Evolutionary Dynamics & Mathematical Biology Teaching

In fall 2009 and 2011, I assisted in teaching Math 153 together with Ivana Bozic. This course is an intro to mathematical biology, focusing on evolutionary dynamics, including virus dynamics and game theory.  Martin Nowak first started teaching the course in 2004.

Below are some resources that may be useful to anyone who is planning to design, teach, or take similar courses in the future. If you find the below problem sets and tutorials helpful in your teaching, please tell me! I am always curious to know where they end up.

You can find this page and other educational resources on mathematics in biology at Drexel's Math Forum.

Prof. Nowak's book, Evolutionary Dynamics, available at Google Books and Amazon.  The text follows much of the course fairly closely.

Virus Dynamics, by Martin Nowak and Robert May, which presents theoretical models of virology and weaves in discussion of experiments.  It is particularly helpful for developing mathematical understanding of HIV infection and drug treatment.

Evolutionary Games and Population Dynamics
, by Josef Hofbauer and Karl Sigmund, thoroughly covering evolutionary dynamics in an infinite-population setting.  Since it has many exercises, it's a great resource for designing problem sets.

Modeling Course in Population and Evolutionary Biology, taught by Sebastian Bonhoeffer and Viktor Müller at ETH Zurich.  The course site includes modules for learning how to use R to model evolutionary and ecological dynamics.

Population Genetics, taught by Dan Hartl, Michael Desai, and Pardis Sabeti at Harvard. The course site includes lecture notes and problem sets on both mathematical theory and applications of population genetics. The most recent version of the course page should be open and not require a Harvard login.

Problem sets as rewritten in fall 2009 are here.

Mathematica tutorials -- How to use Mathematica for modeling evolution:
  • HIV Scenario 1 (.nb) (.pdf) - A tutorial illustrating simple virus dynamics, as described in Chapter 10 of the text.  Covers how to set up, plot, animate, and analyze ODEs in Mathematica.  Also includes step-by-step instructions for how to output results to a text file.
  • HIV Scenario 2 (.nb) (.pdf) - A tutorial illustrating virus dynamics for multiple strains, numerically solving for the diversity threshold, described in Chapter 10 of the text.
    • Additional .pdf for HIV Scenario 2, expanding a section of the Mathematica notebook.  Shows a useful trick for dealing with ridiculously large outputs in Mathematica.
  • Evolutionary Game Scenario - Gives an example of how to set up and plot ODEs describing evolutionary game dynamics in an infinite, well-mixed population.  Uses replicator-mutator dynamics.  Not well-commented, but it's not too complicated either.