Population Biology and Evolutionary Game Theory
is an interdisciplinary research area and a kind of of Applied Mathematics
. The field focuses on the application of mathematical principles and techniques to help understand biological phenomena. Evolutionary Game Theory
(EGT) applies game theory to try to understand the evolution of populations and their phenotypical / genotypical properties. In EGT, a species or phenotype is associated to a strategy.
This course will introduce you to Mathematical Biology and Evolutionary Game Theory. The course will begin with selected results in mathematical biology in order to provide prerequisite knowledge on dynamical systems required for Evolutionary Game Theory. Substantial emphasis will be placed on evolutionary games in the second half of the course.
Instructors: Dr. Christopher Griffin
and Prof. Andrew Belmonte
Spring 2014 Office Hours:
T 11:30 - 12:30P (5 McAllister), W 11:00 - 1:00P (322 McAllister and 2:15P - 3:15P (5 McAllister)
Math 140, 141 and Math 220, or a course in Matrix Algebra or permission of the instructor(s).
- M. Broom and J. Rychtar, Game-Theoretical Models in Biology, Chapman & Hall, CRC Press, 2013.
- J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, 1998
- J. D. Murray, Mathematical Biology I: An Introduction, Springer, 3ed, 2007
- J. Strogatz, Nonlinear Dynamics and Chaos, Westview Press, 2001
In Spring 2014,
We will teach this course as a hybrid online course. If you’re thinking of taking this course with us, you are welcome to e-mail either of us and ask anything you like.
As a general rule, we'll try to focus concepts so that you don't get lost in the math. The goal of this course is to introduce and interest you to mathematical biology with an emphasis on games in mathematical biology. That being said, you will have to do some math (this is an advanced math class), but we hope to make the class accessible to mathematically inclined biological sciences majors as well as math majors who are interested in biological sciences.
By the end of this course you should, ideally, have a very good working knowledge of elements of mathematical biology as well as a refresher / introduction to dynamical systems as they apply to modeling biological systems.
Spring 2014 Syllabus
Class Notes will be posted on Angel as they become available. We recommend these notes be used with one of the books above, but this is not required.
If you want to contact us by anonymous e-mail, follow this link.
Specific topics we'll cover
- Introduction to Differential Equations (with a review of Matrix Topics)
- Predator-Prey Models
- Epidemic Models
- Cellular Automata Models
- Introduction to Game Theory
- Evolutionary Stable Strategies
- Replicator Dynamics
- Alternatives to the Replicator Dynamics
- Spatial Models (Partial Differential Equations)