Theoretical Ecology and Evolution - Topical (PHY444.5)

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.