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3/20/17 An Introduction to Quantitative Genetics I Heather A L awson Advanced G enetics Spring2017 Outline • What is Quantitative Genetics? • Genotypic Values and Genetic Effects • Heritability • Linkage Disequilibrium and Genome-‐Wide Association Quantitative Genetics • The theory of the statistical relationship b etween genotypic variation and phenotypic variation. 1. What is the cause of p henotypic variation in n atural populations? 2. What is the genetic architecture and molecular basis o f p henotypic variation n natural populations? 1 3/20/17 • Genotype • The genetic constitution of an organism or cell; also refers to t he specific set of alleles inherited at a locus • Phenotype • Any measureable characteristic of an individual, such as height, arm length, t est score, hair color, disease status, migration of proteins or DNA in a gel, etc. Nature V ersus Nurture • Is a phenotype the result o f genes or the environment? • False dichotomy • If NATURE: m y genes m ade m e do it! • If NURTURE: m y m other m ade me do it! • The features of an organisms are due to an i nteraction of the individual’s genotype and environment Genetic Architecture: “sum” of the genetic effects upon a phenotype, including additive,dominance and parent-of-origin effects of several genes, pleiotropy and epistasis Different genetic architectures Different effects on the phenotype 2 3/20/17 Types of Traits • Monogenic traits (rare) • Discrete binary c haracters • Modified by genetic and environmental background • Polygenic traits (common) • Discrete ( e.g. bristle number on flies) or c ontinuous ( human height) or binary (disease status) • Modified by genetic and environmental background As t he number of loci controlling a trait increases, the phenotype frequency becomes increasingly continuous Phenotypic Distribution of a Trait 3 3/20/17 Consider a S pecific Locus Influencing the Trait For this locus, mean phenotype = 0.15, while overall mean phenotype = 0 Goals of Q uantitative Genetics • Partition total trait variation into genetic (nature) and environmental (nurture) components • Predict resemblance b etween relatives • If a sib has a disease/trait, what are y our odds? • Find the underlying loci (genes, n ucleotides) contributing to this variation • QTL – quantitative trait loci • GWAS – genome-‐wide association • Deduce molecular basis for genetic trait variation Basic Model of Q uantitative Genetics Phenotypic Value = the v alue observed when a trait is measured on an individual P = G + E Genotypic Value = the average phenotype of those c arrying the specified genotype Environmental D eviation = the deviation of the observed phenotype in an individual from the genotypic v alue 4 3/20/17 If we measure the genotype and the phenotype in the same individuals, we can estimate genotypic values for various phenotypes Genotypic Values • At a single locus, it is t he average phenotype of those carrying the specified genotype • Can be decomposed into: • Additive effects • Dominance effects • Parent of Origin effects Parent-‐of-‐Origin Genetic Effects • With 3 genotypes (A1A1, A1A2, A2A2) you can estimate two genetic parameters (additive and dominance) • To analyze parent-‐o f-‐o rigin dependent effects, you n eed o rdered genotypes (A1A1, A1A2, A2A1, A2A2) • Adds another parameter 5 3/20/17 A1 A2 A1 A1 A1 A2 A1 A2 A1 A2 A2 A2 Arbitrarily assigned g enotypic values Genotype A1A1 A1A2 -‐a A2A2 d Genotypic value +a 0 Genotypic Values weight(g) pg pg +pg ++ 6 12 14 from Example 7.1 Falconer and Mackay 6 3/20/17 Reference point (r) r is the mid-‐point between the two homozygotes pg pg (6g) +pg (12g) ++ (14g) r = 10g Additive genotypic value (a) a is the half-‐the difference between the two homozygotes 7 3/20/17 pg pg (6g) +pg (12g) ++ (14g) r=10g ±a = 4 g Dominance genotypic value (d) d is the deviation from the midpoint between the two homozygotes pg pg (6g) +pg (12g) ++ (14g) r=10g d = 2 g 8 3/20/17 31 Trait Value 3 0 .5 30 = -‐1 .63 2 9 .5 29 2 8 .5 28 2 7 .5 LL LS|SL SS 31 Trait Value 3 0 .5 = -‐0 .49 30 2 9 .5 29 2 8 .5 = 0.75 28 2 7 .5 LL LS|SL SS Genomic Imprinting: Different expression o f alleles i nherited from the mother and father results i n phenotypic d ifferences between reciprocal heterozygotes (A1 A2 ≠ A2 A1) Pat Mat Pat Mat Bi-‐allelic gene A1 A2 = A2 A1 Maternally expressed gene A1 A2 ≠ A2 A1 Paternally expressed gene A1 A2 ≠ A2 A1 Genotypic Values weight(g) pg pg pg + +pg ++ 6 8 12 14 adapted from Example 7 .1 Falconer and Mackay 9 3/20/17 Parent-‐of-‐origin imprinting genotypic value (i) i is half the difference between the two heterozygotes pg pg (6g) +pg (12g) pg+ (8g) ++ (14g) r=10g ±i = 2 g Trait Value 35 30 = 7.5 25 20 15 = 7.5 10 5 0 LL LS SL SS 35 Trait Value 30 = -‐7.5 25 20 15 = -‐7.5 10 5 0 LL LS SL SS 10 3/20/17 Heritability • The proportion o f p henotypic variation that i s attributable to genotypic variation • Penetrance: the percentage of individuals with a specific genotype that possess an associated disease • Categorical, e.g. H untington’s disease • Expressivity: the degree to which individuals with a s pecific genotype display the associated p henotype • Quantitative, e.g. psoriasis Heritability • Phenotype (P) = Genotype (G) + Environment (E) • Var(P) = Var(G) + Var(E) + Cov(G,E) • Broad-‐s ense heritability • H2 = Var(G) / Var(P) • Broad-‐s ense heritability i ncludes additive, dominance, epistatic variance, and parent-‐o f-‐o rigin effects Heritability • Genetic (G) = Additive (A) + Dominance (D) + Imprinted (I) + Epistasis (E) • Var(G) = Var(A) + Var(D) + Var(I) + Var(E) • Narrow-‐s ense heritability • h 2 = Var(A) / Var(P) • Narrow-‐s ense heritability i s the ratio o f the additive genetic variance to the total phenotypic variance 11 3/20/17 Heritability • Ranges from 0 (all environmental) to 1 (all genetic) • Specific to a population in specific environmental circumstances • Highly inbred population with no genetic variation • Heritability of 0 • No environmental variance in an outbred population if all genetic variance is additive • Heritability of 1 • Can decrease by either a decrease in additive variance (VA) or by an increase in environmental variance (VE) Estimating Heritability Analysis of Variance or Regression Heritability F rom Twins For c omparison of m onozygotic (MZ) and dizygotic ( DZ) twins: rmz = A + C rdz = 0.5 * A + C A = 2 * (rmz – rdz ) C = rmz – A E = 1 – rmz Where the c omponents of v ariance are A for additive, C for c ommon environment, and E for unique environment 12 3/20/17 Heritability of Human Traits Missing Heritability GWAS have been successful in identifying c ommon variants involved in c omplex trait aetiology. H owever, for the m ajority of c omplex traits, <10% of genetic variance is explained by c ommon v ariants. Thus only a small part of heritable variaation in a trait c an be explaind – most is m issing! What Explains Missing Heritability? • Genomic regions or classes of variation are not well covered b y existing markers • • • • LD between m arkers and c ausal v ariants Repeats or heterochromatic regions Rare v ariants Local heritability around associated S NPs • Heritability estimates (narrow-‐sense, i .e. additive) are overestimated • Power • De novo mutations • Explains a subset of c ases of autism and other phychiatric disorders • May contribute t o disease incidence b ut n ot to missing h eritability 13 3/20/17 Linkage Disequilibrium Non-‐random association of alleles at different loci Linkage Disequilibrium Haplotype A1B1 A1B2 A2B1 A2B2 A1/A2 B1/B2 Frequency X11 X12 X21 X22 Frequency p1 = X11 + X12 p2 = X21 + X22 q1 = X11 + X21 q2 = X12 + X22 Allele A1 A2 B1 B2 D = X 11 – p 1q 1 Correlation coefficient r = D sqrt(p 1 p 2 q 1 q 2) Decay of Linkage Disequilibrium Human Chromosome 22 14 3/20/17 Linkage and Linkage Disequilibrium Linkage and A ssociation As s ociation Linkage 20 G enerations Whole Genome A ssociation (Linkage Disequilibrium Mapping) 15 3/20/17 GWAS Methodology GWAS Workflow Case-‐Control A ssociation Plot and LD Map Human Chromosome 22 16