Venue: Feynman Lecture Hall
First Meeting: 9 January 2024
Class Timings: Tuesdays and Thursdays from 11:30 AM - 1:00 PM
Course Description: The course will introduce broad topics in theoretical ecology and evolution, but selected sections will include technical results.
- how populations grow: logistic models and frequency dependent growth
- how multiple species coexist: biodiversity, predator-prey and Lotka-Volterra models
- how populations interact: resource competition and cooperation, consumer-resource models
- how ecosystems remain stable: the May bound and the ecological instability transition - random matrix, network science and geometric approaches to ecology
- multistability, stochasticity, and catastrophes in ecosystems
- statistical inference and data-driven approaches to ecology
- spatiotemporal structure and metacommunity ecology
- evolutionary processes: selection, mutation, and drift
- dynamics on fitness landscapes, epistasis and ruggedness
Course Evaluation: Pre-class questions (10%), problem sets (50%), and final exam (40%)
Perquisites: No prior biology knowledge is necessary. Mathematical physics at 1st year graduate student level will be useful.
Textbooks:
- Mark Kot, Elements of Mathematical Ecology (Cambridge University Press, 2012
- Robert May and Angela McLean, Theoretical Ecology: Principles and Applications (Oxford University Press, 2007)
- Kevin S. McCann and Gabriel Gellner, Theoretical Ecology: Concepts and Applications (Oxford University Press, 2020)
- Martin Nowak, Evolutionary Dynamics: Exploring the Equations of Life (Harvard University Press, 2006)
References
Statistical physics and dynamics of evolution
- “Evolution in rapidly evolving populations”, BH Good, Harvard University (2016)
- "Evolutionary dynamics", DS Fisher, Les Houches Course (2006)
- "Statistical Genetics and Evolution of Quantitative Traits", RA Neher and BI Shraiman, Reviews of Modern Physics (2011)
- "Genetic demixing and the evolution in linear stepping stone models", K. S. Korolev, Mikkel Avlund, Oskar Hallatschek, and David R. Nelson,Reviews of Modern Physics (2010)
Course Outcome: By the end of the course, students should be able to:
- use mathematical models to describe the growth of populations under various assumptions.
- describe stable coexistence between multiple species by analyzing the Lotka-Volterra and MacArthur consumer-resource models.
- 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.
- fit various ecological models to data using Bayesian inference methods.
- distinguish between different evolutionary processes, such as selection, drift, and mutations.
- write and analyze stochastic equations describing evolution on high-dimensional fitness landscapes.
- Teacher: Akshit Goyal