Heritability

1. This session
• The theory behind quantitative traits
• Heritability – definition and estimation
• Data preparation
• Lab on data preparation

2. Learning objectives
• Primary
• Know what a quantitative vs. a categorical trait is.
• Be able to calculate heritability from twin correlations
• Explain why heritability is population specific
• Be able to transform a variable to a normal distribution
• Secondary
• Explain why we think quantitative traits are caused by
many genetic variants.
• Evaluate why heritability estimates may not be accurate
• Discuss the importance of sample and trait characteristics.

3. Part 1
The theory of quantitative traits

4. Qualitative traits
• PKU
• Deficiency of phenylalanine hydroxylase.
• Characterized by
– Intellectual disability
– microcephaly
– delayed speech
– seizures
– eczema
– behavior abnormalities

5. Qualitative traits
• Qualitative trait: PKU
• 12q23.2

6. Qualitative traits
• “You have it or you don’t”
0
5
10
15
20
25
30
Affected Not Affected
PKU

7. Qualitative traits
– Not “a bit pregnant”
0
5
10
15
20
25
30
Not Somewhat Pregnant Very pregnant

8. Qualititative traits
– Not “a bit pregnant”
0
5
10
15
20
25
30
Not Somewhat Pregnant Very pregnant

9. Quantitative traits
• Attention Deficit Hyperactivity Disorder
• Characterized by developmentally
inappropriate
– Hyperactivity / impulsivity
– Inattentiveness
• Ever said: I am sure I am ‘a bit ADHD’?

10. Quantitative traits
– A bit ADHD

11. Qualitative vs. Quantitative traits
• Qualitative
• Categorical
• Dichotomous
• Quantitative
• Continuous
• Dimensional
Is it easy to decide whether traits are qualitative
or quantitative?
Autism
Type II Diabetes
Eating disorders
Dissociation disorders

12. “Traits are influenced by many variants of small
effect, no one variant being necessary, nor
sufficient, for the disorder”.
Implications of the dimensional
approach for genetics
Quantitative Trait Loci approach: Quantitative trait
loci (QTLs) are stretches of DNA containing or
linked to the genes that underlie a quantitative
trait

13. • Imagine 1 locus contributing to a trait
• Each locus has 2 Alleles, one of which is the
risk allele
• The presence of each copy of the risk allele
conveys an additional ‘score’ on the trait
• What happens are you add loci?
Why QTLs give rise to a normal
distribution

14. • 1 locus. Aa.
• How many genotypes?
• AA
• Aa
• aa
Why QTLs give rise to a normal
distribution

15. • Given our genotypes, each risk allele gives you
a score of +1 on the phenotype
• If A is the risk allele, what are our phenotype
scores?
• AA
• Aa
• aa
Why QTLs give rise to a normal
distribution
+2
+1
+0
20
21
19
.5
.25
.25
Genotype Effect Trait Frequency

16. Why QTLs give rise to a normal
distribution
0
0.5
1
1.5
2
2.5
19 20 21

17. • 2 locus. Aa / Bb
• 2 risk alleles (A and B)
• Aa / Bb take a value of 20
• Fill in Table 1
Why QTLs give rise to a normal
distribution

18. Why QTLs give rise to a normal
distribution
Genotypes Effect Trait Frequency
AA/BB +4 21 1/16
AA/Bb +3 20 2/16
aA/BB +3 20 2/16
AA/bb +2 19 1/16
aA/Bb +2 19 4/16
aa/BB +2 19 1/16
Aa/bb +1 18 2/16
aa/Bb +1 18 2/16
aa/bb +0 17 1/16

19. • 2 locus. Aa / Bb
• 2 risk alleles (A and B)
• Aa / Bb take a value of 20
• Fill in Table 1
• Sketch out a graph (assuming 16 individuals)
Why QTLs give rise to a normal
distribution

20. 17 18 19 20 21
2
4
6
8
10
12
14
16

21. 1 locus
0
0.1
0.2
0.3
0.4
0.5
0.6
19 20 21

22. 17 18 19 20 21
2
4
6
8
10
12
14
16
2 loci

23. What do you notice about the trait as
the number of loci increases?
*Note: this shows additive
genetic variance. Dominant
genetic variance calculations are
in the resources section.

24. Quantitative traits
– A bit ADHD

25. • Waiting for ‘proof’ that the phenotypes &
genes are the same
• Does not mirror how clinicians work
Controversies of the QTL

26. • Much easier to find study participants
• Can be more powerful
Advantages of the QTL approach

27. • Quantitative traits are normally distributed
traits
• Assumed that these arise from the combined
effects of multiple genetic variants
• Assumption is that finding variants associated
with traits will find genes associated with
disease:
• Attentiveness -> ADHD
• Blood sugar -> T2DM
Quantitative traits in genetic research

28. Part 2
Heritability

29. Heritability is an estimation of the proportion of
observed trait variance, attributable to genetic
influences.
What is heritability?
Trait variance (Vp)
Vp = Variance due to genetics (Vg) +
variance due to non genetics (VE)

30. • Twin studies
• Vp = A + C + E
• A = Genes
• C = Common environment
• E = Unique environment
How do we calculate heritability?

31. • Assumptions of Twin studies
• MZ twins correlate (rMZ) 100% A
• DZ twin correlate (rDZ) 50% A
• MZ and DZ correlate 100% C
• MZ and DZ correlate 0% for E
How do we calculate heritability?

32. • A = h2 = 2 (rMZ – rDZ)
• C = rMZ – A
• E = 1- rMZ
• If rMZ = .8, and rDZ = .4
• A = 2 (.8 - .4 ) = .8
• C= .8 - .8 = 0
• E = 1 = .8 = .2
How do we calculate heritability?

33. Calculate the heritability
rMZ rDZ A C E
.5 .3
.5 .4
.7 .7
.1 .1
.9 .6
.2 .1
.9 .8

34. Calculate the heritability
rMZ rDZ A C E
.5 .3 .4 .1 .5
.5 .4 .2 .3 .5
.7 .7 .0 .7 .3
.1 .1 .0 .1 .9
.9 .6 .6 .3 .1
.2 .1 .2 .0 .8
.9 .8 .2 .7 .1

35. • The equal environments assumption (EEA) (including
prenatal)
• Assortative mating
• Generalizability.
Assumptions of the twin method

36. • Gene environment correlation (rGE)
• Passive rG
• Increase C
• Active rG
• Increases or decreases heritability
• (why does this increase with age?)
• Evocative rG
• Increases or decreases heritability
• Gene environment interaction (G*E)
– Increases E
Limitations of the twin method

37. Our concept of heritability is tied up with
variation, and with our population.
What is heritability?

38. A thought experiment:
• Where do our hearts come from? If you have a heart,
is this from your genetics? Or from the environment?
• What is the heritability of having a heart?
Heritability & Variation

39. • Tonsillectomies (NG martin, 1991)
• Thought experiment: Reading ability
Population specific heritability

40. 1. How much genetics contributes to some trait
that an individual shows.
Heritability?

41. 2. Proportion of trait variation between
individuals in a given population due to genetic
variation.
Heritability?

42. 2 definitions:
1. How much genetics contributes to some trait
that an individual shows.
2. Proportion of trait variation between
individuals in a given population due to
genetic variation.
What is heritability?
What is the difference?

43. Question:
Does a high heritability for a disease mean that
we should target our treatments at genetics?
What is heritability?

44. Qualitative traits
• PKU
• Deficiency of phenylalanine hydroxylase.
• Characterized by
– Intellectual disability
– microcephaly
– delayed speech
– seizures
– eczema
– behavior abnormalities

45. • Parent-offspring
Heritability estimates in non twins
Mid-parent phenotypic trait value
Offspringphenotypictraitvalue
Slope = 0.89
h2= 0.89

46. • If offspring do not resemble parents then best fit line has a slope of approximately zero.
• Slope of zero indicates most variation in individuals due to variation in environment.
• If offspring strongly resemble parents then best fit line will be close to 1.
Heritability estimates in non twins

47. • Most traits in most populations fall somewhere in the middle
with offspring showing moderate resemblance to parents.
Heritability estimates in non twins

48. • Heritability can be ascertained from twin correlations, and parent-
offspring data
• The point heritability is estimate is not exact (not like a mean)
• Furthermore, it applies only to your population, at your time.
Heritability summary

49. Part 3
Lab: Using phenotype data

50. The world of quantitative genetics
• Genetics… without genotype data.
Phenotype data
1. Sample
characterization
2. Quantitative trait
distribution
3. Heritability
Genotype data
– Variant description
– Missing data
– HWE
– LD and haplotypes

51. • Make a table of sample characteristics
• Prepare a quantitative trait for genetic analysis
Goals of this lab

52. Summarize the sample characteristics (covariates) for
our population, often broken down by gender or
ethnicity.
Summarize trait distribution
1. Summarize data characteristics
Why?

53. – Define the population parameters for comparison
of results with those from other samples (i.e.
gender, age, health)
– Help to identify biases in the data
Why summarize sample
characteristics?
LOOK AT THE
TABLE CLOSELY!!!

54. – Population definition
– Generalizability
Why summarize trait distribution?
LOOK AT THE
TABLE CLOSELY!!!

55. ‘Table 1’

56. ‘Table 1’

57. 1. Is the distribution normal?
2. Are there outliers?
2. Prepare a quantitative trait for
genetic analysis

58. 1. What is a normal distribution?
For continuous data we don’t have equally spaced
discrete values so instead we use a curve or function
that describes the probability density over the range of
the distribution.
Continuous data

59. Normal distribution describes a special class of
continous distributions that are symmetric and can be
described by two parameters
(i) μ = The mean of the distribution
(ii) σ = The standard deviation of the distribution
Changing the values of μ and σ alter the positions and
shapes of the distributions.
The normal distribution

60. The normal distribution

61. Deviations from normal - skew
The normal distribution will have a skew of 0

62. Deviations from normal - Kurtosis
‘Tails’ are misshapen
The normal distribution will have a kurtosis of 0

63. Why we care about the normal
distribution
• Assumption of most (including
genetic association) tests.

64. How do we test for a
normal distribution?
• The Chi-square and KS GOF test
(low power).
• Eyeball methods: look at
histogram & look for a skew and
kurtosis -1 - +1
• Shapiro and Wilk formal test
What is the Ho for Shapiro Wilk?

65. What do we do about
non normal distributions
• Run a monotonic transformation
• You can try
• Log
• Square root
• Cube root
• Reciprocal
• STATA: lnskew0 command which
does it for you!

66. Example of a log transformation
Pre transformation Log transformed

67. NOTE
ALWAYS check the
correlation of the
transformed variable with
the original variable.

68. Screening outliers
Screen ‘odd’ or extreme values
Subjective definition: sometimes values 3 or 4 +/- the
mean
Contentious. Positives and negatives.
My personal recommendation ‘sensitivity analysis’

69. Summary
Normal distribution is a symmetrical distribution
Skew and kurtosis represent a deviation from
normality
Most genetic tests require a normal distribution
Therefore we try to transform our distributions

70. Lab Goals
Going to prepare three variables for analysis: fasting
VLDL, LDL and HDL particle size (cardiovascular
disease risk factors)
1. Prepare a summary table, split by gender, for the
trait and relevant covariate characteristics of the
sample
2. Decide if the variables need to be transformed,
and transform if so.
3. Prepare a variable with no outliers (using 2
definitions)

71. Learning objectives
• Primary
• Given an example of a qualitative trait
• Give an example of a quantitative trait
• With rMz = 6 and rDz = 6, what is the heritability?
• Why is heritability is population specific?
• How would you recognize a non-normal variable and transform it
to a normal distribution
• Secondary
• Explain why we think quantitative traits are caused by many genetic
variants.
• Given one reason why heritability estimates may not be accurate
• Why do we need to include covariate characteristics?

72. Slide graveyard

73. Lab Goals
Going to prepare three variables for analysis:
fasting VLDL, LDL and HDL particle size.
Prepare a summary table, split by gender of the
trait distributions and relevant

74. Implications of the dimensional
approach
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
AA/BB
AA/BB
Column1
Column2
Column3
Column4