A comparison of three different stochastic population models with regard to persistence time

Theoretical Population Biology

Volumn 64, Issue 4, 2003, Pages 439-449

  Allen, Linda J S ^a   Allen, Edward J ^a  

^a TEXAS TECH UNIVERSITY   (United States)

Author keywords

Birth and death process; Logistic equation; Markov chain; Persistence time; Stochastic differential equation

Indexed keywords

BIRTH RATE; MARKOV CHAIN; MORTALITY; PERSISTENCE; POPULATION MODELING; STOCHASTICITY;

EID: 0346338100     PISSN: 00405809     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0040-5809(03)00104-7     Document Type: Article

References (46)

1. Allen E.J. Stochastic differential equations and persistence time for two interacting populations. Dynam. Contin., Discrete and Impulsive Systems. 5:1999;271-281.
2. Allen L.J.S. An Introduction to Stochastic Processes with Applications to Biology. 2003;Prentice Hall, Upper Saddle River, NJ.
3. Allen E.J., Victory H.D. Modelling and simulation of a schistosomiasis infection with biological control. Acta Trop. 87:2003;251-267.
4. Busenberg S., Cooke K. Vertically Transmitted Diseases: Models and Dynamics. 1993;Springer, Berlin, Heidelberg, New York.
5. Caswell H. Matrix Population Models. 2nd Edition:2001;Sinauer Assoc. Inc. Pub. Sunderland, Mass.
6. Cushing, J.M., 1998. An Introduction to Structured Population Dynamics, SIAM CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 71, Philadelphia, PN.
7. Cushing J.M., Constantino R.F., Dennis B., Desharnais R.A., Henson S.M. Chaos in Ecology. 2003;Academic Press, Amsterdam, Boston, London, New York.
8. DeAngelis, D.L., Gross, L. (Ed.), 1992. Individual-Based Models and Approaches in Ecology. Chapman & Hall, New York, NY.
9. Dennis B. Allee effects in stochastic populations. Oikos. 96:2002;389-401.
10. Dennis B., Costantino R.F. Analysis of steady-state populations with the gamma abundance model. application to Tribolium Ecology. 69:1988;1200-1213.
11. Dennis B., Munholland P.L., Scott J.M. Estimation of growth and extinction parameters for endangered species. Ecol. Monogr. 61:1991;115-143.
12. Dennis B., Taper M.L. Density dependence in time series observations of natural populations. estimation and testing Ecol. Monogr. 64:1994;205-224.
13. Dushoff J. Carrying capacity and demographic stochasticity. scaling behavior of the stochastic logistic model Theor. Popul. Biol. 57:2000;59-65.
14. Gard T.C. Introduction to Stochastic Differential Equations. 1988;Marcel Dekker, Inc. New York and Basel.
15. Gardiner C.W. Handbook of Stochastic Methods for Physics, Chemistry and the Natural Science. 1985;Springer, Berlin, Heidelberg, New York.
16. Goel N.S., Richter-Dyn N. Stochastic Models in Biology. 1974;Academic Press, New York.
17. Golec, J., Sathananthan, S., 2003. Stability analysis of a stochastic logistic model. Mathematical and Computer Modelling, In press.
18. Hanski I.A., Gilpin M.E. Metapopulation Biology: Ecology, Genetics, and Evolution. 1997;Academic Press, San Diego, CA.
19. Karlin S., Taylor H.M. A First Course in Stochastic Processes. 2nd Edition:1975;Academic Press, San Diego, New York, Boston, London.
20. Karlin S., Taylor H.M. A Second Course in Stochastic Processes. 1981;Academic Press, San Diego, New York, Boston, London.
21. Keeling M.J. Simple stochastic models and their power-law type behavior. Theor. Popul. Biol. 58:2000;21-31.
22. Kloeden P.E., Platen E. Numerical Solution of Stochastic Differential Equations. 1992;Springer, New York.
23. Kloeden P.E., Platen E., Schurz H. Numerical Solution of SDE through Computer Experiments. 1997;Springer, Berlin.
24. Langtangen H.P. Numerical solution of first passage problems in random vibrations. SIAM J. Sci. Comput. 15:1994;977-996.
25. Leigh E.G. The average lifetime of a population in a varying environment. J. Theor. Biol. 90:1981;213-239.
26. Matis J.H., Kiffe T.R. Effects of immigration on some stochastic logistic models: a cumulant truncation analysis. Theor. Popul. Biol. 56:1999;139-161.
27. Matis J.H., Kiffe T.R. Stochastic Population Models A Compartmental Perspective. 2000;Springer, New York.
28. Näsell I. Extinction and quasi-stationarity in the Verhulst logistic model. J. Theor. Biol. 211:2001;11-27.
29. Näsell I. Moment closure and the stochastic logistic model. Theor. Popul. Biol. 63:2003;159-168.
30. Nisbet R.M., Gurney W.S.C. Modelling Fluctuating Populations. 1982;Wiley, Chichester, New York, Brisbane, Toronto, and Singapore.
31. Norden R.H. On the distribution of the time to extinction in the stochastic logistic population model. Adv. Appl. Prob. 14:1982;687-708.
32. Ø ksendal B. Stochastic Differential Equations An Introduction with Applications. 5th Edition:2000;Springer, Berlin, Heidelberg, New York.
33. Ortega J.M. Matrix Theory A Second Course. 1987;Plenum Press, New York.
34. Pielou E.C. Mathematical Ecology. 1977;Wiley, New York.
35. Renshaw E. Modelling Biological Populations in Space and Time. 1993;Cambridge University Press, Cambridge.
36. Richter-Dyn N., Goel N.S. On the extinction of colonizing species. Theor. Popul. Biol. 3:1972;406-433.
37. Roberts J.B. First passage probabilities for randomly excited systems: diffusion methods. Prob. Eng. Mech. 1:1986;66-81.
38. Schurz H. Numerical analysis of stochastic differential equations without tears. Kannan D., Lakshmikantham V. Handbook of Stochastic Analysis and Applications. 2002;237-359 Marcel-Dekker, New York.
39. Sharp W.D., Allen E.J. Numerical solution of first passage time problems using an approximate Chapman-Kolmogorov relation. Probab. Eng. Mech. 13:1998;233-241.
40. Tier C., Hanson F.B. Persistence in density dependent stochastic populations. Math. Biosci. 53:1981;89-117.
41. Tognetti K., Winley G. Stochastic growth models with logistic mean population. J. Theor. Biol. 82:1980;167-169.
42. Tuckwell H.C., Koziol J.A. Logistic population growth under random dispersal. Bull. Math. Biol. 49:1987;495-506.
43. Wissel C. Metastability, a consequence of stochastics in multiple stable population dynamics. Theor. Popul. Biol. 36:1989;296-310.
44. Wissel C., Schmitt T. How to avoid extinction of populations optimally exploited. Math. Biosci. 84:1987;127-138.
45. Wissel C., Stöcker S. Extinction of populations by random influence. Theor. Popul. Biol. 39:1991;315-328.
46. Wissel C., Zaschke S.-H. Stochastic birth and death processes describing minimal viable populations. Ecol. Modelling. 75/76:1994;193-201.