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Navigable Slide Index
 Introduction
 Talk outline
 Suggested reading / references
 Traditional heritability analysis
 Why are we interested in heritability?
 Types of phenotypes
 Definition of heritability
 Human height as an example of heritability
 Modes of inheritance
 Additive model
 Additive model: d=0
 Dominant model: d > 0
 Recessive model: d < 0
 Overdominant model: d > a
 Additivity is the norm
 Some heritabilities
 Ways to measure heritability
 Example: Galton height data (available in R)
 Example: Galton height data
 Measuring relatedness
 Identity by descent (IBD)
 Example coefficients
 The covariance equation (1)
 The covariance equation (2)
 Statistical aside: covariance (1)
 Statistical aside: covariance (2)
 Estimating heritability using the covariance equation
 Parentchild studies: total phenotypic variation
 Parentchild studies: additive variance
 Parentchild studies: estimating heritability
 MZ twins
 MZ and DZ twins: The twin method / ACE model (1)
 MZ and DZ twins: The twin method / ACE model (2)
 Mixed model (1)
 Mixed model (2)
 Mixed model explained
 Instructions for using the mixed model
 Some caveats
 More caveats
 SNPbased heritability analysis
 Problems with pedigreebased heritability estimation
 Theoretical distribution of φ
 Theoretical distribution of φ: relationship table
 Theoretical distribution of φ: identical by decent
 Measuring actual relatedness
 Using actual relatedness for heritability estimation
 Using unrelated individuals
 Using unrelated individuals (advantages)
 Application to human height
 Instructions for estimating heritability for SNPs
 Liability model for binary traits
 The missing heritability problem (1)
 The missing heritability problem (2)
 The missing heritability problem (GWAS)
 SNPbased heritability analysis (height)
 SNPbased heritability analysis (other traits)
 Extensions of SNPbased heritability analysis
 Motivating allelic correlations (1)
 Motivating allelic correlations (2)
 Extensions of SNPbased heritability analysis (list)
 Genome partitioning (1)
 Genome partitioning (2)
 Genebased association testing
 Bivariate analysis
 Bivariate analysis: example
 Summary
Topics Covered
 The concept of heritability
 How to measure heritability based on pedigree information
 How to measure heritability from genetic (SNP) data
 How SNPbased heritability analysis can be used to improve our understanding of complex traits.
Talk Citation
Speed, D. (2016), "Heritability and its uses", in The Biomedical & Life Sciences Collection, Henry Stewart Talks Ltd, London (online at https://hstalks.com/bs/3258/)Talk Information
Other Talks in the Series: Statistical Genetics
Transcript
0:00
My name is Doug Speed,
and I'm a Researcher
at University College
London Genetics Institute.
And today, I will be telling
about Heritability and Its Uses.
And hopefully, I'll convince you
why this is the most
exciting area
in Quantitative Genetics.
0:14
So there are two parts
in this talk.
First, I'll tell you about
traditional heritability
analysis,
and then,
I'll talk to you a bit about
SNPbased heritability analysis,
which is a very recent area
in the last five years,
and hopefully,
I will give you an idea
of all the uses it has in trying
to understand complex trades.
0:30
So first of all,
here are few books and papers
which I find very useful.
The first one is Introduction
to Quantitative Genetics,
and this has more details
on lots of the first part
of this talk.
I've a second too,
Introductory Statistics with R
and Elements of Statistical
Learning are both available
at the author's web pages
to view online.
And then here
I have major papers
in the field of SNPbased
heritability analysis,
and so it'll be useful
for later.
0:56
It's a bit hard to tell
in that previous slide,
so I've just added
a bit of noise
so you can see
the individual SNP genotypes.
So here we see
that adding in copies
of the mutant allele increases
phenotype on average.
So for example,
if an individual has one copy,
so it's genotype AG,
for example,
then their effect is higher
than if they have
zero copies AA.
And then,
if they have two copies GG,
their effect is the
same amount higher still.
And what we can observe
is a linear trend,
so each copy
of the mutant allele
increases for phenotypic effect
by the same quantity.
1:33
So heritability
is a fundamental concept
in quantitative genetics.
Really, if you plan to do
a genetic analysis
of a phenotype,
one of the first things
you should think about is,
what is the heritability
of a trait you wish to study.
If the heritability is zero,
then there's no point
doing a genetic analysis,
because there are
no genetic factors
influencing the trait.
Whereas, if the heritability
is very high,
then this suggests
that your analysis
is likely to be fruitful.
We're often interested
in very broad comparisons,
so for example,
the heritability tells us
how well we might predict
a particular trait.
So this could be in plants,
and animal genetics,
or it could be
in human diseases.
So for example,
if there's two diseases,
and one has heritability
of 20 percent,
and one has heritability
80 percent,
then in theory,
we could predict
the second disease
better than the first.
So there's probably
a good reason to try
and study about
the second trait.
2:26
There are two main types
of phenotypes,
and one of the main
is quantitative phenotype.
So for example, human height,
this is a continuous
valued trait
which takes measurements
between say
one and a half meters
and two meters.
Another major type of trait
is the case control
for binary outcome.
So here values only take
two possible values,
one, if the individual
is affected,
and zero, if he's unaffected.
I'm going to focus mainly
on quantitative trait,
but towards the end,
I'll explain
how most of these ideas
can be applied
to binary traits as well.
As well as quantitative
and binary traits,
there's also count data
and survival data,
but methods for analyzing
these are more complicated.
3:07
So we start with the definition
of heritability.
So we have our phenotype,
which I will represent
with the vector Y,
and we can think of
why it's been made up
of a contribution
of genetic effects vector G,
and environmental noise
vector E.
And therefore, we can consider
a variation in the phenotype Y
as to some
of the genetic variation
and the environmental
noise variation.
So this model assumes
there's no interactions
between genetics
and environments.
So the environmental effects
are independent
of the genetic effects.
With this model, we then get
the broad sense heritability
is the genetic variance divided
by the total
phenotypic variance.
And so H square tells us
what proportion
of the total
phenotypic variation
is attributable to genetics.
However, we often consider
inside the narrow
sense heritability,
and this is a slightly
different model.
Now we assume the phenotype
has contributions from A,
which is the additive
genetic effects,
as well as E which is still
the environmental noise.
And therefore,
the narrow sense heritability,
which is h squared is the total
additive genetic effects
divided by the total
phenotypic variation.
4:18
So to give an example,
for human height,
variation is about
20 centimeters.
So the average height
is maybe 173 centimeters,
variation is about
20 centimeters,
so most people fall
within 10 centimeters above
or 10 centimeters
below the mean.
And we can break down
this total variation
of 20 centimeters
into two components,
the genetic component
explains about
16 centimeters of this variation
and other factors
explain about 4 centimeters.
And therefore, the heritability
of height is 16 divided by 20,
so about 80 percent.
4:53
So I mentioned, we often focus
on the narrow sense,
the additive heritability,
so to explain what that means,
first of all, we'll be looking
a lot at SNP genotypes.
So a SNP genotype is typically
coded as zero, one, or two,
and this number represents
the count of the mutant allele.
So for example, suppose a SNP
has two alleles A and G,
if its genotype is zero,
then this means
it has two copies of A,
the homozygous wildtype allele.
If the genotype is one,
then it means
that it is heterozygous,
it has an A and a G,
and if the genotype is two,
it means it has two copies of G,
a homozygous mutant.
This table below shows
how we can think
of its effect of particular SNP
on the phenotype.
So here we have
three parameters, µ,
the overall mean, A,
the additive effect, and D,
the dominant effect.
And this shows
what the effect is
for each of the three genotypes.
So this might be
a bit confusing,
but hopefully on the next slide
it will make sense.