Genetic Statistics

Statistics/Genetics 536

Fall, 2006

This course introduces the field of population genetics, the science concerned with the genetic structure of populations and the forces that alter that structure. Formally, the course description is

Probability applied to genetic systems; random mating; selection, mutation and migration; theory of inbreeding; effects of finite population size; basic concepts in quantitative genetics; prediction of progress from artificial selection.

Last Update:

Thu Nov 16 14:19:22 CST 2006 Latest News

Lecture quick links:

By week:

wk. 1 (8/22)	wk. 2 (8/29)	wk. 3 (9/5)	wk. 4 (9/12)	wk. 5 (9/19)
wk. 6 (9/26)	wk. 7 (10/3)	wk. 8 (10/10)	wk. 9 (10/24)	wk. 10 (10/31)
coalescent	diversity

Homework quick links:

hw1 | hw2 | hw3 | hw4

Instructor:

Karin S. Dorman

Office:

Snedecor 210C (4-8392); Science II 534 (4-6078)

Office Hours:

On demand

Email:

kdorman_at_iastate.edu

WWW:

http://puga.gdcb.iastate.edu/dormanks/teaching/stat536/fall06
for access to data & and protected documents: login | logout
WebCT

Lectures:

TR 3:40 - 5:00 in MBB 1424

Textbook:

None required. References:

Hartl and Clark. Principles of Population Genetics
Gillespie. Population Genetics: A Concise Guide
Ewens. Mathematical Population Genetics
Weir. Genetic Data Analysis II

Grading:

Homework: 40%
Exams (midterm plus final (12/14/06 at 2:15)): 40%
Final project: 20%

Other:

Disability Statement | Jobs | Recent Publications | Websites

Course Objectives

Formulate the laws of genetic transmission as basic probability models.
Identify and assess the impact of basic forces (mutation, selection, migration) that change the genetics of a population.
Understand and quantitate the role of small population size on genetic change of a population.
Understand the coalescent as a fundamental model of population genetics.
Quantitate the effects of nonrandom mating and population subdivision on the genetics of a population.
And throughout, learn how to use genetic data to estimate the forces of genetic change, compare models, etc.

News

Fri Dec 8 20:15:37 CST 2006
Sample problem solutions posted. These are fairly rushed, and I found a couple of problems with the original problem statements posted last night. There may also be problems with the solutions. Ask questions about any solutions or any questions without solutions.
Thu Dec 7 20:51:25 CST 2006
- Additional coalescent notes posted
- Sample problems for exam preparation posted; no solutions yet
Thu Nov 16 14:18:46 CST 2006
Project detailed description.
Thu Nov 16 08:50:07 CST 2006
Tsetse fly locations.
Mon Nov 13 12:09:03 CST 2006
- Tsetse data set posted last week on WebCT.
- Diversity notes, collected from previous year lectures posted
- Tsetse fly background posted
Wed Oct 18 10:43:00 CDT 2006
- Discovered that link to homework 2 solutions was broken. Tell me!
- Posted homework 3 solutions and R code.
Tue Oct 17 18:35:29 CDT 2006
- Answer to question about stability of 1-m/s for one-island haploid model posted on WebCT.
- Homework 3 solutions posted on WebCT if you have turned them in. See "Homework #3 Solution" under Assignments.
- Old exams posted in exam section.
Mon Oct 16 15:10:01 CDT 2006
There are some posts in WebCT discussion about homework 3.
Sun Oct 8 09:02:59 CDT 2006
I have a question for myself:

In problem 3b, I am asked to compute the viability relative to the heterozygous mutants, but the data contains no genotype information. What am I to do?

"heterozygous mutants" is the wrong phrase. The inbred line are all homozygous. The outbred line is relatively more heterozygous. Compute all viabilities relative to the outbred line.
Sun Oct 8 08:56:33 CDT 2006
Added problem 3 data to homework 3. It took many hours to generate this data (I was trying to simulate a whole chromosome after all), but it really should not take so long to answer the questions. Ask questions if anything is confusing.
Fri Oct 6 12:40:42 CDT 2006
Derivation of E(n₁n₂) for multinomial counts n₁ and n₂ from week 2 lecture material.
Fri Oct 6 00:00:44 CDT 2006
Derivation of formula for Var(D₁) given in Week 3, slides #2.
Tue Oct 3 18:52:52 CDT 2006
Posted solutions for homework 1 matching your data, including the true population parameter values. How good were your estimates?
Sat Sep 16 09:22:06 CDT 2006
Sign on to WebCT for discussions and questions.
Tue Sep 5 11:26:55 CDT 2006
The problem with the account making tool should have been fixed. Let me know if you continue to experience difficulties.
Mon Aug 21 16:23:02 CDT 2006
To read the notes, use acrobat reader.

Lectures

Week 1: slides | probability notes
[Tue Aug 22 2006]
- meiosis
- If you are a complete novice in biology, read DNA from the Beginning.
- Unless you are a biologists, read Human Molecular Genetics 2 Chapters 1-2.
Week 2: Hardy Weinberg Equilibrium
- slides (as handout)
  [Tue Aug 29 2006]
  - Hardy-Weinberg Equilibrium Theorem
  - Estimation of population genotype and allele frequencies
  - Estimation of frequency estimator variances: delta method, Fisher's approximation, jackknife, bootstrap, maximum likelihood theory
Week 3: Hardy Weinberg Equilibrium, Estimation and Testing
- slides #1 (as handout)
  [ Last posted: Sat Sep 16 09:23:35 CDT 2006 ]
  - Obtaining maximum likelihood estimates: Lagrange multipliers, Bailey's method, Newton-Raphson, Expectation-Maximization algorithm
  - Method of moments estimation (simple example: estimating allele correlation)
  - Bayesian estimation (simple example: estimating allele frequency)
- slides #2 (as handout | 2nd version)
  [ Last posted: Thu Sep 14 03:52:34 CDT 2006 ]
  - Statistical hypothesis testing overview
  - Correlation model of Hardy Weinberg DISequilibrium
  - Testing Hardy Weinberg Equilibrium by disequilibrium coefficient D₁: z-test, chi-square, chi-square goodness-of-fit, likelihood ratio test, exact tests, handling multiple alleles, approximate exact tests
  - Power calculations for testing HWE
- Handouts: Lee03.pdf | Guo92.pdf (Access WebCT for these documents if you have trouble here.)
Week 4: linkage disequilibrium
- slides (as handout)
  [ Last posted: Sat Sep 16 03:15:32 CDT 2006 ]
  - Population genetics of genetic linkage or genetic disequilibrium: existence of equilibrium, geometric decay to equilibrium
  - Statistical estimation/testing when phase is known: z, chi-square, exact
  - Trigenic and quadrigenic disequilibria
  - Statistical estimation/testing when phase is unknown: composite digenic disequilibrium
- GenePOP on the Web: GENEPOP is a population genetics software package originally designed by Michel Raymond and Francois Rousset at the Laboratiore de Genetique et Environment, Montpellier, France.
- data set for exact test of HWE
Week 5: natural selection
- Lecture 2: slides (as handout)
  [ Last posted: Thu Sep 21 17:29:54 CDT 2006 ]
  - Estimation of viability using HWE, controlled cross, or multiple generations
Week 6: mutation slides (as handout)
[ Last posted: Tue Oct 3 18:57:34 CDT 2006 ]
- Mutation: recurrence, equilibrium, rate of approach to equilibrium, back mutation, multiple alleles
- Mutation and Selection: haploid, HIV example, diploid recessive, diploid (partial) dominant, cystic fibrosis example
- Haldane-Muller principle: haploids, diploids, genetic load

Week 7: migration slides (as handout)
[ Last posted: Fri Oct 6 00:06:24 CDT 2006 ]
- Migration: of alleles, of genotypes, with linkage disequilibrium, with selection
- Whalund effect: homozygous excess
- Gene flow: estimation
- Models: one-island, island, stepping-stone, general migration matrix

Week 8: genetic drift
- slides (as handout)
  [ Last posted: Thu Oct 12 21:43:50 CDT 2006 ]
  - concepts: neutral theory, inbreeding, genetic drift, allele fixation
  - Wright-Fisher model: inbreeding recursion, heterozygosity
  - Recovery from bottleneck, heterozygosity half-life
  - Mean and variance of allele frequencies over replicate populations
  - Relationship between inbreeding and allele frequency variance
  - Effective population size: for non-selfing populations, for two-sex populations, for monogamous populations, for varying population size, for variation in fitness due to environmental effects
- slides (as handout)
  [ Last posted: Thu Oct 12 21:43:50 CDT 2006 ]
  - infinite isoalleles model: mutation/genetic drift equilibrium
  - finite isoalleles model: nucleotide, protein evolution
  - homozygosity, rate of mutation, recovery from bottlenecks, relation to effective population size
  - one-island model: migration and genetic drift equilibrium
  - island model: migration, mutation, and genetic drift equilibrium
Week 9: genetic drift and selection
- slides (as handout): both are corrected for errors discovered in lecture
  [ Last posted: Tue Oct 24 17:44:29 CDT 2006 ]
  - extinction probability/fixation probability: general offspring pmf, Wright-Fisher model
  - Wright's diffusion approximation: multiplicative selection, complete/partial dominance
Week 10: population structure: slides

Coalescent
- Introduction: slides (handout)
- More results including Tsetse fly background: slides (handout)
- Advance coalescent
Diversity: slides

Homework

Homework 1 (Due 9/14/06): problems | data (you will need to create an account before you can access your data; each student should have a separate account)
- solutions for 2 and 3 (be patient, it is slow): please learn from problem 2 that estimates of allele frequency can be biased if HWE does not apply.
- solution for 4
- solutions for 1, and partial examples for 2 and 3 (use above for complete 2 and 3 solutions)
Homework 2 (Due 10/03/06): problems | data

verbose solutions for a sample data set
R script for all computations; uncomment your data set and run it through R

Homework 3 (Due 10/17/06): problems | data

verbose solutions for a sample data set
R script for all computations; uncomment or enter your data set and run it through R

Homework 4 (Due 11/14/06): problems

Exams

sample problems on coalescent and quantitative genetics (partial solutions)
Old exams:
- 2004 final exam (solutions)
- 2004 midterm with solutions
- 2001 final exam (poor example)
- stat 537 final
- See stat 432 exams for format: 2005 | 2003
midterm (with with solutions)

Supplementary Materials

Population genetics software
- DnaSP: "a software package for the analysis of nucleotide polymorphism from aligned DNA sequence data" (Windows)
- SITES: "a computer program for the analysis of comparative DNA sequence data" (Windows)
- GDA: Genetic Data Analysis for "Computes linkage and hardy-weinberg disequilibrium, some genetic distances, and provides method-of-moments estimators for hierarchical F-statistics."
- Arlequin 3.1: "The goal of Arlequin is to provide the average user in population genetics with quite a large set of basic methods and statistical tests, in order to extract information on genetic and demographic features of a collection of population samples."
- FSTAT: "FSTAT is a computer package for PCs which estimates and tests gene diversities and differentiation statistics from codominant genetic markers."
Statistical genetics programs of study
Background reading materials:
- Human Molecular Genetics 2
- DNA from the Beginning

Jobs in Statistical Genetics

I may list a (noncomprehensive) taste of the kinds of jobs available to people with training in this area during the semester.

Statistical Genetics Websites

Karen Ayres' Statistical Genetics Websites

Disability Statement

Iowa State University complies with the Americans with Disabilities Act and Sect 504 of the Rehabilitation Act. If you have a disability and anticipate needing accommodations in this course, please contact me within the first two weeks of the semester. Retroactive requests for accommodations will not be honored. Before meeting with me, you will need to obtain a SAAR form with recommendations for accommodations from the Disability Resources Office, located in Room 1076 on the main floor of the Student Services Building. Their telephone number is 515-294-7220.

Last Updated: Thu Nov 16 14:19:22 CST 2006