Population Biology
BIOL 763/599 / MATH 599 and SCCC 411B
Spring 1999

Professor Matt Miller
miller@math.sc.edu
Department of Mathematics
University of South Carolina 		Professor Dave Wethey
wethey@biol.sc.edu
Department of Biological Sciences
University of South Carolina

Tuesday / Thursday 2:00-3:15 in CLS 202
Required text: Mathematical Models in Biology by L. Edelstein-Keshet, McGraw Hill, NY, 1988
Recommended text: Population Biology by Alan Hastings, Springer, NY, 1997

  • Differential Equations
  • Jan 12-14: Rate equations, Euler's method of integration
  • Jan 19-21: The logistic model and modifications; Maple
  • Jan 26-28: The chemostat and compartment models
  • Feb 02-04: Dimensional analysis, systems (beginning), predator-prey models
  • Feb 09-11: Systems (continued): equilibria, eigenvalues and eigenvectors, linearization, stability analysis (whew!)
    First Projects selected
  • Feb 16-18: Systems (continued), predator-prey vs. competition models,
    FIRST EXAM (to be turned in by Feb 25 or so)
  • Difference Equations
  • Feb 23-25: Mixotroph model, age structured discrete model (Leslie model)
    Exam 1 due, more or less
  • Mar 02-04: Leslie-Lefkowitch (linear) models; nonlinear models discrete vs. continuous
  • Mar 9-11: SPRING BREAK -- No class
  • Mar 16-18: Non-linear models, bifurcation, stable cycles and the transition to chaos
  • Mar 23-25: FIRST PROJECT ORAL REPORTS (final written version due Apr 6)
  • Mar 30-Apr 01: Jim Cornette, guest speaker, Dept. of Biological Sciences Colloquium: Monday, March 29, at 4 pm in CLS 005
    Analysis of EST-Contigs -- One Gene or More, and Tuesday, March 30 in class demonstration
    FIRST PROJECT ORAL REPORTS (continued, final written version due Apr 6)
  • Apr 06-08: Nicholson-Bailey host parasitoid model, Poisson processes
    Second Projects selected
  • Apr 13-15: Nicholson-Bailey(cont.), genetic modeling
  • Apr 20-27: ESS, SECOND PROJECT ORAL REPORTS (final written version due noon Tuesday, May 2.
  • Exams These are all take-home; they will be distributed on the first listed date,
    and will be due at the beginning of class on the last listed date.
  • Exam 1: Feb 18-25
  • Exam 2: cancelled
  • FINAL EXAM: Apr 22-MAY 1 (2 pm) A boo-boo on the final. With the values given for the E's in problem #7, p = 0.5 is not an equilibrium -- it should be p = 0.167. If one uses p[0] = 0.1 and p[0] = 0.2, one gets the same phenomenon as we indicate, though with all new values, but the easier fix is to swap the values of E[SS] and E[TT].
    • Last modified: May 28, 1999