...................................................................... Reading list for 1996 Probability Intern Program ...................................... A. From David Griffeath -- Durrett, R. (1995) Ten lectures on particle systems. Lectures on Probability Theory, pp. 97-201. Springer Lecture Notes in Math 1608. Some recent developments in interacting stochastic systems, with examples drawn from biology and ecology. Edelstein-Keshet, L. Mathematical Models in Biology. Random House, New York, 1988 My favorite reasonably current introduction to biomathematical modeling; see especially the first chapter and the last section of the book for discussion of discrete paradigms. Ermentrout, G.B. and Edelstein-Keshet, L. (1993) Cellular automata approaches to biological modeling. J. Theor. Biol. 160, 97-133 A nice survey of the beginnings of a CA biomathematics literature. Toffoli, T. and Margolus, N. Cellular Automata Machines. MIT Press, Cambridge, Mass., 1987. The best overview of CA modeling. B. From Tony Ives -- The following books provide good, basic reading on theoretical ecology. They provide a good introduction to the application of theory to basic ecological problems. Prof. Ives' lectures will not deal with these topics in detail, but the ecological background will be useful. Gotelli, N. J. 1995. A primer of ecology. Sinauer Associates, Sunderland, MA. Roughgarden, J., R. M. May, and S. A. Levin. 1989. Perspectives in ecological theory. Princeton University Press, Princeton, N. J., USA. C. From Tom Kurtz -- Kurtz, Thomas G. Relationships between stochastic and deterministic population models, Proceedings of the Heidelberg Conference on Models of Biological Growth and Spread, Lecture Notes in Biomathematics 38, Springer-Verlag, Berlin (1980), 449-467. D. From Simon Levin, Dept. of Ecology and Evolutionary Biology Princeton University -- Gueron, S. and S.A. Levin (1995) The dynamics of group formation. Mathematical Biosciences 128:243-264. Mollison, D. and S.A. Levin (1995) Spatial dynamics of parasitism. pp. 384-398. In: (B.T. Grenfell and A.P. Dobson, eds.) Ecology of Infectious Diseases in Natural Populations. Cambridge University Press, Cambridge, U.K. Durrett, R. and S.A. Levin (1994) Stochastic spatial models: a user's guide to ecological applications. Philosophical Transactions of the Royal Society of London, Series B 343:329-350. Durrett, R. and S.A. Levin. (1994) The importance of being discrete (and spatial). Theoretical Population Biology 46:363-394. In addition, Professor Levin has suplied a large number of preprints of articles in press that will be made available to the participants at the beginning of the program. E. From Hal Caswell -- Caswell, H. and J.E. Cohen (1991) Disturbance, interspecific interaction and diversity in metapopulations. Biol. J. Linnean Soc. 42, 193-218. Caswell, H. and J.E. Cohen. 1996. Red, white and blue: environmental variance spectra and coexistence in metapopulations. Journal of Theoretical Biology 176:301-316. Caswell, H. and R.J. Etter. 1993. Ecological interactions in patchy environments: from patch-occupancy models to cellular automata. pp. 93-109 in S. Levin, T. Powell, and J.H. Steele (eds.) Patch Dynamics. Springer-Verlag. Caswell, H. and J.E. Cohen. 1991. Disturbance and diversity in metapopulations. Biological Journal fo the Linnean Society 42:193-218. Depending on the background of the participants, I might also suggest some older material: Hutchinson, G.E. 1951. Copepodology for the ornithologist. Ecology 32:571-577. Hutchinson, G.E. 1953. The concept of pattern in ecology. Proceedings of the Academy of Natural Sciences, Philadelphia. 105:1-12. Huffaker, C.B. 1958. Experimental studies on predation: dispersion factors and predator-prey oscillations. Hilgardia 27:343-383. Paine, R.T. 1966. Food web complexity and species diversity. American Naturalist 100:65-75. Cohen, J.E. 1970. A Markov contingency table model for replicated Lotka-Volterra systems at equilibrium. American Naturalist 104:547-560.