Martin Nowak | Fall 2023 | Harvard University
This course introduces basic concepts of mathematical biology and evolutionary dynamics: reproduction, selection, mutation, genetic drift, quasi-species, finite and infinite population dynamics, game dynamics, evolution of cooperation, language, spatial models, evolutionary graph theory, infection dynamics, virus dynamics, somatic evolution of cancer.
General
Course Textbook
Evolutionary Dynamics: Exploring the Equations of Life by Martin A. Nowak
Lectures
Additional Chapters from Evolutionary Dynamics
Problem Sets
Final Project
Proposal Instructions
Provide an outline of your proposed final project.
Your final project should both:
- pose a question in evolutionary dynamics or mathematical biology, and
- use the mathematical tools and principles developed throughout the course to address the chosen question (perhaps through a new mathematical model/principle within evolutionary dynamics/mathematical biology/game theory or an application of an existing model/principle to a relevant topic of your choice).
The outline of your final project should include:
- a proposed question that your final project will address,
- a brief literature review (2-5 sources),
- a proposed approach (model or algorithm),
- any preliminary progress (analysis / results), and next steps.
Note that as you continue to research your final project after you submit your proposal, you may adjust your research question and approach (this is common in research!).
Please upload a single PDF of your 2-3 page proposal to Canvas by October 19th, 2023. You may use any formatting or organization that you feel is appropriate, including any reasonable choice of columns, line spacing, and margin size. You may work individually or in groups (max 5 people).
For your proposal, we suggest (but do not require) the following structure:
Group members: If you have group members, only one member needs to submit the proposal, but all group members’ names must be listed.
An informed introduction (~1 page): Use your introduction section to concisely inform the reader about your research question of interest, which should be in some way connected to the course material. Summarize the current state of the literature by discussing and referencing around 2-5 published papers on your topic (including at least 2 mathematical papers if possible), and identify a specific question that remains unresolved.
Your proposed approach (~1 page): Present the model equations or algorithm you propose to study. Your model may be deterministic, stochastic, algorithmic, statistical, computational, game theoretical, or anything else. It may be your own original model or a meaningful modification of an existing model. Be sure to identify the variables and notation, clearly explain each of the model equations, and identify any assumptions underlying the formulation of the model.
Preliminary progress and next steps (~1 page): You are not expected to have any preliminary results (although if you do, feel free to include a very brief summary). Describe how you aim to analyze your model. Do you plan to solve the model equations directly and study the solutions? Do you plan to solve for stability conditions or fixation probabilities? Do you plan to conduct computer simulations, and if so, using what approach?
References: Please cite the papers or materials that you discussed in your proposal. You may use whatever bibliographic format you prefer. For each reference, please also include in-text citations.
Example Final Projects