Problem! When Fisher Did This Work, It Was Virtually Impossible to Identify Any Specific Loci Influencing a Quantitative Trait.

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1 Problem! When Fisher Did This Work, It Was Virtually Impossible to Identify Any Specific Loci Influencing a Quantitative Trait. Therefore, No Genotypes Could be Measured, and No Genotypic Means Could Be Determined. How Did You Measure h 2, etc.? Solution Fisher Devised Several Ways of Estimating The Parameters of His Models Even When No Genotypes Are Measured. This Made His Model Immediately Practical in Agriculture and Medicine. Only Consider Two of His Approaches: 1. Phenotypic Correlations Among Relatives. 1

2 Covariance Measure Phenotypes in Two Individuals, Say X and Y The Covariance between X and Y = Average(X-µ x )(Y-µ y ) Fisher Showed Cov(Parent,Offspring) = 1 / 2 σ a2 Parents and Offspring Share Half Their Genes Covariance Measure Phenotypes in Two Individuals, Say X and Y The Covariance between X and Y = Average(X-µ x )(Y-µ y ) Fisher Showed Cov(Parent,Offspring) = 1 / 2 σ a2 Only This Part of the Phenotypic Variance is Transmissible Through A Gamete 2

3 Correlation Coefficient Is a Standardized Covariance Than Varies From -1 to +1. The Correlation between X and Y = Cov(X,Y)/(σ x 2 σ y2 ) 1/2 Assuming σ p 2 is constant across generations, Fisher Showed Corr(Parent,Offspring) = 1 / 2 σ a2 /(σ p 2 σ p2 ) 1/2 = 1 / 2 σ a2 /σ p 2 = 1 / 2 h 2 Correlation Coefficient Fisher Showed Corr(Sib1,Sib2) = 1 / 2 h / 4 σ d2 /σ p 2 Note, Corr(Parent,Offspring) < Corr.(Sibs) E.g., Systolic Blood Pressure: Corr.(Parent,Offspring) = h 2 = Corr.(Sibs) = > 1 / 2 h 2 Lesson: Two Peas In a Pod Trumps A Chip Off The Old Block 3

4 Misconception about correlation: The Higher h 2, the Less Important the Environment Never True at the Individual Level: an Individual s Phenotype is an inseparable interaction between genes and environment. E.g., h 2 B of mental retardation associated with PKU can be greatly altered by changing the dietary environment. The Higher h 2, the Less Important the Environment Never True at the Deme Level: For example, Environmental Factors can Determine the mean, µ, which has no impact on h 2 4

5 Adoption Study on IQ (Skodak & Skeels, 1949) Correlation Between Biological Mothers and Children = 0.44 Implies h 2 of IQ is 2(0.44) = 0.88 Correlation Between Adoptive Mothers and Children 0 Implies Environment Unimportant? Adoption Study on IQ (Skodak & Skeels, 1949) Biological Mothers (µ = 86, σ = 15.75) Relative Frequency IQ Score 5

6 Adoption Study on IQ (Skodak & Skeels, 1949) Adoptive Mothers (µ = 110, σ = 15) Relative Frequency IQ Score Adoption Study on IQ (Skodak & Skeels, 1949) Adopted Children (µ = 107, σ = 15.1) Relative Frequency IQ Score 6

7 Adoption Study on IQ (Skodak & Skeels, 1949) Adopted Children Relative Frequency Biological Mothers Adoptive Mothers IQ Score Environment 7

8 Strong Biol. Mother- Offspring Correlation No Adoptive Mother- Offspring Correlation 8

9 Adoption Study on IQ (Skodak & Skeels, 1949) 1. IQ has a high heritability and genetic variation is the major cause of differences in IQ among the adopted children 2. The IQ of the adopted children was strongly influenced by socio-economic factors. These Are Not Contradictory! Correlation & Regression the midparent value = 1 / 2 P m + 1 / 2 P f where the subscript m denotes the phenotype of the mother and f the phenotype of the father Cov(midparent, offspring) = Cov( 1 / 2 g am + 1 / 2 g af, 1 / 2 g am + 1 / 2 g af ) = 1 / 4 Var(g am ) + 1 / 4 Var(g af ) = 1 / 2 a 2 ρ p o = σ a 2σ a 1 2 σ p 2 σ p 2 = 1 σ p 2 = 1 2 h 2 2 σ The regression coefficient is: b YX = ρ Y XY 2 σ X b op = ρ p o σ o σ = h 2 = h 2 1 p 2 9

Regression Coefficient 11.0 1978 1976 10.0 9.0 8.0 8.0 9.0 10.0 11.0 Midparent Beak Depth (mm) 2.

10 Regression Coefficient Midparent Beak Depth (mm) 2. Response to Selection b op = h 2 Implies another way of estimating h 2 Offspring Mean Midparen t Phenotype R S Selected Parent Mean Hence, R=Sh 2 10

2. Response to Selection Abdominal Bristle Number in Drosophila melanogaster Unselected Mean=35.3 Selected Mean=40.6 S=40.6-35.3=5.3 Offspring Mean=37.9, so R=37.9-35.3 Hence, h 2 =R/S = 0.

11 2. Response to Selection Abdominal Bristle Number in Drosophila melanogaster Unselected Mean=35.3 Selected Mean=40.6 S= =5.3 Offspring Mean=37.9, so R= Hence, h 2 =R/S = 0.49 Measured vs. Unmeasured Genotypes in Quantitative Genetics In 1918, the only genes identifiable were those with a simple relationship to a phenotype. Genes influencing quantitative variation were not knowable as individual loci. Fisher s genius was that he invented ways of estimating h 2 even though no genotypes were being measured. Today, we can measure genotypes. 11

12 Measured Genotype Approaches Genome-wide mapping Candidate loci. Combination of the two. Both Approaches Are Not Really New, but practicality is. Mapping Approaches To Identifying Genetic Factors Contributing To Disease Risk Linkage Mapping Linkage Disequilibrium Mapping (GWAS: Genome-Wide Association Studies) Admixture Mapping 12

13 Genomic Linkage Mapping Need Pedigree Data (humans) or crosses between strains. Obtain sufficient polymorphic markers scattered throughout the genome such that any locus is close to a marker locus. Genetic resolution is limited by the number of recombination events in a single (or a few) generation(s) in your sample. Genomic Linkage Mapping The markers show an association with phenotypic variation through linkage, not direct causation. The strength of the association in general is inversely proportional to the recombination frequency. Therefore, the markers with the strongest associations identify the areas of the genome with loci that affect the phenotype. These areas are called Quantitative Trait Loci (QTL s). Note, they are not genetic loci, but positions (loci) or regions on the chromosome. 13

Genomic Linkage Mapping When dealing with a polygenic trait and with sufficient markers to cover the entire genome at least at the

14 Genomic Linkage Mapping This is easiest to do when a single locus has a strong (or exclusive) influence on the phenotype. For example, the locus for Huntington s Chorea was identified by linkage within 5 cm to a marker locus. Genomic Linkage Mapping When dealing with a polygenic trait and with sufficient markers to cover the entire genome at least at the resolution of 10 cm, can examine every map position in the genome and evaluate how likely it is that genetic variation is segregating at that site that influences the trait of interest. 14

15 Genomic Linkage Mapping Interval Mapping Observed Marker Genotype Observed Average Phenotype Possible Genotypes When QTL Is Included and The Expected Frequency Assuming Model in Figure 10.2 AB/ab G AB AXB/axb 1 / 2 (1-r) Expected Phenotype Given QTL with Genotype Values of G Xx and G xx G Xx Ab/ab G Ab AXb/axb 1 / 2 (r-r x ) Axb/axb 1 / 2 r x [(r-r x )G Xx +r x G xx ]/r ab/ab G ab axb/axb 1 / 2 r x axb/axb 1 / 2 (r-r x ) ab/ab G ab axb/axb 1 / 2 (1-r) [r x G Xx +(r-r x )G xx ]/r G xx E.g., A Genome Linkage Scan for Persistence of Fetal Hemoglobin in 3,765 Sardinians (Uda et al. 2008) Scanned for Nearly 10,000 SNP s (Single Nucleotide Polymorphisms), With Interval Mapping at Every 0.5 CM Position Threshold for Statistical Significance Location of Hb β Chain Locus (note, Sardinians have a high incidence of Hb-S) Threshold for Statistical Significance Chromosomal Location 15

16 Linkage Disequilibrium Mapping D S U D i s t a n c e (kb) kb Utah Swed AllYor YorBot YorTop Reich et al. (2001 Nature 411: ) Linkage Disequilibrium Mapping or Genome-Wide Association Study (GWAS) The markers show an association with phenotypic variation through linkage disequilibrium, not direct causation. The strength of the association in general is inversely proportional to the recombination frequency (if you have sampled correctly). Therefore, the markers with the strongest associations identify the areas of the genome with loci that affect the phenotype. The analyses are similar to those of pedigree linkage mapping, but you do not need pedigree data (a big cost and logistic advantage). Instead, linkage disequilibrium in the population is used as a proxy for recombination frequency in a pedigree. 16

17 Linkage Disequilibrium Mapping or GWAS The accuracy of the localization of a QTL in the genome depends upon having some recombination between the markers and the QTL under both linkage and disequilibrium mapping. Linkage mapping depends upon recombination events that occurred only in a handful of generations, often just one, and therefore results in a coarse resolution with broad peaks. Disequilibrium reflects the cumulative effects of recombination over human evolutionary history, and therefore potentially results in much finer scale resolution. To take advantage of this finer scale resolution, need to scan the genome with many more markers. E.g., A Genome Linkage Scan for Persistence of Fetal Hemoglobin in 3,765 Sardinians vs. a GWAS on 4,305 (overlapping) Sardinians (Uda et al. 2008) Based on 10K SNP-Chip Based on 500K SNP-Chip 17

18 A Problem For GWAS is Missing heritability Suppose b is a allele that affects the phenotype, but A/a is the marker locus. Even when D =1, not all bears of a have b, so some potential phenotypic association is lost. D = g AB g ab - g Ab g ab = g AB 0-0g ab =0 Initial Gene Pool: A B a B a B Mutation At A Second Site Produces Three Gamete Types: Gene Pool After Mutation: A B a B a b D = g AB g ab - g Ab g ab = g AB g ab - 0g ab = g AB g ab 0 18

Missing Heritability is also induced by statistical corrections to minimize false

Nat Genet 42:565-569, 2010 Corrected for LD Effects and did not try to identify specific

all! Some Heritability may be missing because of the genetic architecture assumed by most

19 Missing Heritability is also induced by statistical corrections to minimize false positives, which increase the rate of false negatives. Yang et al. Nat Genet 42: , 2010 Corrected for LD Effects and did not try to identify specific QTLs and looked at GWAS estimates of h 2 for height: Most of the h 2 was not missing at all! Some Heritability may be missing because of the genetic architecture assumed by most GWAS models: Epistasis is generally ignored, and only primarily examine effects of common alleles with small effects. 19

20 Assumed Model In Standard GWAS 20

21 Assumed Model For Rare Variants Look For Extended Haplotypes 21

22 Look For Extended Haplotypes Impact of Two Extended Haplotypes 22

23 Admixture Mapping Controlled Crosses Are Often Used to Determine the Genetic Basis of Differences Between Populations. When controlled crosses are not an option, can use natural admixture as a substitute, and must use genetic markers to determine the degree of admixture in the sampled individuals. Admixture Between Two Demes Ancestral Gene Pools European Population West African Population A a A a pe qe pw qw 1 M 1-M Gene Pools in Present North America A pe a qe European Americans A pa= MpE+(1-M)pW a qa African Americans 23

24 End-Stage Kidney (Renal) Disease (ESKD) Is A Major Disease In the USA and Other Countries 100,000 Americans develop ESKD each year, and it is associated with high health care costs and high mortality The cumulative life time risk for ESKD varies with ethnicity: 7.5% in African-Americans 2.1% in European-Americans The cause of this increased risk is not explained by social-economic status, lifestyle factors, etc. Admixture Between Two Demes Basic strategy of admixture mapping: Subdivide the African American Sample into Cases (those with ESKD) and Controls (matched for as many other variables as possible, but do NOT have ESKD). Idea: genes increasing risk of ESKD should be in genomic regions of West African Ancestry. 24

Ancestry informative markers are used to compute the ancestry across the chromosomes of cases and controls African European Bercovici S. et.al. Genome Res.

25 Ancestry informative markers are used to compute the ancestry across the chromosomes of cases and controls African European Bercovici S. et.al. Genome Res. 2008;18: by Cold Spring Harbor Laboratory Press Admixture Between Two Demes For this to work you need to have markers that cover the whole genome and that are informative about the population differences between Africans and Europeans. We created a computer algorithm to choose 2,500 SNPs out of 6 million for this purpose (Bercovici, S., D. Geiger, L. Shlush, K. Skorecki, and A. Templeton Genome Res. 18: ). The SNP panel was then run on a sample of 723 Cases and 1,059 Controls at Washington University. An independent sample was run by Kopp et al, and both studies had identical results. 25

26 Results of Admixture Mapping Association analysis in ESKD cohorts with logistic regression for alleles G1 and G2 Both nonsynonymous: D =1, defines a derived APOL1 haplotype called G1 After removing effects of G1, find strong signal in 6-bp deletion in APOL1: Call this G2 After removing effects of G1 and G2, no significant signals remain: call remaining haplotypes at APOL1 WT Tzur et al., Hum Genet 128, (2010); Genovese et al., Science 329, (2010) 26

27 Extended Haplotypes at APOL1 Locus Extended Haplotype Homozygosity Candidate Locus Approach Prior information is used to implicate specific loci as likely to be association with the phenotype of interest From mapping study From knowledge of biochemistry, physiology, and gene function An example is the ApoE study that was presented earlier. 27

However, interactions challenge our usual concepts of causation and scientific

28 A Major Advantage of the Candidate Locus Approach Is That Interactions Between Genes (Epistasis) and Between Genes and Environments Can Be Studied. However, interactions challenge our usual concepts of causation and scientific inference. Epistasis Between ApoE and LDLR HDL particle containing cholesterol ApoE ApoB 28

29 Epistasis Between ApoE and LDLR for LDL Cholesterol LDLR Genotype A1/- Serum LDL Cholesterol (mg/dl) A2/A ApoE Genotype Two Populations Frequency ApoE-4 Allele = Frequency ApoE-3 Allele = 0.77 Frequency LDLR A2 Allele = 0.78 Frequency ApoE-4 Allele = 0.95 Frequency ApoE-3 Allele = 0.03 Frequency LDLR A2 Allele =

{ Epistatic Variance Dominance Variance Additive Variance 50.00 35.00 B. 30.00 40.00 25.00 30.00 20.00 15.00 20.00 10.

30 10/4/12 Quantitative Genetic Components As a Function of Allele Frequencies: A. ε4 allele at ApoE is Rare, A2 at LDLR Common; B. Reversed Genetic Variance A. { Epistatic Variance Dominance Variance Additive Variance B ApoE & LDLR ApoE LDLR ApoE & LDLR ApoE LDLR Interactions Also Exist Between Genetic and Environmental Factors (e.g, Macular Degeneration, the cause of 90% of all legal blindness) 30

31 LD genome scan Macular Degeneration chromosome 10q26 Schmidt, S., M. A. Hauser, et al. (2006). Am J Hum Genet 78(5): Genotype Frequencies in Subjects with MD General Population Macular Degeneration Genotype Frequencies in Subjects without MD Schmidt, S., M. A. Hauser, et al. (2006). Am J Hum Genet 78(5):

32 Macular Degeneration Linkage genome scan Schmidt, S., M. A. Hauser, et al. (2006). Am J Hum Genet 78(5): Autoimmune Diseases & Allergies 32

Hygiene Hypothesis Hygiene Hypothesis Braun-Fahrlander et al (2002) showed that children of farmers in Central Europe that were exposed to high levels of bacterial endotoxin in house dust had low

33 Hygiene Hypothesis Hygiene Hypothesis Braun-Fahrlander et al (2002) showed that children of farmers in Central Europe that were exposed to high levels of bacterial endotoxin in house dust had low levels of allergies & asthma compared to children from the same communities exposed to low levels of endotoxin. This suggests a candidate environment (endotoxin loads in house dust), and a candidate gene, CD14 33

34 Hygiene Hypothesis Hygiene Hypothesis CC has highest risk CC has lowest risk Martinez, in Genetic Effects on Environmental Vulnerability to Disease, Wiley,

35 Interactions of Genes With Other Genes and With Environmental Factors Ensure That The Phrase The Gene For X Is Often False and Actively Misleading. Using Interactions in Treatments GWAS Studies Identified the rs37972 SNP As Being Associated with Asthma. Cell Culture Studies Indicate That This SNP Is Also Associated with the Level of Transcription of the glucocorticoid-induced transcript 1 gene (GLCCI1) Tantisira, K. G. et al. New England Journal of Medicine 365, ,

Using Interactions in Treatments The association of GLCCI1 rs37972 genotypes with changes in forced expiratory volume in 1 second (FEV1) after 4 to 8 weeks of therapy with inhaled glucocorticoids in

36 Using Interactions in Treatments The association of GLCCI1 rs37972 genotypes with changes in forced expiratory volume in 1 second (FEV1) after 4 to 8 weeks of therapy with inhaled glucocorticoids in four replication populations Tantisira, K. G. et al. New England Journal of Medicine 365, , 2011 Using Interactions in Risk Prediction Example: ApoE genotypes and Cholesterol Level (affected by many genes and environmental factors) as retrospective predictors of coronary artery disease (Kardia, S. L. R., Stengård, J., & Templeton, A. R An evolutionary perspective on the genetic architecture of susceptibility to cardiovascular disease. In S. C. Stearns, Ed., Evolution in Health and Disease, pp Oxford: Oxford University Press) 36

37 10 Odds 2 of 1 CAD There Is About A 5-Fold Range Of Incidence Variation With Any One Factor. C-H C-M C-L 4/ 3 2/ 3 3/ C-Hin C-M in C-L in and and and 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 10 Odds 2 of 1 CAD There Is About A 100-Fold Range Of Incidence Variation With The Two Factors Considered Together C-H C-M C-L 4/ 3 2/ 3 3/ C-Hin C-M in C-L in and and and 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 37

38 10 Odds 2 of 1 CAD There Is Much More Information In The Interactions Among Factors Than Just In The Factors Themselves C-H C-M C-L 4/ 3 2/ 3 3/ C-Hin C-M in C-L in and and and 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 10 Odds 2 of 1 CAD C-H C-M C-L 4/ 3 2/ 3 3/ C-Hin C-M in C-L in and and and 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 38

39 10 Odds 2 of 1 CAD C-H C-M C-L 4/ 3 2/ 3 3/ C-Hin C-M in C-L in and and and 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 10 Odds 2 of 1 CAD C-H C-M C-L 4/ 3 2/ 3 3/ C-Hin C-M in C-L in and and and 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 39

40 10 Odds 2 of 1 CAD Individual Predictions Are Much More Informative and Precise When The Genotypic Information Is Placed In An Interactive Context C-H C-M C-L 4/ 3 2/ 3 3/ C-Hin C-M in C-L in and and and 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 4/ 3 2/ 3 3/ 3 Candidate Genes & Human Disease The Major Application of Genetics to Risk Prediction and Treatment Is Not Gene Therapy But Rather In Understanding Genetic and Environmental Interactions. This Requires A Shift In Medicine From Treating The Diseases of Individuals To Treating The Individual With The Disease. 40

41 Interactions Are Both A Challenge and an Opportunity 41

b. (3 points) The expected frequencies of each blood type in the deme if mating is random with respect to variation at this locus.

b. (3 points) The expected frequencies of each blood type in the deme if mating is random with respect to variation at this locus. NAME EXAM# 1 1. (15 points) Next to each unnumbered item in the left column place the number from the right column/bottom that best corresponds: 10 additive genetic variance 1) a hermaphroditic adult develops