Abstract
The importance of linear models in the study of the dynamics of structured populations is great. Yet, probably only a few population phenomena can be assumed to be linear. Nonlinearity arises whenever interaction is incorporated into mathematical models, as for density dependence, predator-prey relationships, competition, external forcing, and spatial effects.
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Literature Cited
Brillinger, D. R., J. Guckenheimer, P. Guttorp, and G. Oster. 1980. Empirical modelling of population time series data: The case of age and density dependent vital rates. Lectures on Mathematics in the Life Sciences 13: 65–90.
Caswell, H. 1989. Matrix Population Models. Sinauer, Sunderland, Mass.
Caswell, H., and A. M. John. 1992. From the individual to the population in demographic models. Pp. 36–61 in D. L. DeAngelis and L. J. Gross, eds., Individual-Based Models and Approaches in Ecology. Chapman & Hall, New York.
Cushing, J. M. 1989. A strong ergodic theorem for some nonlinear matrix models for the dynamics of structured populations. Natural Resources Modeling 3(3): 331–357.
DeAngelis, D. L., and L. J. Gross, eds. 1992. Individual-Based Models and Approaches in Ecology. Chapman & Hall, New York.
Gurney, W. S. C., S. P. Blythe, and R. M. Nisbet. 1980. Nicholson’s blowflies revisited. Nature 287: 17–21.
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.
Metz, J. A. J., and O. Diekmann, eds. 1986. The Dynamics of Physiologically Structured Populations. Lecture Notes in Biomathematics 68. Springer-Verlag, Berlin.
Murdoch, W. W., R. M. Nisbet, S. P. Blythe, W. S. C. Gurney, and J. D. Reeve. 1987. An invulnerable age class and stability in delay-differential parasitoid-host models. American Naturalist 129: 263–282.
Murray, J. D. 1989. Mathematical Biology. Springer-Verlag, Berlin.
Neves, K. W., and S. Thompson. 1992. Software for the numerical solution of systems of functional differential equations with state dependent delays. Journal of Applied Numerical Mathematics 9: 385–401.
Nicholson, A. J. 1954. An outline of the dynamics of animal populations. Australian Journal of Zoology 2: 9–65.
Nisbet, R. M., and W. S. C. Gurney. 1982. Modelling Fluctuating Populations. Wiley, New York.
Readshaw, J. L., and W. R. Cuff. 1980. A model of Nicholson’s blowfly cycles and its relevance to predation theory. Journal of Animal Ecology 49: 1005–1010.
Readshaw, J. L., and A. C. M. VanGerwen. 1983. Age-specific survival, fecundity and fertility of the adult blowfly, Lucilia cuprina, in relation to crowding, protein food, and population cycles. Journal of Animal Ecology 52: 879–887.
Tuljapurkar, S. D. 1989. An uncertain life: Demography in random environments. Theoretical Population Biology 35: 227–294.
Wolfram, S. 1984. Cellular automata as models of complexity. Nature 311: 419–424.
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Val, J., Villa, F., Lika, K., Boe, C. (1997). Nonlinear Models of Structured Populations: Dynamic Consequences of Stage Structure and Discrete Sampling. 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_20
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DOI: https://doi.org/10.1007/978-1-4615-5973-3_20
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