Advanced Mathematical Ecology - Syllabus Fall Math/EEB 681

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1 Advanced Mathematical Ecology - Syllabus Fall 2013 Math/EEB 681 Dr. Louis Gross (gross@nimbios.org) Dr. Chris Remien (cremien@nimbios.org) Home Page: Meeting time: 12:20-1:10 MWF Place: Ayres 112 Objectives: The goal of this course is to expand on the material presented in Math/EEB by discussing, in particular, certain areas of research that were not included in that sequence but which are currently being actively pursued. The emphasis is on developing participants appreciation for research questions in theoretical ecology that were not addressed in the mostly deterministic dynamical systems coverage of The focus of that course sequence was on population and some aspects of community ecology. This course expands on this by including some of the variety of methods used to account for individual behavior as they impact population and community processes. We will also consider some questions in evolutionary ecology, again with a focus on individual-level behaviors rather than overlapping the population-genetics approaches that are covered in Math/EEB583. Another emphasis is to expand on the very limited coverage of stochastic models included in The course presumes mathematical maturity at the level of advanced calculus with prior exposure to basic differential equations, linear algebra, and probability. We will not assume that you have previously had the sequence, but will certainly de-emphasize the overlap in material associated with that course. Some Specific Learning Objectives: Enhancing the breadth of exposure for participants in areas of theoretical ecology beyond those emphasized in Math Encouraging participants to consider methods to confront mathematical models with data and how to evaluate models in this context. Developing an appreciation for stochastic modeling in biology beyond discrete statespace approaches. Developing skill at asking critical questions concerning technical topics in a clear manner, both verbally and in writing. Textbook: The Theoretician's Toolbox: Quantitative Methods for Ecology and Evolutionary Biology by Marc Mangel, Cambridge University Press 2006 We will follow this text fairly closely except that we will skip over sections that are highly similar to those covered in and we will skip the chapter focused on fisheries models. The text will be supplemented by materials from several texts on the accompanying reference list, in addition to papers assigned in class. Topics to be covered are given below, though these may be modified to a certain extent by the interests of class participants. Format: The course will be taught in lecture format, with occasional in-class project and problem discussions. Class participants will be expected to attend some special colloquia related to the topics of the course as they are held during the semester. Participants who audit are expected to attend lectures, do the assigned readings and participate in discussions. Although not required, to expand exposure to other areas of mathematical biology participants are encouraged to attend Math 589 which this semester will focus on models in immunology..

2 Course Grading: We will regularly assign problems related to the course material as homework. You may work on such problems with others from the course, but you must independently write up your results, and make it clear with whom you have collaborated on each homework set. We do not intend to give any formal examinations, but all are expected to attend the scheduled final examination period (12:30-2:30 on Tuesday, December 10) as this will include presentations from participants on their own research projects in a context related to the course material. To encourage reading of material prior to class periods, we expect each participant to prepare a question related to the text weekly. These questions will be presented orally in-class and are expected to be provided in writing to the instructors. Participants will also carry out a project related to their own dissertation work and in relation to some component of the course. These projects are expected to be at current research level, with a written report provided at the end of the semester and a brief oral report provided to the entire class, with accompanying visual material, near the end of the semester. Course grading will be based upon: homework (40% of grade), weekly questions (20%), project (40%). Topic Coverage: Key models in Behavioral Ecology Diet-choice and foraging Evolutionarily Stable Strategies Search and predation Stochastic models and statistics Probability background and important distributions Some applications to search and foraging Bayesian methods Host-parasitoid models Nicholson-Bailey and extensions Evolutionary models and stochastic dynamic programming Disease models and Fishery models (may be included based on participant interest and available time) Basic SIR and extensions Evolution of virulence Vectors and disease Fisheries bioeconomic models Stochastic population models Sample paths and stochastic differential equations General stochastic diffusion processes Extinction time in density independent case Extinction time in density-dependent case Individual-based models (as time allows)

3 Designing a model Cellular automata and IBMs Formulating and implementing a model What we will likely not cover: There are many additional topics within mathematical ecology that are not included in this course or in 581-2, some of which are listed below. Any of these could serve as a basis for inclusion in the individual projects, if they connect to participant s dissertation interests. Biophysical ecology and physiological ecology models Stochastic community models Food web, trophic network, and more general biological network models Spatial community models Species distribution models (also called Niche models) Integro-differential equation models (general delay models) Spatial branching and L-systems Neural nets, genetic algorithms, A-life models Basic Reference List: The below texts are general ones that you may find of most interest relative to the content of this course. Additional references will be given in each section of the course. Allen, L. J. S An Introduction to Stochastic Processes with Applications to Biology. Pearson. Upper Saddle River, NJ. Allen, L. J. S An Introduction to Mathematical Biology. Pearson. Upper Saddle River, NJ. Allman, E. S. and J. Rhodes Mathematical Models in Biology: An Introduction. Cambridge Univ. Press. Cambridge. Brauer, F. and C. Castillo-Chavez Mathematical Models in Population Biology and Epidemiology. Springer. New York. Caswell, H Matrix Population Models. 2nd Edition. Sinauer. Sunderland, MA.. Clark, Colin W Mathematical Bioeconomics: The Optimal Management of Renewable Resources. Wiley. New York. Clark, J. S Models for Ecological Data. Princeton University Press. Cushing, J. M An Introduction to Structured Population Dynamics. SIAM, Philadelphia, PA. Denny, M and S. Gaines Chance in Biology: Using Probability to Explore Nature. Princeton Univ. Press. Princeton, NJ. Edelstein-Keshet, L Mathematical Models in Biology. Random House, New York. (Reissued by SIAM 2005)

4 Ellner, S. P. and J. Guckenheimer Dynamic Models in Biology. Princeton Univ. Press. Princeton, NJ. Gotelli, Nicholas J A primer of ecology. Sinauer Associates, Sunderland, MA. Second Edition Grimm, V. and S. F. Railsback Individual-Based Modeling and Ecology. Princeton Univ. Press. Princeton, NJ. Gurney W.S.C. and Nisbet R Ecological Dynamics. Oxford University Press. New York, NY. Haefner, J. W Modeling Biological Systems: Principles and Applications. Chapman and Hall, NY. (Reissued by Springer 2005) Hallam, T. G. and S. A. Levin (eds.) Mathematical Ecology: an Introduction. Springer- Verlag. Berlin. Hastings, A Population Biology: Concepts and Models. Springer-Verlag, NY. Hastings, A. and Gross L Encyclopedia of Theoretical Ecology. University of California Press, Berkeley and Los Angeles, CA. Hofbauer, J. and K. Sigmund The Theory of Evolution and Dynamical Systems. Cambridge University Press, Cambridge. Jones, D. S. and B. D. Sleeman Differential Equations and Mathematical Biology. Chapman and Hall. Boca Raton, FL. Keeling, M. J and P. Rohani Modeling Infectious Diseases in Humans and Animals. Princeton University Press. Levin, S. A., Hallam, T. G. and L. J. Gross (eds.) Applied Mathematical Ecology. Springer-Verlag. Berlin. Maynard Smith, J Mathematical Ideas in Biology. Cambridge Univ. Press, Cambridge. Maynard Smith, J Models in Ecology. Cambridge University Press, Cambridge. Murray, J. D Mathematical Biology. Springer-Verlag. New York. Okubo, A Diffusion and ecological problems: mathematical models. Springer-Verlag. Berlin. (Reissued with additions as Okubo and Levin, 2004) Otto, S. P. and T. Day A Biologist's Guide to Mathematical Modeling in Ecology and Evolution. Princeton Univ. Press. Princeton, NJ. Pielou, E. C Mathematical Ecology. Wiley. New York. Railsback, S. F. and V. Grimm Agent-Based and Individual-Based Modeling: A Practical Introduction. Princeton University Press. Renshaw, E Modelling Biological Populations in Space and Time. Cambridge University Press. Roughgarden, J Primer of Ecological Theory. Prentice Hall. Upper Saddle river, NJ. Taubes, C. H Modeling Differential Equations in Biology. Prentice Hall. Upper Saddle River, NJ.

5 Key Journals in the Field: The American Naturalist Bulletin of Mathematical Biology Journal of Mathematical Biology Journal of Theoretical Biology Mathematical Biosciences Mathematical Biosciences and Engineering Mathematical Medicine and Biology Theoretical Ecology Theoretical Population Biology