Effects of immigration on some stochastic logistic models: A cumulant truncation analysis

Theoretical Population Biology

Volumn 56, Issue 2, 1999, Pages 139-161

  Matis, James H ^a   Kiffe, Thomas R ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Birth death process; Carrying capacity; Cumulant function approximation; Differential equations; Muskrat spread; Population growth

Indexed keywords

ANIMALIA; MURIDAE; ONDATRA ZIBETHICUS;

EID: 0033213413     PISSN: 00405809     EISSN: None     Source Type: Journal    
DOI: 10.1006/tpbi.1999.1420     Document Type: Article

References (21)

1. Bailey N. T. J. The Elements of Stochastic Processes. 1964;Wiley, New York.
2. Banks R. B. Growth and Diffusion Phenomena. 1994;Springer-Verlag, Berlin.
3. Barbour A. D. On a functional central limit theorem for Markov population processes. Adv. Appl. Probab. 6:1974;21-39.
4. Bartlett M. S., Gower J. C., Leslie P. H. A comparison of theoretical and empirical results for some stochastic population models. Biometrika. 47:1960;1-11.
5. Chandrasekhar F. R. S. A theory of turbulence. Proc. R. Soc. London A. 229:1955;1-19.
6. Hengeveld R. Dynamics of Biological Invasions. 1989;Chapman-Hall, London.
7. Isham V. Assessing the variability of stochastic epidemics. Math. Biosci. 107:1991;209-224.
8. Johnson N. L., Kotz S., Kemp A. W. Univariate Discrete Distributions. 1992;Wiley, New York.
9. Johnson N. L., Kotz S., Balakrishnan N. Continuous Univariate Distributions. 1994;Wiley, New York.
10. Matis J. H., Kiffe T. R., Hengeveld R. Estimating parameters for birth-death-migration models from spatio-temporal abundance data: Case of muskrat spread in the Netherlands. J. Agric. Biol. Environ. Stat. 1:1996;40-59.
11. Matis J. H., Kiffe T. R., Parthasarathy P. R. Using density-dependent birth-death-migration models for analyzing muskrat spread in the Netherlands. J. Indian Soc. Agric. Stat. 49:1997;139-156.
12. Matis J. H., Kiffe T. R., Parthasarathy P. R. On the cumulants of population size for the stochastic power law logistic model. Theor. Popul. Biol. 53:1998;16-29.
13. Nisbet R. M., Gurney W. S. Modelling Fluctuating Populations. 1982;Wiley, New York.
14. Pielou E. C. Mathematical Ecology. 1977;Wiley, New York.
15. Renshaw E. Modelling Biological Populations in Space and Time. 1991;Cambridge Univ. Press, Cambridge.
16. Renshaw E. Saddlepoint approximations for stochastic processes with truncated cumulant generating functions. J. Math. Appl. Med. Biol. 15:1998;1-12.
17. Skellam J. G. Random dispersal in theoretical populations. Biometrika. 38:1951;196-218.
18. Smith P. J. A recursive formulation of the old problem of obtaining moments from cumulants and vice versa. Am. Stat. 49:1995;217-218.
19. van der Bosch F., Hengeveld R., Metz J. A. J. Analyzing the velocity of animal range expansion. J. Biogeogr. 19:1992;135-150.
20. Whittle P. On the use of the Normal approximation in the treatment of stochastic processes. J. R. Stat. Soc. B. 19:1957;268-281.
21. Wolfram S. Mathematica, a System for Doing Mathematics by Computer. 1991;Addison-Wesley, Redwood City.