***=required reading

Once again, we begin with the classics before taking on the more modern approaches.

Lecture 1. Patchy environments.

The first approach we have to looking at spatial questions is to begin
with the classic work of Huffaker, and models of this work. We
will
look first at the results of Huffaker's system, and then develop
models,
in analogy to our work on epidemic modeling, that can be used to help
understand
these dynamics. This work will set the basis for our future
discussions
of metapopulations. Some newer references would be covered in the
Hansk and Gaggiati book.

Gurney,
W.S.C. and Nisbet, R.M. 1978 Predator-Prey fluctuations in patchy
environments. J. Anim. Ecol. 47:85-102.

***Hastings, A. Spatial heterogeneity and the stability of
predator-prey
systems. Theor. Pop. Biol.; 1977, 12: 37-48.

***Huffaker C.B. Experimental studies on predation: dispersion factors
and predator-prey oscillations. Hilgardia; 1958; 27:

343-383.

Levin
S.; R.T. Paine. Disturbance, patch formation, and community structure.
Proc. Nat. Acad. Sci.; 1974; 71: 2744-2747.

see also for a look at more recent work::

Hanski, I. & Gaggiotti, O. (Eds.) 2004. Ecology, genetics, and evolution of metapopulations. Edited by Hanski, I. & Gaggiotti, O. Elsevier Academic Press, Amsterdam, 696 pp.

Hanski, I. & Gilpin, M.E. 1997. Metapopulation Biology: Ecology, Genetics, and Evolution. Academic Press, San Diego, 512 p.

Gilpin, M. & Hanski, I. 1991. Metapopulation Dynamics: Empirical and Theoretical Investigations. Academic Press, London, 336 p.

Lecture 2. Diffusion approaches - introduction. Our goal here will be to present the diffusion models as a way of expressing spatial structure and looking at spatial spread, and to explore the assumptions underlying the model. The examples in Kareiva (1983) will be used to look at the adequacy of the model. The use of the approach to ask other biological questions will be emphasized in future lectures. The review in Hastings et al., 2005 cotnains numerous references that I do not repeat here (see in particular ndow et al.). This topic is a superb example of the theme of what is the level of 'relevant' detail introduced in the first lecture. Also, we explicitly focus on the idea of relating macroscopic behavior (population level) to microscopic behavior (individuals), and to some simple ideas concerning matching of data to model.

Fisher, RA. The wave of advance of advantageous genes. Ann Eugen., Lond,; 1937; 7: 355-369,

**Hastings****,
A.**,
Cuddington,
K., Davies, K.F., Dugaw, C.J., Elmendorf, S., Freestone, A., Harrison,
S., __Ecology Letters __8:91-101

Kareiva, P. 1983. Local movement in herbivorous insects: Applying a passive diffusion mdoel to mark-recapture field studies. OECOLOGIA 57: 322-327

Kierstead, H.; L.B. Slobodkin. The size of water masses containing plankton bloom. J. Mar. Research; 1953; 12: 141-147.

***Levin, S.A. Dispersion and population interactions. Am. Nat.; 1974; 108: 207-228.

***Okubo A. Note: chapter 5 required, do not get caught up in mathematical details (on reserve in library)

Skellam,
J.G. Random dispersal in theoretical populations. Biometrika; 1951; 38:
196-218.