Mathematics of Evolution

Spring 2023--Simon Fraser University

Course Overview

Much of our understanding of evolution, the process shaping the beautiful biological diversity in our world, is grounded in equally elegant mathematics. In this course we will cover the mathematical description of evolution. Involving a wide range of topics, from the analysis of non-linear dynamics to stochastic processes, and game theory, this course will challenge you to take mathematical principals and apply them to the natural world.

What this course is not. This course is not a thurough introduction to popualtion genetics. Don't get me wrong, population genetics is awesome!, but it is only one way of modelling evolution. Instead this course will focus on "going wide" instead of "going deep" exploring how a wide variety of matheamtical approaches can be sued to study type of evolutionary question: the evolution of life history traits. This course is also not an introudction to modelling of biological populations. This too is an importnat topic and a fascinating one, allowing us to model ecology, evolution, and epidemiology (again all topics close to my heart). While we will discuss eco-evolutionaory dynamics in this course we do so through the lense of the evolutionary consequences not necessarily the ecological ones.

Course Content

Class Times

Lecture: Wednesday and Friday 10:30-12:20 (On zoom)
Office Hours: Friday 4-5pm (On zoom)

Holidays

Feb 20-26: Reading week
April 7 & April 10: Easter

Grade Overview

Homework: 6 x 10% each
Presentation 15%
- 5% Presentation content
- 5% Presentation delivery
- 5% Q and A (Asking questions to others and answering questions asked)
Report 25%
- 5% Background & Justification
- 10% Methods & results & figures/tables
- 5% Discussion
- 5% Writing proficancy

Final Project

Choose a peer-reviewed publication examing the evolution of life history and reproduce the results. Part 1: Give a 20 min presentation summerizing the question, methods, and key results. Part 2: 4pg report (not including additional supplemental materials) discussing the background, methods, results, and a possible extension to the model.

Presentation Sign Up

List of Topics

Day(s)	Topic	Refereces
Jan 4,6,11,13	Four Evol. Processes	Crow and Kimura 1970
Jan 18,20	Desnity-Dependent Sln.	Roughgarden 1971
Jan 25,27	Mathematical Demography	Charlsworth 1980 Ch 1.
Feb 1	Semelparity vs. Iteroparity	Young 1981
Feb 3,8	Intro to Adaptive Dynamics	Brännström et al. 2013
Feb 10	Evolution of Senesence and age of reproductive maturity	Charlsworth 1993, Day and Abrams 2020
Feb 15	Evolution of Seed Dormancy	Scott and Otto 2014
Feb 17	Evolution of Epidmeiolgoical Traits
Feb 22,24	Reading week
Mar 1,3	Introduction to Coalescent Theory	Wakeley 2009
Mar 8,10	Eco-evolutionary coalescent models	Griffiths and Tavare 1994, Austerlitz 1997,Kaj and Krone 2003
Mar 15,17	Introduction to Phylogenetics	Zhang 2006 Ch 1,4
Mar 22,24	Diversiction Models: BiSSE	Maddison et al. 2007, Stadler 2010, MacPherson et al. 2021
Mar 29,31, April 5	Presentations Sign Up Here