Lectures:
- The most rudimentary population model with a juvenile and adult
stage(e.g., for amphibians). Hopf bifurcation of periodic
solutions. A simple population model for the Arizonan tiger
salamander.
- Population models with more stages. Persistence and invasion
theory. The role of cannibalism in Arizonan tiger salamanders.
- Discretely structured metapopulation models (with small
subpopulations)
- Transition to continuous structure variables. The Pease/Inaba
influenza model. Measures as state space.
- More general continuously structured population models.
If I find that this is too much material, I will skip (3) and spread
the other topics out. An permeant mathematical theme for (2) to (5)
will be persistence theory (conveniently formulated in terms of
semiflows [dynamical systems]).
- H.R. Thieme: Persistence under relaxed point-dissipativity (with
applications to an endemic model). SIAM J. Math. Anal. 24 (1993),
407-435.
- H.R. Thieme: Uniform weak implies uniform strong persistence
also for non-autonomous semiflows. Proc. Amer. Math. Soc. 127 (1999),
2395-2403.
- H.R. Thieme: Uniform persistence and permanence for non-autonomous
semiflows in population biology, 41 pages (submitted).
For the influenza model:
- C.M. Pease: An evolutionary epidemiological mechanism, with applications
to type A influenza. Theor. Pop. Biol. 31 (1987), 422-452.
- H. Inaba: Mathematical analysis for an evolutionary epidemic model.
in Mathematical Models in Medical and Health Sciences
(M.A. Horn, G. Simonett and G.F. Webb; eds.) Vanderbilt Press 1998,
213-236.
On physiologically structured populations:
- J.A.J. Metz, O. Diekmann: The Dynamics of Physiologically Structured
Populations. Lecture Notes in Biomathematics 68. Springer 1986.
- O. Diekmann, M. Gyllenberg, J.A.J. Metz, H.R. Thieme:
On the formulation and analysis of general deterministic structured
population models. I. Linear theory. J. Math. Biol. (1998), 349-388.
On Metapopulations:
- M. Gyllenberg, I. Hanski, A. Hastings: Structured Metapopulation Models.
In Metapopulation Biology. Ecology, Genetics and Evolution (I. A. Hanski, M. E. Gilpin; eds). Academic Press 1996, Chapter 5.
- A.T. Smith, M.E. Gilpin: Spatially correlated dynamics in a
pika metapopulation. In Metapopulation Biology. Ecology,
Genetics and Evolution (I. A. Hanski, M. E. Gilpin; eds).
Academic Press 1996, 407-428.
Others:
-
O. Diekmann: The many facets of evolutionary dynamics. Preprint.