Effects of the Family Environment Gene.pdf

2008, Vol. 44, No. 2, 305–315

Effects of the Family Environment: Gene–Environment Interaction and

Passive Gene–Environment Correlation

Thomas S. Price and Sara R. Jaffee

University of Pennsylvania

The classical twin study provides a useful resource for testing hypotheses about how the family

environment influences children’s development, including how genes can influence sensitivity to

environmental effects. However, existing statistical models do not account for the possibility that

children can inherit exposure to family environments (i.e., passive gene– environment correlation). The

authors introduce a method to simultaneously estimate the effects of passive gene– environment corre-

lation and gene– environment interaction and use it to investigate the relationship between chaos in the

home and verbal ability in a large sample of 4-year-old twins.

Keywords: twins, epidemiology, gene– environment interaction, gene– environment correlation

Supplemental materials: http://dx.doi.org/10.1037/0012-1649.44.2.305.supp

Developmental psychologists have long been interested in in-

vestigating whether and how children’s family environments in-

fluence their cognitive and behavioral development. Researchers

have demonstrated that environmental factors measured at the

family level, such as socioeconomic status (SES) and geographical

location, are associated with children’s outcomes independent of

individual-level parent or child factors (e.g., Duncan & Brooks-

Gunn, 1997; Leventhal & Brooks-Gunn, 2000) and are often

mediated by more proximal processes (Collins, Maccoby, Stein-

berg, Hetherington, & Bornstein, 2000).

Although many studies have demonstrated associations between

family environmental factors and children’s adjustment, it is

equally true that the effects of family environment can vary from

child to child, even for children raised in the same family. For

example, extreme privation in childhood can cause profound cog-

nitive deficits, but children raised under such conditions vary

widely in terms of their cognitive and socioemotional functioning

(Rutter, O’Connor, & the English and Romanian Adoptees Study

Team, 2004). One possibility is that the effects of adversity are

conditioned by individual differences in children’s resilience or

adaptivity to environmental risk, which may have a genetic basis

E. It has

been demonstrated in animal experiments by researchers showing

differential effects of environmental conditions in groups of ani-

mals stratified by their genetic background (e.g., Bennett et al.,

2002). For obvious reasons, it has been much harder to demon-

strate G E in humans. Whereas in animal studies both genotype

and environmental exposure can be manipulated for experimental

purposes, in human studies interactions must generally be sought

between naturally occurring variations in genotype and environ-

ment. Epidemiological approaches to G E can offer greater

validity than experimental studies, but they do so at the expense of

statistical power and experimental control. One of the drawbacks

of an epidemiological study of G E is the possibility of corre-

lation between genotype and environment: the phenomenon of

gene– environment correlation (rGE). Statistical methods for de-

tecting G E in human populations need to allow for the possible

lack of independence between genetic and environmental risk

factors (Etheredge, Christensen, Del Junco, Murray, & Mitchell,

2005; Liu, Fallin, & Kao, 2004).

Genotype and environment can correlate for various reasons

(Jaffee & Price, 2007), but studies of the effects of family envi-

ronments on children’s outcomes are particularly subject to con-

founding due to passive rGE (Kendler & Eaves, 1986; Plomin,

1986). Passive rGE occurs when the family environment depends

on heritable parental characteristics, so that parents pass on to their

children an environment that correlates with the parental genotype.

Biological parents also pass on the genotype to their children.

When this genotype also influences children’s behavioral or cog-

nitive outcomes, the result is a spurious association between en-

Thomas S. Price, Institute for Translational Medicine and Therapeutics,

University of Pennsylvania; Sara R. Jaffee, Department of Psychology,

University of Pennsylvania.

We have no financial interests or conflicts of interest related to the

material reported in the article. This work was supported by Grant P50

HL81012 from the National Heart, Blood, and Lung Institute to Thomas S.

Price and Grant R01 HD050691 from the National Institute of Child Health

and Human Development to Sara R. Jaffee.

We thank the participants in the Twins Early Development Study

(TEDS), Robert Plomin, and the TEDS research team, especially Andy

McMillan for providing data management support.

Correspondence concerning this article should be addressed to Thomas

S. Price, Institute for Translational Medicine and Therapeutics, University

of Pennsylvania, Room 807 BRB II/III, 421 Curie Boulevard, Philadelphia,

PA 19104. E-mail: tom@spirit.gcrc.upenn.edu

305

Developmental Psychology

0012-1649/08/$12.00 DOI: 10.1037/0012-1649.44.2.305

(Rutter, 2003). Gene– environment interactions (G E) occur

when genetic factors influence sensitivity to environmental effects.

An alternative way of conceptualizing the interaction is to say that

environmental exposure moderates the effect of genetic risk fac-

tors. The existence of such moderating effects would suggest

greater scope for environmental intervention to alter heritable traits

such as cognitive abilities.

However, many challenges remain to identify G

306

PRICE AND JAFFEE

vironment and outcome (Plomin, DeFries, & Loehlin, 1977; Scarr

& McCartney, 1983). In this way, an association between a mea-

sure of the family environment and a childhood outcome can be

partially or totally accounted for by the effects of parental geno-

type. In the absence of passive rGE this association is attributed to

the influence of the family environment on the outcome. Failure to

rule out the possibility that passive rGE accounts for some portion

of the association may result in its misattribution to environmental

causes.

When the association between measured environment and out-

come is accounted for by unobserved genetic factors (namely,

parental genotype), then the association is said to be genetically

mediated . When the association is accounted for by unobserved

environmental factors, then it is said to be environmentally medi-

ated . This terminology is admittedly somewhat confusing. The

terms genetic mediation and environmental mediation as used by

behavioral geneticists do not imply that genes or environments are

intervening variables in the association between the measured

environment and the outcome; clearly, parental genotype is caus-

ally prior to both measured environment and childhood outcome.

Studies of twin children can exploit differences in genetic re-

latedness between monozygotic (MZ) and dizygotic (DZ) pairs to

quantify the degree to which the effects of environmental exposure

at the level of the individual are genetically mediated and envi-

ronmentally mediated, even in the presence of G E (Eaves,

Silberg, & Erkanli, 2003; Rathouz, Van Hulle, Rodgers, & Lahey,

2007). However, current statistical methods for studies of twin

children are uninformative about whether the effects of family-

wide environments are environmentally or genetically mediated

(Turkheimer, D’Onofrio, Maes, & Eaves, 2005). In fact, the meth-

ods that are currently in use implicitly assume the absence of

passive rGE. This problem extends to studies that investigate

possible interactions between genetic influences and the family

environment.

The goal of the current article is to introduce an analytical

method for twin studies that simultaneously estimates G E and

passive rGE for measures of the family environment. The motiva-

tions for developing this method are twofold. First, we have

identified a problem with the statistical methodology that is cur-

rently used to investigate the moderating effects of the family

environment, namely, the assumption that there is no passive rGE.

Therefore, we wish to develop an alternative method that does not

suffer the consequences of violating this assumption. The second

motivation is the prospect that passive rGE can be estimated using

data from child twins under specific circumstances: namely, when

genetic influences on the phenotype both correlate with and are

moderated by a measure of the family environment.

In this study, we analyze simulated datasets to investigate

whether these motivations are justifiable. First, we analyze the

simulated datasets using the existing method for detecting G E

to quantify the problems that arise when passive rGE is present.

Second, we reanalyze the simulated data using the new model to

outline the range of circumstances under which the simulated

parameter values are accurately recovered.

We illustrate the model with an application to the trait of

childhood verbal ability. Below, we review twin studies that have

attempted to demonstrate how family-wide environments such as

SES and parental education moderate genetic influences on chil-

dren’s cognitive outcomes. We highlight methodological problems

in these studies that originate in their failure to account for possible

effects of passive rGE and explain how the new statistical model

may overcome these shortcomings. Finally, we apply the method

to a large sample of twins and show for the first time that such data

can be used to distinguish true environmental effects from passive

rGE.

Studies of G

E and Children’s Cognitive Abilities

A series of twin studies has attempted to quantify and test the

moderating effects of family environmental variables (e.g., paren-

tal education, SES) on genetic factors that influence individual

differences in children’s verbal or cognitive abilities (Asbury,

Wachs, & Plomin, 2005; Fischbein, 1980; Guo & Stearns, 2002;

Harden, Turkheimer, & Loehlin, 2007; Kremen et al., 2005; Rowe,

Jacobson, & Van den Oord, 1999; Scarr-Salapatek, 1971; Turkhei-

mer, Haley, Waldron, D’Onofrio, & Gottesman, 2003). The results

have been contradictory. An analysis of data from the National

Longitudinal Study of Adolescent Health concluded that the her-

itability of verbal ability was greater in families with highly

educated parents (Rowe et al., 1999), although a reanalysis as-

cribed the moderating effect to employment status and race (Guo

& Stearns, 2002). Other studies have also found that the genetic

influences on cognitive abilities are stronger in families in which

parents have more education (Kremen et al., 2005) or higher SES

(Harden et al., 2007; Turkheimer et al., 2003). In contrast, a large

study of 4-year-old twins did not find that heritability estimates

varied as a function of SES (Asbury et al., 2005) but that herita-

bility estimates were higher in high-risk families characterized by

high levels of chaos and poor parent– child communication—

aspects of the environment that typically correlate with low SES

(Asbury et al., 2005; Evans, 2004). Moreover, these reports of G

E have not been confirmed in studies of nontwin families (Nagoshi

& Johnson, 2005; Van den Oord & Rowe, 1997).

The twin studies reviewed above used either a structural equa-

tion modeling framework (e.g., Turkheimer et al., 2003), a mixed

model (Guo & Stearns, 2002), or a DeFries-Fulker regression

model (e.g., Rowe et al., 1999) to test hypotheses about the effects

of the family environment on cognitive outcomes. These methods

estimate the overall association between family environment and

the phenotype but do not distinguish between environmentally

mediated effects and passive rGE (Turkheimer et al., 2005). In

effect, the influences of latent genetic and environmental factors

are estimated from the variation in the phenotype that remains after

estimating a main effect of the measured family environment

(Purcell & Koenen, 2005; Turkheimer et al., 2005). This is equiv-

alent to assuming that the association between the measured family

environment and the child phenotype is mediated entirely through

the shared environment. In the presence of passive rGE this im-

plicit assumption is violated, so that these procedures not only

misspecify the effect of the measured environment but also mis-

specify the effects of the latent shared environmental factor. A

further consequence of the presence of passive rGE is that the

phenotypic variance cannot be resolved into separate genetic and

environmental components in the usual way (Rathouz et al., un-

published manuscript). Crucially, at least two studies have dem-

onstrated that rGEs are likely to account for part of the association

between SES or parental education and offspring cognitive abili-

ties (Neiss, Rowe, & Rodgers, 2002; Tambs, Sundet, Magnus, &

SPECIAL SECTION: EFFECTS OF THE FAMILY ENVIRONMENT

307

Berg, 1989), suggesting that estimates of G E as predictors of

cognitive abilities might be biased. The same problem may apply

to twin studies of G E in other phenotypes: For example, the

relationship between family dysfunction and children’s antisocial

behavior may be genetically rather than environmentally mediated

(Button, Scourfield, Martin, Purcell, & McGuffin, 2005). On the

other hand, studies that have been careful to measure environments

that are not likely to be genetically correlated with the outcome,

such as geographical region, are less vulnerable to this criticism

(e.g., Dick, Rose, Viken, Kaprio, & Koskenvuo, 2001).

Method

Statistical Model

In this section we first outline a model for the effects of a

measured family environment on twin phenotypes that parameter-

izes the effects of passive rGE and explains why it cannot be

successfully estimated. Next, we extend the model to account for

the effects of both G E and passive rGE and show that the

existence of G E allows the main effect of the measured family

environment to be distinguished from passive rGE.

Let us say that we are interested in understanding the sources of

variation in a phenotype like children’s verbal ability. In the

standard biometric model for twin data, the phenotype Y ij for twin

j in family i is determined by the population mean and the values

of the random variables A ij ,C i , and E ij that represent additive

genetics, shared environment, and nonshared environment, respec-

tively. We assume that the latent variables A , C , and E are

independently normally distributed and load on the phenotype with

coefficients a , c , and e , respectively. In order for the model to be

identified, it is necessary to provide an arbitrary location and scale for

the latent genetic and environmental variables. In accordance with

convention, we scale these latent variables to zero mean and unit

variance. Because MZ twins have the same genomic DNA, whereas

DZ twins share half their segregating genes, the genetic factors for

twins in the same family, A i1 and A i2 , are correlated with Coefficient

1 for MZ twins and with Coefficient 0.5 for DZ twins. The nonshared

environments E ij are uncorrelated within members of the same family.

We supplement this model with an additional random variable X

representing a measured family environment—that is, a variable

measured at the family level whose value differs between families

but not within families (e.g., family chaos). X is normally distrib-

uted with zero mean and variance 2 , has a main effect x on the

phenotype, and is correlated with A due to a passive rGE, such that

Cor( X i, A i1 ) Cor( X i, A i2 ) r . Under this model, the value of the

phenotype Y ij for twin j in family i is given by

Need for New Statistical Methods

In this article we suggest a methodological innovation that

addresses the problem we have identified. We introduce a statis-

tical model for the classical twin design that estimates both the

environmentally mediated effects of the family environment and

passive rGE in the presence of G E. The influence of the

measured family environment is modeled as a random effect that

may correlate with genotype rather than a fixed main effect, an

approach that allows both the genetically mediated effects and the

environmentally mediated effects of the measured environment to

be estimated from the data. Similar analytic strategies have been

suggested previously in relation to child-specific environments

(Eaves et al., 2003; Purcell, 2002). Simulation studies have been

performed that quantify the deficiencies of the existing method and

validate the proposed analytical procedure.

We illustrate the new method using data from a large twin study

of early cognitive development. A previous report from this study

found evidence that chaos in the family home and features of

parent– child communication style moderated genetic influences

on verbal ability at age 4 (Asbury et al., 2005). We selected family

chaos for our analysis to facilitate comparison with the existing

literature on the moderating effects of distal family environments

over genetic influences on cognitive development.

Chaos reflects the child’s physical microenvironment, including

the child’s exposure to noise, crowding, and patterns of environ-

mental traffic (Matheny, Wachs, Ludwig, & Phillips, 1995). Fam-

ily chaos may retard cognitive development by causing children to

filter out useful environmental stimuli along with unwanted noise

(Evans, 2006). Parent– child interactions in noisy or crowded

homes are also less conducive to cognitive development because

parents are less responsive to their children (Evans, 2006). Chaos

correlates with SES and may function as a proximal mediator of its

effects (Asbury et al., 2005; Pike, Iervolino, Eley, Price, & Plomin,

2006). It has previously been shown that this measure of the family

environment not only correlates with verbal ability (Petrill, Pike,

Price, & Plomin, 2004; Pike et al., 2006) but also moderates the

effect of genetic influences on verbal ability (Asbury et al., 2005).

Although these findings are premised on the assumption that chaos

has environmentally mediated effects on children’s verbal ability,

an alternative hypothesis is that parents who raise their children in

chaotic home environments also pass along genetic variants that

are associated with poor verbal ability and that, in fact, the asso-

ciation between chaos and children’s verbal ability is partly ge-

netically mediated. In this study, we use a new statistical method

to show that a previously reported association between chaos at

home and early verbal ability cannot be explained by passive rGE.

Y ij aA ij cC i eE ij xX i .

(1)

Because we are interested in the effects of an environmental factor

that differs between families but not within families, it is illumi-

nating to rearrange the model for the phenotypic scores into

separate terms for the half sum (the within-family mean, corre-

sponding to the component of the twins’ phenotypic scores that

differs between families) and the half difference (the component of

the twins’ phenotypic scores that varies within families):

Y i 1 Y i 2

2 a A i 1 A i 2

cC i

2 e E i 1 E i 2 xX i , (2)

Y i 1

Y i 2

2 a

A i 1

A i 2

2 e

E i 1

E i 2

Note that the sum of these terms is Y i1 (i.e., the score for Twin

1 in family i ) and the difference between them is Y i2 (i.e., the score

for Twin 2 in family i ). The variance in the phenotypic scores can

be partitioned into a component of variance due to differences

between families, 2 , accounted for by factors that differ between

308

PRICE AND JAFFEE

families such as the main effect of X , and a component of variance

due to differences within families, 2 , which cannot be accounted

for by the main effect of X because X takes the same value for all

children in a family. Let us assume that the variables follow a

multivariate normal distribution and there are no systematic effects

of birth order. The latter is not generally considered a controversial

assumption for behavioral data simply because twins are so close

in age, although there is some evidence that perinatal risk is

elevated in second-born twins (Armson et al., 2006). Under these

assumptions the following equality holds:

parameters (namely a , c , e , x and r ) to be estimated (the variance

X can be estimated directly from the data). This means that x and

r are not identified: It is not possible to estimate unique values for

these parameters from the data.

Let us now extend the model with additional terms describing

the moderating effects of the measured family environment. We

can model G E by allowing a moderating effect of the measured

environment on the genotype so that the coefficient of genetic

influence on the phenotype is given by a 1 m A X , where m A is

a linear moderation term. Nonzero values for this term imply that

the genetic influences on the phenotype vary across levels of the

measured environmental variable. We can also allow linear mod-

eration of the paths for the shared environment, c 1 m C X , and

nonshared environment, e 1 m E X . The variances of the phe-

notypic sums and differences are now given by:

Var Y i 1 Var Y i 2 b w Var

Y i 1 Y i 2

Var

Y i 1 Y i 2

. (3)

bMZ

a 2

1 m A X

c 2

1 m C X

The variances of the half-sums and half-differences correspond,

respectively, to the between-family variance 2 and the within-

family variance 2 , and are uncorrelated. The values of 2 and 2

depend on the zygosity of the twin pair, because genetic differences

between twins can contribute to within-pair differences for DZ pairs

but not for MZ pairs. It can be shown that the between- and within-

family phenotypic variances for MZ and DZ pairs are given by:

e 2

1 m E X

x 2

2 a 1 m A X x X r , (5)

wMZ

2 e 2

m E X

2 ,

4 a 2

bDZ

1 m A X

c 2

1 m C X

2 e 2

bMZ

a 2

c 2

2 ax X r ,

(4)

2 e 2

1 m E X

x 2

2a 1 m A X x X r ,

2 e 2 ,

wMZ

4 a 2

2 e 2

wDZ

m A X

m E X

2 .

4 a 2

2 e 2

bDZ

c 2

x 2

2 ax X r ,

The covariance between the measured environment X and the

phenotype Y , c XY , comprises terms relating to the environmentally

and genetically mediated effects of the measured environment:

wDZ

4 a 2

2 e 2 .

We can see that a positive association between the measured

family environment and the phenotype increases the variance of

the phenotype between families. This association has two compo-

nents: an environmental component that is mediated solely by the

latent environmental variable X , and a genetic component due to

the passive rGE between A and X . The phenotypic variance ac-

counted for by the environmental component of the association is

simply the square of the main effect of the environmental influence

on the phenotype, x 2

c XY x 2

a 1 m A X X r .

(6)

2 . The phenotypic variance due to passive

rGE equals twice the covariance between A and X 2 ax X r . Note

that the within-family phenotypic variance does not depend on

either x or r . The lack of dependence of within-family variance on

x is not surprising, because we model the effect of the family

environment the same way for both twins in a pair. The reason that

passive rGE makes no contribution to within-family differences

can be understood intuitively as follows. Genetic differences

within DZ twin pairs arise from recombination during meiosis, a

random process that is uncorrelated with the parental genotypes

and hence with the processes that cause passive rGE. As a final

point, it is important to note that the environmentally and geneti-

cally mediated effects of the measured family environment on the

between-family and within-family variances are confounded in

this model. There are four pieces of information, and there are five

The covariance between measured environment and phenotype

due to passive rGE, a 1 m A X X r , is a linear function of X ,

whereas the covariance due to the environmentally mediated ef-

fect, x 2 , is constant with respect to X . Consequently, if it is

known (or can be shown in advance) that there is moderation of the

genetic variance such that m A and a are nonzero, then a model that

estimates the covariance between measured environment and phe-

notype as a linear function of X is identified and allows unique

values for x and r to be estimated from the data. In other words, the

existence of G E allows one to distinguish between the envi-

ronmentally and genetically mediated effects of the measured

family environment. For example, if the environmental exposure X

is binary with values corresponding to exposure/nonexposure, then

the equations in (5) will provide eight pieces of information—four

variances for each value of X —sufficient to estimate the eight

parameters in the model. Naturally, the power to discriminate

between the main effect of the environment and passive rGE will

depend strongly on the values of the genetic path parameter a and

the genetic moderation parameter m A : Power will increase as the

magnitude of these parameters increases.

Because the covariance between X and Y is entirely due to the

covariance between X and the half-sums, which also equals c XY ,

SPECIAL SECTION: EFFECTS OF THE FAMILY ENVIRONMENT

309

the covariances between the variables in our model can be de-

scribed completely by inserting the values from the equations in

(5) and (6) into the following structural equations:

A path diagram corresponding to this model of environmental

mediation and moderation is shown in Figure 1. For simplicity of

presentation, the means model is omitted. The model can either be

implemented within a structural equation modeling paradigm and

estimated by maximum likelihood—an example script is provided

as part of the supplementary materials online in Supplemental

Appendix I, for the freely distributed software package Mx (http://

www.vcu.edu/mx/; Neale, Boker, Xie, & Maes, 1999)— or imple-

mented as a Bayesian model and estimated by Markov chain

Monte Carlo methods. Bayesian models allow very flexible pa-

rameterization: A script for the freely distributed program win-

BUGS 1.4.1 (www.mrc-bsu.cam.ac.uk/bugs/; Spiegelhalter,

Thomas, Best, & Lunn, 2003) is provided online in Supplemental

Appendix II.

MZ : Var

Y i 1 Y i 2

, 1

Y i 1 Y i 2

, X i

bMZ

0c XY

wMZ

, (7)

c XY

DZ : Var

Y i 1 Y i 2

, 1

Y i 1 Y i 2

, X i

bDZ

0 c XY

wDZ

c XY

Data Analysis

The expected vector of means for, respectively, the half-sums,

half-differences, and measured environment is ( , 0, 0) for both

zygosity groups. However, in practice it may be better to estimate

the means for MZ and DZ groups without imposing any con-

straints to capture any mean effects due to zygosity and birth order.

As mentioned previously, the statistical model described by the

equations in (7) can only be estimated when it is already known

that the measured family environment moderates the genetic vari-

ance (i.e., m A 0). For this reason, the full model— containing

both r and m A parameters— cannot, by itself, provide a test for the

(1+ m C X ) 2

C b

s 2

(1+ m A X ) 2

(1+ m E X ) 2

A b

E b

E w

√½ e

½(Y 1 +Y 2 )

½(Y 1 –Y 2 )

(1+ m C X ) 2

s 2

√ 4 / 3 r

(1+ m A X ) 2

C b

(1+ m E X ) 2

A b

E b

E w

(1+ m A X ) 2

√¾ a

A w

√½ e

√¼ a

½(Y 1 +Y 2 )

½(Y 1 –Y 2 )

the variance of

the measured family environment; 1 ⁄ 2 (Y 1 Y 2 ) half sum of twin phenotypes; 1 ⁄ 2 (Y 1 –Y 2 ) half difference

between twin phenotypes; A additive genetics; C shared environment; E nonshared environment; b

suffix between-family variance; w suffix within-family variance; m C linear moderation of shared

environmental path; r correlation due to passive rGE; m A linear moderation of genetic path; a additive

genetic path parameters; c shared environment path parameters; e nonshared environment path parameters;

x environmentally mediated effect of the measured environment.

½(Y 1 +Y 2 )

Figure 1. Path diagrams for monozygotic (MZ) and dizygotic (DZ) twin pairs, showing observed variables

(square boxes), latent variables (circles), regression paths (single-headed arrows) and correlations (double

headed arrows). The means model has been omitted. X measured family environment; x 2

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