Estimation and Partition of Heritability in Human ...emilkirkegaard.dk/en/wp-content/uploads/Estimation-and... · Heritability in Human Populations Using Whole-Genome Analysis

GE47CH04-Vinkhuyzen ARI 29 October 2013 12:1

Estimation and Partition ofHeritability in Human PopulationsUsing Whole-Genome AnalysisMethods

Anna A.E. Vinkhuyzen,1 Naomi R. Wray,1

Jian Yang,1,2 Michael E. Goddard,3,4

and Peter M. Visscher1,2

1The University of Queensland, Queensland Brain Institute, Brisbane, 4072, Queensland,Australia; email: [email protected], [email protected],[email protected] University of Queensland, Diamantina Institute, Translation Research Institute,Brisbane, 4072, Queensland, Australia; email: [email protected] of Food and Agricultural Systems, University of Melbourne, Parkville, 3053,Victoria, Australia4Biosciences Research Division, Department of Primary Industries, Bundoora, 3001,Victoria, Australia; email: [email protected]

Annu. Rev. Genet. 2013. 47:75–95

First published online as a Review in Advance onAugust 22, 2013

The Annual Review of Genetics is online atgenet.annualreviews.org

This article’s doi:10.1146/annurev-genet-111212-133258

Copyright c© 2013 by Annual Reviews.All rights reserved

Keywords

quantitative traits, whole-genome methods, additive genetic variance,genomic relationship, mixed linear model, genetic architecture

Abstract

Understanding genetic variation of complex traits in human populationshas moved from the quantification of the resemblance between closerelatives to the dissection of genetic variation into the contributions ofindividual genomic loci. However, major questions remain unanswered:How much phenotypic variation is genetic; how much of the geneticvariation is additive and can be explained by fitting all genetic variantssimultaneously in one model, and what is the joint distribution of effectsize and allele frequency at causal variants? We review and comparethree whole-genome analysis methods that use mixed linear models(MLMs) to estimate genetic variation. In all methods, genetic variationis estimated from the relationship between close or distant relatives onthe basis of pedigree information and/or single nucleotide polymor-phisms (SNPs). We discuss theory, estimation procedures, bias, andprecision of each method and review recent advances in the dissectionof genetic variation of complex traits in human populations. By usinggenome-wide data, it is now established that SNPs in total account forfar more of the genetic variation than the statistically highly significantSNPs that have been detected in genome-wide association studies. AllSNPs together, however, do not account for all of the genetic varianceestimated by pedigree-based methods. We explain possible reasons forthis remaining “missing heritability.”

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Complex trait: a traitfor which variation is aresult of multiplegenes andenvironmental factors(quantitative andcategorical)

Genetic relationship:the expected or actualproportion of thegenome identical bydescent (pedigree orwithin-family design)or by state (populationdesign)

Genetic architecture:description of thenumber of geneticvariants, allelicfrequencies, and effectsizes of variants thataffect a trait and theirmode of gene action

INTRODUCTION

The discipline of quantitative genetics, or thegenetics of complex traits, aims to understandand exploit genetic variation in continuouslyvarying traits, such as height (stature), bloodpressure, and cognitive ability in humans.However, relatives often share both genes anda similar environment, making it difficult tocompletely separate the genetic variance fromthe variance due to the shared environment.

Technological advances now allow individ-uals to be assayed for more than one milliongenetic markers [usually single nucleotide poly-morphisms (SNPs)] covering DNA variationthat spans the whole genome. These SNP datacan be used in two ways: to map genes that affecta complex trait and to estimate the genetic re-lationship between individuals more accuratelythan can be done from their known pedigree.Estimating genetic relationships between indi-viduals from SNP data allows us to estimategenetic variance from supposedly unrelated in-dividuals without confounding by shared envi-

ESTIMATING HERITABILITY FOR DISEASE

Categorical traits (e.g., disease traits) are sometimes inherited in asimple Mendelian manner, but often they behave like continuoustraits in that they are influenced by many genes and environmen-tal factors. Unlike quantitative traits, the phenotypic variance ofa disease trait depends on the population mean, i.e., the diseaseprevalence. To facilitate comparison of estimates across studies,heritability of disease is generally estimated for the liability un-derlying the disease (48) in a threshold model (21). In a thresholdmodel, the disease status (measured on a 0/1 scale) is superim-posed onto a distribution of liability in which a threshold of li-ability for disease is determined that bisects the distribution toreflect the proportion of affected and unaffected individuals inthe population (20).

Estimates derived from linear mixed model analysis can betransformed to a liability scale by adjusting both for scale and forascertainment of the data. Estimation methods for heritability ofdisease have recently been reviewed by Tenesa & Haley (75), anda detailed description of estimating heritability for disease traitsin a population design is provided by Lee et al. (45).

ronment and allows dissection of the geneticarchitecture of complex traits. Genetic archi-tecture refers to the description of the number,frequencies, and effect sizes as well as the modeof gene action of causal variants.

Our focus here is on the theory and ap-plication of whole-genome analysis methodsto estimate genetic variance in human popula-tions and to elucidate the genetic architectureof complex traits. In all of the analysis methodsthat we review, mixed linear models (MLMs)form the basis of the analysis. The focus is onhuman populations because large genetic datasets are available, allowing accurate empiricalvalidation of new genomic analysis methods. Inthe discussion of the analysis methods, we fo-cus on analyses of quantitative traits; variationsof these methods have been developed to al-low application to discrete traits (see sidebar,Estimating Heritability for Disease).

We start with a concise history to placequantitative genetics and whole-genome meth-ods in context. We then review and comparethree different designs and methods for esti-mation of genetic variance and discuss preci-sion and potential sources of bias of the esti-mates. The three designs are referred to as thepedigree design, the within-family design, andthe population design. Briefly, to estimate her-itability, the pedigree design utilizes observedand expected similarity of identical [monozy-gotic (MZ)] and nonidentical [dyzgotic (DZ)]twin pairs, the within-family design utilizes re-alized variation around expected genetic simi-larity for full-sibling pairs, and the populationdesign utilizes realized genetic similarity be-tween distant relatives. There are other pedi-gree designs that can be used to estimate ge-netic variance, e.g., parents and offspring orextended family pedigrees, but in this reviewwe focus on the twin design. Similarly, thereare other within-family designs that could beused, e.g., families with half-siblings, but herewe focus on families with full siblings. For eachmethod, we summarize an example study on themodel trait human height. We chose to selectexamples for human height because height is ahighly (∼80%) heritable trait (e.g., see 70, 85)

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Whole-genomeanalysis methods:methods that utilizeinformation from thewhole genome toestimate geneticparameters, often incombination withphenotypicinformation

Mixed linear model(MLM): a linearmodel that jointlyaccounts for fixed andrandom effects

and has been studied for more than a century(24), and large empirical data sets are availableto demonstrate analysis methods and statisticalinference. Finally, we discuss to what extent thewhole-genome methods have contributed to abetter understanding of the genetic architectureof complex traits in human populations and howdevelopments in analysis methods and DNA se-quencing technology can contribute further.

A BRIEF HISTORY OF COMPLEXTRAIT GENETICS IN HUMANPOPULATIONS

Quantitative genetic methods build on theprinciples of genetics described by Mendel andon statistical methods developed initially byGalton. Whereas Mendel in his experimentswith peas focused on discrete traits, Galtonpioneered statistical methods to study theresemblance between relatives and introducedconcepts of regression and correlation to studycontinuous variation in a population. In hisbook Hereditary Genius (23), Galton stated thatif a trait is heritable, then the closer the familialrelatedness of two individuals, the more thesepeople phenotypically resemble each other.Several articles have been published on con-tinuous distribution of quantitative traits andthe observed resemblance between relatives(7, 59, 96), and a comprehensive theory toexplain these observations was presented inR.A. Fisher’s landmark paper “The Correla-tion Between Relatives on the Supposition ofMendelian Inheritance,” published in 1918(22). Fisher showed that the seemingly contra-dictory hereditary properties of discrete traits(e.g., Mendel’s peas) and continuous traits (e.g.,Galton’s height) were consistent if quantitativetrait variation is caused by a combination ofmany genetic loci, each with a small effect andinherited in a Mendelian manner, togetherwith environmental effects. The article byFisher marks the beginning of the disciplineof quantitative genetics. According to Fisher’sinfinitesimal model, many segregating genes,each with a very small (infinitesimal) effect onthe trait, lead to a normal distribution of genetic

values and, provided environmental effects arenormally distributed, a normal distributionof phenotypes in the population. The theoryimplied that genetic and nongenetic sourcesof variation can be estimated by quantifyingthe correlation between relatives, without anyknowledge of specific genes affecting the trait.Further important theoretical developments onthe genetics, selection, and evolution of quan-titative traits were made by Wright (90), Crow& Kimura (10), and many others (e.g., 21, 49).

With the advent of molecular genetics,quantitative genetics, as with many other dis-ciplines in biology, has become a more empiri-cal, data-driven science. New data can be usedto answer old questions about the genetic archi-tecture of complex traits. Whereas, for example,in the past expected values of genetic similar-ity were used to estimate heritability from rela-tives, it is now possible to estimate empiricallythe realized genetic similarity between close ordistant relatives and to estimate heritability ex-ploiting that information.

SOURCES OF VARIATION

Total phenotypic variation between individuals(VP) is a directly observable measure in a pop-ulation. Many systematic and random factorsare expected to contribute to that variation. Wecan partition total phenotypic variation into agenetic (VG) and non-genetic (VR) componentof variation:

V P = VG + V R. (1)

Equation 1 represents the simplest partitioningof VP in which no specific factors are identi-fied that contribute to VG and VR. For a com-plex trait, however, many genetic and environ-mental factors are likely to contribute to thevariance, and VG and VR can be partitionedfurther.

We may partition VR into variance due to ef-fects shared by children in a nuclear family thatlive together (common environment, VC) and aremaining residual variance (VE), although fur-ther variance components could be partitionedout from the residual variance, for example, to

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account for genotype by environment interac-tion and measurement error:

V R = VC + V E . (2)

Similarly, the genetic component for a complextrait likely comprises multiple genetic factors.These genetic factors may simply add up butcould also interact with each other (i.e., non-additivity). Nonadditivity refers to interactionbetween alleles at the same locus (dominance)or at different loci (epistasis). Under this model,the total genetic variance of a complex trait isdefined as the sum of all additive and nonaddi-tive genetic components:

VG = V A + V D + V I , (3)

where VG is the total genetic variance, VA isthe additive genetic variance, VD is the domi-nance variance, and VI is the epistatic variance.VD and VI are collectively referred to as non-additive genetic variance (21, 49). Nonadditivevariance can be further partitioned in interac-tions between additive and nonadditive variancecomponents and between nonadditive and non-additive variance components:

VG = V A + V D + V AA + V AD (4)

+V AAA + V DD + V AAD + · · ·We can consider the covariance between

pairs of relatives. For example, the expected co-variance between MZ twins and DZ twins (orfull siblings) is respectively (21, 49)

Covmz = VG + VC (5)

and

Covd z = 12

V A + 14

V D + 14

V AA

+ 18

V AD + 18

V AAA + 116

V DD

+ 116

V AAD + · · · + VC . (6)

Therefore, theoretically, many variance com-ponents can be partitioned from the expectedcovariance between close relatives. However,because there are in theory more componentsthan data points and because a number of thesecomponents are confounded (e.g., VD and VAA

in the covariance between DZ twin pairs or full

sibling pairs), not all components are estimablewith current experimental designs.

In this review, we focus on estimation ge-netic variance, in particular the additive geneticvariance. The contribution of nonadditive ge-netic variation to phenotypic variation for com-plex traits in human populations continues to bedebated (8, 35, 97) and is still unresolved, mostlybecause current experimental designs lead to bi-ased and imprecise estimates. When we refer toheritability (h2), we refer to the proportion ofthe phenotypic variance that is attributable toadditive genetic variance.

To estimate additive genetic variance, wespecify an additive statistical model (see below)that superimposes a defined variance structureonto the underlying (unknown) variance com-position. In all methods described, we test howwell the statistical model summarizes the ob-served data. It is crucial to recognize that evenwhen the data fit the statistical model well, theconclusions we draw may not be true becausethe statistical model is a simplified version ofthe true underlying variance structure. For eachmethod, we discuss whether nonadditive varia-tion can be estimated, what the challenges are,and how potential bias from nonadditive andshared family variance may affect the estimateof the additive genetic variance.

THE MIXED LINEAR MODEL

A cornerstone of the theory and application ofquantitative genetics is the linear mixed model(16) of the form

y = f + a + e . (7)

In this model, y represents the measured quan-titative trait or phenotype, f represents knownfixed nongenetic variables (such as overallmean, sex, and age), and a and e represent therandom additive genetic and residual effects, re-spectively. Residual effects refer to effects thatare not accounted for by the fixed and randomeffects specified in the model, e.g., measure-ment error. The model is called mixed becauseit jointly accounts for fixed ( f ) and random(a and e) effects and called linear because the


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Breeding value: thesum of the additiveeffects of anindividual’s genes. Inhuman genetics we usethe term additivegenetic value instead

Best linear unbiasedpredictor (BLUP):a method forprediction of therandom effects in alinear mixed model

Identity-by-descent(IBD): situation inwhich two alleles areinherited from acommon ancestor

various terms are additive in their effect on thetrait.

In matrix notation, the linear mixed modelrepresented in Equation 7 can be generalized as

y = Xf + Za + e, (8)

where y is a vector containing the phenotypicvalues, f is a vector of fixed effects with inci-dence matrix X, a is a vector of random additivegenetic effects with incidence matrix Z, and e isa vector of residuals. The elements in the inci-dence matrices are either zero or one, depend-ing on whether the relevant effect is present inthe individual.

Crucially, elements in the vector a are corre-lated because individuals share genes by descentfrom a common ancestor. We define the covari-ance matrix for the vector a of genetic effects asG and the covariance matrix for the vector e ofresiduals as R. The covariance matrix for thevector of phenotypic values y is then

V = ZGZT + R, (9)

where the term ZGZT represents the variance-covariance matrix attributed to the random ge-netic effects, and R represents the variance-covariance attributed to the residual effects. Ifwe assume that the residual effects are indepen-dent and have constant variance, R is a diagonalmatrix (R = σ 2

EI). However, this assumptiondoes not hold if there are shared environmentaleffects between subsets of individuals, such asfamilies. In that situation the general form R,or an equivalent model that includes the sharedenvironmental effect, must be used.

The statistical and computational analysis ofmore advanced versions of Equation 8 for largedata sets was facilitated by C.R. Henderson (33,34), who developed efficient algorithms to si-multaneously obtain estimators of the fixed ef-fects [best linear unbiased estimator (BLUE)]and predictors [best linear unbiased predictor(BLUP)] of the random effects. In animal andplant breeding, BLUP is widely used to pre-dict the breeding value of individuals in selec-tion programs (25), whereas in human genetics

BLUP could be used to make predictions ondisease susceptibility (56).

The main objective of the applications re-viewed here is to estimate and partition geneticand environmental variance. When variancesare known, the MLM allows the simultaneousestimation of the fixed effects (BLUE) andprediction of the random effects (BLUP). Inpractice, the variance components are usuallyestimated using maximum likelihood (ML) orrestricted maximum likelihood (REML) (58),and the estimates of the variance componentsare subsequently used to obtain the BLUEand BLUP estimators of the fixed and randomeffects. Estimates of variance components frommaximum likelihood are biased, in particularwhen there are many fixed effects in the modelrelative to the number of observations. REMLdoes not suffer from this bias. In applicationsto human data sets, the number of fixed effectsis usually small relative to sample size and MLand REML estimates are very similar.

The genetic effect (a) for an individual per-son is the sum of all effects at causal loci in thegenome and is assumed to be drawn from a spec-ified distribution, usually a normal distribution.We define a as the additive genetic value of theindividual and hence its variance as the additivegenetic variance. Note that nonadditive geneticvariation is ignored in this model.

The differences between the three methodswe discuss are reflected in the genetic relation-ship matrix G used in the MLM to estimategenetic variance (Equation 9). In pedigreedesigns without genetic-marker data, elementsof G are the coefficients of expected geneticrelatedness between relatives, derived fromthe probabilities of identity-by-descent (IBD)on the basis of the recorded pedigree, e.g., inthe classical twin design, 1 for MZ twin pairs,1/2 for DZ twin pairs, and 0 for unrelatedindividuals. In the within-family design, wherethe pedigree is known and genetic-marker dataare available, elements of G are the realizedor actual coefficients of relatedness, and thesecoefficients vary around 1/2 for full siblings andare zero for individuals from different families.In the population design in which the pedigree


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bPedigree design4 individuals from 2 families,including 1 MZ twin pair and1 DZ twin pair

G =

1100

100

10.5 1

Within-family design4 individuals from 2 families,including 2 full sibling pairs

G =

10.543

00

100

10.476 1

Population design4 ‘unrelated’ individualsfrom the same population

G =

1.002–0.016–0.0030.015

1.018–0.0060.021

0.994–0.011 0.983

a

Den

sity

Genetic relatedness

80

0

0.0 0.2 0.4 0.6 0.8 1.0

20

40

60

MZ and DZtwin pairsSibling pairsUnrelated

Figure 1(a) Distributions of the off-diagonal elements for the genetic relationship matrix G in the pedigree design using monozygotic (MZ) anddizygotic (DZ) twin pairs ( green), the within-family design using full-sibling pairs ( pink), and the population design using unrelatedindividuals (blue). The distribution of off-diagonal elements for the genetic relationship matrix G for the pedigree design represents theexpected proportion of genome-wide identity-by-descent (IBD) for MZ (=1) and DZ (=0.5) twin pairs. The distribution of the actualproportion of the genome that is shared IBD within full-sibling pairs in the within-family design varies around 0.5, whereas thedistribution of the actual proportion of the genome that is shared identity-by-state (IBS) for individuals not knowingly related to eachother varies around zero. IBD and IBS estimates for the within-family design and the population design, respectively, are derived fromdata from the Framingham Heart Study (FHS). Mean IBD was estimated at 0.5028 with a standard deviation of 0.0368 for full siblings.Mean IBS was estimated at −0.0002 with a standard deviation of 0.0046 for pairs of unrelated individuals. Only full-sibling pairs wereselected for the IBD estimation in the within-family design, whereas for the IBS estimation in the population design only one siblingper family was selected and one member of each of the remaining pairs of individuals that had an estimated genetic relationship of morethan 0.025 was removed. Estimates of IBS are relative to an arbitrary base population with an average relationship between all pairs ofindividuals of zero. In this analysis, the sample under study is used as the base population; consequently, the average relationshipbetween all pairs of individuals is zero, and the average relationship of an individual with him or herself is one. (b) Examples of thegenetic relationship matrix G for four individuals in the pedigree design (upper matrix), the within-family design (middle matrix), andthe population design (lower matrix). Diagonal elements in matrix G represent an individual’s estimated genetic relatedness with him orherself. Off-diagonal elements in matrix G represent genetic similarity between individuals. Note that matrix G is symmetrical and thatfor clarity only elements in the lower triangular are provided. In the pedigree design, off-diagonal elements represent expectedgenome-wide IBD sharing for four individuals (one MZ twin pair and one DZ twin pair) from two independent families in whichparents are assumed to be unrelated. In the within-family design, the off-diagonal elements represent actual variation around theexpected genome-wide IBD sharing [E(π ) = 0.5] for two independent full-sibling pairs. In the population design, the off-diagonalelements represent actual genome-wide IBS for four (i.e., six pairs) individuals that are not knowingly related. In the population design,an individual’s genetic relatedness with him or herself (diagonal elements) is an estimate of 1 + F, with F being the inbreeding coefficientrelative to the base population.

is unknown but dense genetic-marker data areavailable, G contains estimates of coefficientsof additive genetic covariance between pairsof individuals that are captured by the markersused to construct G. These coefficients arescaled to vary around zero for pairs of indi-viduals that are not knowingly related. SeeFigure 1b for graphical representation ofmatrix G for the three designs.

In all the designs we review, the samplingvariance of the estimate of heritability is a func-tion of sample size and the variation amongthe elements of G; more variation impliessmaller sampling variance (see Figure 1a for agraphical representation of the distribution ofelements in matrix G). In extended or complexpedigrees, the coefficients in matrix G are1/2k for individuals and descendants who are


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Table 1 Precision of estimates of heritability from whole-genome methods

Design Sampling variance of estimate ReferencesPedigree design including an equalnumber of MZ and DZ twin pairs

var(h2) ≈ 4(

1m

+ 1m

)= 4

(2m

)= 8

m= 32

NNA

Within-family design including fullsibling pairs

var(h2) ≈ 2m × var(π )

var(π ) ≈ 0.0015

var(h2) ≈ 4N ∗0.0015

≈ 2667N

(65, 83, 85)

Population design including onlydistantly related individuals (e.g.,pair-wise genetic relationship<0.025)

var(h2) ≈ 2N 2 × var(π )

var(π ) ≈ log(4 × N e × L)(2 × N e × L)

≈ 2 × 10−5

var(h2) = 1 × 105/N 2

(68, 82)

(25)

Abbreviations: DZ, dyzgotic, h2, heritability estimate; L, total map length over all autosomes (L = 35) (41); m, number of MZ, DZ, or full sibling pairs;MZ, monozygotic; N, number of individuals; π , estimated proportion of genome-wide identity-by-descent; Ne, effective population size and is assumed tobe 10,000; var, variance.

Intraclasscorrelation: thecorrelation betweenmeasures within agroup (e.g., MZ orDZ twins)

Narrow-senseheritability:proportion of thephenotypic variancethat is explained byadditive geneticvariance

k generations apart. Hence, sampling variationin a (human) pedigree design using close rela-tives is small compared with designs using moredistant relatives. Bias, however, is more likelyto come with analyses of close relatives andis generally of more concern than precision.To obtain tractable and comparable approxi-mations, we have assumed that the populationvalue of heritability is small (i.e., < .40). Whenthe true population value is large (e.g., as it is forheight: h2 = .80) (70, 85), the actual samplingvariance is smaller than our approximation.Table 1 summarizes the precision of the esti-mates of genetic parameters for all methods.

ESTIMATING HERITABILITYFROM EXPECTED GENETICRELATEDNESS OF RELATIVESIN A PEDIGREE DESIGN

Design

In pedigree studies, genetic parameters are es-timated from phenotypic similarity betweenknown relatives (21, 49). Twin studies are aspecial case of pedigree studies and have beenused to estimate heritability for a wide variety oftraits, including disease susceptibility, anthro-pometric traits, and behavioral phenotypes (6).

Heritability estimates vary widely (0 to 0.8), butfor many traits heritability is estimated as mod-erate to high (in the range of 0.4–0.8).

In the pedigree design, the phenotypicresemblance [often denoted as the intraclasscorrelation (t)] of MZ and DZ twin pairs isutilized to estimate the contribution of geneticand environmental variation to the phenotypicvariation of a trait. MZ twins share 100% oftheir genomic variation IBD, whereas DZtwins share on average 50% of their genomeIBD. Hence, the matrix G has pair-wise coef-ficients of 1 (MZ twins), 1/2 (DZ twins), and 0(individuals from different families). Assumingthat the common environmental variance isequal for MZ and DZ twins, narrow-senseheritability can be estimated as twice thedifference between phenotypic correlations forMZ and DZ twin pairs (21). In practice, max-imum likelihood methods are used to estimate(co)variance components (e.g., see 54), and theMLM (Equation 8) is augmented with addi-tional random effects, e.g., the effect of a sharedenvironment or nonadditive genetic effects.

Precision

An approximate asymptotic expression forthe sampling variance of the estimate of


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Broad-senseheritability:proportion of thephenotypic variancethat is explained byboth additive andnonadditive geneticvariance

narrow-sense heritability from the classicaltwin design, assuming an equal number (m) ofMZ and DZ twin pairs, is 4(1/m + 1/m) = 32/N(Table 1) (80), with N being the total numberof individuals with a measured phenotype(N = 4m). For example, for 200 MZ and200 DZ pairs (800 samples in total), theapproximate standard error of the estimate ofheritability is

√(32/800) = 0.2.

Limitation and Potential Bias

A limitation of the classical twin design (withMZ and DZ twin pairs) is that it allows esti-mation of only three variance components (in-cluding residual variation) because there areonly two estimates of correlation (one for MZpairs and one for DZ pairs) from which vari-ance components are estimated. Consequently,if the true population variance contains morethan three sources of variance, they cannot allbe estimated simultaneously in the model. Forinstance, if MZ twins share a more similar en-vironment than DZ twins, this effect cannot beseparated from the increased genetic similaritybetween MZ twins compared with DZ twins.Similarly, nonadditive genetic effects decreasethe correlation for DZ twins relative to the cor-relation of MZ twins and therefore may lead tooverestimation of the narrow-sense heritabil-ity, whereas shared environmental effects in-crease the correlation for DZ twins relative tothe correlation of MZ twins and may lead tounderestimation of the broad-sense heritabil-ity. Limitations of this design lead to strong as-sumptions about causes of family resemblance,e.g., absence of nonadditive genetic variance(21, 49, 97), and consequently broad-sense andnarrow-sense heritability cannot reliably be dis-tinguished. Extending the classical twin designto other relatives, such as parents, spouses, and(adopted) children of the twins, allows a widerrange of models to be fitted and allows test-ing of some, but not all, assumptions (e.g., 40,51, 79). However, collection of large cohorts isdifficult.

Example for Human Height

In a comparative study on human height mea-sured in Caucasian twin cohorts from eight dif-ferent countries, Silventoinen et al. (70) esti-mated heritability from MZ and DZ twin pairresemblance. Data were available for 30,111complete pairs. MZ twin correlations rangedfrom 0.87 to 0.94 in both men and women,whereas same-sex DZ twin correlations rangedfrom 0.42 to 0.57 in men and from 0.49 to0.56 in women. Opposite-sex DZ twin corre-lations ranged from 0.30 to 0.50 but were notincluded in the modeling. Maximum likelihoodwas used to estimate the contribution of geneticand environmental effects. The contribution ofshared environmental factors was generally lowand nonsignificant in most cohorts. Heritabilityestimates ranged from 0.70 to 0.87 in men andfrom 0.68 to 0.93 in women. Although substan-tial variation was observed in mean body heightacross different cohorts, the relative contribu-tion of genetic factors was very similar betweenpopulations. Both the observed resemblancebetween close relatives, including parents andoffspring, and the inference on heritability forhuman height have been consistent for morethan a century (84). Empirical observations onthe resemblance between twins and other closerelatives suggest that most phenotypic variationin human height in the population is genetic andthat most genetic variation is additive.

ESTIMATION OF HERITABILITYFROM ACTUAL GENETICRELATEDNESS IN AWITHIN-FAMILY DESIGN

Design

In pedigree studies (e.g., twin and other familystudies), additive genetic variance is estimatedfrom expected genome-wide IBD sharingbetween relatives. These studies are basedon strong assumptions about the covariancebetween individuals within and betweenfamilies. For the estimation of additive genetic


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variation, these assumptions can be bypassed byutilizing only within-family information if verylarge data sets are available.

Through Mendelian segregation, fullsiblings of non-inbred parents share zero, one,or two copies of the alleles at each autosomallocus, with probabilities of 1/4, 1/2, and 1/4,respectively. The total expectation of IBD in apopulation then becomes 1/2 with variance of1/8 for a single locus. The variance becomessmaller when the number of loci increases (30,36, 64), with the expected proportion of IBDsharing being equal to the actual proportion ofIBD sharing if genetic variance were due to aninfinite number of independent loci. However,the number of loci is limited, and geneticlinkage causes dependent segregation of lociin the pedigree, maintaining variation aroundthe expected genetic similarity for all pairsof relatives, apart from MZ twin pairs (whoalways share both alleles IBD) and parents andoffspring (who always share one allele IBD).Using genetic-marker data, we can preciselyestimate the amount of the genome shared by apair of relatives and can estimate narrow-senseheritability by simply regressing phenotypicsimilarity on their genome-wide geneticsimilarity.

By using information from exactly two fullsiblings per family, the matrix G in this design isblock diagonal and contains off-diagonals thatare estimates of the realized or actual propor-tion of the genome that is shared IBD (πG)for a pair of siblings. Elements for individu-als from different families are zero (Figure 1a).Estimates of locus or genome-wide IBD areobtained from genetic-marker data, and effi-cient algorithms exist to calculate probabilitiesof IBD, in particular for small pedigrees (e.g.,see 1, 17, 43).

For analysis of the within-family design,Equation 8 is augmented by a random effectthat models the covariance between full siblingsthat is the same for all pairs; irrespective of theproportion of their genome, they share IBD.This random effect is included because theobjective of the analysis is to estimate additivegenetic variation from the deviation of the

expected value of IBD, which is 1/2 for all pairs.The covariance between sibling pairs i and j is

cov(yi , y j ) = πGi j σ2A + σ 2

C , (10)

where σ 2A is the additive genetic variance

and σ 2C represents the sibling covariance not

explained by additive genetic effects, such aseffects of dominance, epistasis, and the sharedfamily environment. Because the heritabilityin this design (85) is estimated solely fromsegregation within families without any as-sumptions regarding underlying factors thatcause between-family variance, the estimate ofadditive genetic variance is free of confoundingby environmental differences between families.As is the case for the pedigree design, theestimate of additive genetic variance from thewithin-family design is biased upwards whenthere are nonadditive genetic effects and whentheir variance is not estimated simultaneouslywith the variance of additive effects.

Precision

The sampling variance of the estimate ofnarrow-sense heritability of this design is ap-proximately 2/(m∗var(πG)), with m being thenumber of full-sibling pairs and var(πG) be-ing the variance in pair-wise-realized geneticrelationships between the siblings. Theoreticalstudies provide an approximation of variationin realized relationships of full-sibling pairs:var(πG) ≈ 1/(16L)−1/(3L2), where L is the to-tal length of the genetic map (in Morgans) (85).For humans, the total map length for the 22 au-tosomes is L ≈ 35 (41), and so var(πG) ≈ 0.0392,which is close to what has been reported empir-ically (65, 83, 85). Hence, around the expectedproportion of shared IBD (i.e., 1/2), there isa standard deviation of roughly 4%. Becausethe number of recombination events per chro-mosome is small (27), genome-wide IBD shar-ing between full siblings can be estimated withonly a few markers per chromosome. The ap-proximate sampling variance of the estimate ofheritability of the full-sibling design is 2667/N,given a number of assumptions, with N being


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Genome-wideassociation study(GWAS): a studydesign in whichhundreds of thousandsof genetic variants inthe genome (usuallySNPs) are tested forassociation with thetrait

Linkagedisequilibrium (LD):a measure ofassociation betweenalleles at different loci

the total number of individuals with a pheno-type (Table 1).


The limitation of the within-family designis the large sample size required to estimateparameters with sufficient precision. For thesame number of people with a phenotype, thisdesign is approximately 80 times less efficientthan the twin design with equal numbers of MZpairs and DZ pairs. For 10,000 full-sibling pairs(20,000 phenotypes), the approximate standarderror is 0.37. Potential bias may come fromnonadditive genetic effects that are not mod-eled because limited sample size does not allowa reliable distinction between additive and non-additive effects. Both additive genetic varianceand nonadditive genetic variance are estimatedfrom variation around the expected coefficientof relatedness; for full siblings, the expected co-efficient of relatedness is 1/2 for additive geneticvariance and 1/4 for dominance genetic vari-ance and additive × additive genetic variance(21). In theory, this design allows estimationof genetic dominance deviation. However,because the coefficients for additive varianceand dominance variance are highly corre-lated [theoretical value is 0.89 (85)], a strongsampling correlation between the estimatesis expected, which implies that even largersample sizes are required to reliably distinguishnonadditive from additive genetic variance.


In a study on human height measured in 3,375quasi-independent sibling pairs, Visscher et al.(85) estimated heritability by correlating phe-notypic similarity and genome-wide IBD shar-ing between siblings. Actual genome-wide IBDfor full siblings ranged from 0.374 to 0.617 witha mean of 0.498 (with a standard deviation of0.036). Two models were fitted: a full modelthat included a genome-wide additive effect, ashared environmental effect, and a residual ef-fect, and a reduced model that excluded thegenome-wide additive effect. Maximum like-

lihood was used to estimate the contributionof genetic and environmental effects using theMLM as previously described. Heritability wasestimated at 0.80 (95% confidence interval;0.46–0.85), with the remaining variance com-pletely attributable to the residual effect, whichis very similar to estimates and inference fromtwin and family studies (70). The within-familydesign, however, facilitated a complete separa-tion of genetic and environmental factors andcan therefore be seen as an independent valida-tion study for estimating the heritability of hu-man height from pedigree studies. A subsequentstudy with more than 10,000 full-sibling pairsreported a similar value and also partitioned ad-ditive genetic variation into contributions fromindividual chromosomes (83). Results showedthat the data were consistent with a model inwhich variance explained by a chromosome isproportional to the length of that chromosome.

ESTIMATING HERITABILITYFROM POPULATION-BASEDESTIMATES OF GENETICRELATEDNESS

Design

Advances in genotyping technologies have ledto arrays of SNPs that can genotype hundredsof thousands to millions of markers in a sin-gle assay (3). These SNP chips form the basisof genome-wide association studies (GWASs),which have revolutionized human genetics inthe past six years (e.g., see 87). Table 2 showsGWAS results for a selection of quantitativetraits.

In a GWAS, association between each SNPand the trait is tested, and the paradigm is basedon the existence of linkage disequilibrium (LD)between ungenotyped causal variants and SNPsin the analysis. LD refers to a nonrandomassortment of alleles at two loci and occurs ina finite, random mating population becausechromosomal segments are descended from acommon ancestor without any recombination.Consequently, chromosomes that carry thesame allele at a locus that affects a complex


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Table 2 Proportion of variance explained by genetic factors for a number of selected quantitative traits

Trait h2 pedigree designa h2 GWAS hitsb h2 population designc

Height 0.80 (70) 0.10 (42) 0.45 (91, 95)Body mass index 0.45–0.80 (67) 0.02 (73) 0.17 (95)von Willebrand factor 0.66–0.75 (12, 57) 0.13 (71) 0.25 (95)Bone mineral density 0.61 (2) 0.06 (18) 0.16 (93)General intelligence- Children (∼12 years)- Adults

0.40–0.60 (4, 32)0.80 (32, 61)

0 (5)0 (9)

0.22–0.64 (5)0.40–0.50 (11)

Red blood cell phenotypes- Hemoglobin concentration- Sodium

0.84 (19)0.50 (88)

0.02 (76)0.02 (93)

0.16 (93)

Personality- Neuroticism- Extraversion

0.13–0.58 (38)0.34–0.57 (38)

0 (13)0 (13)

0.06 (78)0.12 (78)

aHeritability in the pedigree design is estimated by comparing expected and observed monozygotic and dyzogotic twin pair resemblance.bHeritability from genome-wide association study hits represents the total variation explained by all of the single nucleotide polymorphisms thatindividually reached genome-wide significance in genome-wide association studies.cHeritability in the population design is estimated from the single-nucleotide-polymorphism-derived genetic similarity between pairs of individuals thatare not knowingly related.

Type-1 error:rejection of the nullhypothesis when thenull hypothesis is true

trait are also likely to carry the same alleleat a nearby SNP, generating an associationbetween the SNP alleles and the trait (55).

Because of the large number of tests con-ducted in a genome-wide survey, very stringenttype-1 error rates are used [∼5 × 10−8 (14, 26)]to avoid false positives and to ensure that re-ported associations are robust and are likely toreplicate in other samples from the same popu-lation. This stringent threshold minimizes falsepositives but leads to many false negatives be-cause a causal variant with a small effect or weakLD with SNPs on the chip does not generate anassociation between any one SNP and the traitthat is large enough to be declared significant.In practice, the effect of these false negativeshas been found to be dramatic. For most traits,the SNPs that are declared significant explain intotal 10% or less of the genetic variance. Thishas been referred to as the “missing heritabil-ity” paradox (52).

Instead of testing the effect of each SNP in-dependently on the trait, it is possible to esti-mate the variance explained by fitting all theSNPs simultaneously. This is equivalent to es-timating the relationship between individuals

from the SNPs and using this relationship ma-trix to estimate the genetic variance (25, 74,77). A method described by Yang et al. (91, 92)utilizes LD between genotyped SNPs and un-known causal variants to capture additive ge-netic variation underlying phenotypic variationin a random sample of unrelated individuals inthe population. In this design, matrix G rep-resents genetic similarity between individuals jand k from m genotyped SNPs:

Gjk = 1m

m∑i=1

(xi j − 2pi )(xik − 2pi )2pi (1 − pi )

, (11)

where p is the frequency of the reference alleleand xi is the genotype indicator of the ith SNP(xi = 0, 1, or 2). Estimates of genetic similarityare the genetic relationships expressed relativeto a base population; in this method, the studysample is the base (whereas in pedigree studies,the base is the set of founders with no recordedor inferred relationships to older individuals).In the equation above, the average similarity iszero if the allele frequencies ( p) are estimatedfrom the sample because the expected value ofx is 2p. This is also the matrix that is used for


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principal component analysis to infer popula-tion structure from SNP data (62).

The basic idea behind this method is to esti-mate additive genetic variance by including allthe SNPs in the model without focusing on in-dividual SNPs. In other words, it is an estima-tion rather than a hypothesis-testing paradigm.Variance explained by causal variants that arein LD with genotyped SNPs, but whose effectsizes are too small to reach genome-wide sig-nificance in a conventional GWAS, is includedin the heritability estimate derived through thismethod.

Yang et al. (91) showed that estimates of ad-ditive genetic variation using this method di-rectly address the perceived problem of miss-ing heritability (52, 53). Estimates of additivegenetic variation quantify how much variationis captured by all SNPs, and therefore quantifyhow much variation would be explained by aGWAS when the sample size is so large that allvariants that are associated would be statisticallysignificant (86, 91, 92).

Precision

As mentioned above, sampling variance in-creases with decreasing variation among thecoefficients of G, assuming all else is equal.With expected coefficients being 1/2k (forkth degree relatives), the population design withonly distant relatives yields only little variation.However, whereas G in the pedigree design isblock diagonal with coefficients of expected orrealized IBD for within-family pairs and coeffi-cients of zero for all other elements represent-ing pairs of unrelated individuals, G in the pop-ulation design is filled with estimates for all pairsof individuals. The number of pairs in the pop-ulation design is (N 2 − N)/2, which is a multipleof the number of pairs in the pedigree design( = 1/2 N for pairs of twins). The precisionin the population design comes from the veryprecise estimate of genetic similarity and fromthe large number of pair-wise comparisons inthe sample.

Theory borrowed from linkage analysis ofquantitative traits (68, 82) predicts that the sam-

pling variance of the estimate of heritabilityfrom the mixed model analysis is approximately100,000/N2 (Table 1), hence a standard errorof 315/N. We validated this by simulations us-ing GWAS data of the Atherosclerosis Risk inCommunities Study (ARIC) cohort (63, 95).The simulation results are provided in the sup-plemental material (follow the SupplementalMaterial link from the Annual Reviews homepage at http://www.annualreviews.org).


A limitation of this design is that genetic vari-ance contributed by causal variants that are notin sufficient LD with the genotyped SNPs isnot included in the heritability estimate. If LDbetween the genotyped SNPs and the causalvariants is incomplete, the genetic similarity be-tween individuals j and k at the causal vari-ants is different from the genetic similaritybetween those individuals estimated from thegenotyped SNPs (89). Consequently, geneticvariance from untagged causal variants is notaccounted for by the genetic similarity calcu-lated from genotyped SNPs. This is where thematrix G differs from the previous applications.In the pedigree and within-family designs, thecoefficients of relatedness are based on IBD andare blind to allele frequencies of causal variants(if DNA segments in a pair of individuals areIBD, then any variant in that segment, commonor rare, is shared). In contrast, the population-based estimate of SNP sharing relies on LD andis sensitive to allele frequencies. In the extremecase that all causal variants in the genome areat low allele frequency in the population, andtherefore not in LD with common variants (89),the pedigree and within-family design estimatestotal heritability, whereas the SNP-based esti-mates are zero (and a GWAS would not workeither). Recently, Speed et al. (72) proposed amethod in which the contribution of the SNPsto the estimate of genetic similarity between apair of individuals is weighted according to theLD with their neighboring SNPs, aiming to re-duce potential bias and to increase the precisionof the heritability estimate.


Supplemental Material

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http://www.annualreviews.org

http://www.annualreviews.org/doi/suppl/10.1146/annurev-genet-111212-133258


Bias may also come from a shared environ-ment that is not modeled in this design. If indi-viduals who share SNP genotypes more oftenthan the average also tend to share a commonenvironment, then the heritability explained bythe SNPs will be overestimated. This would beexpected if closely related people (e.g., cousins,siblings) were included in the sample. However,if closely related people are excluded from theanalysis, this source of bias should be small be-cause among distantly related people, genomicsimilarity is poorly correlated with pedigree re-lationship, and it is only the pedigree relation-ship that might be correlated with environmen-tal similarity.

Another possible source of bias may ariseif the population consists of subpopulationsthat differ both genetically and environmen-tally. This bias is usually avoided by testing forpopulation structure and eliminating it from thedata or correcting for it in the analysis (e.g., byincluding the first few principal components ofthe relationship matrix as fixed effects in theMLM). Biases attributable to population struc-ture and genotyping artifacts, such as plate andbatch effects, are more likely to be a problemin case-control analyses than quantitative traitanalyses because confounding with the binaryphenotype is not uncommon (44, 45).


Yang et al. (91) estimated the heritability ofhuman height from 294,831 SNPs genotypedon 3,925 unrelated individuals. The data werefitted in an MLM, and REML was used toestimate the variance explained by the SNPs.All the SNPs were considered simultaneouslyin the model and the proportion of phenotypicvariance explained by the SNPs was 0.45(SE 0.08), with remaining variance due tononfamilial environmental factors and possiblemeasurement error. This estimate of geneticvariance forms the lower boundary of totalnarrow-sense heritability because only geneticvariation due to causal variants that are insufficient LD with the genotyped SNPs isincluded in the estimate. Using simulated data,

the authors show that incomplete LD betweenthe causal variants and the genotyped SNPscan explain all of the remaining heritability.This study showed that the so-called “missingheritability” (52) for height is not missing buthidden. The finding that, together, commonvariants explain a substantial proportion of theheritability proves that GWASs to date havebeen underpowered to detect individual SNPswith small effects. Results from this studyindicate that much larger sample sizes arerequired to detect those individual commonSNP effects in a GWAS. The observed strongrelationship between the experimental samplesize of a GWAS and the number of significantloci detected (81) is consistent with thatconclusion. Causal variants in low LD with thegenotyped SNPs may be identified throughwhole-genome sequencing studies.

A SUMMARY AND COMPARISONOF THE METHODS

We have reviewed three different methods toestimate heritability from genetic similarity be-tween pairs of relatives. The methods differin the parameters estimated. The use of thetwin (pedigree design) and full-sibling (within-family design) data leads to an estimate of totalheritability, whereas the use of SNPs to con-struct a relationship matrix (population design)estimates the additive genetic variance (andtherefore heritability) explained by the SNPs.The proportion of genetic variance explainedby the SNPs depends on the structure of thedata. In a population of unrelated individuals,this proportion depends on the LD betweenSNPs and causal variants. Although individualsare not known to be related, they could sharedistant ancestors and therefore some chromo-some segments that are IBD. Thus, the estimateof genetic variance from all SNPs can be con-sidered as driven by LD or by distant realizedrelationships: The two descriptions are equiva-lent. In fact, the variance of the SNP-based re-lationship is equal to the LD averaged over allpairs of SNPs. The within-family design, whichuses variation in realized relationships between


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pairs of SNPs, can be described as using LDgenerated by the inheritance of large chromo-some segments from parents to offspring withina family. Consequently, this design estimatesthe full heritability because in this design theSNPs track all causal variants.

Heritability estimates derived through thesedesigns differ in precision and possible bias.Generally, close relatives give more precisionbut potentially more bias, whereas distantrelatives give less precision and less bias. Biasin analyses of close relatives may come fromenvironmental variation that is confoundedwith additive genetic variation within fam-ilies, or in the case of siblings, confoundedwith nonadditive genetic effects. Precisionin parameter estimates depends on the totalnumber of individuals with a phenotype andthe variation in relationship (close or distant).

The heritability estimated in the pedigreedesign has generally small sampling variance, asmuch variation exists among the coefficients ofrelatedness. In this design, however, potentialbias is of greater concern and generally has alarger impact on the estimate than precision.The heritability estimated from variationaround the expected genetic similarity of fullsiblings in a within-family design is free ofassumptions about variation between families,but relative to the classical twin design, the sam-pling variance is large. Inflation of the estimateof narrow-sense heritability by nonadditive ge-netic variation is a concern in both the pedigreeand the within-family design. In the pedigreedesign, this is caused by confounding withenvironmental factors. In the within-familydesign, this is caused by a strong correlationof sampling variance between additive andnonadditive genetic variation. Consequently,the power to estimate nonadditive geneticvariance is generally insufficient. Heritabilityestimated in the population design is unbiased:Distant relatives are unlikely to share variationdue to environmental factors or variation dueto nonadditive effects. Sampling variance isrelatively small due to a large number of pair-wise comparisons that can be achieved withthe large sample sizes that are available to date.

The population design is as efficient as a twindesign when tens of thousands of individualswith phenotypic and SNP data are available.Estimating heritability from genetic similarityof distant relatives requires smaller samplesizes compared with the within-family designto obtain similar precision. However, a muchlarger number of genetic markers is requiredto accurately estimate the genetic similarityof distant relatives in the population design.SNP chips available to date are adequatelydesigned to ensure sufficient LD betweengenotyped variants and ungenotyped causalvariants. Hence, heritability can be estimatedfrom distant relatives without much error,especially when heritability is high.

GENETIC ARCHITECTURE

Numerous pedigree studies have revealedmoderate-to-large heritability estimates fora wide variety of complex traits in humanpopulations. After the completion of theHuman Genome Project, considerable successof GWASs was anticipated. After six years ofGWAS discovery, however, much of the ge-netic variance estimated from pedigree studieshas not been accounted for by the geneticvariants discovered from GWASs. For complextraits, typically less than 10% of the geneticvariation is explained by SNPs, although thereare exceptions: For age-related macular de-generation, an eye disease, approximately 50%of genetic variation has been accounted for byonly five loci (31), and for Crohn’s Diseaseand ulcerative colitis, two inflammatory boweldiseases, very large experimental sample sizes(∼15,000 cases) have led to the discovery ofhundreds of loci by GWASs, which in combina-tion with known less common variants explainapproximately 20% of genetic variation (39).

Several explanations have been raised toanswer the case of the missing heritability (52).Possible explanations are that (a) pedigreestudies have overestimated the heritability by,for example, bias due to nonadditive and/orenvironmental effects, that (b) causal variantsindividually explain such a tiny amount of


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variation that their effects do not reach statis-tical significance in GWASs to date, and/orthat (c) causal variants are not in sufficient LDwith the genotyped SNPs and therefore theireffects are not fully captured by the genotypedSNPs in GWASs. Quantifying the differencebetween (b) and (c) is informative with respectto the allelic spectrum of causal variants, i.e.,the frequency of risk alleles in the population.Causal variants that are in low frequencyin the population are not in high LD withgenotyped SNPs. Consequently, variationcaused by variants that are not in sufficient LDwith SNPs cannot be captured and thereforeremains undetected in GWAS.

Whole-genome methods utilizing an ex-pected or realized genetic relationship betweenindividuals have increased our understandingof the genetic variation that underlies complextraits. A short recapitulation for human height,pedigree studies using data from MZ andDZ twin pairs have repeatedly reported heri-tability estimates of approximately 80% (e.g.,50, 70), an estimate confirmed by Visscher et al.(83, 85) utilizing empirical genome-wide IBDsharing of full-sibling pairs (the within-familydesign). Using realized genetic similaritybetween unrelated individuals, Yang et al. (91,95) have demonstrated that 45% to 55% of thephenotypic variance can be explained by com-mon SNPs when taking the individual SNPeffects together. The largest GWAS on heightto date (42) has identified 180 genetic loci thattogether explain ∼10% of the phenotypic vari-ation. Together, these results suggest that forhuman height the genetic variance is additiveand involves many loci of small effect. Thedifference between ∼50% and 10% is due toSNP associations with height that are too smallto reach the stringent significance level used inGWASs. Individual loci do not explain much ofthe genetic variation because otherwise theseeffects would have been identified by GWASsto date. The variance unaccounted for (80% −50% = 30%) is likely to be mainly due to thesegregation of causal variants at low frequency.Bias due to nonadditive genetic effects orenvironmental variation seems unlikely for

human height given the similar heritabilityestimates derived from different study designsand additive genetic models that fit the datawell in all three study designs. Nevertheless,the power to test for absence of nonadditivevariance in any of the reviewed designs remainslow so even if the data are consistent with aparsimonious additive model, it doesn’t provethat there is no variation due to dominance ofepistasis.

We summarize the proportion of varianceexplained from pedigree analyses, genome-wide significant SNPs, and population-basedanalyses using estimated pair-wise genomic re-lationships for a selection of quantitative traitsin Table 2. Traits other than height, such asbody-mass index and cognitive ability, followthe same trend, i.e., the estimates of heritabil-ity from pedigree designs is large, genome-widesignificant loci explain none or a small propor-tion of phenotypic variation, and variance esti-mated from genomic relationships captures 1/3to 2/3 of pedigree heritability. For height, heri-tability estimates derived from pedigree studieshave been confirmed by other study designs,and biased estimates are unlikely. For othertraits, however, inflated (e.g., due to nonad-ditive genetic variation) estimates from pedi-gree studies are a possible cause of part of themissing heritability. The contribution of non-additive genetic variation to phenotypic varia-tion for complex traits in human populationscontinues to be debated (8, 35, 97) and is un-resolved, mostly because current experimentaldesigns lead to biased and imprecise estimates.

DISCUSSION

One of the aims of quantitative genetics hasbeen to quantify the amount of variation incomplex traits that is due to genetic varia-tion and the amount due to environmentalvariation. This is difficult in humans becausepeople who share genes also tend to shareenvironments. Traditional designs, such asthe pedigree design, at least partly overcomethis problem. The availability of genome-wideSNP data has allowed the use of new designs,


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such as the within-family design, throughwhich we can estimate the genetic varianceunderlying the trait without the confoundingof the environment. Within-family studieshave tended to confirm traditional estimatesfor height but their low power means thatthe standard errors on estimated heritabilityhave been high. Consequently, this design wasinfeasible for many traits for which sample sizeswere too small. Designs based on a populationsample of unrelated people can also overcomethe confounding of genes and environmentbut only estimate the proportion of geneticvariance explained by the SNPs, which istypically 1/3 to 2/3 of the traditional estimate.

Population designs to estimate geneticvariation in a two-stage procedure, by firstestimating relatedness from genetic markersand then estimating heritability by contrastinggenetic similarity to phenotypic similarity, arenot new. Ritland (66) proposed this for studiesin natural populations in which obtainingpedigree information may be impossible. Theinitial idea of this design was to detect IBDbetween close relatives (e.g., full siblings andhalf siblings) from a small number of markersand then correlate estimated relatedness withphenotypic covariance. Conceptually, thisapproach is more similar to the pedigreedesign, whereby the pedigree is inferred fromIBD sharing of large chromosome segments,than the within-family and population designswe have discussed. However, there is no fixedpoint at which an inferred pedigree designbecomes a population design that relies on LD:Increasing marker density allows the estimationof more distant relationships at the expenseof a potential loss of information due to im-perfect LD between the markers used to inferrelatedness and causal variants for the trait.

The new (population-based) whole-genomemethods have shown that numbers of geneticvariants with small effect explain a substantialproportion of the heritability for complex traits.These common variants account for the dif-ference between the heritability explained byGWAS hits and the heritability estimated fromall of the SNPs in the population design (see

Table 2). From this, we can conclude thatlarge sample sizes lead to detection of more in-dividually significant SNPs. Augmenting SNPgenotypes with genome sequence data shouldhelp to find the remaining missing heritabil-ity, i.e., the difference between the heritabilityestimates from pedigree studies and the heri-tability estimated from SNPs. In particular, se-quence data should be more powerful wherecausal variants are rare and hence not in highLD with any SNPs on the SNP chip. Althoughthe individual effect size of such a rare variantcan be large, each of these variants is expectedto explain a small amount of variance simplybecause they are rare.

Population-based methods can also be usedin a multivariate setting to estimate genetic co-variance that can be captured by all the SNPs.In the pedigree and within-family designs,genetic covariance is usually estimated by par-titioning phenotypic covariance on individualswho have multiple phenotypic measurements.In the population design, however, geneticcovariance can also be estimated from SNPdata on unrelated individuals that have only oneof the phenotypes measured. That is, geneticcovariance can be estimated from two or moreindependent groups of unrelated individuals,with each group being measured on a differentphenotype. Coefficients of the SNP-basedGRM are the expected genetic covariance be-tween a pair of individuals, and this covariancecan be for the same trait or for different traits.Multivariate analysis using SNP data facilitatesthe quantification of pleiotropy among com-plex traits and might be of particular interestfor traits that cannot be measured on the sameindividual, such as two different diseases (e.g.,see 46, 47). Another goal of research on the ge-netics of complex traits is to identify individualcausal variants and to elucidate their biologicalmechanisms. GWASs have identified manygenes and even some causal sites within thesegenes that contribute to variation in particulartraits (e.g., see 15, 29, 37). Further researchwill no doubt identify more individual causalvariants. Given that the variance explained bymany individual causal variants is so small, it


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may never be possible to identify all of them.A slightly different aim is to describe the prop-erties of causal variants as a class rather thanto identify them all individually. For example,we would like to know the joint distribution ofallelic effects and allele frequencies, and to beable to infer this relationship not all causal vari-ants need to be known. This joint distributionis of interest because it reflects the evolutionaryprocesses underlying complex trait variation,including natural selection, the distributionof effect sizes of new mutations, and past andpresent population size. Moreover, under-

standing the allelic spectrum of causal variantsallows us to provide realistic predictions of thenumber of genetic variants that are presentin the genome and their effect sizes, and hencethe sample size that is required to detectthe variants. That is, knowledge on the jointdistribution of effect size and allele frequencyleads to useful information on experimentaldesigns to further dissect complex trait vari-ation. The whole-genome methods reviewedhere will bring us closer to this goal and willhelp in the identification of individual causalvariants.

SUMMARY POINTS

1. Expected or realized genetic similarity between relatives (either close or distant) can beused to estimate heritability of complex traits in human populations. Estimates based onclose relatives generally yield high precision but may come with bias because of strongassumptions that are violated. Estimates based on distant relatives generally have less biasbut lower precision.

2. Whole-genome methods increase our understanding of the genetic variation underlyingcomplex traits in humans. These methods have shown that a substantial proportion ofgenetic variation is additive and that 1/3 to 2/3 of additive genetic variation is capturedby common SNPs.

3. Whole-genome methods have shown that the postulated genetic architectures involvingonly rare variants are not consistent with the data for many complex traits (see alsoTable 2).

FUTURE ISSUES

1. For many complex traits, most of the heritability is hidden rather than missing. Empiricaldata analyses and simulation studies suggest that future gene-mapping endeavors shouldfocus on both common and rare variants.

2. Whole-genome methods utilizing a realized genetic relationship as reviewed here couldbe exploited for the use of whole-genome sequencing data to unravel the combined effectsof rare variants underlying complex traits.

3. GWAS data that are widely available to date allow investigation of genetic pleiotropybetween different traits (and/or diseases). Whereas in the pedigree design two correlatedtraits are generally measured in the same individuals, the population design also allowsestimation of genetic correlation when the two traits are measured in different individuals,thereby increasing flexibility and possibilities in the study.

DISCLOSURE STATEMENT

The authors are not aware of any affiliations, memberships, funding, or financial holdings thatmight be perceived as affecting the objectivity of this review.


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ACKNOWLEDGMENTS

The Framingham Heart Study is conducted and supported by the National Heart, Lung,and Blood Institute (NHLBI) in collaboration with Boston University (Contract NumberN01-HC-25195). This manuscript was not prepared in collaboration with investigators ofthe Framingham Heart Study and does not necessarily reflect the opinions or views of theFramingham Heart Study, Boston University, or NHLBI. Funding for SHARe Affymetrixgenotyping was provided by NHLBI Contract N02-HL-64278. SHARe Illumina genotypingwas provided under an agreement between Illumina and Boston University. The AtherosclerosisRisk in Communities Study is carried out as a collaborative study supported by NHLBI contracts(HHSN268201100005C, HHSN268201100006C, HHSN268201100007C, HHSN2682011-00008C, HHSN268201100009C, HHSN268201100010C, HHSN268201100011C, and HH-SN268201100012C), R01HL087641, R01HL59367, and R01HL086694; National HumanGenome Research Institute contract U01HG004402; and National Institutes of Health contractHHSN268200625226C. The authors thank the staff and participants of the ARIC study for theirimportant contributions. Infrastructure was partly supported by grant number UL1RR025005,a component of the National Institutes of Health and NIH Roadmap for Medical Research. Theauthors would like to thank Gibran Hemani for the IBD estimation of the Framingham siblingpairs and Bill Hill for his valuable comments on an earlier version of this review. This research wassupported by the Australian Research Council (FT0991360, DP1093502, and DP130102666),the Australian National Health and Medical Research Council (APP1011506, APP1047956,APP1048853, and APP1052684), and the National Institutes of Health (GM099568, GM075091,and MH100141).

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GE47-FrontMatter ARI 2 November 2013 9:9

Annual Review ofGenetics

Volume 47, 2013

Contents

Causes of Genome InstabilityAndres Aguilera and Tatiana Garcıa-Muse � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1

Radiation Effects on Human HeredityNori Nakamura, Akihiko Suyama, Asao Noda, and Yoshiaki Kodama � � � � � � � � � � � � � � � � � � �33

Dissecting Social Cell Biology and Tumors Using Drosophila GeneticsJose Carlos Pastor-Pareja and Tian Xu � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �51

Estimation and Partition of Heritability in Human Populations UsingWhole-Genome Analysis MethodsAnna A.E. Vinkhuyzen, Naomi R. Wray, Jian Yang, Michael E. Goddard,

and Peter M. Visscher � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �75

Detecting Natural Selection in Genomic DataJoseph J. Vitti, Sharon R. Grossman, and Pardis C. Sabeti � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �97

Adaptive Translation as a Mechanism of Stress Responseand AdaptationTao Pan � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 121

Organizing Principles of Mammalian Nonsense-MediatedmRNA DecayMaximilian Wei-Lin Popp and Lynne E. Maquat � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 139

Control of Nuclear Activities by Substrate-Selectiveand Protein-Group SUMOylationStefan Jentsch and Ivan Psakhye � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 167

Genomic Imprinting: Insights From PlantsMary Gehring � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 187

Regulation of Bacterial Metabolism by Small RNAsUsing Diverse MechanismsMaksym Bobrovskyy and Carin K. Vanderpool � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 209

Bacteria and the Aging and Longevity of Caenorhabditis elegansDennis H. Kim � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 233

The Genotypic View of Social Interactions in Microbial CommunitiesSara Mitri and Kevin Richard Foster � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 247

SIR Proteins and the Assembly of Silent Chromatin in Budding YeastStephanie Kueng, Mariano Oppikofer, and Susan M. Gasser � � � � � � � � � � � � � � � � � � � � � � � � � � � � 275

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GE47-FrontMatter ARI 2 November 2013 9:9

New Gene Evolution: Little Did We KnowManyuan Long, Nicholas W. VanKuren, Sidi Chen, Maria D. Vibranovski � � � � � � � � � � � 307

RNA Editing in Plants and Its EvolutionMizuki Takenaka, Anja Zehrmann, Daniil Verbitskiy, Barbara Hartel,

and Axel Brennicke � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 335

Expanding Horizons: Ciliary Proteins Reach Beyond CiliaShiaulou Yuan and Zhaoxia Sun � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 353

The Digestive Tract of Drosophila melanogasterBruno Lemaitre and Irene Miguel-Aliaga � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 377

RNase III: Genetics and Function; Structure and MechanismDonald L. Court, Jianhua Gan, Yu-He Liang, Gary X. Shaw, Joseph E. Tropea,

Nina Costantino, David S. Waugh, and Xinhua Ji � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 405

Modernizing the Nonhomologous End-Joining Repertoire:Alternative and Classical NHEJ Share the StageLudovic Deriano and David B. Roth � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 433

Enterococcal Sex Pheromones: Signaling, Social Behavior,and EvolutionGary M. Dunny � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 457

Control of Transcriptional ElongationHojoong Kwak and John T. Lis � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 483

The Genomic and Cellular Foundations of Animal OriginsDaniel J. Richter and Nicole King � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 509

Genetic Techniques for the ArchaeaJoel A. Farkas, Jonathan W. Picking, and Thomas J. Santangelo � � � � � � � � � � � � � � � � � � � � � � � 539

Initation of Meiotic Recombination: How and Where? Conservationand Specificities Among EukaryotesBernard de Massy � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 563

Biology and Genetics of Prions Causing NeurodegenerationStanley B. Prusiner � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 601

Bacterial Mg2+ Homeostasis, Transport, and VirulenceEduardo A. Groisman, Kerry Hollands, Michelle A. Kriner, Eun-Jin Lee,

Sun-Yang Park, and Mauricio H. Pontes � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 625

Errata

An online log of corrections to Annual Review of Genetics articles may be found athttp://genet.annualreviews.org/errata.shtml

vi Contents

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ANNUAL REVIEWSIt’s about time. Your time. It’s time well spent.

ANNUAL REVIEWS | Connect With Our ExpertsTel: 800.523.8635 (US/CAN) | Tel: 650.493.4400 | Fax: 650.424.0910 | Email: [email protected]

New From Annual Reviews:

Annual Review of Statistics and Its ApplicationVolume 1 • Online January 2014 • http://statistics.annualreviews.org

Editor: Stephen E. Fienberg, Carnegie Mellon UniversityAssociate Editors: Nancy Reid, University of Toronto

Stephen M. Stigler, University of ChicagoThe Annual Review of Statistics and Its Application aims to inform statisticians and quantitative methodologists, as well as all scientists and users of statistics about major methodological advances and the computational tools that allow for their implementation. It will include developments in the fi eld of statistics, including theoretical statistical underpinnings of new methodology, as well as developments in specifi c application domains such as biostatistics and bioinformatics, economics, machine learning, psychology, sociology, and aspects of the physical sciences.

Complimentary online access to the fi rst volume will be available until January 2015. TABLE OF CONTENTS:• What Is Statistics? Stephen E. Fienberg• A Systematic Statistical Approach to Evaluating Evidence

from Observational Studies, David Madigan, Paul E. Stang, Jesse A. Berlin, Martijn Schuemie, J. Marc Overhage, Marc A. Suchard, Bill Dumouchel, Abraham G. Hartzema, Patrick B. Ryan

• The Role of Statistics in the Discovery of a Higgs Boson, David A. van Dyk

• Brain Imaging Analysis, F. DuBois Bowman• Statistics and Climate, Peter Guttorp• Climate Simulators and Climate Projections,

Jonathan Rougier, Michael Goldstein• Probabilistic Forecasting, Tilmann Gneiting,

Matthias Katzfuss• Bayesian Computational Tools, Christian P. Robert• Bayesian Computation Via Markov Chain Monte Carlo,

Radu V. Craiu, Jeff rey S. Rosenthal• Build, Compute, Critique, Repeat: Data Analysis with Latent

Variable Models, David M. Blei• Structured Regularizers for High-Dimensional Problems:

Statistical and Computational Issues, Martin J. Wainwright

• High-Dimensional Statistics with a View Toward Applications in Biology, Peter Bühlmann, Markus Kalisch, Lukas Meier

• Next-Generation Statistical Genetics: Modeling, Penalization, and Optimization in High-Dimensional Data, Kenneth Lange, Jeanette C. Papp, Janet S. Sinsheimer, Eric M. Sobel

• Breaking Bad: Two Decades of Life-Course Data Analysis in Criminology, Developmental Psychology, and Beyond, Elena A. Erosheva, Ross L. Matsueda, Donatello Telesca

• Event History Analysis, Niels Keiding• Statistical Evaluation of Forensic DNA Profi le Evidence,

Christopher D. Steele, David J. Balding• Using League Table Rankings in Public Policy Formation:

Statistical Issues, Harvey Goldstein• Statistical Ecology, Ruth King• Estimating the Number of Species in Microbial Diversity

Studies, John Bunge, Amy Willis, Fiona Walsh• Dynamic Treatment Regimes, Bibhas Chakraborty,

Susan A. Murphy• Statistics and Related Topics in Single-Molecule Biophysics,

Hong Qian, S.C. Kou• Statistics and Quantitative Risk Management for Banking

and Insurance, Paul Embrechts, Marius Hofert

Access this and all other Annual Reviews journals via your institution at www.annualreviews.org.

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