Description: The first half of the course concentrates on classical population genetics. We introduce topics such as Hardy-Weinberg equilibrium, models of selection for populations of infinite size and population subdivision.
The second half of the course focuses on coalescent theory, covering migration, changes in population size and recombination. We provide guidelines how these models can be used in to infer population genetic parameters. Finally, some recent results and methods from the population genetic literature are discussed.
Description: It is an exciting time for research in population genetics. Technological advances are making it increasingly possible to obtain large numbers of genotypes from individuals in a population, and theoretical and algorithmic advances are improving the prospects for obtaining detailed inferences about populations and their evolutionary history. To make use of these dramatic advances in the field, it is important to understand the processes that act on populations and affect the properties of the genotypes that will eventually be drawn from these populations. In this course, by learning the mathematical models used in population genetics, students will learn how various population-genetic phenomena influence the properties of genetic variation. Students will also gain an understanding of the statistical methods used for analysis of population-genetic data.
The course is split into two major sections. The first section covers classical population genetics, including subjects first introduced by RA Fisher and S Wright. We cover Hardy-Weinberg equilibrium, natural selection in infinite and finite populations, stochastic effects in finite populations (drift), recombination and linkage disequilibrium, and admixture and population subdivision. Moreover, we cover the most commonly used models of mutation, such as the infinite sites model and the infinite alleles model. The goal of this section is to give students a broad understanding of the statistical principles underlying population genetics and to provide a connection between these classical results and modern challenges in statistical genetics.
In the second section of the course we cover coalescent theory. We introduce the basic coalescent model for constant Wright-Fisher populations. We then introduce commonly used extensions of this model to scenarios with recombination, population expansion and population subdivision. We introduce methods of parameter inference based on these models, including both simple method-of-moments estimates as well as more sophisticated Monte-Carlo based estimation methods. The goal of this section is to give students the ability to design realistic simulation algorithms and perform population genetic inference.
Classes on population structure and population admixture (~4) will be taught by Noah Rosenberg.
In the biweekly homeworks, we expect the students to be able to apply and extend the presented theory. Early in the course, each student will select a topic for a project; the student is expected to work on this project throughout the semester and to give at the end of the semester a written project report and a 20-minute presentation on the results of his analysis. Typical projects are
" Simulate a model of rare variants under mutation-selection balance and estimate power for rare variants testing methods.
" Calculate the contribution of low frequency variants to heritability in structured populations
" Perform a principal components analysis on genetic data
" Explore recent resequencing data for signs of natural selection.
Prerequisites: Biostat 601, Biostat 602, Biostat 666 or Perm. Instr.
Description: Advanced topics in quantitative genetics with emphasis on models for gene mapping, pedigree analysis, reconstruction of evolutionary trees, and molecular genetics experiments, computational mathematics, and statistical techniques such as Chen-Stein Poisson approximations, hidden Markov chains, and the EM algorithm introduced as needed.