We have now ahd an introduction to some of the general ideas that come
up when dealing with nonlinear models, and will trun to the more specialized
case of age structure. We think that age structure plus density dependence
should elad to cycles, and the goal will be to see if we can distinguish
among different kinds of biological causes for the cycles. We'll
approach this in two ways -- by looking at a way to get a relatively simple
model for age dependent interactions using differential delay equations.
We'll then look at the question from a much more general viewpoint (the
Higgins et al. approach). If time permits, we'll finish by looking
at Tribolium dynamfrom several points of view.
MORE TO COME.
*The Systematic Formulation of Tractable Single-Species Population Models Incorporating Age Structure. W. S. C. Gurney, R. M. Nisbet, J. H. Lawton. Journal of Animal Ecology, Vol. 52, No. 2. (Jun., 1983), pp. 479-495.
Dependence and Age Structure: Nonlinear Dynamics and Population Behavior.
Kevin Higgins, Alan Hastings, Louis W. Botsford. American Naturalist,
Vol. 149, No. 2. (Feb., 1997), pp. 247-269.
and Continuous Insect Populations in Tropical Environments
H. C. J. Godfray, M. P. Hassell
Journal of Animal Ecology, Vol. 58, No. 1. (Feb., 1989), pp. 153-174.
Demographic Dynamics: Mathematical Models, Statistical Methods, and Biological
Brian Dennis, Robert A. Desharnais, J. M. Cushing, R. F. Costantino
Ecological Monographs, Vol. 65, No. 3. (Aug., 1995), pp. 261-282.