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Home , Pleiotropy, Quantitative genetics

3/20/17

An Introduction to Quantitative I Heather A Lawson Advanc ed Genetic s Spring2017

Outline

• What is ?

• Genotypic Values and Genetic Effects

•

• and -Wide Association

Quantitative Genetics

• The theory of the statistical relationship between genotypic variation and phenotypic variation.

1. What is the cause of phenotypic variation in natural populations?

2. What is the and molecular basis of phenotypic variation n natural populations?

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• • The genetic constitution of an organism or cell; also refers to the specific set of inherited at a

• • Any measureable characteristic of an individual, such as height, arm length, test score, color, disease status, migration of or DNA in a gel, etc.

Nature Versus Nurture

• Is a phenotype the result of or the environment?

• False dichotomy

• If NATURE: my genes made me do it!

• If NURTURE: my mother made me do it!

• The features of an organisms are due to an inte raction of the individual’s genotype and environment

Genetic Architecture: “sum” of the genetic effects upon a phenotype, including additive, and parent-of-origin effects of several genes, and

Different genetic architectures

Different effects on the phenotype

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Types of Traits • Monogenic traits (rare) • Discrete binary characters • Modified by genetic and environmental background

• Polygenic traits (common) • Discrete (e.g. bristle number on flies) or continuous (human height) or binary (disease status) • Modified by genetic and environmental background

As the number of loci controlling a trait increases, the phenotype frequency becomes increasingly continuous

Phenotypic Distribution of a Trait

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Consider a Specific Locus Influencing the Trait

For this locus, mean phenotype = 0.15, while overall mean phenotype = 0

Goals of Quantitative Genetics

• Partition total trait variation into genetic (nature) and environmental (nurture) components • Predict resemblance between relatives • If a sib has a disease/trait, what are your odds? • Find the underlying loci (genes, ) contributing to this variation • QTL – quantitative trait loci • GWAS – genome-wide association • Deduce molecular basis for genetic trait variation

Basic Model of Quantitative Genetics

Phenotypic Value = the value observed when a trait is measured on an individual P = G + E

Genotypic Value = the average phenotype of those carrying the specified genotype Environmental Deviation = the deviation of the observed phenotype in an individual from the genotypic value

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If we measure the genotype and the phenotype in the same individuals, we can estimate genotypic values for various

Genotypic Values • At a single locus, it is the 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 (A1A1, A1A2, A2A2) you can estimate two genetic parameters (additive and dominance)

• To a n a l y z e p a r e n t -of-origin dependent effects, you need ordered genotypes (A1A1, A1A2, A2A1, A2A2) • Adds another parameter

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A1 A2

A1 A1 A1 A2 A1

A2 A1 A2 A2 A2

Arbitrarily assigned genotypic values

Genotype

A1A1 A1A2 A2A2

-a d +a

Genotypic 0 value

Genotypic Values pg pg +pg ++

weight(g) 6 12 14

from Example 7.1 Falconer and Mackay

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Reference point (r)

r is the mid-point between the two homozygotes

pg pg +pg ++ (6g) (12g) (14g)

r = 10g

Additive genotypic value (a)

a is the half-the difference between the two homozygotes

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pg pg +pg ++ (6g) (12g) (14g)

r=10g ±a = 4g

Dominance genotypic value (d)

d is the deviation from the midpoint between the two homozygotes

pg pg +pg ++ (6g) (12g) (14g)

r=10g d = 2g

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31

30.5

30

29.5 = -1.63

29

28.5 Trait Value

28 27.5 LL LS|SL SS 31

30.5

30 = -0.49

29.5

29

28.5 Trait Value 28 = 0 .7 5 27.5 LL LS|SL SS

Ge nomic Imprinting: Different expression of alleles inherited from the mother and father results in phenotypic differences

between reciprocal heterozygotes (A1 A2 ≠ A2 A1) Pat Mat Pat Mat

Bi-allelic A1 A2 = A2 A1 Maternally expressed gene A1 A2 ≠ A2 A1

Paternally expressed gene A1 A2 ≠ A2 A1

Genotypic Values pg pg pg + +pg ++

weight(g) 6 8 12 14

adapted from Example 7.1 Falconer and Mackay

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Parent-of-origin imprinting genotypic value (i)

i is half the difference between the two heterozygotes

pg pg pg+ +pg ++ (6g) (8g) (12g) (14g)

r=10g ±i = 2g

35

30 25 = 7.5 20

15

Trait Value 10 = 7.5

5 0 LL LS SL SS

35 30 25 = -7.5 20 15 10 = -7.5 Trait Value 5 0 LL LS SL SS

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Heritability • The proportion of phenotypic variation that is attributable to genotypic variation

• Penetrance: the percentage of individuals with a specific genotype that possess an associated disease • Categorical, e.g. Huntington’s disease

• : the degree to which individuals with a specific genotype display the associated phenotype • Quantitative, e.g. psoriasis

Heritability

• Phenotype (P) = Genotype (G) + Environment (E)

• Var(P) = Var(G) + Var(E) + Cov(G,E)

• Broad-sense heritability • H2 = Var(G) / Var(P)

• Broad-sense heritability includes additive, dominance, epistatic variance, and parent-of-origin effects

Heritability

• Genetic (G) = Additive (A) + Dominance (D) + Imprinted (I) + Epistasis (E)

• Var(G) = Var(A) + Var(D) + Var(I) + Var(E)

• Narrow-sense heritability • h2 = Var(A) / Var(P)

• Narrow-sense heritability is the ratio of the additive genetic variance to the total phenotypic variance

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Heritability

• Ranges from 0 (all environmental) to 1 (all genetic)

• Specific to a population in specific environmental circumstances

• Highly inbred population with no • 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 From Twins

For comparison of monozygotic (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 components of variance are A for additive, C for common environment, and E for unique environment

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Heritability of Human Traits

Missing Heritability

GWAS have been successful in identifying common variants involved in complex trait aetiology. However, for the majority of complex traits, <10% of genetic variance is explained by common variants. Thus only a small part of heritable variaationin a trait c an be explaind – most is missing!

What Explains Missing Heritability?

• Genomic regions or classes of variation are not well covered by existing markers • LD between markers and causal variants • Repeats or heterochromatic regions • Rare variants • Local heritability around associated SNPs • Heritability estimates (narrow-sense, i.e. additive) are overestimated • Power • De novo • Explains a subset of cases of and other phychiatric disorders • May contribute to disease incidence but not to missing heritability

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Linkage Disequilibrium

Non-random association of alleles at different loci

Linkage Disequilibrium

Haplotype Frequency Frequency A1B1 X11 A1 p1 = X11 + X12 A1B2 X12 A2 p2 = X21 + X22 A2B1 X21 B1 q1 = X11 + X21 A2B2 X22 B2 q2 = X12 + X22

D = X 11 – p1q1 A1/A2 Correlation coefficient r = D B1/B2 sqrt(p1 p2 q1 q2)

Decay of Linkage Disequilibrium Human 22

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Linkage and Linkage Disequilibrium

Linkage and Association

As s oc iation

Linkage

20 Generations

Whole Genome Association (Linkage Disequilibrium Mapping)

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GWAS Methodology

GWAS Workflow

Case-Control Association Plot and LD Map Human

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