Mathematical Biology
Mathematical Biology
Mathematics 496-896
Fall Semester 2002
Textbook
W. S. C. Gurney and R. M. Nisbet, Ecological Dynamics, Oxford U. P. 1998.
References
There are many excellent texts on mathematical biology and ecology. Here is a short list:
- D. Alstad, Basic Populus Models of Ecology , Prentice-Hall 1999.
- F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology
and Epidemiology, Springer-Verlag 2001.
- L. Case, T., An Illustrated Guide to Theoretical Ecology, Oxford UP 2000
- L. Edelstein-Keshet, Mathematical Models in Biology, McGraw-Hill
- A. Hastings, Population Biology, Springer-Verlag
- M. Kot, Elements of Mathematical Ecology, Cambridge U. P. 2001
- J. Mazumdar, An Introduction to Mathematical Physiology and Biology , Cambridge U. P. 1999
- J. Murray, Mathematical Biology Vol 1, Springer-Verlag 2002
- C. Taubes, Modeling Differential Equations in Biology , Prentice-Hall 2000
Topics in Course
- Ecology and population biology (discrete and continuous)
- Pharmacokinetics and compartmental analysis
- Life history theory and energy budgets
- Epidemiology and infectious disease spread
- Structured models; stochasticity
Prerequisites
The prerequisites are Calculus I and Calculus II (derivatives and integrals). Calculus I may
suffice for some; please see me. A large part of the course will involve differential and
difference equations, topics that will be developed in a biology context.
Grading
One Project (30 percent), Assigned Exercises (50 percent), and a final examination (20 percent).
The final examination will be "open book" and will be comprehensive. It will cover some of the basic exercises
assigned in the course.
Project and Laboratory
The class will be divided into several 4-person teams for a small research project that will involve a
laboratory project (with tribolium confusum ).
A formal report from each team, typed in Latex or an equivalent, is due Wednesday, November 27.
A sample paper, to show the format of your report,
is available as a PDF file.
Professor Janet Andersen of Hope College was kind enough to share some of the lab activities that she used in
her mathematical biology course. I learned about these
at her talk in Knoxville at the annual Society of Mathematical
Biology meeting. You can view the tribolium confusum lab protocol .
Adam Shaver of our class found several articles on tribolium cofusum. You can view these as PDF files:
T. Park, Q. Rev. Biol. 1934 .
T. Park and M. Frank, Ecology, 1948. .
J. Ford, J. Animal Ecology, 1937..
N. Taylor, Ecology, 1965. .
N. Taylor, Ecology, 1967.
This last paper is "A mathematical model for tribolium confusum populations".
Assigned Exercises from Gurney & Nisbet
These exercises should be kept in a separate, loose leaf, notebook so they can be easily removed and checked:
Chapter 2 (page 46): 1, 2, 3, 4, 5, 6. Project 1.
Chapter 3 (page 74): 1, 2, 3, 6.
Chapter 4 (page 114): 1, 2.
Chapter 5 (page 145): 1, 2, 3, 4.
Chapter 6 (page 180): 1, 2, 3, 4, 5, 6.
Chapter 7 (page 218): 1, 2.
Exercise Comments
Chapter 2, no. 3: no factor of V in Q_/infinity.
Chapter 2, no. 6: assume S is less than one.
Technology Skills
As a part of the course, students will learn to use technological aides including:
Programming and use of a calculator (a TI-86, TI-89, or TI-92 is strongly suggested)
Learning to program in a computer algebra package (Matlab or Maple)
Using an ODE solver (pplane5.m or Populus)
Learning Tex or Latex
Reading a Research Paper
Another strong suggestion is to read a research paper in the area. This exercise often
gives students a true idea what research in mathematical biology really involves.
A good paper in mathematical ecology that fits well with the lab project is:
D. Crouse, L. Crowder, and H. Caswell, Stage-based population model for loggerhead sea
turtles and implications for conservation, Ecology 68(5), 1412-1423 (1987).
The paper can be downloaded if you wish.
Download Loggerhead Turtle Paper .
Other References
Populus can be downloaded from http://ecology.umn.edu/populus
The inexpensive populus manual
is available through Prentice-Hall, or it can be downloaded from the populus web site.
pplane5.m (a Matlab program) can be downloaded from
http://www.math.rice.edu/~polking/ . The SOLVER program (see the preface of the text), written by Gurney
and Nisbet, can also be used to solve differential and difference equations.
Research Teams
Team 1: Flores, Kochsiek, McMahon, Rieke
Team 2: M. Dvorak, Bradley, Reyes, Windle
Team 3: Drayton, Miller, Brockett, Hulme
Team 4: Bartels, deBuers, Shaver, Wiltgen, Dall-Olmo
Team 5: Coleman, Nissen, Stohs, Cox
Team 6: Kuo, Norgard, D. Dvorak, deVries
Other Literature on Flour Beetles
Benoit, H.P., E. McCauley, J.R. Post.1998. Testing the demographic consequences of
cannibalism in Tribolium confusum. \emph{Ecology} 79(8): 2839-2851.
Borror, D.J., D.W., Delong, C.A. Triplehorn. 1981. \emph{An introduction to the study of
insects}, 5th edition. Saunders College Publishing.
Park, Thomas, D.B. Mertz, W. Grodzinski, and T. Prus. 1965. Cannibalistic Predation in
Populations of Flour Beetles. \emph{Physiol. Zool.}, 38: 289-321.
Young, Allen M. 1970. Predation and abundance in Populations of Flour Beetle.
\emph{Ecology} 51(4): 602-619.
Arthur, F.H. 2000. Impact of food source on survival of red flour beetles and confused flour beetles exposed to
diatomaceous earth, \emph{J. Econ. Entomol} 93(4), 1347-1356.
Wade, M.J. 1980. Group selection, population growth rate, and competitive ability in the flour beetles, Tribolium SSp,
\emph{Ecology} 61(5), 1056-1064.