Content

This course is an introduction to evolutionary game theory and population dynamics, biologically motivated by questions in evolutionary biology and behavioral ecology and mathematically based in the theories of nonlinear dynamical systems and differential geometry. Topics include general Lotka-Volterra systems, normal-form games, replicator dynamics, evolutionarily stable strategies, adaptive dynamics, and the evolution of cooperation.

Audience

The course is suitable for theoretically and mathematically-minded science and engineering students. Applied mathematicians, statisticians, computer scientists, and engineers are especially welcome, as are students of biology, ecology, evolution, epidemiology, environmental sustainability, economics, social sciences, and bioinformatics with suitable mathematical backgrounds.

Prerequisites

Students should have the equivalent of four semesters of calculus (including ordinary differential equations and multivariable calculus), a working knowledge of elementary linear algebra and probability, and computer literacy appropriate for mathematically-minded science or engineering students. Some homework problems will involve numerical computations or simulations. If you are not certain as to whether you meet the course prerequisites, contact Prof. King to inquire.

Work required

You must attend lectures and complete the assigned homework exercises, which will be collected & graded. Your final course grade will be determined from the sum of points earned on the homework (40%), on the midterm examination (20%), and on the final examination (40%).

Writing

Because mathematical reasoning is an essentially linguistic activity, a subsidiary but very important aim of the course is to improve your mathematical writing ability. Feedback on your written work will be aimed at bringing your reasoning and writing to a high standard of excellence. The following guidelines are provided to assist you in achieving this goal:

  1. Make each submission self-contained. It should be possible for someone to pick up, read, and understand your submission without having to find and read any other document. This will help you to make your thinking more rigorous and systematic and your exposition clearer. It will also make your written work a more valuable supplement to your notes, as you will be able to read and understand it years hence.
  2. Never turn in a rough draft. It will typically be necessary to write at least one rough draft before preparing a final copy for submission. Scratch work, notes to self, dead ends, and minor calculations, such as are found in a rough draft, do not belong on the final copy.
  3. Write for your peers. The final copy may end up being substantially more concise than the rough draft. For example, though there is no single standard, it is generally not necessary to include every step of a mathematical argument in the final copy. A good guideline is to write not for the professor but rather for an audience composed of your peers, with similar background, preparation, and skill level. Not only is this an intuitive guideline to follow, doing so will increase the value of your written work as a supplement to your notes.

You will not be expected to reach this standard immediately. Rather, expect constructive criticism about not only the content, but also the style, of your written work. As the course progresses, you will be expected to incorporate these lessons into your writing.

Course Information

Instructor

Aaron A. King, Ph.D.
Nelson G. Hairston Collegiate Professor
Department of Ecology & Evolutionary Biology
Center for the Study of Complex Systems
Department of Mathematics
Office: 3038 Biological Sciences Building
WWW: https://kinglab.eeb.lsa.umich.edu/
Email:
Telephone: +1.734.936.7861

Class meetings

Tuesdays and Thursdays, 16:00–17:20 in 296 Weiser Hall.

The nature of the course is such that attendance at lectures is required. Lectures will be recorded so that those forced to miss the occasional lecture will be able to catch up. Viewing lecture recordings will not prove to be an adequate substitute for attendance.

Office hours

Mondays 11:00–12:00, Wednesdays 16:30–17:30, and by appointment.
Office hours will be conducted via Zoom: the Zoom links are available via the course Canvas.

Course Slack channel

We will have a dedicated Slack channel, which will use this for all online communication about the course, including:

  • Questions and answers
  • Announcements
  • Direct messaging (DM) with the instructor and fellow students for communications about the course
  • Organizing study activities

To contact the instructor, use DM over this Slack channel in preference to email.

Honor pledge

All submitted course work must be accompanied by the following signed pledge:
“Upon my honor, I have neither given nor received any unauthorized aid on this [examination/problem set].”
Work that is not accompanied by a signed pledge will not be graded.

Homework assignments

Homework Exercises will be assigned from time to time during the lectures. Each Exercise will be posted to the course Canvas immediately after the lecture in which it was assigned. It will be due approximately one week after it is assigned. These should be uploaded to Gradescope on time: The late penalty is 25% per day or portion thereof.

Examinations

There will be two timed take-home examinations. Each will be made available at an announced time and will have a fixed deadline for submission. The exams will be downloaded from Gradescope, completed within a specified amount of time, and uploaded again to Gradescope. The goal of the exams is to probe depth of understanding, thoroughness of reasoning, and clarity of expression and not speed. Accordingly, a generous amount of time will be allotted for completion of the exam.

Text

In the past, we have used the text, Evolutionary Games and Population Dynamics by Josef Hofbauer and Karl Sigmund (Cambridge University Press, 1998, DOI: 10.1017/CBO9781139173179), and the exposition follows that of those authors to some extent, but this text will not be required. Occasionally, I will select readings, which will provided on the course Canvas, but the course lecture notes are meant to be self-contained.

Bookshelf

The following are some reference materials that you may find useful.

Course policies

Academic integrity

The University of Michigan community functions best when its members treat one another with honesty, fairness, respect, and trust. The college promotes the assumption of personal responsibility and integrity, and prohibits all forms of academic dishonesty and misconduct. All cases of academic misconduct will be referred to the LSA Office of the Assistant Dean for Undergraduate Education. Being found responsible for academic misconduct will usually result in a grade sanction, in addition to any sanction from the college. For more information, including examples of behaviors that are considered academic misconduct and potential sanctions, please see lsa.umich.edu/lsa/academics/academic-integrity.html.

Course Recordings

Students are prohibited from recording/distributing any class activity without written permission from the instructor. Approved recordings will be only for the student’s own private use.

Incompletion

Students in good standing (i.e., grade of B or better), forced by circumstances beyond their control to withdraw entirely from school after the withdrawal deadline may request a grade of Incomplete. The instructor may request proof of the necessitating circumstances and will, in consultation with the student, set the terms for the timely completion of course requirements.

Disability Statement

The University of Michigan is committed to providing equal opportunity for participation in all classes, programs, services and activities. Requests for accommodations by persons with disabilities may be made by contacting the Services for Students with Disabilities (SSD) Office located at G664 Haven Hall. The SSD phone number is 734-763-3000. Once your eligibility for an accommodation has been determined you will be issued a verified individual services accommodation (VISA) form. Please present this form to me at the beginning of the term, or at least two weeks prior to the need for the accommodation (i.e., examination).

Mental Health and Well-Being

University Students may experience stressors that can impact both their academic experience and their personal well-being. These may include academic pressures and challenges associated with relationships, mental health, alcohol or other drugs, identities, finances, etc. If you are experiencing concerns, seeking help is a courageous thing to do for yourself and those who care about you. If the source of your stressors is academic, please contact me so that we can find solutions together. For personal concerns, U-M offers a variety of resources, many which are listed on the Student Well-being webpage.

Sexual Misconduct Policy

Title IX prohibits discrimination on the basis of sex, which includes sexual misconduct—including harassment, domestic and dating violence, sexual assault, and stalking. I understand that sexual violence can undermine your academic success, so I encourage anyone dealing with sexual misconduct to talk to someone about their experience, so they can get the support they need. Confidential support and academic advocacy can be found with the Sexual Assault Prevention and Awareness Center (SAPAC) on their 24-hour crisis line, 734.936.3333 and at sapac.umich.edu.

Violations can be non-confidentially reported to the Office for Institutional Equity (OIE) at .