Department of Mathematics and Statistics
Concordia University

Fall 2008

MAST 679/MAST 881: Probabilistic Methods in Biology

M 14:45-17:00, H-539-2 (SGW)

Instructor: Lea Popovic
Office: LB 921-29 (SGW)
Phone: (514) 848-2424 Ext 5854

Office Hours: TBA

Course Outline

This course will give an account of useful mathematical results in population genetics. Population genetics studies how genetic variability is shaped by natural selection, demographic factors and random genetic drift. A lot of results in this field are obtained by simulation, however in a wide number of instances mathematical formulas for desired quantities are available and can be used to understand the dependence on the underlying parameters.
We will start with an introduction to the basic biological terminology and genetic models. We will then consider the theory of neutral evolution in a homogeneously mixing population of constant size, then work through more complicated models of population size changes and population subdivison. We will also study diffusion approximations to these models which are used to compute fixation probabilities, expected fixation time, and the site frequency spectrum. Some statistics used to test whether data is consistent with model assumptions will be discussed. The course will cover:
  • Basic models in population genetics: Wright-Fisher and Moran model, Infinite alleles and Infinite sites model, the coalescent
  • Population complications: population growth, effective population size, models of population subdivision
  • Diffusion processes: hitting probabilities and hitting times, models for gene duplication
  • Statistical estimation and testing for population models


Understanding of probability and some familiarity with Markov chains and Poisson processes


"Probability Models for DNA Sequence Evolution" by R. Durrett (Springer, 2008, 2nd edition)


Combination of homework problems and individual projects for students from different departments.

Important Dates

Oct 6 - no class

Project Papers: