Mathematical Biology 3380

Fall 2002

Tuesday 10:30-11:50; Thurs 12:00-1:20

3RD FLR CONF ROOM, Thackeray Hall

Bard Ermentrout

Recommended books

Evolutaionary Dynamics Martin Nowak, 2006
Mathematical Biology II J.D. Murray, Springer, 2004

Prerequisites

Mathematics
- Some differential equations
- Some basic linear algebra (eigenvalues, etc)
- Some Fourier series
Computing. You will be required to do many computer exercises. Free software XPPAUT is available that will allow you to do most of the exercises.

Grading

Homework 60%
Final Project 40%

Syllabus

Introduction: Discrete dynamics
- Ecological models - Birth and Death
  - Simple first and second order maps
    - Logistic map
    - Discrete predator-prey
  - Coherence and extinction Paper by Earn and Levin
  - Periodic emergence of cicadas: Hoppensteadt and Keller Science 194:335-337,1976
- Ecological models: Intro to ODE models
  - Predator Prey
  - Competition
  - Oscillations
- Evolutionary dynamics
  - Chapt 2 (Nowak)
  - Some homework
  - The ODE file
  - and the table
  - Chapt 3,4 home work Assignment 2 Due Feb 15
  - Prisoners dilemma in a population with reactive strategies. Here is is a zipped file with code for simulating 100 strategies. I have included a few tables of values which have interesting dynamics showing a switch fromm ALLD to TFT to GTFT.
  - A really fun paper on bimatrix games We will do this paper the week of Feb 12. I have written an ODE file for the paper and here it is
  - Neutral drift and finite populations Chapter 5
  - Here is an XPP file and set file to reproduce figure 7.9d in Nowak ODE file and set file
  - Games on graphs Evolution on graphs and supplementary stuff - proofs etc See also tutorial on evolution on graphs
  - Spatial games: Virtual labs 2x2 games
    - An overview of spatial games
    - Qi Mi has written a NetLogo version for 2 player spatial games Download
    - Pair approximation for spatial models
    - Pair approx for TFT/ALLD lattice
    - Pretty cool 1D lattice TFT model
  - HIV modeling ODE file for HIV mode
  - Virulence modeling ODE file for virulence (Note the ode file is named for this! )