Using Extended Genealogy to Estimate Components of
Heritability for 23 Quantitative and Dichotomous Traits
Noah Zaitlen1*, Peter Kraft2,3,4, Nick Patterson4, Bogdan Pasaniuc5, Gaurav Bhatia2,3,4,
Samuela Pollack2,3,4, Alkes L. Price2,3,4*
1Department of Medicine, Lung Biology Center, University of California San Francisco, San Francisco, California, United States of America, 2Department of Epidemiology,
Harvard School of Public Health, Boston, Massachusetts, United States of America, 3Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts,
United States of America, 4Broad Institute of Harvard and Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America,
5Interdepartmental Program in Bioinformatics Pathology and Laboratory Medicine, University of California Los Angeles, Los Angeles, California, United States of America
Important knowledge about the determinants of complex human phenotypes can be obtained from the estimation of
heritability, the fraction of phenotypic variation in a population that is determined by genetic factors. Here, we make use of
extensive phenotype data in Iceland, long-range phased genotypes, and a population-wide genealogical database to
examine the heritability of 11 quantitative and 12 dichotomous phenotypes in a sample of 38,167 individuals. Most previous
estimates of heritability are derived from family-based approaches such as twin studies, which may be biased upwards by
epistatic interactions or shared environment. Our estimates of heritability, based on both closely and distantly related pairs
of individuals, are significantly lower than those from previous studies. We examine phenotypic correlations across a range
of relationships, from siblings to first cousins, and find that the excess phenotypic correlation in these related individuals is
predominantly due to shared environment as opposed to dominance or epistasis. We also develop a new method to jointly
estimate narrow-sense heritability and the heritability explained by genotyped SNPs. Unlike existing methods, this approach
permits the use of information from both closely and distantly related pairs of individuals, thereby reducing the variance of
estimates of heritability explained by genotyped SNPs while preventing upward bias. Our results show that common SNPs
explain a larger proportion of the heritability than previously thought, with SNPs present on Illumina 300K genotyping
arrays explaining more than half of the heritability for the 23 phenotypes examined in this study. Much of the remaining
heritability is likely to be due to rare alleles that are not captured by standard genotyping arrays.
Citation: Zaitlen N, Kraft P, Patterson N, Pasaniuc B, Bhatia G, et al. (2013) Using Extended Genealogy to Estimate Components of Heritability for 23 Quantitative
and Dichotomous Traits. PLoS Genet 9(5): e1003520. doi:10.1371/journal.pgen.1003520
Editor: Peter M. Visscher, The University of Queensland, Australia
Received September 27, 2012; Accepted April 6, 2013; Published May 30, 2013
Copyright: ? 2013 Zaitlen et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This work was funded by NIH grant R03HG005732 (NZ and ALP), NIH fellowship 5T32ES007142-27 (NZ), and the Rose Traveling Fellowship Program in
Chronic Disease Epidemiology and Biostatistics (NZ). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: email@example.com (NZ); firstname.lastname@example.org (ALP)
Although genome-wide association studies (GWAS) have
resulted in the discovery of thousands of novel associations of loci
to hundreds of phenotypes , concerns have been raised about
the finding that these loci appear to explain a relatively small
proportion of the estimated heritability, the fraction of phenotypic
variation in a population that is due to genetic variation . This
has led to considerable speculation by researchers about the
genetic basis of complex human phenotypes and the ‘‘missing
heritability’’, i.e. the fraction of heritability not accounted for by
the associations discovered to date [3,4,5,6,7,8,9]. Among the
proposed explanations for missing heritability is the existence of
many presently unidentified common variants with small effect
sizes, rare variants not captured by current genotyping platforms,
structural variants, epistatic interactions, gene-environment inter-
actions, parent-of-origin effects, or inflated heritability estimates
[3,5,10]. Studies that examine the sources of missing heritability
can help researchers to evaluate the prospects of future studies
focusing on common versus rare variation and thereby devise
effective strategies to discover the remaining sequence variants that
affect disease risk and other aspects of phenotypic variation in
The narrow-sense heritability of a phenotype (h2) is the fraction
of phenotypic variance that can be described by an additive model
over the set of SNPs that are functionally related to the phenotype
(i.e. the causal SNPs) . It is commonly estimated by comparing
the phenotypic correlation of monozygotic (MZ) to that of
dizygotic (DZ) twins. The difference between h2and the fraction
of phenotypic variance accounted for by variants discovered by
means of GWAS (h2
gwas) is the so-called missing heritability.
Recently, Yang et al  developed a method to estimate the
variance explained by all SNPs on a genotyping platform including
those that are not genome-wide significant (h2
limit of h2
gwasfor infinite sample size.
There are two major challenges in comparing h2and h2
g), representing the
quantify missing heritability. First, there is the potential for
inflation of h2estimates based on closely related individuals such as
MZ/DZ twins. It is well known that epistatic interactions can
inflate heritability estimates in studies of related individuals .
PLOS Genetics | www.plosgenetics.org1May 2013 | Volume 9 | Issue 5 | e1003520
Recent work from Zuk et al  has examined this in detail.
Other factors that could also lead to inflated estimates of h2using
closely related pairs of individuals include dominance and shared
environment. Second, there is a tradeoff between inflation and
sampling variance when estimating h2
component approach described by Yang et. al results in inflated
[12,14,15,16,17]. However, removing related individuals reduces
the sample size, resulting in a larger standard error around the
estimate [18,19]. Both of these issues can adversely affect estimates
of missing heritability.
Here, we analyze the heritability of 23 complex phenotypes in
an Icelandic cohort of 38,167 individuals, leveraging both a
population-wide genealogical database and genotype data from
over 300,000 SNPs that have been long-range phased across and
between chromosomes (i.e. where not only the phase, but also the
parental origin of alleles has been determined) . Importantly,
we develop an approach that allows h2to be estimated on the basis
of both closely and distantly related pairs of individuals. We find,
for all of the quantitative phenotypes, that our estimates of h2are
smaller than those from the literature that were based on MZ/DZ
twins . Our results indicate that previous estimates were
inflated by the impact of epistasis or shared environment.
We further introduce a new variance components method that
provides simultaneous estimates of h2and h2
principal advantages. First, by adequately taking account of both
closely and distantly related pairs of individuals, it minimizes the
standard error of the estimates, whilst avoiding the upward bias that
canresultfromcalculations based on closely related pairs.Second, it
produces both estimates of heritability for the same population
sample, ensuring that h2and h2
gare directly comparable.
For most of the 23 phenotypes examined here, our results show
identified many SNPs with large effect sizes (i.e. h2
gwasby a considerable margin, it follows that
g. The recent variance
g. This method has two
gaccounts for more than half of h2. As GWAS have not
gwasis small), and
gis greater than h2
there must be many associated sequence variants that remain to be
discovered, i.e. these phenotypes are highly polygenic. Currently,
only common variants are well captured by the genotyping arrays
used in most GWAS studies. As the difference between h2
is likely due to common and rare variants not captured by the
genotyping array , it may be assumed that a fair number of
association signals remain to be identified through more compre-
hensive approaches, such as whole genome-sequencing. However,
our estimates of h2
gshow that GWAS genotyping arrays capture a
greater proportion of h2than indicated by previous twin-based
estimates of h2.
Overview of methods
Below, we provide an overview of the approaches we used to
estimate various components of heritability. The details of these
approaches are provided in the Methods section.
We used a linear mixed model approach to estimate compo-
nents of heritability. In this approach, each phenotype is modeled
using a multivariate normal distribution. Each of the components
of heritability that we estimated corresponds to a different model
of the phenotypic covariance.
Narrow-sense heritability (h2) estimates from variance compo-
nent models rely on covariance matrices specifying the genome-
wide genetic relatedness of individuals in the data set. An estimate
of h2can be obtained by using an identity-by-descent (IBD) based
covariance matrix, which is trivial to obtain from long-range
phased genotype data (see below).
The fine-scale estimates of IBD used here rely on long-range
phasing data that are not available in most data sets. An estimate
of h2can also be obtained by using an identity-by-state with
threshold (IBS.t) based covariance matrix with all values below a
threshold t set to 0, i.e. focusing on closely related individuals. An
alternative is to use the full IBS based covariance matrix to obtain
an estimate of the heritability explained by genotyped SNPs (h2
however, this requires removing related individuals . If related
individuals are included, the resulting estimate is neither an
estimate of h2nor an estimate of h2
Previous approaches to estimating the heritability explained by
genotyped SNPs (h2
g) required filtering related individuals, thereby
increasing the standard error of the estimates. However, joint
estimates of h2and h2
gcan be obtained using two covariance
matrices based on IBS.t and IBS. The first component provides
an estimate of h2, and the second provides an estimate of h2
approach removes the need to filter related individuals. Alternate-
ly, joint estimates of h2and h2
covariance matrices based on IBD and IBS, where here IBD
replaces IBS.t to estimate h2.
Broad-sense heritability (H2) is the sum of additive, dominant,
and epistatic components of heritability. The additive, dominant,
environmental (ADE) model can be used to obtain joint estimates
of dominance and additive components of heritability, using two
covariance matrices based on IBD2 (two copies shared IBD) and
Below, we investigate all of these modeling approaches. Table
S1 contains definitions of all parameters quantifying components
of heritability that are used in the text.
gcan be obtained using two
Estimates of narrow-sense heritability (h2)
Ideally, estimates of narrow-sense heritability of a particular
phenotype would be based on a genetic relationship matrix
Phenotype is a function of a genome and its environment.
Heritability is the fraction of variation in a phenotype
determined by genetic factors in a population. Current
methods to estimate heritability rely on the phenotypic
correlations of closely related individuals and are poten-
tially upwardly biased, due to the impact of epistasis and
shared environment. We develop new methods to
estimate heritability over both closely and distantly related
individuals. By examining the phenotypic correlation
among different types of related individuals such as
siblings, half-siblings, and first cousins, we show that
shared environment is the primary determinant of inflated
estimates of heritability. For a large number of pheno-
types, it is not known how much of the heritability is
explained by SNPs included on current genotyping
platforms. Existing methods to estimate this component
of heritability are biased in the presence of related
individuals. We develop a method that permits the
inclusion of both closely and distantly related individuals
when estimating heritability explained by genotyped SNPs
and use it to make estimates for 23 medically relevant
phenotypes. These estimates can be used to increase our
understanding of the distribution and frequency of
functionally relevant variants and thereby inform the
design of future studies.
Components of Heritability via Extended Genealogy
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