Migration effects in a stochastic multipopulation model for African bee population dynamics

Environmental and Ecological Statistics

Volumn 4, Issue 4, 1997, Pages 301-319

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

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Carrying capacity; Coupled logistic model; Cumulants; Density dependent growth; Quasiequilibrium distribution

Indexed keywords

APIS MELLIFERA; APOIDEA; APIDAE; APIS MELLIFERA SCUTELLATA; HYMENOPTERA;

AFRICANIZED HONEY BEE; MIGRATION; MODELLING; POPULATION DYNAMICS;

USA;

EID: 0031428434     PISSN: 13528505     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1018590915942     Document Type: Article

References (26)

1. Banks, R.B. (1994) Growth and Diffusion Phenomena. Springer-Verlag, Berlin.
2. Bartlett, M.S., Gower, J.C. and Leslie, P.H. (1960) A comparison of theoretical and empirical results for some stochastic population models. Biometrika, 47, 1-11.
3. Gilpin, M. and Hanski, I. (1991) Metapopulation Dynamics: Empirical and Theoretical Investigations. Academic Press, London.
4. Hastings, A. (1993) Complex interactions between dispersal and dynamics: lessons from coupled logistic equations. Ecology, 74, 1362-72.
5. Johnson, N.L., Kotz, S. and Kemp, A.W. (1992) Univariate Discrete Distributions. 2nd edn. Wiley, New York.
6. Kaplan, J.K. (1996) Buzzing across the border. Agricultural Research, 44, 4-10.
7. Knipling, E.F. (1979) The basic principles of insect population suppression and management. Agricultural Research Service No. 512. US Department of Agriculture, Washington, DC.
8. Matis, J.H. and Kiffe, T.R. (1996) On approximating the moments of the equilibrium distribution of a stochastic logistic model. Biometrics, 52, 980-91.
9. Matis, J.H., Rubink, W.L. and Makela, M. (1992) Use of the gamma distribution for predicting arrival times of invading insect populations. Environmental Entomology, 21, 436-40.
10. Matis, J.H., Kiffe, T.R. and Otis, G.W. (1994) Use of birth-death-migration processes for describing the spread of insect populations. Environmental Entomology, 23, 18-28.
11. Matis, J.H., Yang, S., Castiaux, N., Westbrook, J.K., Beerwinkle, K.R. and Lopez, J. D. Jr (1995a) Predicting the date of first catch of the corn earworm, Helicoverpa zea, in central U.S. In Proceedings of Applied Statistics in Agriculture, J. Schwerke (ed.), Kansas State University Press, Manhattan, KS.
12. Matis, J.H., Zheng, Q. and Kiffe, T.R. (1995b) Describing the spread of biological populations using stochastic compartmental models with births. Mathematical Biosciences, 126, 215-47.
13. Matis, J.H., Kiffe, T.R. and Hengeveld, R. (1996) Estimating parameters for birth-death-migration models from spatio-temporal abundance data: Case of muskrat spread in the Netherlands. Journal of Agricultural, Biological, and Environmental Statistics, 1, 40-59.
14. Matis, J.H., Kiffe, T.R. and Parthasarathy, P.R. (1997) On the cumulants of population size for the stochastic power law logistic model. Theoretical Population Biology. To appear.
15. Otis, G.W. (1991) Population biology of the Africanized honey bee. In The 'African' Honey Bee, M. Spivak, D.J.C. Fletcher and M.D. Breed (eds), Westview, Boulder, CO, pp. 213-34.
16. Pielou, E.C. (1977) Mathematical Ecology. Wiley, New York.
17. Ratnieks, F.L. W. (1991) Africanized bees: Natural selection for colonizing ability. In The 'African' Honey Bee, Westview, Boulder, CO, pp. 119-36.
18. Renshaw, E. (1991) Modeling Biological Populations in Space and Time. Cambridge University Press, New York.
19. Rowell, G.A., Makela, M.E., Villa, J.D., Matis, J.H., Labougle, J.M. and Taylor, O. R., Jr. (1992) Invasive dynamics of Africanized honeybees in North America. Naturwissenschaften, 79, 281-3.
20. Ruxton, D.G. (1996) Density-dependent migration and stability in a system of linked populations. Bulletin of Mathematical Biology, 58, 643-60.
21. Sparks, A.N., Westbrook, J.K., Wolf, W.W., Raulston, J.R. and Pair, S.D. (1989) The potential importance of insect migration to management strategies of maize arthropods. Acta Phytopathologia et Entomologica Hungarica, 24, 195-206.
22. Spivak, M., Fletcher, D.J.C. and Breed, M.D. (1991) The 'African' Honey Bee. Westview, Boulder, CO.
23. Westbrook, J.K., Allen, C.T., Plapp, F.W. Jr. and Multer, W. (1990) Atmospheric transport and pyrethroid-resistant tobacco budworm, Heliothis virescens, in western Texas in 1985. Journal of Agricultural Entomology, 7, 91-101.
24. Westbrook, J.K., Wolf, W.W., Lingren, P.D., Raulston, J.R., Lopez, J.D. Jr., Matis, J.H., Eyster, R.S., Esquivel, J.F. and Schlieder, P.G. (1997) Early-season migratory flights of corn earworm. Environmental Entomology, 26, 12-20.
25. Wissel, C. and Stocker, S. (1991) Extinction of populations by random influences. Theoretical Population Biology, 39, 315-28.
26. Wolfram, S. (1991) Mathematica, A System for Doing Mathematics by Computer. 2nd edn, Addison-Wesley, Redwood City, CA.