MATH 599 / BIOL 703A / SCCC 412A -- Spatial Ecology

Professor Matt Miller
miller@math.sc.edu
Tu 4:30 -- 5:45 and Th 3:30 -- 4:45 in CLS 202 (excpt for 2/20, 3/20, 4/15)

Note: If this page looks out of date, please Reload (or Refresh) it.

  • Class topics and assignments
  • Jan. 13-15, 20, 27-29. Overview, Levins and Skellam articles and relevant math (Taylor series, point source solution for diffusion equation, problems dealing with t = 0). Homeworks #1 and #2. Step through the Maple worksheet levins-skellam.mws. Jim's presentation of Hanski's modification of the Levins model to the mainland / island "patch" configuration. We missed one class due to the snow day; I would like to make it up, possibly in the time slot scheduled for the final exam (a Friday), or the day before (which is probably more convenient).
  • Feb 4-6. Gabe's presentation of the Levins-Okubo model of windborne dispersal of seeds. Discussion of Skellam 3.1 and 3.2, with emphasis on steady state analysis, effects of boundary conditions, critical habitat size as a function of the diffusion coefficient and the intrinsic rate of increase of the population. More detailed examination of the derivation of the diffusion equation. Homework #3.
  • Feb. 11-13. Pam's presentation of the first part of the KLvdD article. You may find kernels.mws of interest. Also do Homework #4.
  • Feb. 18-21. Conclusion of discussion of KLvdD. Straud's presentation of the Appendix. Introduction to traveling wave solutions in general.
  • Feb. 25-27. Conclusion of Straud's presentation and discussion of KLvdD, Appendix A on speed of the wave front. Traveling wave solutions of the diffusion model and of advection models. Homework #5.
  • Mar. 4-6. Discussion of the WEK paper on ant trails; leaders Sarah and Mark.
  • Mar. 11-13. No class (Spring Break)
  • Mar. 18-20. Continuation of WEK paper discussion.
  • Mar. 25-27. Hanski's approach to metapopulation biology as presented in chapter 2 of Tilman and Kareiva's collection; the rescue effect; discussion leaders Jim and Gabe.
  • April 1-3. Conclusion of Hanski reading; discussion leader Pam. Beginning of second ant paper (WEK2); discussion leader Sarah.
  • April 8-10. Conclusion of model set-up of WEK2. Large chunk of time taken up by discussion of r bar calculation and the general idea of expected value. Straud lead discussion of the results section of the paper.
  • April 15-17. Discussion of the Wissel paper on a grid based model for the spread of rabies. Holmes paper (Tilman-Kareiva chapter 5) on a CA epidemiology SIR model.
  • April 22-24. Conclusion of Holmes, oral presentation of projects.
  • April 29. Oral presentation of projects (conclusion). Assignment of final exam. You may finf the Maple worksheet Bessel.mws to be of some use in problem 4.
  • Make-up day: one of 6-9 May. Discussion of VMW and the final exam, and general remarks on the course as a whole.

  • Exams and Projects
  • FIRST EXAM: to be distributed 27 Feb, and turned in by 5 pm on 7 March to my LeConte mailbox.
  • PROJECT: articles to be examined will be distributed the week of March 18; oral presentations (time limit: 25 minutes) 22, 24 and 29 April. Final written versions due 2 May by 2:30 pm at my office or my LeConte mailbox. Just in case you are wondering just what I am looking for, here's a quick rundown. These are the elements; they don't have to be strictly in this order.
  • Above all remember this is a course in spatial modeling. You must analyse that aspect of the model, though you may want to range into other aspects.
  • First give a brief summary of what the authors say they did: their assumptions, their model, their simulations, their comparison with data (if any), their conclusions. You must include a copy of the paper with your report, so you may refer to Figure 3.2 or equation (6.1) without having to copy these over.
  • Next make a critical assessment of what they did. Does the model accurately reflect the assumptions? Do there appear to be any unstated assumptions? Did they give you enough information that you could implement their model (given enough time, computer capacity, and programming skill)? Do the conclusions that they draw follow in fact from the results that they present? To the extent possible fill in missing steps, for example, of the derivation of steady state solutions, or of equilibria, or verification of the model equations and boundary conditions. If you can, check their simulation, vary parameter values, and so forth.
  • Answer questions that they should have asked themselves, but forgot to (for example, if a certain parameter value is increased, what will happen? what was the initial condition?).
  • Finally give a critical assessment of the overall paper(s), or paper segment(s). Does the model appear to be an appropriate one for the biological system that they claimed to study? Would another type of model perhaps do a better job, or does the given model just need some tinkering (reasoned suggestions would strengthen your case, naturally).
  • Type (or word process) your paper as much as possible. Give me a clean version, without all the dead end scratchwork. Where you fill in by hand make it legible. It would be surprising if you could do all this in less than 5 pages; but I don't want to read 20 either. Probably 8-12 would be good, depending on your layout, font size, number of graphs, figures, and tables.
  • FINAL EXAM: to be distributed 28 April, and turned in by 5 pm, 5 May.

    • Last modified: April 28, 2003