Genetic Statistics

Statistics/Genetics 536

Fall, 2004

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.

though we may stray a bit beyond the limits of this description. Perhaps more helpfully, you will learn to:

• discuss the laws of genetic transmission and derive the genetic equilibriums obtained under ideal conditions,
• identify the forces (selection, mutation, migration) that change the genetics of a population,
• predict the impact of small population size on the genetics of a population and its impact relative to other forces,
• identify types of sequence data and carry out standard sequence comparison techniques, including phylogenetic reconstruction, and
• understand the basic ideas of the coalescent as a model of molecular population genetics.

• Thu Dec 23 16:12:39 CST 2004
  Course grades and final exam grades posted. Course grades will be submitted as late grades.
• Wed Dec 22 19:23:38 CST 2004
  I picked up the final exams at 6pm today. I'll post grades tomorrow.
• Wed Dec 22 12:45:25 CST 2004
  I have not received final exams from Mayo (there may be some difficulties with delivery due to closed offices -- I know they were sent), but will check before I leave home tonight. However, due to this delay final grades may not be posted today.
• Wed Dec 22 12:43:55 CST 2004
  Project grades posted.
• Tue Dec 21 16:32:19 CST 2004
  Final exam and solutions posted (only accessible to those who have completed the exam).
• Mon Dec 20 12:08:54 CST 2004
  Because distance students are taking the final exam tomorrow after grades are due, all students will receive N (Not Reported) on their grade reports. I will enter late grades next Monday when late grades will be first accepted. By Wednesday (Dec. 22) I will post your grades on this website.
• Sat Dec 18 15:37:50 CST 2004
  Homework 4 solutions re-posted (incorrect math in inbreeding calculation for autosomal locus). Does not effect grades.
• Thu Dec 16 17:17:45 CST 2004
  Homework 4 solutions re-posted (typo in Chapter 5, Exercise 3 solution).
• Sun Dec 12 21:46:28 CST 2004
  Homework 4 solutions posted.
• Mon Dec 6 21:24:53 CST 2004
  An updated midterm solutions posted. Note, the last news was wrong. Midterm solutions are now up-to-date.
• Sat Dec 4 13:12:57 CST 2004
  Midterm grades posted.
• Sun Nov 14 13:25:29 CST 2004
  Homework 4 (a short one) posted.
• Thu Nov 4 11:53:55 CST 2004
  First (incomplete) version of midterm solutions posted.
• Tue Nov 2 09:05:25 CST 2004
  Data files for answering homework 2 questions 2 & 3 were posted (as per a request).
• Tue Nov 2 08:52:02 CST 2004
  Chapter 7 posted for distance students or if you want an electronic copy.
• Wed Oct 27 22:19:06 CDT 2004
  All homework 2 grades posted.
• Wed Oct 27 15:28:44 CDT 2004
  Some homework 2 scores and homework 3 scores posted (no distance yet).
• Wed Oct 27 13:24:50 CDT 2004
  Homework 4 posted.
• Tue Oct 19 21:51:42 CDT 2004
  Corrected (again) homework 2 solutions posted. The EM algorithm for f does not work. There was a bug in the original perl code that made it seem that it had converged on, unfortunately, the value I expected. Sorry to anyone who had a correct working EM algorithm heading to 0, but heard from me that it shouldn't head to 0. Homework 3 solutions also reposted with minor revisions. All R code reposted with minor revisions and some additions. Additions include alternative ways to compute things and answer questions based on what students did in their homework.
• Fri Oct 15 13:28:46 CDT 2004
  Corrected homework 2 solutions and added some more code for finding solutions.
• Thu Oct 14 16:55:11 CDT 2004
  Posted reading assignment for genetic drift.
• Thu Oct 14 12:23:52 CDT 2004
  Posted reading assignment for inbreeding. Sorry, it was an oversight.
• Wed Oct 13 23:48:39 CDT 2004
  Posted homework 3 solutions. Mayo students don't yet have access.
• Mon Oct 11 18:19:26 CDT 2004
  Posted homework 2 solutions. Mon Oct 11 18:19:42 CDT 2004
• Mon Oct 11 14:33:54 CDT 2004
  Posted some more sample code for homework 1
• Sat Oct 9 13:20:19 CDT 2004
  Homework 1 grades posted.
• Fri Oct 1 17:14:04 CDT 2004
  Homework 3 is posted.
• Thu Sep 30 13:07:53 CDT 2004
  Mutation chapter posted.
• Thu Sep 30 09:50:56 CDT 2004
  Second version of homework 1 solutions posted. You only care about this if you looked at the earlier version. There was a correction to the code to calculate method of moments estimator f. Actually estimate was right, the code and bootstrap figure were wrong.
• Wed Sep 29 20:40:38 CDT 2004
  First version of homework 1 solutions posted. Hopefully more will come later.
• Mon Sep 27 14:31:36 CDT 2004
  There was a typo in homework 2, problem 4, part a and typos corrected in lecture 4, pages 20, 21, and 22.
• Thu Sep 23 11:16:49 CDT 2004 The reading for natural selection has been posted.
• Sat Sep 18 16:06:41 CDT 2004
  Lectures and homework are now password protected. Please open an account (there should be a link) on the login page. If you receive the message "sorry", email me. You need to enter the email listed on your ISU record.
• Sat Sep 18 11:21:00 CDT 2004
  Homework 2 posted. You have two weeks to complete it. Due Friday, October 1 for on-campus students, Friday, October 8 for off-campus students.
• Thu Sep 9 20:07:43 CDT 2004
  Lecture 6 was reposted to correct some errors that became evident during today's taping.
• Tue Sep 7 17:07:59 CDT 2004
  On campus office hours tomorrow 9/8/04 are rescheduled to 9-10am in Snedecor 210C due to a scheduling conflict with the regular time. Also, if you need last minute help with homework, you can contact me by email any day, but I will also be in Science II 534 all day next Monday except for a morning meeting 9-10:30am and the statistics seminar at 4:10pm.
• Tue Sep 7 17:04:19 CDT 2004
  Lecture 5 posted is slightly modified from lecture to correct typos or mistakes (pp. 7, 10, 28, 36, 37) and minor wording or content (pp. 6, 39).
• Sat Sep 4 22:31:43 CDT 2004
  First homework posted. Due Tuesday, September 14 for on-campus students, Friday, September 20 for Mayo students.
• Fri Sep 3 16:32:37 CDT 2004
  First homework posting is postponed until tomorrow. You will have more than a week to do it and you can relax Labor Day weekend. Enjoy!
• Wed Aug 25 09:20:10 CDT 2004
  Reading assignment posted along with slightly corrected (percentages sum to 100% and misspelling errors) version of lecture 1 notes.
• 2004-08-24
  To read the notes, use acrobat reader.

Lectures

• Lecture 30 (12/09/04): Review II
  [ Last post: Thu Dec 9 16:35:46 CST 2004 ]
  • FSTAT
  • Weir's problem 5.4
  • Weir's problem 5.4 output
  • See the calculation of Weir and Cockeram's F statistics with confidence intervals by bootstrap.
• Lecture 29 (12/07/04): Review I
  [ Last post: Tue Dec 7 17:08:12 CST 2004 ]
  • Mendel website
  • Mendel examples
    • Examples:
      • 6a: allele frequency calculation
      • 6b: allele frequency calculation at a sex-linked locus
      • 10a: coefficient of kinship calculations on a specified pedigree
      • 11a: HWE and LE test at two loci
      • 11b: haplotype data with LE test for all pairs of loci
    • Input files
      • Control file: use to specify input and output file names and the type of analysis. Relevant analysis options:

        ANALYSIS_OPTION = Allele_frequencies	Compute allele frequencies and HWE
        ANALYSIS_OPTION = Kinship_matrices	Compute coefficients of kinship
        ANALYSIS_OPTION = Genetic_equilibrium	Test for genetic equilibrium (HWE and LE depending on circumstance and option NUMBER_OF_MARKERS_INCLUDED and MODEL)
        NUMBER_OF_MARKERS_INCLUDED = [integer]	Window size for testing for linkage equilibrium within. If 1, only test HWE. If 2, test for LE and HWE. If 3, compare all pairs within window for HWE and LE.
        MODEL = [1|2]	If set to 1, computes Fisher exact tests of independence. If 2, data must be haplotype and then tests for LE between all pairs of loci.

      • Locus file: use to define all loci, all alleles at each locus, and all possible phenotypes; also defines factors

      						[locus name] [AUTOSOME|X-LINKED] [number of alleles] [number of phenotypes]
      						[allele 1 name] [optional allele frequency]
      						[allele 2 name] [optional allele frequency]
      						...
      						[phenotype 1 name] [number of genotypes with this phenotype]
      						[genotype 1 for phenotype 1 entered as allele_name/allele_name]
      						[genotype 2 for phenotype 1 entered as allele_name/allele_name]
      						...
      						[phenotype 2 name] [number of genotypes with this phenotype]
      						[genotype 1 for phenotype 2 entered as allele_name/allele_name]
      						...
      						

      • Map file: use to input recombination fractions between loci, if known

      						[locus name 1]
      						[recombination fraction between locus 1 and locus 2]
      						[locus name 2]
      						[recombination fraction between locus 2 and locus 3]
      						[locus name 3]
      						...
      						

      • Pedigree file: use to input pedrigrees

        						format line 1
        						format line 2
        						[number of people in pedigree] [pedigree name] [number of pedigrees in data set of this same form]
        						[person 1's name] [person 1's mother] [person 1's father] [sex] [list of phenotypes and factors...]
        						[person 2's name] [person 2's mother] [person 2's father] [sex] [list of phenotypes and factors...]
        						...
        						

• Lecture 28: Coalescent II
  [ Last post: Fri Dec 3 15:54:57 CST 2004 ]
  • Estimating t_MRCA
• Lecture 27: Coalescent I
  [ Previous post: Tue Nov 30 14:42:23 CST 2004 Last post: Tue Nov 30 16:45:01 CST 2004 (1 update) ]
  • Reading: Rosenberg and Nordborg, 2002
• Lecture 26: Analysis of Genetic Variance and Example
  [ Last post: Thu Nov 18 17:38:44 CST 2004 ]
  • Covariance <-> correlation
  • ANOVA framework (components of variance)
  • Link between parameterizations
  • ANOVA for random mating systems
  • ANOVA with Population subdivision
  • Example: tsetse fly gene flow
• Lecture 25: Selection and Genetic Drift and Analysis of Genetic Variance
  [ Last post: Tue Nov 16 18:32:58 CST 2004 ]
  • Equilibrium with mutation
  • Equilibrium with migration
  • Equilibrium with selection and mutation
  • Variation among alleles in a single population : Cockerham, 1969
• Lecture 24: Selection and Genetic Drift
  [ Previous post: Thu Nov 11 16:40:48 CST 2004 Last post: Wed Nov 17 09:16:16 CST 2004 (1 update) ]
  • Description of project
  • Multiplicative selection with Wright diffusion model
  • General dominance with Wright diffusion model (numerical solutions)
  • Equilibrium distribution - exact solution
• Lecture 23: Selection and Genetic Drift
  [ Last post: Tue Nov 9 14:52:38 CST 2004 ]
  • Review since finite population
  • Drift vs. selection
    • Probability of extinction vs. selection
    • Branching process approximation
    • Wright model with selection
    • Wright model diffusion approximation
• Lecture 22: Population Structure
  [ Previous post: Thu Nov 4 14:50:49 CST 2004 ; Last post: Thu Nov 4 16:48:57 CST 2004 (1 update) ]
  • Random populations - haploid
    • ANOVA
    • Estimation of F_ST aka θ
    • Extension to multiple alleles and multiple loci
    • Time of divergence of subpopulations from the common ancestor
    • Bootstrap to estimate sampling variance of F_ST estimator
    • Permutation test for population differentiation
  • Random populations - diploid
    • ANOVA
    • Estimation of F_ST and F_IT
    • Extension to multiple alleles and loci
    • Bootstrap and permutation
    • Estimation of F_IS
• Lecture 21: Comparing Genetic Drift
  [ Last post: Tue Nov 2 17:55:04 CST 2004 ]
  • Island model with migration and mutation
    • Recurrence relations
    • Equilibrium solution
    • Extensive interpretation of the equilibrium
    • Equilibrium in the absence of mutation
    • Differentiation between subpopulations
  • ANOVA for fixed populations: definitions and table
• Lecture 20: Comparing Genetic Drift
  [ Last post: Thu Oct 28 18:32:47 CDT 2004 (1 update) ]
  • Reading Assignment: Felsenstein's Chapter 7
  • Topics:
    • Genetic drift and mutation
      • Infinite isoalleles model
      • Finite isoalleles model
      • Infinite vs. finite isoalleles model
      • Homozygosity, inbreeding and infinite isoalleles model
      • Rate of observable mutation in Wright infinite isoalleles model
      • Bottlenecks in finite populations with mutation
    • Genetic drift and migration
      • One island model
      • Island model (introduction only)
    • Rules of thumb for finite populations with mutation and migration
• Lecture 19: Genetic Diversity
  [ Previous post: Tue Oct 26 14:51:10 CDT 2004 ; Last post: Tue Oct 26 16:55:30 CDT 2004 ]
  • Total variance (including genetic variation) of allele frequency estimates
  • Bias of average gene diversity
  • Total variance of per-locus gene diversity
  • Estimating total variance of average gene diversity from single populations
  • Population structure : detecting genetic differences between fixed populations (without considering genetic variation)
    • Contigency tables
    • Numerical resampling (bootstrap): overlapping confidence intervals
    • Permutation tests (approximate exact methods): conditional probability derivation and procedure
• Lecture 18: Genetic Diversity
  [ Last post: Thu Oct 21 14:54:02 CDT 2004 (1 update) ]
  • Code:
    • R code for allele variance and inbreeding figures.
    • R code for varying population size figure.
  • Topics:
    • Measures of diversity
    • Average heterozygosity
      • Sampling variance
      • Total variance (including genetic variation)
      • Estimating total variance from multiple alleles, one population
      • In analysis of variance (ANOVA) context: components of variance
        • Variance at a locus within a population
        • Total variance of average heterozygosity
    • Gene diversity
      • Per-locus bias
      • Per-locus sampling variance
      • Sampling Variance of average gene diversity
• Lecture 17: Genetic Drift II
  [ Last post: Tue Oct 19 14:32:44 CDT 2004 ]
  • Plots of predicted allele frequency 95% confidence intervals and inbreeding probabilities for various population sizes
  • Effective population size for varying levels of variability in the number of offspring per adult (fertility variation caused by environmental effects)
  • Hierarchical population structure
    • Relative probabilities of non-ibd alleles (H_IT, H_IS, H_ST)
    • Relative inbreeding coefficients (F_IT, F_IS, F_ST)
    • Example: infinite population split into infinitely many subpopulations of size N.
    • Relative inbreeding coefficients in random mating populations.
    • Relative inbreeding coefficients as relative correlations.
    • Diversity
      • Heterozygosity
        • Per locus and average heterozygosity
        • Sampling variance
        • Bias
• Lecture 16: Genetic Drift
  [ Previous post: Thu Oct 14 16:54:09 CDT 2004 (1 update) ; Last post: Wed Nov 17 19:33:14 CST 2004 (2 updates; correct p. 11 binomial formula) ]
  • Rate of loss of alleles in finite populations.
  • Change of inbreeding at current generation relative to amount of inbreeding left before complete homogeneity achieved.
  • Bottlenecks
  • Time required to lose a target amount of heterogeneity or achieve a target level of inbreeding.
  • Wright-Fisher Model
    • Mean allele frequency
    • Fixation probabilities
    • Variance of allele frequencies
    • Relation between inbreeding and genetic drift
  • Violating Wright-Fisher Assumptions and effective population size N_e
    • Distinct parents (no selfing)
    • Distinct sexes
    • Monogamy
    • Changing population size N_t
• Lecture 15: Inbreeding II
  [ Previous post: Tue Oct 12 14:45:03 CDT 2004 ; Last post: Tue Oct 12 17:05:11 CDT 2004 (1 update) ]
  • Reading assignment: Felsenstein Chapter 6
  • Topics:
    • Regular systems of inbreeding
      • Self-fertilization
      • Full-sib mating
      • Offspring-parent mating
      • Half-sib mating
      • Repeated backcross
    • Conserving genetic variability
    • Inbreeding depression and population mean relative fitness
    • Finite population size and genetic drift (introduction): allele fixation, haploid version of Wright model
• Lecture 14: Inbreeding
  [ Previous post: Thu Oct 7 14:43:12 CDT 2004 ; Last post: Thu Oct 7 16:44:57 CDT 2004 (1 update) ]
  • Reading assignment: Felsenstein Chapter 5
  • Topics:
    • The concept of offspring randomly selecting ancestors from previous generations
    • Computing inbreeding coefficients on pedigrees
      • Definition and notation of pedigree
      • Malecot's inbreeding coefficient
      • Path analysis for computing the inbreeding coefficient F_X
      • Examples of path analysis
      • Coefficient of kinship
        • With yourself F_XX
        • In relation to inbreeding coefficient
        • For full sibs
        • A child with a non-descendent
        • Set of rules for computing coefficients of kinship
• Lecture 13: Migration
  [ Previous post: Tue Oct 5 16:39:59 CDT 2004 ; Last post: Tue Oct 5 14:49:56 CDT 2004 (1 update) ]
  • Migration and linkage disequilibrium.
  • Gene flow
  • Estimating migration
  • One island model
  • Island model
  • Stepping-stone model (briefly)
  • Migration and selection
  • Properties of locally adaptive alleles
  • Inbreeding introduction: autozygotes, allozygotes, base population, inbreeding coefficient
• Lecture 12: Mutation II
  [ Previous post: Thu Sep 30 14:24:27 CDT 2004 ; Last post: Thu Sep 30 16:53:40 CDT 2004 (1 update) ]
  • Reading: Felsenstein Chapter 4: Migration (read through p. 138 to start)
  • Topics:
    • Example application: pre-existence of HIV drug resistant mutants prior to therapy.
    • Mutation/selection balance in diploids: recessive, partial dominant
    • Example: cystic fibrosis
    • Haldane-Muller principle/mutational load: cost of mutation on a population
    • Relation between mutation and linkage disequilibrium
    • Migration
      • Equations for allele frequencies
      • Equations for genotype frequencies
      • Whalund effect: excess of homozygotes
• Lecture 11: Finish Natural Selection, Then Mutation
  [ Previous post: Tue Sep 28 14:48:30 CDT 2004 ; Last post: Wed Sep 29 17:00:58 CDT 2004 (1 update) ]
  • Web link: Biology of mutations
  • Reading: Felsenstein Chapter 3: Mutation
  • Topics:
    • Detecting selection by sampling multiple generations
      • Estimating relative viability using ratios of genotype frequencies: homozygotes to heterozygotes
      • Estimating relative fitness Using ratios of allele frequencies
      • Maximum likelihood estimation of the full model
    • Introduction to mutation types and control mechanisms (see external link.
    • Recurrence relations for mutation
    • Change in allele frequencies due to mutation
    • Equilibrium, stability, and rate of approach to equilibrium
    • Neglecting back mutation
    • Extension to multiple alleles
    • Mutation/selection balance
    • Haploid population: q_e = u/s
    • Diploid population (also in lecture 12): recessive vs. partial dominant
• Lecture 10: Natural Selection
  [ Previous post: Thu Sep 23 14:53:30 CDT 2004 ; Last posted: Thu Sep 23 16:44:22 CDT 2004 (1 update) ]
  • Meaning of mean allele fitness in diploid populations
  • Extending selection equations to multiple alleles: equations, equilibrium and stability
  • Population mean relative fitness: the effect of selection on a population, cost of diploidy
  • Detecting selection: deviation from HWE and estimating relative viability
    • Method 1: in a population satisfying other HW assumptions
    • Method 2: in a controlled cross where equal proportions of two offspring types are expected
• Lecture 9: Natural Selection
  [ Previous post: Tue Sep 21 14:47:58 CDT 2004 ; Last posted: Tue Sep 21 16:51:55 CDT 2004 (1 update) ]
  
  • Some really silly examples of R scripts used to generate graphics in lectures:
    • Wt.R: R script for modeling asexual population absolute growth N_A(t) over time.
    • Pt.R: R script for modeling asexual population relative allele frequency p_A(t)/p_a(t) over time.
    • p_A.t.R: R script for plotting allele frequency p_A(t) as a function of time t.
  • Reading assignment
    • pp. 33-66 of Felsenstein's Chapter 2 all except differential equations stuff.
    • start reading Chapter 8 at p. 274 of Weir's book.
  • Topics covered
    • Fitness (W) components: viability (v), fertility (f)
    • Haploid selection
      • Recurrence relations
      • Mean absolute fitness
      • Relative fitness (w and s): advantages and different parameterizations
      • Change per generation in allele frequency
      • Time course and rate of change in allele frequencies
    • Motivation: examples of selection detection
    • Diploid selection
      • Gametic pool
      • Allele frequencies post-viability selection, post-fertility selection
      • Recurrence relations
      • Relative fitness, mean relative fitness, mean allele fitness
      • Change per generation in allele frequency
      • Types of diploid selection: geometric (multiplicative), additive, recessive, dominant, overdominant, underdominant
      • Equilibrium allele frequencies and stability
• Lecture 8: Linkage Disequilibrium II
  [ Previous post: Thu Sep 16 14:46:41 CDT 2004 ; Last posted: Thu Sep 16 18:12:52 CDT 2004 (1 update) ]
  • Linkage disequilibrium for physically unlinked loci
  • Generalization of linkage disequilibrium to multiple alleles
  • Normalized linkage disequilibrium
  • Other possible statistical associations between two loci
    • Trigenic associations: definition, estimation, testing
    • Composite digenic association for data without phase information: estimating, testing
  • Other exact tests for genetic count data
    • Genotype independence across loci
    • Linkage equilibrium and HWE simultaneously
  • Multiple tests for multiple loci
    • implementation and interpretation
    • Bonferroni correction
  • Tests for homogeneity
  • Natural selection in asexual populations
    • change in a single generation (recurrence relation)
    • relative fitness
    • environmental effects
    • selection coefficients s
    • detecting selection (examples)
• Lecture 7: Linkage Disequilibrium I
  [ Previous post: Tue Sep 14 14:55:08 CDT 2004 ; Last posted: Tue Sep 14 17:46:37 CDT 2004 (1 update) ]
  • Meisosis Animation
  • Topics:
    • Recurrence relation for gamete frequencies
    • Recurrence relation for linkage disequilibrium
    • Rate of approach to linkage equilibrium
    • Haplotypes vs. gametes
    • Pratical consequences of linkage disequilibrium
    • Testing linkage disequilibrium D_AB
      • Phase information available:
        • likelihood function
        • bias
        • sampling variance
        • z test
        • chi-square test
        • exact test
        • power and sample size calculations
• Lecture 6: Disequilibrium II
  [ Previous post: Thu Sep 9 20:06:36 CDT 2004 (1 update) ; Last posted: Mon Oct 11 11:22:35 CDT 2004 (2 updates) ]
  • GenePop: site for computing exact tests
  • Second update corrected notation in last few slides from P_AB to p_AB since gamete frequencies are supposed to be identified by small p. Thanks for the correction.
  • Topics:
    • Equilibrium allele frequency for sex-linked locus
    • Equilibrium genotype frequencies for sex-linked locus
    • Other mating systems
    • Tests for HWE with multiple alleles
      • Chi-square test for complete equilibrium
      • z-test for partial equilibrium
      • Likelihood ratio test statistic for partial equilibrium
      • Exact tests
    • Power calculations: chi-square test, exact tests
    • Linkage: introduction
• Lecture 5: Disequilibrium I
  [ Previous post: Tue Sep 7 17:03:49 CDT 2004 Last posted: Tue Dec 7 09:48:27 CST 2004 (1 update; better formatting) ]
  • standard normal distribution: site for computing p-values from tail areas
  • Topics:
    • Statistical hypothesis testing
    • Hardy-Weinberg disequilibrium
    • HWD as covariation between alleles
    • Additive disequilibrium D_A
      • Testing additive disequilibrium H₀: D_A=0
      • Bias
      • Sampling variance
      • z-test
      • Alternative hypotheses
      • Chi-square test; chi-square goodness-of-fit test; cautions
      • Exact tests
      • Likelihood ratio and likelihood ratio test
      • Multiplicative model of Hardy-Weinberg disequilibrium (log-linear)
    • Sex linkage: persistence of disequilibrium, equilibrium solution (repeated and cont'd)
• Lecture 4 (9/02/04): Frequency Estimation III
  [ Previous post: Thu Sep 2 16:59:35 CDT 2004 ; Last posted: Mon Sep 27 14:27:47 CDT 2004 (1 update) ]
  • Another iterative solution for maximizing likelihood: EM Algorithm
  • Method of Moments
  • Bayesian Estimation
  • HWE Generalization: different genotype frequencies in two sexes
• Lecture 3 (8/31/04): Frequency Estimation II
  [ Last posted: Wed Sep 1 09:52:33 CDT 2004 ]
  • Hardy-Weinberg Equilibrium
  • Linear recurrence relations
  • Maximum likelihood estimation: (1) brute force calculus, (2) Lagrange multipliers and (3) Bailey's method
  • Iterative solution for maximizing likelihood: (1) grid search and (2) Newton-Raphson
• Lecture 2 (8/26/04): Frequency Estimation
  [ Previous post: Tue Aug 31 09:32:28 CDT 2004 Last posted: Tue Dec 7 08:46:00 CST 2004 (1 update) ]
  • Building a genetic model, e.g. Mendel's model
  • Statistical estimation and statistical sampling
  • Multinomial sampling distribution applies in frequency estimation
  • Allele and genotype frequency simple estimators, variance, and covariance formulas direct from Multinomial distribution
  • Constructing confidence intervals
  • Fisher's approximate variance formula
  • Resampling methods for estimating variances: (1) jackknife and (2) bootstrap
• Lecture 1 (8/24/04): Course Introduction
  [ Last posted: Wed Aug 25 09:17:39 CDT 2004 ]
  • Links:
    • Human Molecular Genetics 2
    • DNA from the Beginning
    • K. A. Crandall's 1995 J. Virol. figure from the paper on dental transmission of HIV. Nodes labeled D represent HIV sequences from the dentist. Nodes labeled PA through PH represent HIV sequences from his patients. Nodes labeled Q or by numbers alone are local controls, HIV sequences from patients with no known contact with the dentist. The numbers along the branches indicate the number of mutations separating the sequences.
  • Reading assignment:
    • Read Chapter 1 of Weir. Begin reading Chapter 2 if you like to stay ahead of lecture.
    • If you need biological review, take a little extra time to read through DNA from the Beginning for a real gentle, but entertaining introduction and chapters 1-2, 5, and 6.1-6.3 of Human Molecular Genetics 2. Finally, also read section 11.2 of HMG 2 and Chapter 12 from the online book Modern Genetic Analysis to learn about the different genetic markers. This is not a required reading assignment, but highly recommended if you are new to biology. You won't have much fun with this material if you don't learn these basics.