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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?
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• 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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 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
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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
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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
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Linkage and Linkage Disequilibrium
Linkage and A ssociation
As s ociation
Linkage
20 G enerations
Whole Genome A ssociation (Linkage Disequilibrium Mapping)
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GWAS Methodology
GWAS Workflow
Case-­‐Control A ssociation Plot and LD Map
Human Chromosome 22
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