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
Dr. David Wethey -- Office: 704 EWS -- Phone: 777-3936  Email: wethey at biol.sc.edu
Dr. Matt Miller -- Office:  -- Phone: 777-3690 Email: miller at math.sc.edu

Date

Topic

Readings 
Off Campus Access

Homework

Worksheets

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

LesliePlot.mws,

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

 

 

chaos_demo

Sep 22

Work on Projects

 

 

 

Sep 27

Harvesting Models

Case Chap 10

 

 

Sep 29

Predator-prey models - behavior

Case Ch 12 to p277

 

volterra.mws

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

FALL BREAK

 

 

 

Oct 25

Host Parasitoid Models

 

Choose Projects on multiple species dynamics

blowflies.mws NBaddendum.mws

Oct 27

Competition models - behavior

Case Ch 14

 

competition.mws

Nov 01

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

 

 

DE_system.mws

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

THANKSGIVING BREAK

 

 

 

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

 

 

 

 
 Grading:

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: http://www.biol.sc.edu/~wethey/763/index.html