Abstract
Classical models for the dynamics of biological populations, such as the famous logistic and Lotka-Volterra equations, involve population-level statistics and parameters. In the “structured” population models of this book, individual members of the population are classified in some manner, usually by means of certain physiological characteristics, and the distribution of individuals based upon this classification is dynamically modeled.
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Literature Cited
Allee, W. C. 1931. Animal Aggregations. University of Chicago Press.
Clark, C. W. 1976. Mathematical Bioeconomics: The Optimal Management of Renewable Resources. Wiley, New York.
Costantino, R. F., and R. A. Desharnais. 1991. Population Dynamics and the’ Tribolium’ Model: Genetics and Demography. Monographs on Theoretical and Applied Genetics 13. Springer, Berlin.
Costantino, R. F., J. M. Cushing, B. Dennis, and R. A. Desharnais. 1995. Experimentally induced transitions in the dynamic behaviour of insect populations. Nature 375: 227–230.
Crowe, K. M. 1991. A discrete size-structured competition model. Ph.D. diss. University of Arizona, Tucson.
Cushing, J. M. 1988a. Nonlinear matrix models and population dynamics. Natural Resource Modeling 2(4): 539–580.
Cushing, J. M. 1988b. The Allee effect in age-structured population dynamics. Pp. 479–505 in T. G. Hallam, L. J. Gross, and S. A. Levin, eds., Mathematical Ecology. World Scientific Press, Singapore.
Cushing, J. M. 1991a. A simple model of cannibalism. Mathematical Biosciences 107(1): 47–72.
Cushing, J. M. 1991b. Some delay models for juvenile vs. adult competition. Pp. 177–188 in S. Busenberg and M. Martelli, eds., Differential Models in Biology, Epidemiology, and Ecology. Springer-Verlag, Berlin.
Cushing, J. M. 1995. Nonlinear matrix models for structured populations. Chapter 26 in O. Arino, D. Axelrod, M. Kimmel, and M. Langlais, eds., Mathematical Population Dynamics III: Mathematical Methods and Modelling of Data. Wuerz, Winnipeg.
Cushing, J. M., and J. Li. 1989. On Ebenman’s model for the dynamics of a population with competing juveniles and adults. Bulletin of Mathematical Biology 51: 687–713.
Cushing, J. M., and J. Li. 1991. Juvenile versus adult competition. Journal of Mathematical Biology 29: 457–473.
Cushing, J. M., and J. Li. 1992. Intra-specific competition and density dependent juvenile growth. Bulletin of Mathematical Biology 54(4): 503–519.
Cushing, J. M., and Zhou Y. 1995. The net reproductive number and stability in linear structured population models. Natural Resource Modeling 8: 297–333.
Dennis, B. 1989. Allee effects: Population growth, critical density, and the chance of extinction. Natural Resource Modeling 3: 481–538.
Dennis, B., R. Desharnais, J. M. Cushing, and R. Costantino. 1995. Nonlinear demographic dynamics: Mathematical models, statistical methods, and biological experiments. Ecological Monographs 65: 261–281.
Ebenman, B. 1987. Niche difference between age classes and intraspe-cific competition in age-structured populations. Journal of Theoretical Biology 124: 25–33.
Ebenman, B. 1988a. Competition between age classes and population dynamics. Journal of Theoretical Biology 131: 389–400.
Ebenman, B. 1988b. Dynamics of age-and size-structured populations: In-traspecific competition. Pp. 127–139 in B. Ebenman and L. Persson, eds., Size-Structured Populations: Ecology and Evolution. Springer-Verlag, Berlin.
Ebenman, B., and L. Persson, eds. 1988. Size-Structured Populations: Ecology and Evolution. Springer-Verlag, Berlin.
Gantmacher, F. R. 1960. The Theory of Matrices. Vol. II. Chelsea,New York.
Impagliazzo, J. 1980. Deterministic Aspects of Demography. Springer, Berlin.
Lauwerier, H. A. 1986. Two-dimensional iterative maps. Pp. 58–95 in A. V. Holden, ed., Chaos. Princeton University Press, Princeton, N.J.
Loreau, M. 1990. Competition between age classes, and the stability of stage-structured populations: A re-examination of Ebenman’s model. Journal of Theoretical Biology 144: 567–571.
May, R. M., G. R. Conway, M. P. Hassell, and T. R. E. Southwood. 1974. Time delays, density-dependence and single-species oscillations. Journal of Animal Ecology 43: 747–770.
Rabinowitz, P. H. 1971. Some global results for nonlinear eigenvalue problems. Journal of Functional Analysis 1(3): 487–513.
Sokoloff, A. 1974. The Biology of ‘Tribolium’. Vol. 2. Oxford University Press.
Tschumy, W. O. 1982. Competition between juveniles and adults in age-structured populations. Theoretical Population Biology 21: 255–268.
Usher, M. B. 1966. A matrix approach to the management of renewable resources with special reference to forests. Journal of Applied Ecology 3: 355–367.
Usher, M. B. 1972. Developments in the Leslie matrix model. Pp. 29–60 in J. M. R. Jeffers, ed., Mathematical Models in Ecology. Blackwell, London.
Wiggins, S. 1990. Introduction to Applied Nonlinear Dynamical Systems and Chaos. Tests in Applied Mathematics, Vol. 2. Springer, Berlin.
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Cushing, J.M. (1997). Nonlinear Matrix Equations and Population Dynamics. In: Tuljapurkar, S., Caswell, H. (eds) Structured-Population Models in Marine, Terrestrial, and Freshwater Systems. Population and Community Biology Series, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5973-3_6
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