University of South Carolina       

Department of Biological Sciences Department of Mathematics

MATH523/BIOL763 ---Population Biology aka Mathematical Biology --- Fall 2011
Time: Tuesday/Thursday 9:30 - 10:45 -- 302 Coker Life Science
David Wethey -- Office: 704 EWS -- Phone: 777-3936  Email: wethey at
Dr. Matt Miller -- Office:  -- Phone: 777-3690 Email: miller at



Off Campus Access



Aug 18

Introduction / Unconstrained Population Growth

Case Ch1, Appendix 1

Complete Worksheet 1


Aug 23

Unconstrained Growth/ Introduction to transformations




Aug 25

Introduction to Maple, eigenvalue/eigenvector analysis

Case p45-54,
Running R

P 63-64: Prob 2,3  Worksheet 2

intro.mws ,intro.R transformations.mws transformations.R

Aug 30

Eigenvalue/eigenvector analysis


eigen.mws, eigen.R


Sep 01

Eigenvalue/eigenvector analysis




Sep 06

Growth of age-structured populations

Case  p64 -end of chapter


leslie.mws, leslie.R

Sep 08

Growth of stage-structured populations


p77: Prob 4,5


Sep 13

Continuous logistic population growth

Case Chap 5 Science 269:341-346


cohen.mws growth.mws

Sep 15

Discrete logistic population growth

Science 186: 645-647  AmNat 110:573-599

p135: Prob 6-11 Choose Projects on single species dynamics

may.mws may.R, nonlinear.mws

Sep 20

Discrete logistic continued / stability analysis




Sep 22

Work on Projects




Sep 27

Harvesting Models

Case Chap 10



Sep 29

Predator-prey models - behavior

Case Ch 12 to p277



Oct 04

Predator-prey models – linear stability analysis

 Case Ch 13 to p 301


 linearization.mws localstab.mws

Oct 06

Disease Models




Oct 11

Project Presentations




Oct 13

Project Presentations




Oct 18

Predator-prey models – linear stability analysis

 Case Ch 13 to p 301

Single Species Project Papers Due


Oct 20





Oct 25

Host Parasitoid Models


Choose Projects on multiple species dynamics

blowflies.mws NBaddendum.mws

Oct 27

Competition models - behavior

Case Ch 14



Nov 01

Maple analysis of equilibria, phase plots, linear stability, isocline plots, etc




Nov 03

Trace/Determinant Analysis; Work on projects




Nov 08

Chemostats - Dimensional Analysis




Nov 10

Chemostats continued / work on projects




Nov 15

Project Presentations




Nov 17

Project Presentations




Nov 22

Disease Models


Multiple Species Project Papers Due


Nov 24





Nov 30

Metapopulation Models

Case Ch 16 Biol J Linn Soc 42:17-38



Dec 01

Age Structured Metapopulation Models

FinalExam Handed Out



Dec 06

FINAL EXAM 5:00 pm  TAKE HOME Due at end of exam period





100 pts - First Project
100 pts - Second Project
100 pts - Take Home Final
300 pts - Total

Learning Outcomes: Students will gain the mathematical tools needed to evaluate theoretical models reported by environmental scientists in their published papers. Students will learn how to take apart published models and ask "what-if" questions about them using altered data and parameters, in order to test ecological hypotheses. See Biology Dept Curriculum Goals.

This page last modified August 17, 2011 URL: