Stochastic Methods of Population Genetics, 5 credits
(graduate course)
Objective:
Changes of human DNA over time is a combination of random inheritance
(Mendelian laws),
recombination of maternal and paternal DNA, mutations and selection
principles.
This is conveniently described using tools from probability theory and
stochastic processes.
The population genetic models so obtained are important for
understanding variation of DNA
between individuals and populations. This in turn has applications for
1) human ancestry and estimating
age of populations 2) locating genes that increase risk for inheritable
diseases (gene mapping).
The course will focus on mathematical and statistical principles of
population genetics. We have
the genetic applications in mind, but also study these models as
interesting mathematical objects
of their own.
Contents:
Basic concepts of genetics (nucleotides, alleles, recombination,
Mendelian laws, the genetic code, phenotypes
and penetrance).
Population genetic models (Wright-Fisher, Moran, infinite alleles,
infinite sites, Hoppe's urn model and
random permutations).
Coalescence theory.
Ancestral recombination graphs.
Varying and effective population size.
Population subdivision.
Selection models.
Applications: Statistical inference of model parameters (mutation
rates, time to most recent common ancestor, ...),
mapping of disease causing genes (association analysis).
Prerequisites:
Familiarity with random variables, distributions, Markov processes in
discrete and continuous time,
statistical tests and estimators.
(Corresponding to two courses in probability theory (total of 10
credits), one course in
stochastic processes (5 credits) and one course in statistical
inference theory (5 credits).)
No prior knowledge of genetics is required.
Literature:
Durrett, R. (2002). Probability Models for DNA Sequence Evolution.
Springer, New York. ISBN 0-387-95435-X.
Articles handed out during the course.
Other course material:
Statistics primer for those
with less statistics background.
Genetic glossary for those with less
genetics background (updated version Sep 05).
Reading guide.
List of typos (updated version Oct 10).
Examination:
Three written home assignments will be handed out during the course:
Home assignment 1: Handed out Sep
12, last day of return Sep 26. (Updated with credits per exercise Sep
14.)
Home assignment 2: Handed out Oct
3, last day of return Oct 17.
Home assignment 3: Handed out Oct
17, last day of return November 7.
You may do these individually or in groups (maximum size 2). Required
number of credits for each home assignment is 50%.
Further, a mandatory 45 minutes oral
presentation of a topic relevant for the course.
Here are some
suggestions of seminar topics
(updated version Sep 26).
The lectures are not mandatory but at least 2/3 of the other
participants' presentations must be attended.
Ola Hössjer, Mathematical Statistics, SU. ola@math.su.se
Schedule/Location:
We meet once a week Mondays 13.15-15.00, starting September 5. See schedule for further details.
Dept of
Mathematics, SU, the Cramér Room (Room 306), House 6,
Kräftriket.
List of seminars:
Tue Nov 8:
10.15-11.00: Mathias Lindholm, Coalescence with varying population size
11.15-12.00: Francois Besnier, Gene mapping via the ancestral
recombination graph
Mon Nov 14:
13.15-14.00: Björn Larsson, Diffusion
Processes for Prosaists
14.15-15.00: Patricia Geli, Markov processes with continuous state
space- population genetic applications
Mon Nov 21:
13.15-14.00: Ali Tofigh, Statistical inference through Monte Carlo in
population genetics
14.15-15.00: Andreas Nordvall Lagerås, Paintbox constructions and
stochastic flows of bridges - representations of coalescent processes
Mon Nov 28:
13.15-14.00: Hedvig Norlen, Allelic spectrum and common variant common
disease hypothesis
14.15-15.00: Martin Linder, Tests for neutral evolution
Interested?
Then, it would be very good if you could send me an email in advance, so that I can estimate the number of participants.
Welcome to the course!
Ola
| Ola Hössjer ola  math.su.se
|
Updated: October 17, 2005 |