Demonstrating the validity of twin research in criminology
Abstract
In a recent article published in Criminology, Burt and Simons (2014) claimed that the statistical violations of the classical twin design render heritability studies useless. Claiming quantitative genetics is “fatally flawed” and describing the results generated from these models as “preposterous,” Burt and Simons took the unprecedented step to call for abandoning heritability studies and their constituent findings. We show that their call for an “end to heritability studies” was premature, misleading, and entirely without merit. Specifically, we trace the history of behavioral genetics and show that 1) the Burt and Simons critique dates back 40 years and has been subject to a broad array of empirical investigations, 2) the violation of assumptions in twin models does not invalidate their results, and 3) Burt and Simons created a distorted and highly misleading portrait of behavioral genetics and those who use quantitative genetic approaches.
DEMONSTRATING THE VALIDITY OF TWIN
RESEARCH IN CRIMINOLOGY∗
J. C. BARNES,1JOHN PAUL WRIGHT,1,6 BRIAN B. BOUTWELL,2
JOSEPH A. SCHWARTZ,3ERIC J. CONNOLLY,4
JOSEPH L. NEDELEC,1and KEVIN M. BEAVER5,6
1School of Criminal Justice, University of Cincinnati
2School of Social Work, Saint Louis University
3School of Criminology and Criminal Justice, University of Nebraska at Omaha
4Criminal Justice Department, Pennsylvania State University, Abington
5College of Criminology and Criminal Justice, Florida State University
6Center for Social and Humanities Research, King Abdulaziz University,
Jeddah, Saudi Arabia
KEYWORDS: assumptions, behavior genetics, biosocial, empirical, quantitative, twins
In a recent article published in Criminology, Burt and Simons (2014) claimed that
the statistical violations of the classical twin design render heritability studies useless.
Claiming quantitative genetics is “fatally flawed” and describing the results generated
from these models as “preposterous,” Burt and Simons took the unprecedented step
to call for abandoning heritability studies and their constituent findings. We show that
their call for an “end to heritability studies” was premature, misleading, and entirely
without merit. Specifically, we trace the history of behavioral genetics and show that 1)
the Burt and Simons critique dates back 40 years and has been subject to a broad array
of empirical investigations, 2) the violation of assumptions in twin models does not in-
validate their results, and 3) Burt and Simons created a distorted and highly misleading
portrait of behavioral genetics and those who use quantitative genetic approaches.
“The flaws of twin studies are not fatal, but rather seem no worse (and may be better)
than the flaws of the typical causal study that relies on observational data.”
(Felson, 2012: ii)
Behavioral genetic research has existed for more than 100 years (Maxson, 2007). Since
its inception, it has been a lightning rod of criticism, especially by scholars who are inal-
terably opposed to linking biology with behavior. Over this time, numerous critics (e.g.,
∗Additional supporting information can be found in the listing for this article in the Wiley Online
Library at http://onlinelibrary.wiley.com/doi/10.1111/crim.2014.52.issue-4/issuetoc.
We wish to thank each of the five anonymous reviewers for their scholarly insight. In addition, we
would like to acknowledge Mara Brendgen, Francis Cullen, Lisabeth DiLalla, Christopher Fer-
guson, Judith Rich Harris, Kenneth Kendler, Terrie Moffitt, Christopher Patrick, Steven Pinker,
Stephen Tibbetts, Catherine Tuvblad, and Anthony Walsh for their comments, suggestions, and
feedback on previous drafts of this article. Of course, all errors and omissions are ours and ours
alone. Direct correspondence to J. C. Barnes, School of Criminal Justice, University of Cincinnati,
Cincinnati, OH 45221 (e-mail: jc.barnes@uc.edu).
C2014 American Society of Criminology doi: 10.1111/1745-9125.12049
CRIMINOLOGY Volume 00 Number 0 1–39 2014 1
2 BARNES ET AL.
Joseph, 2004; Lewontin, Rose, and Kamin, 1984) have leveled various charges against
twin designs and the assumptions on which they are based. Beginning in the 1970s, polit-
ically motivated critics of behavioral genetics launched an all-out crusade against such
methods, the findings emanating from them, and even on the researchers themselves
(Segerstr˚
ale, 2000). These critics called for an end to the idea that biology had anything
to do with behavior, noting that sociobiology was a “dangerous idea.” Relying heavily
on anecdotes, opinions, and the occasional mathematical example, critics of behavioral
genetics were unrelenting in their attack.
In response, a small but growing force of behavioral geneticists, statisticians, and other
scholars launched a prolonged effort to collect larger samples of twins, other geneti-
cally related relatives, and adoptees. They used these samples to test, retest, and re-
fine behavioral genetic models. Throughout the 1980s, behavioral geneticists published
study after study documenting the robustness of behavioral genetic methods, especially
those designed to assess heritability (Floderus-Myrhed, Pederson, and Rasmuson, 1980;
Paul, 1980; Pederson et al., 1985; Rice, Cloninger, and Reich, 1980; Rushton et al., 1986;
Scarr, Scarf, and Weinberg, 1980). These studies quickly multiplied, eventually leading
behavioral geneticists to “lose their identity” because they became so integrated within
psychology and other fields (Scarr, 1987). By the end of the 1980s, the war was over with
a large body of research findings supporting the general thrust of behavioral genetic mod-
eling (Plomin and Bergeman, 1991). As time went on, isolated critics (e.g., Joseph, 2004)
emerged only to be greeted by even more empirical evidence in favor of the validity of
the findings stemming from behavioral genetic studies. Today, behavioral genetic stud-
ies inform a broad range of fields, including medicine, psychiatry, psychology, education,
and even criminology. Summarizing the large body of behavioral genetic findings that had
emerged prior to 2002, Pinker (2002: 374) observed:
The results [of heritability studies] come out roughly the same no matter what is
measured or how it is measured. . . . All of this translates into substantial heritability
values, generally between .25 and .75. A conventional summary is that about half of
the variation in intelligence, personality, and life outcomes is heritable.
The collective body of biosocial evidence thus directly aligns with the “reality” of find-
ings from every other discipline. Broadly speaking, biosocial criminologists have found
that approximately 50 percent of the variance in antisocial phenotypes can be attributed
to genetic influences, followed by unique environmental influences and, to a lesser extent,
common (or shared) environmental influences (Beaver, 2013; Ferguson, 2010; Moffitt,
2005).
These findings, and others, however, find themselves once again imperiled. A recent
publication in Criminology by Burt and Simons (2014; hereafter Burt and Simons) called
for criminologists to abandon heritability studies and effectively to jettison them from
the discipline. In doing so, Burt and Simons called for a de facto form of censorship.
Their logic was straightforward: Twin studies are fatally flawed, the findings cannot be
trusted, old findings should be placed on the scrapheap of scientific history, and new find-
ings only reify what is known to be untrustworthy. As a result, no bona fide criminolog-
ical journal should publish twin-based research moving forward. Joining history’s critics
(Joseph, 2004), Burt and Simons critiqued heritability studies and those who use behav-
ioral genetics models. Although their arguments were multifaceted, they bear a striking
VALIDITY OF TWIN RESEARCH 3
resemblance to the arguments leveled against behavioral geneticists in the 1970s. Even so,
their argument was powerful, emotionally appealing, and seductive, especially for those
uninformed about behavioral genetics and for those ideologically opposed to biology.
Burt and Simons argued that behavioral genetic methods are fundamentally flawed
because violation of “crucial assumptions” and “technical limitations” inevitably leads
to upwardly biased estimates of heritability and to downwardly biased estimates of the
common environment. Burt and Simons detailed a series of methodological arguments
against heritability studies, arguing, for instance, that violations of the equal environ-
ments assumption (EEA; “the environment of MZ co-twins is no more similar than that
of DZ co-twins”) are “flatly contradicted by both empirical evidence and common sense”
(p. 231).1Indeed, they even told us “behavioral geneticists acknowledged that the EEA
was invalid” (p. 232). Yet the EEA was just one of many behavioral genetic assumptions
attacked by Burt and Simons. Because twin research rests on critical assumptions, as-
sumptions Burt and Simons argued are always violated, findings from heritability studies
are “biologically nonsensical” (p. 225). After purportedly scrutinizing prior studies, Burt
and Simons went on to brand entire bodies of carefully collected and meticulously ana-
lyzed scientific evidence as useless, and even “preposterous” (p. 236). Burt and Simons
then proceeded to tell readers that behavioral genetic findings are “implausible” and that
behavioral genetic research rests on a “dubious foundation” (p. 223). In the end, they
claimed to have exposed the critical flaws of behavioral genetic research.
But did they expose any fundamental flaws of behavioral genetics? Did they present the
readers of Criminology a fair and impartial assessment of behavioral genetics research?
Did they delve deeply into the vast body of behavioral genetic literature, into the technical
aspects of assumption violation, biased parameter estimates, and erroneous conclusions?
Or, instead, did they join past critics and reify arguments already shown to be unsubstan-
tiated by empirical evidence? Clearly, as even Burt and Simons recognized, “most of the
arguments” in their article “are not original” (p. 225). Does repeating arguments origi-
nally proposed in the 1970s, and refuted shortly thereafter, make them relevant today? In
short, can we believe Burt and Simons have ascertained unbiased and definitive proof that
behavioral genetic models are wrong? Have they done something no other statistician,
theorist, or behavioral geneticist in the last four decades has been able to accomplish?
In the following pages, we show that the criticisms of behavioral genetic models ad-
vanced by Burt and Simons have not only been answered by dozens of prior studies but
also that they are wrong. We show this mathematically, with an in-depth examination
of the basis of twin designs, with our own simulation models that directly illustrate the
impact of violating assumptions on heritability estimates, and by examining 61 empirical
studies that have tested one of the “critical assumptions” pointed out by Burt and Simons:
the EEA. In the end, we show that the violations of behavioral genetic assumptions hardly
qualify as “fatal flaws” that can be used as a justification to abandon heritability studies.
Indeed, the evidence to this fact is overwhelming and should reduce any confidence read-
ers extended to the Burt and Simons article.
If showing mathematically that Burt and Simons grossly exaggerated their claims is
not sufficient, we then examine the scholarship underpinning their critique of heritability
studies. We show, in detail, where they misquoted scholars, where they misrepresented
1. MZ =monozygotic and DZ =dizygotic.
4 BARNES ET AL.
study findings, and where they labeled political ideologues as “experts” in behavioral ge-
netics. We show where they selectively cited some studies, relied heavily on others, and
at the same time failed to recognize a voluminous literature that would temper, or even
wholly disprove, their claims. Finally, we will show their call for a “post-genomic” crim-
inology to be superfluous, even fanciful, serving only to distract criminologists from the
hard work yet to be done in the “genomic” age.
We acknowledge that Burt and Simons critiqued other aspects of behavioral genetic re-
search designs including adoption-based designs and twins reared apart designs. Although
the literature has provided ample support for these additional designs and the validity of
the findings stemming from them (Bouchard et al., 1990; Pinker, 2002; Plomin, DeFries,
et al., 2013), we do not thoroughly discuss this line of research for four reasons. First, and
as Burt and Simons acknowledged, the classical twin design is the “main ‘workhorse’ used
in behavioral genetics to estimate heritability” (p. 229). Second, comprehensive overviews
and empirical assessments of both adoption (Heath et al., 1985; Kendler et al., 2013;
Sacerdote, 2004) and twins reared apart studies (Bouchard et al., 1990; Gottfredson, 2010;
Segal, 2012) have been completed previously. Third, findings garnered from studies using
the classical twin design, the adoption design, and the twins reared apart design largely
converge, revealing that genetic influences explain approximately 50 percent of the vari-
ance in antisocial phenotypes (Ferguson, 2010; Mason and Frick, 1994; Miles and Carey,
1997; Rhee and Waldman, 2002). Fourth, there is simply insufficient space to provide a
thorough discussion of these additional research designs in this article.
ASSUMPTIONS OF THE CLASSICAL TWIN DESIGN
The classical twin design, like any statistical model, rests on a foundation of testable as-
sumptions. If those assumptions fail, then estimates drawn from the classical twin design
may be upwardly or downwardly biased. For this reason, the popular adage “all models
are wrong but some are useful” (Box and Draper, 1987: 424) is important to keep in mind
when considering the suitability of the classical twin design or, for that matter, any sta-
tistical model examining human behavior. In addition to the standard probability theory
assumptions that permeate all methods of statistical inference, several assumptions are
unique to the classical twin design. The heart of the Burt and Simons attack on behavioral
genetic studies rests on the violations of assumptions of the classical twin design, particu-
larly the EEA. Although we provide a discussion of other assumptions in appendix A in
the online supporting information, in the following sections, we offer a detailed analysis
of the EEA (which will upwardly bias heritability estimates when violated) along with
what is perhaps the other most frequently discussed assumption of classical twin designs:
random mating (which will downwardly bias heritability estimates when violated).2Un-
like Burt and Simons, who did not provide any empirical evidence of the consequence(s)
of violating the assumptions underlying classical twin designs, we also provide a compre-
hensive presentation of the available literature including the results of empirical studies
that provide direct estimations of the degree to which parameter estimates will be biased
when such assumptions are violated.
2. Additional supporting information can be found in the listing for this article in the Wiley Online
Library at http://onlinelibrary.wiley.com/doi/10.1111/crim.2014.52.issue-4/issuetoc.
VALIDITY OF TWIN RESEARCH 5
MODEL IDENTIFICATION AND THE ACE MODEL
In much the same way that a criminologist might partition variance within individuals
and between individuals in a data set with a multilevel model, a behavioral geneticist seeks
to partition variance in a measured trait into genetic and environmental components.
The total variance in any trait results from five separate influences: 1) additive genetic
factors (A), 2) dominant genetic factors (D), 3) epistatic genetic factors (I), 4) common
(or “shared”) environmental factors (C), and 5) nonshared environmental factors (E).
Thus, the total variance of any trait (referred to as a phenotype;Vp) can be expressed as
(for a detailed discussion presented by Purcell, see Plomin, DeFries, et al., 2013: 373–7):
V
p=A+D+I+C+E+2Cov(A,D)+2Cov(A,I)+2Cov(A,C)
+2Cov(A,E)+2Cov(D,I)+2Cov(D,C)+2Cov(D,E)+2Cov(I,C)
+2Cov(I,E)+2Cov(C,E)(1)
where Ais the additive genetic effect, Dis the dominant genetic effect, Iis the epistatic ge-
netic effect, Cis the common (shared) environmental effect, Eis the nonshared environ-
mental effect and error, Cov(A,D) is the covariance between Aand D, Cov(A,I) is the co-
variance between Aand I, Cov(A,C) is the covariance between Aand C, Cov(A,E)isthe
covariance between Aand E, Cov(D,I) is the covariance between Dand I, Cov(D,C)is
the covariance between Dand C, Cov(D,E) is the covariance between Dand E, Cov(I,C)
is the covariance between Iand C, Cov(I,E) is the covariance between Iand E, and
Cov(C,E) is the covariance between Cand E.
The solution for Vpis intuitive and in line with standard probability/counting theory
that notes the variance of a sum is calculated as the summation of the unique variance of
variable 1, the unique variance of variable 2, and two times their covariance. Several prac-
tical issues have prevented researchers from estimating all parts of the equation simulta-
neously. As noted by Purcell (in Plomin, DeFries, et al., 2013: 377), “by definition, the
additive genetic influences are independent of dominance deviations. That is, Cov(A,D)
will necessarily equal zero.” Thus, this term may be omitted safely. A similar conclusion
can be reached for the Cov(A,I) parameter and the Cov(D,I) parameter. In terms of the
environmental parameters, common (shared) environmental factors cannot, by definition,
overlap with nonshared environmental factors, allowing us to omit the Cov(C,E) param-
eter. Of the remaining parameters, Dand Iare often omitted by making an additional
assumption (see appendix A in the online supporting information). Similarly, the remain-
ing covariance parameters [i.e., Cov(A,C), Cov(A,E), Cov(D,C), Cov(D,E), Cov(I,C),
and Cov(I,E)] often are omitted by making additional assumptions (see appendix A in
the online supporting information). Relying on these assumptions, we are left with the
well-known ACE model:
V
p=A+C+E
Once we have simplified the equation into the A, C, and Eparameters, two additional
assumptions are necessary to identify the model. These two assumptions, along with the
consequences of violating them, are outlined in the next section.
6 BARNES ET AL.
ASSUMPTION 1: HUMANS MATE RANDOMLY (NO ASSORTATIVE MATING)
Assumption
The assumption of random mating is required to fit the classical twin design because
this assumption defines the variance–covariance matrix for DZ twins. As is shown in ap-
pendix B in the online supporting information, the covariance between DZ twins for any
trait is expressed as ½A+C. The assumption of random mating defines the ½portion of
the equation. When two humans reproduce, germ cells formed through meiosis (which
is the process of genetic mixing for sexual reproduction) fuse and form the zygote that
will eventually develop into an independent and genetically unique human (Carey, 2003;
McConkey, 2004). As a consequence of meiosis and fertilization, a quasi-random 50 per-
cent of the genes from each parent (i.e., a random 50 percent maternally and a random
50 percent paternally) are combined to create the offspring, which will not be genetically
identical to either parent at all genetic loci. Thus, one may assume that any offspring pro-
duced by two humans will be 50 percent similar to their mother and 50 percent similar to
their father at the distinguishing loci. Based on this logic, full siblings and DZ twins are
50 percent similar, on average, within the distinguishing regions of the genome.
Given that the violation of this assumption actually deflates heritability estimates, it
represents an important counterpoint to the assumptions that are frequently listed as
producing inflated heritability estimates. Against this backdrop, it is somewhat surpris-
ing that Burt and Simons did not include any discussion of the consequences of violating
the assumption of random mating in their article.3Perhaps Burt and Simons omitted a dis-
cussion of assortative mating because they were unaware of the assortative mating litera-
ture. In a prior study, however, Simons et al. (2002: 404) noted, “Past research on dating
and mate selection has demonstrated strong support for the idea of assortative mating
(Collins, 1985).” In the same paper, Simons and colleagues tested for assortative mating,
found evidence of mate assortment, and ultimately criticized existing theories for not hav-
ing incorporated a discussion of assortative mating. Why the issue of assortative mating
was not given direct attention in the Burt and Simons critique is, therefore, unclear.
The Impact of Assumption Violation
The process of meiosis ensures that, on average, full siblings and DZ twins will share
50 percent of their distinguishing genotype if mating is random. If mating is not random,
then the 50 percent figure may be an underestimate, which would lead to underestimates
of the Aparameter in the ACE model. To see why this is the case, consider the impact
of assortative mating (i.e., nonrandom mating) on the DZ variance–covariance matrix.
Substituting hypothetical values and solving for Aclearly indicates that a trait that is
completely influenced by additive genetic factors (A) will produce a heritability estimate
3. Burt and Simons provided an indirect acknowledgment of the assumption of random mating by
stating that classical twin designs assume “[t]he genes of MZ twins are 100 percent identical and are
approximately 50 percent identical for DZ twins” (Burt and Simons: 230). Although this statement
necessitates the assumption of random mating, this point is not made clear by Burt and Simons
and is perhaps even obfuscated by lumping the assumption of 100 percent genetic similarity of MZ
twins together with the assumption of 50 percent (on average) genetic similarity for DZ twins. The
former relies on principles of molecular biology that define the DNA structure of MZ twins.
VALIDITY OF TWIN RESEARCH 7
for the Aparameter that is below 1.00 because of a violation of this assumption. Specif-
ically, if a hypothetical trait were completely the result of additive genetic factors, then
we should expect estimates of Ato, on average, hover around 1.00. But, if the assump-
tion of random mating is violated, then the ½Avalue in the DZ correlation matrix will
be too low, producing an overall estimate of Athat is below 1.00 because the correlation
for MZ twins will be 1.00 but the correlation for DZ twins will be above the expected
.50; the value will reflect the amount of genetic correlation that is actually present. When
this occurs in practice, the ACE model (which uses the ½A) attributes any portion of the
DZ correlation that is above .50 to the shared environment (C). Thus, violation of the
random mating assumption leads to inflated estimates of the shared environment effect
and deflated estimates of heritability.
Empirical Evidence of Assumption Violation
An impressive body of research exists regarding mate similarity across a variety of de-
mographic factors (Vandenburg, 1972) and other traits/behaviors such as level of educa-
tion (Domingue et al., 2014; Mare, 1991) and political affiliation (Alford et al., 2011). One
may have expected such correlations among these factors, but the focus for this discus-
sion is on whether mates tend to correlate in their antisocial behavior (or across important
correlates of antisocial behavior, such as self-control). Mental illness, addiction, and drug
use display a pattern of similarity between mates that suggests the presence of assortative
(or nonrandom) mating for antisocial behavior to some degree (Jacob and Bremer, 1986;
Merikangas and Spiker, 1982; Rhule-Louie and McMahon, 2007). Findings from a diverse
line of scholarship, moreover, suggest humans select mates who display similar levels of
antisocial and aggressive behavior (e.g., Boutwell and Beaver, 2010; Boutwell, Beaver,
and Barnes, 2012; Capaldi, Kim, and Owen, 2008; Haynie et al., 2005; Krueger et al., 1998;
Rhule-Louie and McMahon, 2007; Rowe and Farrington, 1997). Despite some variation,
each of these analyses has reported a positive and statistically significant correlation be-
tween mates for antisocial outcomes, and there is relative consistency in the strength of
the observed associations across studies. Krueger and colleagues (1998) reported mating
assortment for antisocial behavior in couples that was around r=.50. This correlation
is similar in magnitude (depending on the trait in question) to the correlations reported
in other studies (Boutwell and Beaver, 2010; Boutwell, Beaver, and Barnes, 2012; Rowe
and Farrington, 1997). In short, empirical evidence shows that sexual partners do not mate
randomly, and thus, the assumption of random mating is likely consistently violated in the
classical twin design on many behavioral phenotypes (Alford et al., 2011).
Calculating and Simulating the Impact of Assumption Violation
To demonstrate the consequences of violating the assumption of random mating in the
ACE model, we followed a two-pronged approach. First, we created a simple script in
the computer program Rthat would estimate A, which will be referred to with the her-
itability estimate notation of h2to reduce confusion (i.e., Awill be used to refer to the
“actual” or “true” level of additive genetic influence and h2is used to refer to the “esti-
mated” level of additive genetic variance that is retrieved from the ACE model). The
coefficient for h2was estimated for different levels of “true” Aand at different val-
ues of the degree to which DZ twins actually overlap in distinguishing genes that influ-
ence the trait in question. The latter element—the actual level of genetic overlap for
8 BARNES ET AL.
Table 1. Impact of Violating the Assumption of Random Mating on h2
Estimates
“True” Parameter Values
A=.25, C=.50 A=.50, C=.25
Difference Difference
from “True” from “True”
Calculation Results h2Estimate Parameter h2Estimate Parameter
Genotypic similarity of DZs =.50 .250 .000 .500 .000
Genotypic similarity of DZs =.52 .240 –.010 .480 –.020
Genotypic similarity of DZs =.54 .230 –.020 .460 –.040
Genotypic similarity of DZs =.56 .220 –.030 .440 –.060
Genotypic similarity of DZs =.58 .210 –.040 .420 –.080
Genotypic similarity of DZs =.60 .200 –.050 .400 –.100
Average h2Average c2Average h2Average c2
Simulation Results Estimate Estimate Estimate Estimate
Genotypic similarity of DZs =.50 .252 .497 .503 .246
90 percent range (.162–.339) (.417–.577) (.395–.610) (.143–.344)
Genotypic similarity of DZs =.55 .222 .526 .447 .301
90 percent range (.131–.318) (.441–.610) (.333–.561) (.195–.410)
Genotypic similarity of DZs =.60 .200 .548 .401 .347
90 percent range (.116–.293) (.468–.623) (.305–.513) (.249–.439)
DZ twins—was set to range between .50 (i.e., no violation of the assumption) and .60
(a fairly substantial departure from the assumption). These values were chosen because
the evidence presented previously suggests the level of assortative mating for antisocial
outcomes is likely to range between r=.25 and r=.50, which may translate to a DZ geno-
typic relatedness score that ranges between .01 and .10 higher than the assumed level of
.50 (Lynch and Walsh, 1998: 158). The Rscript is provided in appendix E in the online
supporting information. The results from the calculations are presented in table 1 under
the panel labeled “Calculation Results.”
As shown in table 1, the h2estimate decreases as the level of genotypic similarity for
DZ twins increases above .50 (i.e., as the assumption begins to fail). Interestingly, the de-
gree of bias is greater under conditions where additive genetic factors account for more
variance in the trait; bias is greater when “true” A=.50 compared with when “true”
A=.25. When “true” Ais set to .50, then a .01 increase in the genotypic similarity of
DZs translates to a reduction in the h2estimate of 1 percentage point. The same increase
in the genotypic similarity of DZs amounts to a reduction in the h2estimate of .5 per-
centage points when “true” A=.25. The results from the calculations also are presented
graphically in figure 1.
Our second approach to demonstrating the impact of violating the assumption of no
assortative mating was to produce two series of computer simulations: once where the
“true” parameters were set to A=.25, C=.50, and E=.25 and a second time where
the “true” parameters were set to A=.50, C=.25, and E=.25. In both simulations,
the actual level of genetic overlap for DZ twins was set to vary among .50, .55, and .60.
Variance–covariance matrices from 500 simulated data sets—each with 500 MZ twin pairs
VALIDITY OF TWIN RESEARCH 9
Figure 1. Heritability Bias at Different Levels of Random Mating
Violation and Different Levels of “True” Aand “True” C
0.50 0.52 0.54 0.56 0.58 0.60
−0.10 −0.08 −0.06 −0.04 −0.02 0.00
Parameter Bias Due to Assortative Mating
Genotypic Similarity of DZs
Amount of Bias in h2
"True" A=0.25, "True" C=0.50
"True" A=0.50, "True" C=0.25
and 500 DZ twin pairs—for each condition were analyzed with the latent variable ACE
modeling program provided in the OpenMx package (Neale and Maes, 2004) available in
R. As shown in the bottom panel of table 1, the simulations confirmed the results from the
calculations discussed previously by revealing that the Aparameter is underestimated and
that the Cparameter is overestimated when the random mating assumption is violated.
When the level of genotypic similarity among DZ twins is set to .55 (i.e., a violation of
the assumption), the ACE model underestimates the Aparameter by roughly 3 percent-
age points, on average, when “true” A=.25. The simulations revealed that heritability
estimates are approximately 5 percentage points lower than the “true” value when the
genotypic similarity of DZ twins is .55 and “true” A=.50. As the genotypic similarity
among DZ twins is set to higher values, the degree of underestimation of Aincreases. In-
versely, the Cparameter is consistently overestimated as the level of genotypic similarity
among DZ twins increases.
Conclusion:When the assumption of random mating fails, a portion of the variance that
should be attributed to Ais instead attributed to C, and this bias is more substantial for
traits with higher levels of “true” additive genetic variance. Assortative mating therefore
downwardly biases heritability estimates (i.e., h2) and upwardly biases the estimate of the
10 BARNES ET AL.
common/shared environment (i.e., c2). These results are contrary to the general thrust of
the critique offered by Burt and Simons.
ASSUMPTION 2: THE EQUAL ENVIRONMENTS ASSUMPTION
Assumption
Genetic factors are solely responsible for the increased similarity between MZ twins
relative to DZ twins. This assumption is well known and often is referred to as the equal
environments assumption (EEA). In terms of the equations presented in appendix B in the
online supporting information, the EEA allows one to solve for A,C, and Eby assuming
C(i.e., the shared environment) carries a similar influence across all sibling pairings (MZ
and DZ twins in the current example). Given that the crux of the Burt and Simons critique
rests on the violation of this assumption, we pay close attention to the issue. We also
should note that should this assumption prove valid or if violations of the assumption have
a trivial influence on heritability estimates, then the Burt and Simons argument against
the validity of heritability studies will be drawn into serious question.
The Impact of Assumption Violation
If the EEA fails, then the ACE model equations along with the variance–covariance
equations will be biased. The most likely direction of bias vis-`
a-vis an EEA violation is
that Awill be overestimated, Cwill be underestimated, and Eshould be unaffected. The
logic behind this conclusion is simple: If certain types of siblings/twins receive more C
than other types of siblings/twins, then those siblings will be more similar to one another
as a result of having greater levels/impacts of C. This becomes problematic for the classi-
cal twin design because critics often argue that MZ twins will receive greater levels of C
relative to DZ twins because they tend to look more similar to one another. In addition,
MZ twins are the same sex but roughly half of all DZ twins are opposite sex. For these
reasons, critics claim the greater similarity observed for MZ twins may simply be because
they receive more similar treatment from the environment rather than their greater level
of genetic similarity, effectively violating the EEA. Directly related to these observations,
critics of twin research have correctly pointed out that MZ twins tend to have more envi-
ronments in common relative to DZ twins, including parental treatment (Kendler et al.,
1994), closeness with one another (Horwitz et al., 2003; Lykken et al., 1990), belonging
to the same peer networks (McGuire and Segal, 2013), being enrolled in the same classes
(Cronk et al., 2002), and being dressed similarly (Cronk et al., 2002; Loehlin and Nichols,
1976).
In light of these observations, the EEA has been the subject of much debate and has
sparked the production of a large literature that spans several decades and cuts across
multiple fields of study (e.g., Allison et al., 1996; Bulik, Sullivan, and Kendler, 1998; Con-
ley et al., 2013; Cronk et al., 2002; Derks, Dolan, and Boomsma, 2006; Eaves, Foley,
Silberg, 2003; Felson, 2014; Hannagan and Hatemi, 2008; Hatemi et al., 2009; Kendler
and Gardner, 1998; Kendler et al., 2000; Littvay, 2012; Rose et al., 1988; Scarr and Carter-
Saltzman, 1979). Certain critics have cited violations of the EEA as a damning limita-
tion for twin research in sociology (Horwitz et al., 2003), political science (Beckwith and
Morris, 2008; Charney, 2008; Suhay and Kalmoe, 2010), educational psychology
(Richardson and Norgate, 2005), and social psychology (Simons, Beach, and Barr, 2012).
VALIDITY OF TWIN RESEARCH 11
Perhaps the most aggressive critic of twin studies has been Joseph (2004, 2006, 2010) who
questioned the findings of heritability studies because of the presence of unequal environ-
ments (i.e., a violated EEA). Burt and Simons simply echoed Joseph’s (2004) sentiments,
stating: “[W]e think it is unquestionably the case that violations of the EEA are inflating
heritability and decreasing shared environmental effects to a substantial degree” (p. 236,
emphasis added). Like many before them, Burt and Simons failed to acknowledge that
their discussion of the potential effects of violating the EEA was an empirically testable
issue (Littvay, 2012).
Empirical Evidence of Assumption Violation
To assess the current empirical reality, we performed an exhaustive search of the lit-
erature bearing directly on the EEA. Appendix D in the online supporting information
displays all of the studies that have examined the EEA and that were located through a
systematic search of the literature using ProQuest, Web of Science, and PsycINFO. Key
search words and terms used to locate such studies included “EEA,” “equal environ-
ments assumption,” and “unequal environments.” Any matches that provided an empiri-
cal assessment or comprehensive overview of the EEA were selected. In total, this search
process, along with the inclusion of publications that were cited by Burt and Simons, gen-
erated 61 pieces of scholarship.
The bolded studies at the top of appendix D in the online supporting information rep-
resent the studies that were cited by Burt and Simons. As shown, Burt and Simons cited
a total of nine studies, only two of which included an empirical analysis.4One of these
studies (Horwitz et al., 2003) examined whether the EEA was violated but did not ex-
amine the effect of such violations on heritability estimates. The other empirical study
(Cronk et al., 2002) included by Burt and Simons was actually miscited. Burt and Simons
cited this study as evidence of a violated EEA, but the primary conclusions of the study
clearly indicated (even within the abstract) that controlling for the presence of unequal
environments did not result in a significant change in the heritability estimates for any of
the examined outcomes. Indeed, the average change in heritability estimates was only .02
(or 2 percentage points). Based on the consistency of their findings, Cronk et al. (2002)
concluded that “[o]ur results support the validity of the assumptions of equal environments,
upon which conclusions from these twin studies are based” (p. 836; emphasis added).
A close inspection of appendix D in the online supporting information reveals Burt
and Simons cherry-picked studies that align directly with their argument that violations
of the EEA are pervasive and undermine heritability estimates. The studies included in
appendix D in the online supporting information tested for violations of the EEA across
1,233 environments and violations were detected in only 112 of them (9 percent). Of the
61 studies available, only 13 concluded that the EEA was invalid (21 percent), but of these
only 6 performed any empirical analysis (10 percent), and none of these studies actually
estimated the impact of the presence of unequal environments on heritability estimates.
However, several studies examined directly the effect of violating the EEA on heritabil-
ity estimates. Appendix D in the online supporting information includes 11 studies that
4. One of the cited articles (Richardson, 2011) was a summary piece published in an online, non–peer-
reviewed newsletter, GeneWatch. Another study is unpublished and three others are books that
provide no new data. After taking these citations into account, Burt and Simons cited a total of two
empirical pieces of literature, only one of which actually tested the impact of unequal environments
on heritability or shared environmental estimates.
12 BARNES ET AL.
estimated the impact of unequal environments on heritability estimates, with the average
effect being an upward bias of about .012 (or about 1 percentage point) in the heritabil-
ity estimate. What this necessarily means is that the widely cited heritability estimate of
.50 for antisocial behaviors may be upwardly biased by .012 and the “true” Ais actually
closer to .488. However, we should note that these estimates do not take into account
violations of other assumptions (e.g., assortative mating; the presence of evocative gene–
environment correlation) that may downwardly bias heritability estimates. Nonetheless,
as appendix D in the online supporting information indicates, Burt and Simons did not
provide readers with a systematic and unbiased account of the EEA literature.
The results presented in appendix D in the online supporting information are reveal-
ing and show convincingly that the EEA likely has little-to-no influence on heritability
estimates. These conclusions are echoed by Felson (2014; see also Felson, 2012: ii), who
performed “the most comprehensive evaluation of the equal environments assumption
to date.” Using the Midlife Development in the United States (MIDUS) survey, Felson
examined 32 outcomes that tapped a range of psychological and sociological domains. In
addition, he examined a diverse set of environmental similarity measures that included
similarity of childhood environment, proportion of lives lived together, frequency of con-
tact, level of psychological intimacy, and how often each twin shared advice with his or
her co-twin. Importantly, these environmental similarity measures contain several experi-
ences that are cited often as evidence of unequal environments. The results revealed that
only 1 of the 58 estimated models led to a significant change in h2estimates after account-
ing for the similarity measures. Although the remaining models revealed nonsignificant
differences, such differences were still modest averaging around .10 (or 10 percentage
points). Importantly, the changes in h2after accounting for the environmental similarity
measures did not follow any discernable pattern and were not consistent over time, in-
dicating that any potential bias introduced is likely random and does not systematically
bias h2or c2estimates. Felson (2012: ii) concluded that “[t]he flaws of twin studies are not
fatal, but rather seem no worse (and may be better) than the flaws of the typical causal
study that relies on observational data.”5
Although numerous studies examining the potential moderating effects of environmen-
tal similarity on h2and c2estimates have found that violations of the EEA result in sta-
tistically nonsignificant parameter deviations (e.g., Allison et al., 1996; Borkenau et al.,
2002; Bulik, Sullivan, and Kendler, 1998; Cronk et al., 2002; Felson, 2014; Hettema, Neale,
and Kendler, 1995; Kendler et al., 1994; Kendler and Gardner, 1998; Klump et al., 2000;
Littvay, 2012; Loehlin and Nichols, 1976; Morris-Yates et al., 1990; Plomin, Willerman,
and Loehlin, 1976; Scarr and Carter-Saltzman, 1979), additional methodologies also have
been employed. Perhaps the most empirically rigorous method of assessing the validity
of the EEA is through the use of misclassified twin samples. More specifically, in samples
where zygosity is determined via responses to self-report questionnaires tapping confus-
ability, misclassifications can occur where MZ twins are initially classified as DZ twins
and vice versa. Once genotyping tests are conducted, however, these classifications are
corrected. Several studies have drawn on this unique situation to employ a more robust
test of the EEA (Conley et al., 2013; Gunderson et al., 2006; Kendler et al., 1993; Xian
5. As with the empirical assessments listed in table 2, Felson (2012) came to this conclusion without
assessing the impact of violating other assumptions (e.g., assortative mating) that may downwardly
bias heritability estimates.
VALIDITY OF TWIN RESEARCH 13
et al., 2000). This situation presents an ideal way to test whether the EEA is violated and
whether such violations result in meaningful changes in estimates of h2and c2. Assuming
that unequal environments result in biased h2estimates, DZ twins that are mistaken as
MZ twins should more closely resemble one another across the phenotypes of interest
relative to correctly identified DZ twins. Similarly, if critics of twin studies are correct,
then MZ twins incorrectly classified as DZ twins should be less similar to one another
across the examined phenotypes relative to correctly classified MZ twins.
In the most recently performed misclassification study, Conley et al. (2013) used three
distinct samples—the National Longitudinal Study of Adolescent Health (Add Health),
the Child and Adolescent Twin Study in Sweden, and the Minnesota Twin Family Study
(MTFS)—to examine whether unequal environments (measured as zygosity misclassifi-
cation) produce biased h2estimates. Importantly, Conley et al. examined a wide range of
outcome measures, many of which are commonly used by criminologists, including height,
weight, body mass index, depression, attention deficit hyperactivity disorder, delinquency,
and high-school GPA. The results revealed that heritability estimates are not significantly
inflated when the EEA is violated (such as when twins are misclassified). In addition, vio-
lating the EEA actually resulted in artificially deflated heritability estimates in some of the
estimated models, leading the authors to conclude that “it seems reasonable to take re-
sults from an ACE model more or less at face value” (p. 425). Once again, these findings
indicate that any potential bias stemming from violations of the EEA is likely random,
as evidenced by the significant deflation of h2estimates in some models. Importantly,
these results directly align with previous studies that analyzed misclassified twin pairs
(Gunderson et al., 2006; Kendler et al., 1993; Xian et al., 2000), revealing a consistent
overall pattern of findings.6
Germane to the discussion of random bias because of a violation of the EEA is the
premise by Burt and Simons that including opposite-sex DZ twins is a methodologically
unsound practice of twin research. To justify their argument, they relied on two points.
First, they referred to a “voluminous” literature regarding differences in experiences be-
tween sexes. However, they offered no citations to contextualize the type of experiences
to which they refer nor did they discuss how those differences in experiences are relevant
to their argument against twin studies in terms of the effect on heritability estimates. This
oversight is important because it is left to the reader’s imagination to figure out those
experiences and the ways in which such experiences could affect heritability estimates.7
Second, Burt and Simons suggested that heritability estimates are always inflated by
including opposite-sex twins in statistical analyses. This, however, is not the case. In-
cluding opposite-sex twins in genetic analysis is a conventional practice as it allows for
the testing of sex differences in heritability and environmental influences. Statistical
6. Another interesting manner by which the EEA has been assessed was recently completed in two
studies by Segal and colleagues (Segal, 2013; Segal, Graham, and Ettinger, 2013). In these studies,
the authors employed a sample of genetically unrelated look-alikes (i.e., non-kin doppelganger
pairs). Critics of twin studies have noted that a violation of the EEA is likely to result in part
because of the degree to which people (MZs) who look more alike are treated more similarly
(compared with DZs). Segal and her colleagues illustrated that there was virtually no concordance
across a wide variety of personality characteristics among the unrelated look-alike pairs, suggesting
the EEA is upheld.
7. Although it may seem intuitive that including different-sex twins may produce biased results, sci-
ence advances based on empirical evidence and not on intuition or common sense. Therefore, such
a claim requires evidence of the effect of including different-sex twins on estimates of heritability.
14 BARNES ET AL.
modeling strategies have been developed and others have been modified to handle sam-
ples containing opposite-sex twin pairs (e.g., Purcell and Sham, 2003). Even more re-
vealing is that there is not consistent evidence showing significant sex differences when it
comes to heritability estimates (Meier et al., 2011; Viding et al., 2004), which indicates that
opposite-sex twin correlations are not significantly different from same-sex twin correla-
tions. The findings generated from studies that analyze samples containing opposite-sex
twin pairs showed exactly this, with opposite-sex twin correlations commonly not being
significantly different from same-sex twins (Meier et al., 2011). Interestingly, and in direct
contradiction to what Burt and Simons claimed, sometimes the opposite-sex twin correla-
tions are greater in magnitude when compared with same-sex twin correlations (Saudino,
Ronald, and Plomin, 2005).
Burt and Simons cited two studies (Meier et al., 2011; Saudino, Ronald, and Plomin,
2005) to support their claim that including opposite-sex twins in studies results in a vi-
olation of the EEA. Interestingly, the findings and conclusions drawn from these two
studies provide evidence that runs counter to the Burt and Simons claim. More specifi-
cally, although Meier et al. (2011) found significant differences in cross-twin correlations
between same-sex and opposite-sex DZ twins wherein same-sex DZ twins (both males
and females) possessed greater levels of concordance relative to opposite-sex DZ twins
across some of the examined outcomes, they also reported that the correlations were not
significantly different between opposite-sex and same-sex twins for some outcomes. The
other study cited by Burt and Simons (Saudino, Ronald, and Plomin, 2005) reported find-
ings wherein opposite-sex twin correlations were greater than same-sex twin correlations
for some of the examined outcomes. The key takeaway points are that 1) the inclusion
of opposite-sex twins is not an unconventional practice in behavioral genetic studies, 2)
these types of twin pairs can provide information as to potential etiological differences be-
tween males and females, and 3) including opposite-sex twins in statistical analyses does
not seem to have any consistent effect on biasing variance component estimates in any
systematic direction.
Calculating and Simulating the Impact of Assumption Violation
In an effort to provide a more direct example of the biasing effects of EEA violations
on estimates of h2and c2, Burt and Simons argued that “if the shared environmental effect
is .3 for MZ twins and .2 for DZ twins, then heritability estimates will be inflated by 20%”
(p. 232). These values were garnered from an unpublished manuscript by Suhay and
Kalmoe (2010), and even though they represent arbitrary values from a hypothetical ex-
ample, Burt and Simons presented them as empirical evidence favoring an inflated h2
estimate and deflated c2estimate stemming from a violation of the EEA. However, this
example is overly simplistic and highly problematic in two important ways. First, the de-
gree to which an EEA violation inflates h2is directly tied to the degree to which shared
environmental influences actually affect the trait (i.e., “true” C). As “true” C decreases,
the biasing effect of the EEA decreases. This information has bearing on the Suhay and
Kalmoe calculation because they arbitrarily chose values for the MZ and DZ correlations
but did not specify the “true” value for C. So, the reader is left without a baseline value
in which to determine how much h2has been inflated and c2deflated.
In addition, the amount of error introduced by the EEA in Suhay and Kalmoe’s (2010)
calculations is understated, erroneously leading to the conclusion that a small violation
VALIDITY OF TWIN RESEARCH 15
amounts to large biases. The authors stated: “[t]o see more clearly why this is the case,
imagine a small amount of environmental error has crept into the relevant MZ and
DZ trait correlations” (Suhay and Kalmoe, 2010: 5). They then provided a hypothetical
example where c2MZ =.3 and c2DZ =.2. The “small amount of environmental error” is
reflected in the MZ correlation being 50 percent higher than the DZ correlation: hardly a
“small amount of environmental error.” Moreover, their mathematical discussion of the
biasing impact of the EEA is too simplistic. Violations of the EEA will operate by “down
weighting” the Cparameter for DZ twins. To see why this is the case, recall that the EEA
assumes the amount of Cis equivalent across MZ and DZ twins. If the assumption fails,
then the only logical outcome (speaking both conceptually and mathematically) is that
MZ twins will receive 100 percent of Cbut DZ twins will receive less. Thus, we must
“down weight” the proportion of Cthat is received by the DZ twins to test the violations
from the EEA. In this way, Suhay and Kalmoe’s example is misleading because the values
assigned for the cross-twin correlations correspond to DZ twins sharing only 67 percent
of Ccompared with the amount of Cshared by MZ twins. This represents a significant
violation of the EEA and begs the question of whether the seemingly innocuous example
is realistic.
Because of the problematic and overly simplistic nature of the example offered by
Suhay and Kalmoe (2010), we provided a more realistic and comprehensive test of the
EEA using a series of calculations and computer simulations. Mathematically, violations
of the EEA were introduced to the model by “down weighting” the Cparameter for DZ
twins. Thus, the level of Cpresent in the MZ variance/covariance matrix is the “true” level
of Cand the amount of Cpresent in the DZ variance/covariance matrix must be “down
weighted” to demonstrate an EEA violation (see appendix B in the online supporting
information for the variance/covariance matrices).
When this strategy was applied to the calculations introduced previously (see appendix
E in the online supporting information for the Rscript), evidence was produced to support
the notion that EEA violations will inflate h2as a function of the degree to which the
EEA is violated. Table 2, which is structured similarly to table 1, presents the results from
a series of calculations where the EEA was purposely violated under two conditions:
1) where “true” A=.25 and “true” C=.50 and 2) where “true” A=.50 and “true”
C=.25. Also, consistent with the previous analysis, the results from the calculations were
plotted and are presented in figure 2. As shown in both the table and the figure, departures
from the EEA consistently lead to overestimates of h2and underestimates of c2. Note,
however, that the bias in h2was weaker when “true” Cwas set to the lower value.
The results from the computer simulations—again, 500 simulated data sets were
generated for each condition and the ACE model was estimated using OpenMx in R—
corroborated the results presented in the calculations portion of the table. Both the calcu-
lations and the simulation results indicate that departures from the EEA lead to overes-
timates for h2and underestimates of c2, but these biases are weaker as the “true” impact
of shared environmental factors decreases.
Conclusion:Taken together, this body of findings provides clear evidence suggesting
that the EEA is typically not violated and that estimates of h2and c2garnered from
behavioral genetic models are relatively unbiased. Even in situations where the EEA is al-
most certainly violated (e.g., misclassified twins), such studies have indicated that estimates
of h2and c2are highly robust and experience only substantively minor changes (Carey,
16 BARNES ET AL.
Table 2. Impact of Violating the Equal Environments Assumption on h2
Estimates
“True” Parameter Values
A=.25, C=.50 A=.50, C=.25
Difference Difference
from “True” from “True”
Calculation Results h2Estimate Parameter h2Estimate Parameter
% C shared by DZ =100 .250 .000 .500 .000
% C shared by DZ =98 .270 .020 .510 .010
% C shared by DZ =96 .290 .040 .520 .020
% C shared by DZ =94 .310 .060 .530 .030
% C shared by DZ =92 .330 .080 .540 .040
% C shared by DZ =90 .350 .100 .550 .050
Average Average Average Average
Simulation Results h2Estimate c2Estimate h2Estimate c2Estimate
% C shared by DZ =100 .246 .502 .496 .252
90 percent range (.163–.331) (.419–.582) (.391–.599) (.147–.355)
% C shared by DZ =95 .302 .448 .528 .222
90 percent range (.206–.397) (.362–.538) (.413–.639) (.118–.333)
% C shared by DZ =90 .348 .401 .548 .201
90 percent range (.251–.460) (.297–.483) (.439–.676) (.081–.302)
2003). When differences in h2were detected, no discernable pattern emerged in such differ-
ences indicating that any potential bias introduced was likely random (Cronk et al., 2002;
Eaves et al., 2003; Felson, 2012, 2014). Additionally, in instances where Burt and Simons
argued there is an obvious violation of the EEA (i.e., inclusion of opposite-sex DZ twins),
the effect on heritability estimates also seems to be random. Simulations and an analysis
of all of the existing data on the EEA converge to reveal that when the EEA is violated,
estimates are inflated by between 1 and 5 percentage points.
This conclusive set of findings is perhaps one potential explanation for the minimal dis-
cussion of the EEA within the criminological literature. The debate has been settled and
the EEA is not a sufficient reason to dismiss heritability studies or the estimates gleaned
from these studies. Similar to how a large literature stretching back several decades has
clearly defined the robustness of the assumptions that accompany simple linear regression
and the minimal biasing effects that may result when such assumptions are violated, a sim-
ilar line of research has demonstrated that the EEA does not result in any systematic bias
within h2and c2estimates. We are certain that by using the vague and subjective inclu-
sion criteria Burt and Simons relied on to accumulate biosocial studies critiqued in their
article we could identify hundreds of criminological studies that have actively violated
the basic assumptions of linear regression (e.g., the assumption that errors are identically
[normally] and independently distributed across the sample space) and have not formally
acknowledged such assumptions. It is important to note, however, that all the studies
included in the Burt and Simons table (pp. 234–5) referenced scholarship bearing on the
classical twin design assumptions and that the authors of those studies have written exten-
sively about these assumptions (Beaver, 2009, 2013). Although Burt and Simons painted
VALIDITY OF TWIN RESEARCH 17
Figure 2. Heritability Bias at Different Levels of EEA Violation and
Different Levels of “True” Aand “True” C
1.00 0.98 0.96 0.94 0.92 0.90
0.00 0.02 0.04 0.06 0.08 0.10
Parameter Bias Due to EEA Violation
% C Shared by DZs
Amount of Bias in h2
"True" A=0.25, "True" C=0.50
"True" A=0.50, "True" C=0.25
a picture of deception at the hands of biosocial criminologists, the truth is that the EEA is
frequently not discussed because it has no consistent or meaningful impact on heritability
estimates.
Despite the presence of a cohesive set of empirical findings that span multiple litera-
tures and decades, indicating that the EEA does not systematically bias heritability es-
timates, Burt and Simons failed to acknowledge the existence of this literature. Rather,
they cited sources that did not include analyses capable of backing their claims. In the
interest of scholarly transparency, we have brought the full body of literature that em-
pirically assesses the EEA to light. After assessing this body of evidence, our sentiments
align closely with those of Carey (2003: 301, emphasis in original)8:
Taken together, all these lines of evidence suggest that the equal environments as-
sumption meets the definition of a robust assumption. A robust assumption is one
that might actually be violated, but the effect of violating the assumption is so small
8. Our reading of the available evidence also aligns with that of Rowe and Osgood (1984: 534) who
stated, “Although [the EEA] is often questioned, the empirical evidence is largely supportive.”
18 BARNES ET AL.
that the estimates and substantive conclusions are not altered. For example, Newto-
nian physics is incorrect, but one can use Newtonian principles to build a bridge or
design a skyscraper. In these situations, the assumptions of Newtonian physics are
robust even though they are technically wrong.
JOINT VIOLATION OF THE RANDOM MATING ASSUMPTION AND THE
EEA
As revealed in the calculations and simulation results presented previously, violations
of the random mating assumption and violations of the EEA lead to opposite-sign effects
on heritability estimates. This result is not surprising. Indeed, it is both intuitive and has
been anticipated by scholars for more than two decades. Raine (1993: 58–9) noted:
It is concluded that methodological problems of twin studies are just as likely to de-
crease heritability estimates as they are to artificially inflate them. Rutter et al. (1990)
have suggested that in all probability these effects will tend to cancel each other out.
It is important, therefore, not to ignore research findings from twin studies. In spite of
its limitations, the study of twins remains a key method in the field of behavior genet-
ics, and future twin studies of crime using up-to-date biometric modeling are likely to
make increasingly important contributions to genetic research on crime.
The finding of opposite-sign effects leads to at least two important questions or con-
cerns that warrant close consideration. First is the question of whether one assumption
is more likely to be violated than the other, and if so, what are the “downstream” con-
sequences of this reality? Given the evidence presented in this analysis, a conservative
answer is one that acknowledges the violation of both assumptions in everyday practice.
This leads to a second question or concern. Specifically, if both assumptions are violated
in practice, then how much and in which direction are heritability estimates biased? This
question is empirical, meaning it can be tested using the calculations above and using the
same simulations described previously. To be brief, we augmented the calculations and
simulations to include violations of both assumptions simultaneously. We estimated the
calculations and simulations twice: 1) where “true” A=.25 and “true” C=.50, and 2)
where “true” A=.50 and “true” C=.25. Figures 3 and 4 reveal the findings from these
analyses in three-dimensional space. First, figure 3 shows the joint impact of violating the
assumption of random mating and violating the EEA when “true” A=.25 and “true”
C=.50. As was noted, when the two assumptions were analyzed separately, the EEA
tends to have a greater biasing impact at lower values of “true” Aand higher values of
“true” Ccompared with violations of the assumption of random mating under these same
conditions. The three-dimensional plot displays this same finding.
The plane presented in the box in figure 3 represents all of the h2estimates gleaned
from calculations under the different permutations of the two conditions. Note that the
plane touches the vertical axis closest to the reader, and this intersection represents the
“true” Avalue (i.e., h2=.25). If we follow the horizontal axis to the right, the axis la-
beled “% CShared by DZs,” we see that h2estimates tend to increase as the EEA Bias
increases (which is reflected by lower values of Cfor DZs). If we follow the horizontal
axis to the left, the axis labeled “Genotypic Similarity of DZs,” we see that h2estimates
tend to decrease as the assumption of random mating is violated. The overestimates of
VALIDITY OF TWIN RESEARCH 19
Figure 3. Three-Dimensional Plot of the Joint Bias of EEA Violation
and Random Mating Violation
"True" A=0.25, "True" C=0.50
0.90
0.92
0.94
0.96
0.98
1.00
0.50
0.52
0.54
0.56
0.58
0.60
−0.05
0.00
0.05
0.10
% C Shared by DZs
Genotypic Similarity of DZs
Amount of Bias in h2
h2that are presented on the right side of the box are more substantial at the right edge
of the plane, representing a case where the EEA is violated but the assumption of ran-
dom mating is not violated. As we move toward the center of the plane, we see the h2
estimates are not as inflated, representing the “cancelling out effect” of violating the
assumption of random mating. At the back corner of the box, where the plane touches
the vertical axis, h2is estimated to be .30 (.05 points higher than the “true” A). This
point represents the case when both assumptions are violated in their most extreme form
(at least in terms of the parameters set for this study). Thus, the evidence presented in
figure 3 suggests that violations of the EEA, even when the assumption of random mat-
ing is violated, may lead to slightly overestimated values of h2when “true” Ais in the
moderate-to-low range and “true” Cis in the moderate-to-high range.
The same exercise was repeated for the case when “true” A=.50 and “true” C=
.25. The results from this set of calculations are presented in three-dimensional space in
figure 4. In a general sense, the results reported in figure 4 mirror those from figure 3.
The vertical axis closest to the reader reflects the “true” A(i.e., h2=.50). The horizontal
axis to the right reveals the impact of EEA bias, and the horizontal axis to the left reveals
the impact of assortative mating (i.e., violating the assumption of random mating). The
primary difference between figure 3 and figure 4 is the latter indicates that violations
of the assumption of random mating are more consequential for h2estimates compared
with violations of the EEA. Figure 4 clearly displays a steeper downward slope on the
20 BARNES ET AL.
Figure 4. Three-Dimensional Plot of the Joint Bias of EEA Violation
and Random Mating Violation
"True" A=0.50, "True" C=0.25
0.90
0.92
0.94
0.96
0.98
1.00
0.50
0.52
0.54
0.56
0.58
0.60
−0.10
−0.05
0.00
0.05
% C Shared by DZs
Genotypic Similarity of DZs
Amount of Bias in h2
left horizontal axis compared with the upward slope on the right horizontal axis. Finally,
the point at which the plane touches the vertical axis in the far corner of the box shows
the impact of violating both assumptions in their most extreme form (at least in terms
of the parameters set for this study). Here, the h2estimate (h2=.45) is lower than the
“true” Aby .05 points. Thus, when “true” Ais in the moderate-to-high range and “true”
Cis in the moderate-to-low range, the cumulative effect of jointly violating the EEA and
the assumption of random mating is that h2will tend to be underestimated.
Conclusion:When the assumptions of random mating and the EEA are considered in
tandem, calculation and simulation results reveal that violations of one assumption tend
to counterbalance violations of the other. Based on these results, we cannot conclude
that violations of the EEA will overstate heritability because violations of the assump-
tion of random mating lead to underestimates. Scholars should, therefore, be skeptical
of the unilateral dismissal of heritability studies by Burt and Simons because of, among
other reasons, their lack of a discussion of the assumption of random mating. Our conclu-
sions therefore reinforce the comments of Rowe and Osgood (1984: 537) who stated that,
“Although individual studies can be faulted on one ground or another, the overall pattern
of results is so regular that to ignore genetic factors requires either outlandish assumptions
or a very selective reading of the literature.”
VALIDITY OF TWIN RESEARCH 21
CERTAIN ASSUMPTIONS NEED NOT APPLY: ALTERNATIVE METHODS OF
ESTIMATING h2
The Burt and Simons claim that EEA violations bias h2estimates was dramatically
overstated, especially in light of random mating assumption violations and the finding
that the level of bias depends on the values of the “true” parameters. The available em-
pirical literature, along with the results from our calculations and simulations, support the
current position of the classical twin design representing a robust method. Nonetheless,
staunch critics may still argue that the EEA limits the viability of the classical twin de-
sign. As a result, we offer one final point. Allegations of an inflated heritability estimate
in twin studies can be assessed using methodologies that do not rely on the assumptions
of the twin method. If these methodologies produce results that align closely with those
produced by the classical twin design, then previous concerns over violations of the EEA
and violations of the assumption of random mating can be alleviated. One such alter-
native method for generating heritability estimates for phenotypic variance is known as
genome-wide complex trait analysis (GCTA; Yang et al., 2011). In an oversimplified state-
ment, GCTA “scans” the entire genome for every individual in the sample (sample sizes
often number in the thousands) and runs thousands of statistical analyses (correcting the
pvalues for multiple testing bias). Next, the association between the measured genes and
the total trait variance can be used to estimate the portion of variance in the trait that is a
result of genetic factors. Importantly, GCTA does not employ kinship pairs as it exploits
chance genetic similarity in single-nucleotide polymorphisms (SNPs) between unrelated
individuals to calculate heritability estimates for phenotypic variance (Plomin, DeFries,
et al., 2013; Yang et al., 2010). Given that GCTA does not employ the types of kinship
pairs that prevail in the classical twin design, the assumptions of the classical twin design,
including the EEA, need not apply.9
Because GCTA is a cutting-edge technique, the number of published studies employing
the method to estimate the heritability of various phenotypes is limited. In the first study
using GCTA, Yang et al. (2010) generated an estimate of the proportion of variance in
height explained by more than 300,000 SNPs garnered from more than 3,900 unrelated
respondents. The results of the GCTA analysis indicated that these 300,000+SNPs ex-
plained 45 percent of the variance in height. To be clear, unlike twin-based studies, the
GCTA assesses the collective additive influence of the measured SNPs to estimate her-
itability. In this way, the heritability estimates gleaned from a GCTA can be compared
with those provided by twin-based studies to establish the amount of “missing heritabil-
ity” between the two methods.10 Thus, the 45 percent figure represents the amount of
variance in height that is caused by the SNPs included in the GCTA. Of crucial impor-
tance is a comment about the study made by the authors in a subsequent publication.
9. Except, of course, the assumption that non-kin doppelgangers will only be as similar as their genetic
profiles (see footnote 6).
10. Therefore, unlike what Burt and Simons claimed, researchers in behavioral and molecular genetics
have such strong confidence in the results of twin-based studies that they create novel methods
to assess the difference between the broad heritability estimates produced by twin-based studies
and the minimal effects observed in genome-wide association studies (GWAS) and single-gene
association studies. In other words, far from calling for an end to twin-based studies that produce
estimates of heritability, these experts employed such estimates as a benchmark from which to
assess sophisticated molecular genetic analyses.
22 BARNES ET AL.
Visscher, Yang, and Goddard (2010) provided their rationale for excluding close relatives
by indicating their desire to ensure that any observed effect was a result of genetic fac-
tors rather than of nongenetic factors captured by the shared environment. The authors
noted, however, that “leaving these few pairs [of close relatives] in or out made very little
difference to the results” (Visscher, Yang, and Goddard, 2010: 521). Consequently, the
GCTA study by Yang et al. (2010) supports two conclusions of twin-based research on
the variance in height: 1) Variance is primarily caused by genetic effects and 2) shared
environmental effects have little influence on the variance. Although this study is limited
to assessing variance in height, it illustrates that the twin-based method is not hopelessly
biased as there is convergence in illustrating the effect of genetic factors.
GCTA also has been employed in assessments of schizophrenia (Lee et al., 2012) and
other psychiatric disorders (Lee et al., 2013), components of personality (Vinkhuyzen
et al., 2012), behavioral inhibition (McGue et al., 2013), and intelligence in both child-
hood (Benyamin et al., 2013) and adulthood (Davies et al., 2011). The findings across
these studies illustrate that variance in the phenotypes under examination is influenced
by variance in the SNPs included in the analyses. As noted, these types of studies are not
susceptible to the assumptions of the twin-based research; yet they produce estimates of
h2that often are within the confidence intervals produced by the classical twin design.
In an effort to assess directly the relationship between GCTA studies and the twin-based
methodology, Plomin, Haworth, et al. (2013) compared estimates of heritability produced
by the two methodologies for a variety of phenotypes (weight, height, general cognitive
ability, nonverbal cognitive ability, verbal cognitive ability, and language ability) within
the same sample. The results of the analyses indicated that at least 40 percent of the h2
estimates gleaned from the classical twin design were accounted for by the genetic effects
captured by the GCTA (see table 1 in Plomin, Haworth, et al., 2013). In terms of general
cognitive ability, the authors found that approximately two thirds of the h2estimate pro-
duced by the classical twin design also was identified by the GCTA. Overall, the study
provided strong support for the methodologies employed in twin-based studies. Indeed,
the authors (p. 566) concluded by noting:
Although GCTA analysis and other DNA-based methods are exciting additions to
behavioral genetic research, we suggest that traditional quantitative-genetic methods,
such as twin studies and adoption studies, will continue to make important contribu-
tions to understanding how genotypes become phenotypes, in part because twin and
adoption studies are as much studies of environmental influence as they are of genetic
influence.
Specific to the study of criminal behavior, an examination by Bentley and colleagues
(2013) employed a technique similar to GCTA called “candidate systems of genes (CSG)”
(p. 1074). Using data from the Nurse Family Partnership Program, Bentley and col-
leagues examined the variance in a latent antisocial variable that was a function of
variance in a latent genetic variable (based on eight different polymorphisms). The re-
sults of the analyses indicated that the latent genetic variable was significantly predictive
of antisocial behavior (β=.413, p=.006) and that the latent genetic variable explained
16 percent of the variance in antisocial behavior. When compared with genome-wide
association studies on antisocial behaviors where single SNPs have rarely reached sta-
tistical significance (e.g., Tielbeek et al., 2012), these results are remarkable. Selecting
VALIDITY OF TWIN RESEARCH 23
just eight polymorphisms (out of a potential pool numbering in the thousands), the au-
thors were able to account for a considerable proportion of the variance in antisocial
behavior.
Conclusion:When multiple divergent methods converge to illustrate a consistent finding,
it is logically reasonable and empirically sound to accept as valid the results of the diver-
gent methods. The primary reason for such a conclusion is the nonoverlapping assumptions
underlying the various methods. This dynamic is illustrated in the convergence in findings
between classical twin design studies and various molecular genetics methodologies. GCTA
and CSG studies are examples of methodologies that are not subject to the same assump-
tions as classical twin designs and yet provide convergence in terms of the differential influ-
ence of genetic and environmental factors on a variety of behavioral phenotypes, including
antisocial behavior. In direct contrast to the appraisal provided by Burt and Simons, the
most cutting-edge research emanating from molecular genetics relies heavily on the find-
ings of classical twin design studies and is continually providing empirical support for the
validity of such studies.
SOCIAL CONSTRUCTION OF BIOLOGICAL REALITY
We have shown empirically that violations of the assumptions of behavioral genetics
studies do not invalidate heritability estimates. This is not a matter of opinion but a
matter of mathematical evidence. Under certain conditions, our calculations and simu-
lations revealed that heritability estimates will be slightly upwardly biased (probably no
more than 5–10 percentage points). Under other conditions, heritability estimates will
be downwardly biased (probably no more than 5–10 percentage points). Under the most
likely condition, where multiple violations occur simultaneously, the biasing influences of
assumption violations wash out, with upwardly biasing factors canceling downwardly bi-
asing factors. Moreover, the overall pattern of findings flowing from the 61 studies exam-
ining the EEA revealed the same conclusions offered by our calculations and simulation
data. Needless to say, no “fatal flaw” in behavioral genetic methodologies or assumptions
has been discovered and the conclusion that “all of these models are biased toward inflat-
ing heritability and underestimating shared environmental influences” (Burt and Simons,
2014: 226, emphasis in original) is unequivocally incorrect.
We turn now to secondary critiques of the Burt and Simons article. Next, we show
where Burt and Simons presented a misleading portrait of the behavioral genetics liter-
ature. We examine their oversights, beginning with their misrepresentation of the litera-
ture and their misunderstanding of the value of heritability in modern behavioral genetics
research (i.e., epigenetics). Although less important than the presented mathematical ev-
idence validating heritability studies, these problems highlight the various distortions of
evidence and prior scholarly work endemic in the Burt and Simons article.
SELECTIVE CITING AND MISREPRESENTING RESEARCH
The questions raised against heritability studies by Burt and Simons are empirical issues
that can be addressed with available data. Burt and Simons, however, did not empirically
assess the veracity of their criticisms. Instead, and as we have already shown, Burt and
Simons supported their criticisms by selectively citing from the literature, pulling snippets
of information from a study that seem to support their beliefs, or citing heavily from
24 BARNES ET AL.
scholarship that was dismantled long ago in other fields of study, practices that some may
refer to as the “social construction of reality.”
For example, the selection criteria for the studies included in table 1 in the Burt and Si-
mons (pp. 234–5) article were highly subjective. After a closer examination, we identified
three primary issues with their table and the search criteria used to create it. First, when
we attempted to replicate the vague search criteria offered by Burt and Simons, Google
Scholar revealed dozens of relevant studies, all of which were excluded from their table
1. Unsurprisingly, many of the omitted studies do not necessarily conform to the primary
thrust of the Burt and Simons article (e.g., Barnes, Beaver, and Boutwell, 2011; Beaver
et al., 2008) and were not identified by Burt and Simons. For example, despite identifying
numerous studies conducted by Beaver et al., they overlooked at least two of his stud-
ies that directly estimated the heritability of crime and/or delinquency and that included
multiple measures of the environment (Beaver, 2011a; Beaver, DeLisi, et al., 2009). One
such paper, for example, directly examined gene–environment interactions with 13 envi-
ronmental measures drawn from the Add Health data (Beaver, 2011a).11 In addition, at
least two omitted studies were published in Criminology (Barnes, Beaver, and Boutwell,
2011; Beaver et al., 2008). Second, Burt and Simons gave no empirical reason why they
used a 2008 cut-off. Had they searched Criminology prior to 2008, they would have had
to include additional studies, studies that also found heritability estimates on delinquency
of .50 (e.g., Haynie and McHugh, 2003).12 Third, some of the information included in
their table 1 is highly misleading or even completely incorrect. More specifically, in their
discussion of studies that produce heritability estimates, Burt and Simons said the follow-
ing: “[These studies] compare individual phenotypes across varying degrees of genetic re-
lationships and use these comparisons to estimate genetic and environmental influences
without actually measuring either” (p. 229, emphasis in original). We point out that 50
percent of the studies they chose to include in the table actually did measure an environ-
mental variable.
In addition to arguing against the replication of twin studies, Burt and Simons singled
out the Add Health data set as being problematic because it is used in most heritability
studies by biosocial criminologists. They pointed out that the entire twin sample nested
within the larger probability sample includes only 289 MZ twin pairs and 452 DZ twin
pairs for a total of N=1,482 twins. We are somewhat perplexed by this as Simons has built
his career on the FACHS data that include a little more than 800 respondents. In terms of
sample size, the twin subsample of the Add Health data dovetails nicely with the FACHS
data. We should further note that it is not uncommon for entire perspectives, theories,
and disciplines (at certain times) to be guided by only one data set. For example, Far-
rington’s work in developmental/life-course research has been based on data from a little
more than 400 males from England (Piquero, Farrington, and Blumstein, 2007), Sampson
11. In addition, Burt and Simons failed to acknowledge a special issue in Journal of Criminal Justice
that includes multiple heritability studies and that was available online in early 2013 (Tuvblad and
Beaver, 2013).
12. Although Haynie and McHugh (2003) claimed to have completely accounted for heritability in
subsequent models, these subsequent models were estimated incorrectly. As a result, the conclu-
sion of this study should have been that the heritability of delinquency is approximately .50, not
.00, and that the loss of statistical significance was caused by inflation in the standard error relative
to the drop in coefficient resulting from the incorrect application of the DeFries–Fulker analysis.
VALIDITY OF TWIN RESEARCH 25
and Laub’s (1993) life-course work has been based on 1,000 White males from Boston,
and the National Youth Survey guided much of what was known about criminological
theory for 10–15 years. To our knowledge, there has not been any serious attempt to limit
publications on these samples or to isolate the scholars who have used such data. Burt
and Simons continued to disparage the Add Health data by pointing out that the mea-
surement of key constructs is less than ideal. Perhaps this is partially true, but fallibility
in the measures would simply deflate heritability estimates because measurement error is
captured by the nonshared environmental estimate (i.e., e2). What makes these criticisms
all the more surprising is that Simons has pointed out in no less than five separate publica-
tions that the Add Health data represent an ideal data set to examine genotypic influences
on social behaviors (Simons, Beach, and Barr, 2012; Simons and Lei, 2013; Simons et al.,
2011, 2012, 2013).
Beyond the omission of relevant research and curious selective derision of the Add
Health data, Burt and Simons also selectively quoted scholars, resulting in an overall
distortion of such scholars’ original intentions. This is particularly salient when Burt and
Simons quoted Moffitt’s (2005) seminal review. Burt and Simons (p. 226, emphasis in
original) wrote:
Although evidence from the different methods are used to “provide convergent find-
ings,” given that “each of the primary designs used by behavioral geneticists has its
own Achilles heel(s)” (Moffitt, 2005: 57), we show that all of these models are biased
toward inflating heritability and underestimating shared environmental influences.”
Burt and Simons used Moffitt’s words to make the argument that heritability estimates
are biased and, as a result, should be abandoned. However, when reading Moffitt’s words
from the original article, we see that the actual quote was (Moffitt, 2005: 57):
A fundamental assumption guiding this review is that sturdy inferences ought to be
drawn from a cumulative body of studies whose methods differ as much as possible,
but provide convergent findings about the same construct. As we have seen, each of
the primary designs used by behavioral geneticists has its own Achilles heel(s), but
fortunately, each design’s idiosyncratic flaws are offset by compensatory strengths
of the other designs. As a consequence, although particular studies and particular
designs may be subject to critique, this does not invalidate inferences derived from
the entire cumulative evidence base.
A second example of misrepresentation of previous scholarship by Burt and Simons is
evident when they argued that biosocial criminologists frequently ignore the assumptions
of the classical twin design, particularly the EEA. To reinforce this, they quoted Beaver
(2011b: 86 [sic]) as saying “the only reason that MZ twins should be [sic] more similar
than DZ twin pairs [sic] is because they share twice as much genetic material” (Burt and
Simons: 236). Clearly, Burt and Simons are highlighting that Beaver (2011b), and other
biosocial criminologists, strategically failed to inform readers about twin-based assump-
tions that, if violated, could be causing MZ twins to be more similar to each other than
DZ twins. Again, however, if we go to the original Beaver (2011b: 87) article, we see that
the full, unedited quote reads: “As a result, if the assumptions of twin-based research are
met, the only reason that MZ twins should be phenotypically more similar than DZ twins
is because they share twice as much genetic material” (emphasis added). Burt and Simons
26 BARNES ET AL.
therefore edited the Beaver (2011b) quote and misrepresented his words in such a way
as to provide support for their argument. When the actual unedited quote from Beaver
(2011b) is read, the statement flatly contradicts their claim that biosocial criminologists
ignore the assumptions of twin-based research.
Where Burt and Simons selectively cited some studies and incorrectly cited and quoted
others, they also relied heavily on highly questionable sources. They cited Joseph (1998,
2001, 2004, 2006, and 2010), for example, an amazing 70 times in their article and online
supporting information. This averages out to one citation of Joseph per page. Relying
so heavily on a single source makes it difficult to see how Burt and Simons introduced
anything that Joseph had not already discussed. Moreover, Burt and Simons cited as evi-
dence an unpublished manuscript (Suhay and Kalmoe, 2010) and a newsletter (Richard-
son, 2011) from a website constructed and maintained by individuals politically opposed
to gene-behavior research. Their selection of just a few sources of information becomes
more suspect when juxtaposed against appendix D in the online supporting information,
which indicates that Burt and Simons could have easily selected from the 60+scholarly
studies that empirically assessed the EEA.
As we have shown, the call by Burt and Simons for a biosocial criminology “rooted in
reality” rests on a social construction of reality (p. 14). The oversights, misrepresentations,
anecdotes, distortions, and misquotes paint a carnival-mirror-like picture of heritability
studies, their uses, and their findings. Studies that would complicate their narrative were
left out of their discussion. Scholars that support their narrative were given tremendous
weight. Quotes taken from others were highly edited, even to the point that a reading of
the original quote goes on to provide conclusions directly counter to their position.
FAILURE TO APPRECIATE THE BENEFITS OF HERITABILITY STUDIES
FOR MODERN BEHAVIORAL RESEARCH
It was not until biosocial criminologists challenged the discipline to take seriously ge-
netic and biological influences that the sociological tide turned to a more integrated focus
(Beaver and Wright, 2013). With the use of behavioral genetic approaches, including her-
itability studies, biosocial criminologists brought empirical evidence to a field uninitiated
in the use of twin and extended-family designs. Most criminologists have simply ignored
the findings flowing from such studies, but notable exceptions exist (Benson, 2013; Cullen,
2011). This lack of acknowledgment, occurring against a longstanding backdrop of disci-
plinary bias, likely encourages criminologists to accept the Burt and Simons assertions
despite the evidence we provide (Walsh and Ellis, 2004). Before scholars make this jump,
however, we encourage readers to consider the following benefits of heritability studies.
First, heritability studies are the “first step” in a long march toward a true biosocial
criminology, a criminology that is disinterested in whether biology or the environment
gets the credit for causing crime but instead cares about getting the puzzle pieced to-
gether correctly. Biosocial criminologists have published an array of studies on gene
×environment interactions (GxEs) and gene–environment correlations (rGEs) (Barnes,
Beaver, and Boutwell, 2013; Beaver, Wright, and DeLisi, 2008; Schwartz and Beaver,
2011), they have published studies using extended family designs with alternative be-
havioral genetic assessments (Beaver et al., 2009; Connolly and Beaver, 2014), and they
have published studies using molecular markers in search of direct and interactive ef-
fects (Beaver et al., 2013; Schwartz and Beaver, 2014; Wright et al., 2012). Moreover,
VALIDITY OF TWIN RESEARCH 27
they have written books on the interlocking qualities of nature and nurture over the life
course (Benson, 2013; Wright, Tibbetts, and Daigle, 2008). Heritability studies thus rep-
resent only one part of the arsenal of biosocial criminologists, an arsenal that is growing
in size and complexity.
Second, all statistical models have evolved and all have assumptions that are, more or
less, meaningful if violated. This applies equally to social statistics, which has undergone
evolution over time and is subject to a range of important assumptions. Hypothesis test-
ing, for example, encouraged the development of the general linear model, which mor-
phed into truncated variation models, which helped form the basis for complex trajectory
and other latent grouping analyses. Unsatisfied with the statistical limits of each approach,
scholars developed new approaches, such as hierarchical linear modeling and latent class
analysis. Not only did scholars develop each approach, we note, but also they empirically
tested what happens when each underlying statistical assumption is violated. Ordinary
least-squares (OLS) regression is undoubtedly the most used statistical technique in the
social sciences. The assumptions of OLS are known and have been tested thoroughly.
They are so well known that almost no scholar now discusses the assumptions of OLS
in their studies, even though most scholars continually violate those assumptions, such as
homoskedasticity and normally distributed errors. Should OLS regression be abandoned?
Of course not.
In a similar way, ACE models have evolved over time. They now can be used to exam-
ine the genetic and environmental covariation between traits (Loehlin, 1996) and can test
for sex differences (Boisvert et al., 2013). Highly complex behavioral genetic designs, in-
cluding genetic growth curves (McArdle and Plassman, 2009), Bayesian integration to as-
sess GxEs (Eaves, Foley, and Silberg, 2003), and “children of twins” designs (D’Onofrio
et al., 2007) emerged out of basic heritability studies. Our point is as follows: Scholars
should not abandon research or research methods; instead, they should work to revise
their methodologies and statistical models to address known problems.
Third, heritability studies and their partitioning of variance into genetic and en-
vironmental sources have led scholars to a better, more nuanced understanding of
environmental factors. For example, family processes and parenting behaviors tied to
offspring conduct are clearly tangled in the complex web of biology and environment
(Harris, 1998). As McGue (2010) and others (Pinker, 2002) have noted, by ignoring bio-
logical influences scholars were led to erroneous conclusions about the effects of parents
and families on crime—conclusions that brought harm to the lives of parents and chil-
dren. Scholars were so locked into their standard social science paradigm, however, that
it took the work of Rowe (1994) and subsequently Harris (1998) to show how the ele-
ments of the nonshared environment were important to understanding why some children
were influenced by family processes while other children in the same household were not.
Heritability studies provided these insights, and they led to more refined studies into par-
enting and families (Beaver, 2008; Harris, 1998; Rowe, 1994; Wright and Beaver, 2005).
If that example is insufficient, then consider that heritability studies provided the first
evidence that drug addiction and alcoholism were not the products of “bad morals”
but of genetically influenced sensitivity to substances. Heritability studies also provided
the first evidence that ADHD, conduct disorder, obsessive-compulsive disorder, autism
spectrum disorders, and other psychiatric problems were not caused by faulty environ-
ments or poor mothering but instead were strongly influenced by genetics. We could
go on, but the point should be clear: Behavioral genetics research has led to important
28 BARNES ET AL.
discoveries and to a more refined understanding of the types of environmental factors that
matter, the types that do not, and the types that matter for some people or in some con-
ditions but not in others. In short, lives have been improved by the results of behavioral
genetic studies. They have humanized domains of behavior, have led to more effective
social and pharmaceutical interventions, and have been instrumental in destigmatizing
complex social behaviors like homosexuality.13
Yet, Burt and Simons criticized the classical twin design by drawing on examples where
the logic of classical twin studies seems to break down. For example, they tell us that
“eyedness” shows the limited utility of heritability. They argue that our genome equips
all humans with two eyes and yet heritability estimates of “eyedness” based on standard
twin equations would be zero (.00). This is correct. Heritability estimates would be zero
(.00). However, counting eyes does not amount to quantifying and explaining variance;
in fact, in their example, “eyedness” is a constant and mathematical constants cannot
be explained by variables, including genetic variables, regardless of the methodological
design being used.14 The example is logically flawed.
They also argued that the partitioning of variance into genetic and environmental
sources is nearly impossible because of the constant interaction between genes and the
environment. Both Plomin, DeFries, et al. (2013) and Harris (2006) have responded to
this criticism and have dismantled the often-cited example of trying to quantify the area
of a rectangle (phenotype) by discussing the relative contributions of the width (genes)
and the height (environment). Clearly, the area of a rectangle is the product of width
and height. As Plomin, DeFries, et al. (2013: 89–92) noted, though, “if we ask not about
a single rectangle but about a population of rectangles, the variance in areas could be
due entirely to length, entirely to width, or both.” In the “damned rectangle” example,
as Harris (2006) called it, width and height (similar to genes and environment) are being
applied to a single rectangle. In reality, behavior geneticists examine samples contain-
ing numerous “rectangles” of many different sizes. When viewed in this way, it makes
sense to quantify variance in the area of rectangles based on differences in length and
height. What this necessarily means is that for a single individual, his or her genes and
environment in interaction contribute to his or her phenotypic score, but when examin-
ing phenotypic variance in a sample of individuals, it is possible to partition variance into
genetic and environmental components.
Instead of partitioning variance, biosocial criminologists, according to Burt and Simons,
should explore GxEs, epigenetic processes, and social neuroscience. The problem, how-
ever, is that much of the GxE literature is under heavy criticism and epigenetics is in its in-
fancy. Unfortunately, Burt and Simons couched their discussion of epigenetics and GxEs
in language that makes it seem as if this body of research is generally accepted and easily
13. We thank Steven Pinker (2002, and personal communication) for pointing out that behavioral
genetic research helped to remove the blame from parents for every “pathology” and helped to
dispel archaic ideas such as the belief that homosexuality is a contagious choice.
14. Unless, of course, the sample included Oedipus Rex and Moshe Dayan (thanks to Steven Pinker
[personal communication] for this tongue-in-cheek example). In this case, eyedness would vary as
a result of environmental factors. The most important point is that heritability explains variance,
not innateness or species-wide traits. Both variance and species-wide traits can be genetically in-
fluenced, but only the former is addressed by the classical twin design and behavior geneticists.
VALIDITY OF TWIN RESEARCH 29
replicated by neuroscientists, geneticists, and epigeneticists. In reality, nothing could be
further from the truth. Yet, Burt and Simons followed the lead of many before them who,
as Smith (2011: 539) stated, use epigenetics as “the currently fashionable response to any
question to which you do not know the answer.” Contrary to the picture painted by Burt
and Simons, epigeneticists are urging social scientists to be more cautious when discussing
epigenetic influences on social behavior. In the words of two preeminent epigeneticists,
Heijmans and Mill (2012: 4): “[E]pigenetics will not be able to deliver the miracles it is
sometimes claimed it will.” Perhaps unknown to sociologists who have hung their future
of the field on epigenetics, epigeneticists are confronted with the same problems genomic
and biosocial scientists are encountering. In addition, the GxE literature has been plagued
by failures to replicate, especially for novel GxEs (for an overview of the literature, see
Duncan, Pollastri, and Smoller, 2014), with some recent studies indicating that greater
than 90 percent of detected GxE effects are likely false positives (Duncan and Keller,
2011). As a result, some top journals have adopted screening criteria for GxE studies that
require replication of a novel GxE before the paper is considered for publication (Hewitt,
2012).
These points draw attention to one final issue worth considering. Specifically, we argue
that heritability studies are not biased and that scholars reconsider the call by Burt and
Simons for an “end” to heritability studies. There is still much to be gained from heri-
tability studies and the classical twin design. For instance, recent heritability studies have
shown that genetic factors underlie the etiology of criminological variables that may have
otherwise been assumed to be purely social in origin (e.g., Beaver, 2011b). Additionally,
twin studies provide an avenue by which scholars can more accurately estimate the impact
of environmental factors on antisocial behavior. Twin studies can be used to control for
genetic influences so that the impact of an environmental variable on antisocial behavior
can be analyzed without the confounding influence of genetic factors (e.g., Burt et al.,
2010). Thus, the value of the classical twin study has not depreciated.
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J. C. Barnes is an associate professor in the School of Criminal Justice at the Univer-
sity of Cincinnati. He is a biosocial criminologist whose research seeks to understand how
genetic and environmental factors combine to impact criminological phenomena. Recent
works have attempted to reconcile behavioral genetic findings with theoretical develop-
ments in criminology.
John Paul Wright is a professor of criminal justice in the School of Criminal Justice at
the University of Cincinnati. He is also a scholar in the Center for Social and Humani-
ties Research, King Abdulaziz University, Jeddah, Saudi Arabia. His work examines the
biological connections to violence.
Brian B. Boutwell is an associate professor of criminology and criminal justice in the
School of Social Work at Saint Louis University. His research interests include the evolu-
tion of complex outcomes including intelligence, violence, and chronic criminality.
Joseph A. Schwartz is an assistant professor in the School of Criminology and Criminal
Justice at the University of Nebraska at Omaha. His research interests include behavior
genetics, biosocial criminology, the association between intelligence and behavior, and
additional factors involved in the etiology of criminal behavior.
Eric J. Connolly is an assistant professor in the Department of Criminal Justice at
Pennsylvania State University, Abington. He received his Ph.D. in criminology and crim-
inal justice from Florida State University. His research interests include biosocial crimi-
nology, life-course/developmental criminology, and quantitative behavior genetics.
Joseph L. Nedelec is an assistant professor in the School of Criminal Justice at the
University of Cincinnati. He received his Ph.D. in criminology from Florida State Uni-
versity. His research interests include biosocial criminology, evolutionary psychology, in-
telligence, quantitative behavior genetics, and cybercrime.
Kevin M. Beaver is a professor in the College of Criminology and Criminal Justice at
Florida State University and Visiting Distinguished Professor in the Center for Social and
Humanities Research at King Abdulaziz University. His research focuses on the biosocial
underpinnings to antisocial behaviors.
VALIDITY OF TWIN RESEARCH 39
SUPPORTING INFORMATION
Additional Supporting Information may be found in the online version of this article at
the publisher’s web site:
Appendix A. Discussion of Additional Assumptions of Twin-Based Research
Appendix B. Mathematical Foundations of Behavioral Genetics
Appendix C. Latent Variable ACE Model
Appendix D. Comprehensive List of Studies Examining the Equal Environments
Assumption
Appendix E. RScript for Carrying Out Calculations of Assumption Violations
- CitationsCitations42
- ReferencesReferences169
- "In a series of simulations, the assumptions of differential susceptibility models were used to generate virtual data for large samples of monozygotic and dizygotic twins, and the results were compared with those reported in the empirical literature. Importantly, this method sidesteps possible issues concerning the validity of twin designs and their assumptions (for recent discussions see Barnes et al., 2014; Johnson, Penke, & Spinath, 2011). The question is whether the processes postulated by differential susceptibility models can reproduce the findings of twin studies when the data are analyzed in a comparable way, regardless of the validity of the underlying assumptions. "
[Show abstract] [Hide abstract] ABSTRACT: According to models of differential susceptibility, the same neurobiological and temperamental traits that determine increased sensitivity to stress and adversity also confer enhanced responsivity to the positive aspects of the environment. Differential susceptibility models have expanded to include complex developmental processes in which genetic variation interacts with exposure to early environmental factors, such as prenatal stress hormones and family conflict. In this study I employed a simulation approach to explore whether, and under what conditions, developmental models of differential susceptibility are compatible with the cumulative findings from twin studies of personality and behavior, which consistently show sizable effects of genetic and nonshared environmental factors and small to negligible effects of the shared environment. Simulation results showed that, to a first approximation, current alternative models of differential susceptibility are all equally compatible with the evidence from twin research; that sizable interaction effects involving individual differences in plasticity are plausible, but only if direct environmental effects are correspondingly weak; and that a major role of shared environmental factors is plausible in early development (consistent with the developmental mechanisms postulated in the differential susceptibility literature), but not in later development. These results support the general plausibility of differential susceptibility models and suggest some realistic constraints on their assumptions.- "This method of determining genetic risk rests on the Equal Environments Assumption (EEA), which suggests that " the environmental factors that are etiologically relevant to a given phenotype are no more likely to be shared by MZ twin pairs than DZ twins pairs " (LoParo and Waldman, 2014, p. 606). Importantly, recent meta-analyses have revealed that the vast majority of empirical examinations of the EEA support it (see Barnes et al., 2014; Felson, 2014), and that the assumption holds specifically in the case of childhood conduct problems (see LoParo and Waldman, 2014). "
[Show abstract] [Hide abstract] ABSTRACT: Rationale: A sizable body of research has examined associations between breastfeeding and various facets of offspring development, including childhood behavioral problems. Notwithstanding the number of studies on the topic, breastfeeding has not consistently been linked to child misbehaviors. Moreover, empirical examinations of whether breastfeeding is differentially predictive of conduct problems among individuals with varying degrees of genetic risk are lacking. Objective: The present study examines whether a short duration of breastfeeding and genetic risk interact to predict conduct problems during childhood. Methods: A genetically informative design is employed to examine a subsample of twins from the Early Childhood Longitudinal Study: Birth Cohort (ECLS-B), a nationally representative sample of American children. Results: The findings suggest that a shorter duration of breastfeeding only enhances the risk of offspring conduct problems among children who possess high levels of genetic risk. Conversely, longer breastfeeding durations were found to protect against childhood behavioral problems when genetic risk was high. Conclusions: Indicators of genetic risk may help to distinguish individuals whose behavioral development is most sensitive to the duration of breastfeeding. Future research should seek to replicate and extend these findings by considering genetic factors as potential markers of differential susceptibility to breastfeeding duration.- "Much of this research has focused on the etiological development of behavioral phenotypes, including the pervasiveness of genetic influences (Polderman et al., 2015; Turkheimer, 2000); the complex interplay between genetic and environmental influences (Dick et al., 2015; Duncan and Keller, 2011); and the intermediate role of various neurological, physiological, and hormonal processes in connecting genetic influences to behavioral outcomes (Raine, 2008). The field of criminology has also directly experienced the benefit of biosocial integration with studies demonstrating the collective and robust influence of both biological and environmental factors on various forms of criminal and antisocial behavior (Barnes et al., 2014), as well as many of the primary correlates emphasized in mainstream criminological theory and existing research (Harden and Tucker-Drob, 2011; Kendler and Baker, 2007). Although the speed with which such integration has occurred should be applauded, most of these efforts have been exclusively focused on the etiological development of various behavioral phenotypes. "
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