Encyclopedia of Personality and Individual Differences

Living Edition
| Editors: Virgil Zeigler-Hill, Todd K. Shackelford

Twin Studies

  • Frank M. SpinathEmail author
  • Juliana Gottschling
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-28099-8_1353-1



Twin studies are a key tool in quantitative behavioral genetic research. They rely on the fact that monozygotic and dizygotic twins share genes and environments to varying degrees. Models utilizing data from twins range from simple univariate genetic models to complex multivariate models dealing with cross-sectional as well as longitudinal information. More recent extensions of twin studies incorporate data from twins and their families.


Twin studies are considered a key tool in quantitative behavioral genetic research methods, in which genetically informative data (i.e., data from sibling pairs, families, and pedigrees) are used to infer on genetic and environmental causes of individual differences in one or more measured variables (i.e., phenotypes). Galton’s pioneering use of twins to study inheritance (Galton 1869) marks the beginning of the systematic investigation into the sources of individual psychological differences. The development of the twin method is usually also ascribed to Galton (1876) although it is uncertain whether Galton was aware of the distinction between monozygotic and dizygotic twins (see Boomsma et al. 2002).

Twin studies rely on the fact that monozygotic (identical; MZ) and dizygotic (fraternal; DZ) twins systematically vary in the extent to which they share genes and environmental influences. While MZ twins are assumed to share 100% of their genes, DZ twins share on average 50% of their segregating genes, the same percentage as non-twin siblings (Plomin et al. 2013). Twins also share many aspects of their environment, e.g., uterine environment, parental behavior, socioeconomic status, culture, or neighborhood.

Twin studies compare the resemblance of MZ and DZ twins in a given trait to explore the effects of genetic and environmental variance on a phenotype by leveraging on the known differences in genetic similarity between MZs and DZs (Neale and Maes 2004). Assuming the validity of the equal environment assumption (i.e., the assumption that the environments of MZs and DZs do not differ in any systematic way that would affect the trait under study; Plomin et al. 2013), greater phenotypic similarity between MZ twins compared to DZ twins is taken as evidence of the importance of genetic effects for the trait under consideration. Effectively, quantitative behavior genetic research has demonstrated that all human behavioral traits are heritable, that the effect of common environmental influences (i.e., the effect of being raised in the same family) is smaller than the effect of genes, and that a considerable portion of the variation in complex human behavioral traits is accounted for by environmental effects that are not shared by members of a family. These findings, termed the three laws of behavior genetics by Turkheimer (2000), marked the end of the so-called nature-nurture debate and led to a shift in behavior genetic research from investigating main effects of genes and environments to a more integrated understanding of the interplay of genes and environments.

However, rapidly developing novel molecular genetic methodologies and the availability of measured DNA newly stirred up the discussion as to whether the era of twin studies or, more generally, the classical quantitative behavioral genetic approach has come to an end (e.g., Charney 2012). In this regard, Turkheimer and Harden (2014) argue that molecular genetic methodologies themselves have a number of methodological difficulties and that there is no reason to “move on from one poorly understood method to the next, motivated not by the theoretical completion of the old paradigm but rather by the availability of new technology” (p. 160). Moreover, they make the case that figuring out how “heritable” traits are, had never been the core motivation of behavioral genetic studies of human complex traits. Heritability itself is defined as the proportion of the total phenotypic variation in a given trait accounted for by the total effect of the genotype (broad-sense heritability) or by the additive effect of the genotype (narrow-sense heritability). With that in mind, it becomes clear that heritability, as a standardized variance component, is not invariant across times and populations and, thus, is not a meaningful indicator of a causal effect from genotype to phenotype (Turkheimer and Harden 2014). The power of the twin design, even in times of molecular genetics, rather arises from the possibility to analyze associations between phenotypic traits while controlling for the heritability of these traits. That way, twin studies generate a significant but imperfect quasi-experimental control over nonexperimental phenotypic associations (Turkheimer and Harden 2014). Further, more recent developments in twin modeling extend the analytic focus to (step)parents, (half-)siblings, children, and partners of twins. By utilizing such extended twin family designs, researchers can investigate, e.g., the effect of assortative mating, the direct effects from parents on children, or the correlation between genes and environment. Finally, twin studies are also still important to investigate the interplay between genes and environments.


Quantitative behavioral genetic methods exploit familial relationships to estimate the contributions of genetic and environmental factors to individual differences in observed phenotype(s) (Franić et al. 2012). Every individual’s phenotype is determined by a genetic effect (G) and an environmental effect (E; also including measurement error) on the phenotype P (Plomin et al. 2013).
$$ P=G+E $$

Two genetic effects are distinguished, namely, additive genetic effects (A), which encompass the sum of all allelic effects within and across genes, and nonadditive genetic effects, which represent effects of alleles (dominance, D) or loci (epistasis, I) that interact with other alleles or loci. Both nonadditive genetic effects are completely shared in MZ twins, while DZ twins, on average, share only 25% of the dominance and 0% of the epistatic effects. However, as epistatic effects are hard to detect in nonexperimental designs, they are typically not estimated in twin studies. With respect to environmental effects, shared environmental effects (C; common environment) comprise all environmental conditions and experiences that contribute to the resemblance of family members. In contrast, non-shared environmental effects (E) are unique to each family member and therefore contribute to their phenotypic dissimilarity. It is important to note that environmental influences are defined in terms of their effect. Even if twins are exposed to the same event (e.g., parental divorce), the impact of this event on each individual twin may be different and would therefore contribute to the non-shared rather than the shared environmental effect. The best-known design to infer on those genetic and environmental effects is the classical twin design (CTD), which is based on the analyses of reared-together MZ and DZ twins (Boomsma et al. 2002).

The Classical Twin Design

Within the CTD, the known differences in the genetic resemblance of MZ and DZ twins are used to estimate the effects of unmeasured genetic and environmental factors by analyzing the patterns of similarities among MZ and DZ twins within an observed phenotype. A first indication of the relative impact of genetic and environmental influences can be obtained based on the observed phenotypic MZ and DZ twin similarity. The similarity is typically calculated as intraclass correlations (ICC; Shrout and Fleiss 1979), which partitions the total variance into within pair and between pair components (Neale and Maes 2004). Assuming that reared-together MZ twins share both, all of their genes and all shared environmental influences, any observed differences between them must be due to random (unique) effects. The ICC between MZ twins therefore provides an estimate of A + C. Reared-together DZ twins also share all of their common environment, but on average only 50% of their segregating genes. For any particular trait, then:
$$ {ICC}_{MZ}=A+C $$
$$ {ICC}_{DZ}=\frac{1}{2}A+C. $$
With a little bit of algebra, one can derive estimates for the A, C, and E components as follows (Falconer’s formula; Falconer and Mackay 1996):
$$ A=2\left({ICC}_{MZ}-{ICC}_{DZ}\right) $$
$$ C=2\ {ICC}_{DZ}-{ICC}_{MZ} $$
Because MZ twins only differ due to unique environmental effects (Plomin et al. 2013), E can be calculated as:
$$ E=1-{ICC}_{MZ} $$

The validity of the CTD is depending on specific assumptions (for an exhaustive discussion of this topic, we refer the reader to the literature, e.g., Plomin et al. 2013), i.e., the accuracy of the equal environments assumption and the absence of assortative mating, gene-environment interactions, gene-environment correlations, and nonadditive genetic effects, which are confounded with C in the CTD (Neale and Maes 2004). In more complex designs, however, it becomes feasible to estimate those effects directly, and also to tease apart shared environmental and nonadditive genetic effects.

In any case, quantitative behavioral genetics is never about any one individual. Rather, the focus is on disentangling the causes of phenotypic differences (i.e., the variance) in a population: for example, one could ask why some individuals develop a depression or become alcoholic. In a genetically informative sample, it is possible to estimate the variances of P, G, and E (Plomin et al. 2013), which gives:
$$ {V}_P={V}_A+{V}_C+{V}_D+{V}_E $$

Beginning in the late 1970s, quantitative behavioral genetics transitioned to modeling genetic covariance structures using maximum likelihood methods (Martin and Eaves 1977). Within this structural equation modeling (SEM) approach, genetic and environmental effects are modeled as the contribution of unmeasured (latent) variables to the phenotypic differences between individuals (Boomsma et al. 2002; Franić et al. 2012; Neale and Maes 2004). This model-fitting approach has numerous benefits, such as the possibility to test for gender and age effects, to compute confidence intervals on parameters, or to explicitly compare models.

The simplest model is the univariate twin model which can easily be extended to multiple variables, measurement occasions, and/or groups. Although not the focus of the current chapter, it should be noted that it is also possible to model any measured environmental and (or) genetic information directly.

Univariate Twin Modeling

The basis of model-fitting is the construction of a model that describes an observed data pattern. The fit of a model can then be used to evaluate how well the assumed model matches the data, whereby it is also possible to drop parameters from the model and to test such nested models against the full model. The observed data in the CTD consists of the variance-covariance matrices of MZ and DZ twins, resulting in six unique statistics:
$$ \left[\begin{array}{cc}\hfill {Var}_1^{MZ}\hfill & \hfill\ \hfill \\ {}\hfill {Cov}_{12}^{MZ}\hfill & \hfill {Var}_2^{MZ}\hfill \end{array}\right] $$
$$ \left[\begin{array}{cc}\hfill {Var}_1^{DZ}\hfill & \hfill\ \hfill \\ {}\hfill {Cov}_{12}^{DZ}\hfill & \hfill {Var}_2^{DZ}\hfill \end{array}\right] $$
The path diagram that is assumed to describe the two variance-covariance matrices of the MZ and DZ twins is depicted in Fig. 1.
Fig. 1

Univariate path diagram. Only C or D can be estimated in the CTD

The model specifies that the phenotypes of twin 1 (P1) and twin 2 (P2) regress on their respective latent A, C, (D), and E variance components. The path diagram reflects the basic assumptions of the twin model. The freely estimated parameters of this model are the regression coefficients, a, c, (d), and e, and the mean, while the variances of, and the covariance between, the latent variables are fixed to a priori values (Neale 2009). For instance, the A and D components correlate differently for MZ and DZ twins in accordance to their assumed genetic similarity. The C component covaries with a value of 1.00 for both zygosity groups which is the translation of the equal environment assumption. Typically, the phenotypic means and variances are assumed to be equal within twin pairs and across zygosity groups (a testable assumption of the twin model; Franić et al. 2012). Because a simultaneous estimation of C and D is not possible in the CTD, one can either fit an ACE or ADE model (or submodels thereof) to the data, whereby the DE model is biologically implausible (Falconer and Mackay 1996). Taking the ACE model as an example, the variance-covariance matrix for MZ and DZ twins is modeled as:
$$ \left[\begin{array}{cc}\hfill {a}^2+{c}^2+{e}^2\hfill & \hfill \rho {a}^2+{c}^2\hfill \\ {}\hfill \rho {a}^2+{c}^2\hfill & \hfill {a}^2+{c}^2+{e}^2\hfill \end{array}\right] $$
where ρ is 1.00 in MZ and 0.50 in DZ pairs.

In general, all SEM software tools, such as Mplus (Muthén and Muthén 1998–2010), can be adapted to fit twin models. However, the OpenMx package (Neale et al. 2016) for R (R Core Team 2016) provides a flexible matrix syntax well suited for the model requirements of family data (Neale and colleagues 2003) provide an introduction into twin modeling based on matrix algebra).

Analyses based on the univariate twin model have contributed to our understanding of the causes of individual differences in a plethora of human traits, such as cognitive abilities, personality, and psychopathology (see Polderman et al. 2015). However, as Martin and Eaves (1977) already outlined 40 years ago, a powerful extension of the model lies in the possibility to analyze multivariate phenotypes. The following section is intended to provide a basic introduction into the principles of multivariate genetic modeling. The description covers the most commonly used models but is by no means exhaustive. For more advanced models and further reading of the formal quantification of such models, the reader is referred to the pertinent literature (e.g., Neale et al. 2003, 2016).

Multivariate Modeling

The univariate twin model can easily be extended to a multivariate model in which the covariance between multiple traits is analyzed. That way, for example, researchers can investigate whether the phenotypic association between depression and anxiety is due to genes that influence both traits, or rather due to environmental influences that may act as risk factors for both, depression and anxiety. In the simplest case of a bivariate genetic model with two traits, X and Y, measured in twins 1 and 2, the variance-covariance matrix would be:
$$ \left[\begin{array}{cccc}\hfill Var\left({X}_{t1}\right)\hfill & \hfill\ \hfill & \hfill\ \hfill & \hfill\ \hfill \\ {}\hfill Cov\left({X}_{t1}{X}_{t2}\right)\hfill & \hfill Var\left({X}_{t2}\right)\hfill & \hfill\ \hfill & \hfill\ \hfill \\ {}\hfill Cov\left({X}_{t1}{Y}_{t1}\right)\hfill & \hfill Cov\left({X}_{t2}{Y}_{t1}\right)\hfill & \hfill Var\left({Y}_{t1}\right)\hfill & \hfill\ \hfill \\ {}\hfill Cov\left({X}_{t1}{Y}_{t2}\right)\hfill & \hfill Cov\left({X}_{t2}{Y}_{t2}\right)\hfill & \hfill Cov\left({Y}_{t1}{Y}_{t2}\right)\hfill & \hfill Var\left({Y}_{t2}\right)\hfill \end{array}\right] $$
Cov(X t1 X t2) and Cov(Y t1 Y t2) are the univariate cross-twin covariances of trait X and Y, respectively; the phenotypic covariance of X and Y for the first and second twin is Cov(X t1 Y t1) and Cov(X t2 Y t2). The crucial new pieces of information are the cross-twin cross-trait covariances Cov(X t1 Y t2) and Cov(X t2 Y t1). If more than two traits are analyzed, the matrix extends to a 2n × 2n matrix, where n is the number of observed traits. Figure 2 shows the corresponding path diagram for the bivariate model (or correlated factors model).
Fig. 2

Bivariate ACE path diagram

Within multivariate models, the phenotypic correlation between two (or more) traits (X and Y) can be decomposed into genetic and environmental components. For instance, the genetic contribution to the observed correlation is a function of the two sets of genes that influence X and Y, i.e., the genetic correlation (r A ) between X and Y (Neale and Maes 2004). The genetic correlation between traits X and Y (r A,XY ) is derived as the genetic covariance between X and Y (a xy ) divided by the square root of the product of the genetic variances of traits X (a xx ) and Y (a yy ):
$$ {r}_{A, XY}=\frac{a_{xy}}{\sqrt{a_{xx}\times {a}_{yy}}} $$
A genetic correlation of 1.00 would imply that the two sets of genes overlap completely, or put differently, all genetic influences on trait X also influence trait Y. Note that a large genetic correlation does not imply that the overlapping genes influence both traits to the same extent or that they act in the same manner (i.e., additively or nonadditively) for both traits (Posthuma 2009). The same reasoning applies to the shared (r C ) and non-shared environmental correlation (r E ):
$$ {r}_{C, XY}=\frac{c_{xy}}{\sqrt{c_{xx}\times {c}_{yy}}} ; {r}_{E, XY}=\frac{e_{xy}}{\sqrt{e_{xx}\times {e}_{yy}}} $$
A shared environmental correlation of 0.00 would therefore imply that the environmental influences that make twins more similar on trait X are independent of the environmental influences that make twins more similar on trait Y (Plomin et al. 2013). The phenotypic correlation consequently is the sum of the genetic contribution and environmental contributions and is calculated as:
$$ r={r}_{A, XY}\times \sqrt{\frac{a_{xx}}{\Big({a}_{xx}+{c}_{xx}+{e}_{xx\Big)}}}\times \sqrt{\frac{a_{yy}}{\Big({a}_{yy}+{c}_{yy}+{e}_{yy\Big)}}\ } $$
$$ + {r}_{C, XY}\times \sqrt{\frac{c_{xx}}{\Big({a}_{xx}+{c}_{xx}+{e}_{xx\Big)}}}\times \sqrt{\frac{c_{yy}}{\Big({a}_{yy}+{c}_{yy}+{e}_{yy\Big)}}\ } $$
$$ + {r}_{E, XY}\times \sqrt{\frac{e_{xx}}{\Big({a}_{xx}+{c}_{xx}+{e}_{xx\Big)}}}\times \sqrt{\frac{e_{yy}}{\Big({a}_{yy}+{c}_{yy}+{e}_{yy\Big)}}\ } $$
A re-parametrization of the correlated factors model is the so-called Cholesky factorization (Loehlin 1996). This model does not assume an underlying structure of the genetic and environmental influences and tests for common and independent genetic and environmental effects on variance in two or more traits (Neale and Maes 2004). Figure 3 depicts a three-variate twin model as Cholesky factorization.
Fig. 3

Three-variate twin model: Cholesky factorization

The first latent factors (genetic, shared, and non-shared environmental) load on all observed variables, the second on all except the first, and so on. It is important to note that the order of the observed variables is arbitrary in cross-sectional data and that the model merely allows for inferences about the genetic and environmental overlap between the variables. Only with genetically informative longitudinal data it can, e.g., be tested whether new genetic influences become important over time (by testing whether the influence of the second genetic factor on the second measurement significantly differs from zero) or whether genetic amplification is present, i.e., when the paths from the first genetic factor to the respective traits are equal (Posthuma 2009). For example, Klump et al. (2007) used trivariate genetic modeling to investigate the emergence of new genetic effects in disordered eating symptoms between the ages 11 and 18. They found that genetic factors accounted for a small proportion of variance at age 11 (6%), but that genes increased in importance at ages 14 and 18, explaining almost half of the variance in disordered eating. The authors conclude that their findings highlight the transition from early to mid-adolescence as a critical time for the emergence of a genetic diathesis for problematic eating behavior.

The Cholesky model is just identified, which means that no additional paths can be estimated. However, different models that make different assumptions about the underlying nature of the traits can be fitted to test whether a more parsimonious explanation fits the data without significant loss of fit (Plomin et al. 2013). Two commonly used models in behavior genetics are the independent and common pathway models (see Fig. 4, all path coefficients have been omitted to avoid cluttering). The independent pathway model tests the assumption that each measure has specific genetic and environmental effects (subscript “S”), as well as common genetic and environmental effects (subscript “C”) that underlie the correlations between all measures. In the common pathway model, all observed traits are indicators of one common latent factor which is influenced by genetic and environmental effects. The independent pathway model is nested in the general multivariate model described above; the common pathway model is nested in both, which makes it feasible to test the models against each other. More complex multivariate models can be designed as extensions of the previously described models, e.g., hierarchical genetic factor models.
Fig. 4

Three-variate independent (left) and common pathway model (right). Path coefficients have been omitted. Only one twin displayed for simplicity

Further Applications of Twin Studies

Behavior genetic studies based on twin data have revealed a plethora of alternative parameterizations of multivariate or more complex designs. Some of these are described below.

Direction of Causation and Random Effects Models

Under certain conditions (see Heath et al. 1993; Gillespie and Martin 2005), cross-sectional twin data are also informative about the direction of causation between two traits, that is, whether trait A causes trait B or vice versa. For example, Gillespie et al. (2012) used this approach to examine the direction of causation between disrupted sleep, anxiety, and depression.

With recourse to phenotypic random effects models (also known as hierarchical linear models or mixed effects models; see Raudenbush and Bryk (2002) for an introduction), cross-sectional twin data can also be used to augment classic linear regression analyses. Rather than studying the genetic and environmental effects on the respective traits, the goal of such regression-based analyses of twin data is to estimate the part of the regression that is independent of the heritability of the traits (see Turkheimer and Harden (2014) for a detailed description of this approach).

Sex-Limitation Models

Twin studies are also concerned with the question whether sex moderates the genetic and environmental effects on a trait; these models are known as sex-limitation models. The CTD provides the information to further investigate (1) the magnitude of genetic and environmental effects on male and female phenotypes (quantitative sex differences) and to (2) determine whether or not the same genetic factors or shared environmental experiences influence a trait in males and females (qualitative sex differences; Neale and Maes 2004). The second question, however, can only be studied when data from opposite-sex DZ twin pairs are available (Eaves et al. 1978). Various studies in different domains of genetic research, e.g., psychopathology, intelligence, personality, and well-being, indicate the absence of substantial sex-related differences. One exception is a study by Rettew et al. (2006) showing that different genes may be involved in the variation of neuroticism in males and females.

Gene-Environment Interaction

Thus far, all of the described models relied, among other things, on the assumption that genes operate in the same manner across different levels of environmental variables. However, it is understood that the exposure to a given environment can moderate the importance of genetic and/or environmental contributions for a given phenotype (Neale and Maes 2004). This gene-environment interaction (GxE) may have a biasing effect on parameter estimates derived in the CTD (Purcell 2002). The most widely used continuous moderator model (Purcell 2002) tests whether the genetic and environmental effects found within the CTD change as a linear function of the moderator after accounting for the main effect of the moderator on the outcome. For example, the heritability of cognitive ability appears to vary as a function of family socioeconomic status in US samples, with higher heritability at the socially valued end of the distribution (Tucker-Drob and Bates 2016). The classic GxE model has recently been extended by van der Sluis and colleagues to address some methodological drawbacks inherent in the modeling procedure of the continuous moderator model (van der Sluis et al. 2012).

Longitudinal Designs

When a trait is measured repeatedly for each twin in a pair, these data can be utilized to disentangle the genetic and environmental contributions to stability and change in a trait over time. Different methods have been developed for serially correlated longitudinal data. In the Cholesky factorization, the multiple trait measures are treated in a multivariate genetic analysis framework (Posthuma 2009). Markov chain (or simplex) models assume that future values of the trait solely depend on the current trait values, not on the entire past history (Dolan et al. 1991). Also, growth curve models can be applied to longitudinal twin data to investigate the role of genetic and environmental factors in growth and change (Neale and McArdle 2000).

Multi-Group Designs

A powerful extension of the CTD arises from the incorporation of data from other groups of family members. Nuclear models are based on data from parents and children, while extended family models (such as stealth and cascade) also rely on data from nonnuclear family members such as uncles or cousins (see Keller et al. 2009). The benefit of such models lies for one thing in the possibility to simultaneously estimate A, D, and E while decomposing C into multiple components, including an environment common to all family members and a twin-specific environment. It is also possible to estimate additional types of effects, such as gene-environment correlations (the effect that certain genotypes are selectively found in certain environments, represented by a correlation among genetic and environmental factors) and vertical cultural transmission (the effects of parents on offspring due to environmental factors). Further, the genetic effects can be adjusted for potential assortative mating among parents.


Twin studies remain a powerful tool in quantitative behavior genetic research. New modeling techniques and flexible SEM procedures can be extended to incorporate more complex effects in order to deal with some of the limitations of the CTD that arise from the underlying assumptions or power-related issues inherent in the CTD (e.g., Visscher 2004). However, it is not possible to include all these modifications at the same time, and researchers are advised to select the model to be fitted based on a net of a priori-derived hypotheses.



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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of PsychologySaarland UniversitySaarbrueckenGermany

Section editors and affiliations

  • Matthias Ziegler
    • 1
  1. 1.Humboldt Universität zu BerlinBerlinGermany