Relation of transition probabilities in the Leslie model to those from experimental cumulative distributions

  • Yanan Yu
  • Harvey J. Gold
  • Ronald E. Stinner
Article
  • 24 Downloads

Summary

We explore the relationship between transition probabilities in the Leslie model and those derived from experimental cumulative distributions. The nature of the two kinds of probabilities are discussed, and a formula derived for converting from one to the other. A numerical example is given to illustrate the differences.

Key Words

population dynamics Leslie model development transition probability 

References

  1. Artzrouni, M. A. (1985) Generalized stable population theory.J. Math. Biology 21: 363–381.CrossRefGoogle Scholar
  2. Gold, H. J. (1977)Mathematical Modeling of Biological Systems. Wiley, New York.Google Scholar
  3. Hansen, P. E. (1989) Leslie matrix elements.Biometrics 45: 683–686.CrossRefGoogle Scholar
  4. Kendall, D. G. (1949) Stochastic processes and population growth. Symposium on stochastic processes.J. Royal Statistical Society, Series B 11: 230–264.Google Scholar
  5. Leslie, P. H. (1945) On the use of matrices in certain population mathematics.Biometrika 35: 183–221.CrossRefGoogle Scholar
  6. Logan, J. A., D. J. Wollkind, S. C. Hoy and L. K. Tanigoshi (1976) An analytic model for description of temperature dependent rate phenomena in arthropods.Environ. Entomol. 5: 1133–1140.Google Scholar
  7. Miller, R. G., Jr., (1981)Surviva Analysis. John Willey & Sons, New York.Google Scholar
  8. Plant, R. E. (1986) A method for computing the elements of the Leslie matrix.Biometrics 42: 933–939.CrossRefGoogle Scholar
  9. Plant, R. E. and L. T. Wilson (1986) Models for age structured populations with distributed maturation rates.J. Math. Biology 23: 242–262.CrossRefGoogle Scholar
  10. Roberts, F. S. (1976)Discrete Mathematical Models. Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
  11. Schaalje, G. B. and H. R. van der Vaart (1989) Relationships among recent models for insect population dynamics with variable rates of development.J. Math. Biol. 27: 399–428.CrossRefGoogle Scholar
  12. Schneider, S. M. and H. Ferris (1986) Estimation of stage-specific developmental times and survivorship from stage frequency data.Res. Popul. Ecol. 28: 267–280.Google Scholar
  13. Sharpe, J. H. and D. W. DeMichele (1977) Reaction kinetics of poikilotherm development.J. Theor. Biol. 64: 649–670.PubMedCrossRefGoogle Scholar
  14. Sokal, R. R. and F. J. Rohlf (1981)Biometry. W. H. Freemand & Company, San Francisco.Google Scholar
  15. Stinner, R. E., G. D. Butler, Jr., J. S. Bacheler and C. Tuttle (1975) Simulation of temperature-dependent development in population dynamics models.Can. Entomol. 107: 1167–74.CrossRefGoogle Scholar

Copyright information

© Society of Population Ecology 1991

Authors and Affiliations

  • Yanan Yu
    • 1
  • Harvey J. Gold
    • 2
  • Ronald E. Stinner
    • 3
  1. 1.Mathematics DepartmentAlabama State UniversityMontgometryUSA
  2. 2.Biomathematics Program, Department of StatisticsNorth Carolina State UniversityRaleighUSA
  3. 3.Department of Entomology and Biomathematics ProgramNorth Carolina State UniversityRaleighUSA

Personalised recommendations