Venue: Feynman Lecture Hall
Class Timings: Tuesdays and Thursdays from 11:30 AM - 1:00 PM
First Meeting: 13 January 2026 (Tuesday)
Topics:
The course will introduce broad topics in theoretical ecology and evolution, but selected sections will include technical results.
1. How populations grow: logistic models and frequency dependent growth.
2. How multiple species coexist: biodiversity, predator-prey and Lotka-Volterra models.
3. How populations interact: resource competition and cooperation, consumer-resource models.
4. How ecosystems remain stable: the May bound and the ecological instability transition - random matrix, network science and geometric approaches to ecology.
5. Multistability, stochasticity, and catastrophes in ecosystems.
6. Statistical inference and data-driven approaches to ecology.
7. Spatiotemporal structure and metacommunity ecology.
8. Evolutionary processes: selection, mutation, and drift.
9. Dynamics on fitness landscapes, epistasis and ruggedness
Books:
1. Mark Kot, Elements of Mathematical Ecology (Cambridge University Press, 2012.
2. Robert May and Angela McLean, Theoretical Ecology: Principles and Applications (Oxford University Press, 2007).
3. Kevin S. McCann and Gabriel Gellner, Theoretical Ecology: Concepts and Applications (Oxford University Press, 2020).
4. Martin Nowak, Evolutionary Dynamics: Exploring the Equations of Life (Harvard University Press, 2006)
Course Outcome:
By the end of the course, students should be able to:
1. Use mathematical models to describe the growth of populations under various assumptions.
2. Describe stable coexistence between multiple species by analyzing the Lotka-Volterra and MacArthur consumer-resource models.
3. Explain the nonlinear dynamical phases of ecosystems with a large number of species, using approaches from random matrix theory, linear algebra, perturbation theory and high-dimensional geometry.
4. Fit various ecological models to data using Bayesian inference methods.
5. Distinguish between different evolutionary processes, such as selection, drift, and mutations.
6. Write and analyze stochastic equations describing evolution on high-dimensional fitness landscapes
Course Evaluation:
Pre-class questions (10%), homeworks (40%) mid-term (20%) and final exam (20%)
- Teacher: Akshit Goyal