charlesworth B. Evolution in Age-structured Populations. 2nd Edition:1994;Cambridge University Press, Cambridge.
4. Chesson P.L. The stabilizing effects of a random environment. J. Math. Biol. 15:1982;1-36.
5. Chesson P.L., Ellner S. Invasibility and stochastic boundedness in monotonic competition models. J. Math. Biol. 27:1989;117-138.
6. Cohen D. Optimizing reproduction in a randomly varying environment. J. Theor. Biol. 12:1966;119-129.
7. Cohen D., Levin S.A. Dispersal in patch environments. the effects of temporal and spatial structure Theor. Popul. Biol. 39:1991;63-99.
8. Haccou P., Iwasa Y. Establishment probability in fluctuating environments. a branching process model Theor. Popul. Biol. 50:1996;254-280. doi:10.1006/tpbi.1996.0031.
9. Hanski I. Inferences from ecological incidence functions. Am. Nat. 139:1992;657-662.
10. Johst K., Wissel C. Extinction risk in a temporally correlated fluctuating environment. Theor. Popul. Biol. 52:1997;91-100. doi:10.1006/tpbi.1997.1322.
11. Karlin S., Taylor H.M. A first course in stochastic processes. 2nd ed:1975;Academic Press, New York.
12. Keiding N. Extinction and exponential growth in random environments. Theor. Popul. Biol. 8:1975;49-63.
13. Ludwig D. A singular perturbation problem in the theory of population extinction. Soc. Ind. Appl. Math.-Am. Math. Soc. Proc. 10:1976;87-104.
14. MacArthur R.H. Geographical Ecology. 1972;Harper and Row, New York.
15. MacArthur R.H., Levins R. Theory of Island Biogeography. 1967;Princeton University Press, Princeton.
16. Maynard Smith J. Evolution and the Theory of Games. 1982;Cambridge University Press, Cambridge.
17. Mode C., Jacobson M.E. On estimating critical population size for an endangered species in the presence of environmental stochasticity. Math. Biosci. 85:1987;185-209.
18. Mountford M.D. Population survival in a variable environment. J. Theor. Biol. 32:1971;75-79.
19. Mountford M.D. The significance of clutch-size. Bartlett M.S., Hiorns R.W. The Mathematical Theory of the Dynamics of Biological Populations. 1973;315-323 Academic Press, London.
20. Petrov V.V. Sums of Independent Random Variables. 1975;Springer, Berlin.
21. Smith W.L. Necessary conditions for almost sure extinction of a branching process with random environments. Ann. Math. Statist. 39:1968;2136-2140.
22. Smith W.L., Wilkinson W.E. On branching processes in random environments. Ann. Math. Statist. 40:1969;814-827.
23. Turelli, M., 1980. Niche overlap and invasion of competitors in random environments II. The effects of demographic stochasticity. In: Jäger, W., Rost, H., Tautu, P. (Eds.), Biological Growth and Spread, Lecture Notes in Biomathematics. Springer, Berlin, pp. 119-129.