A surprising finding emerging from genetic studies across diverse learning disabilities is that most genetic influences are shared: They are “generalist” rather than “specialist” (Plomin & Kovas 2005). We know this because multivariate genetic analysis of twins yields genetic and environmental correlations among traits; high genetic correlations point to a shared genetic etiology and frame a “generalist genes” hypothesis. Although recent advances in molecular genetics, such as genome-wide association, are revealing the genetic variants that are responsible for these common influences (Wellcome Trust Case Control Consortium 2007), we are beginning to realize that the genetic and environmental architecture of psychological traits is far more complex than previously imagined. Just as Cramer et al. highlight the difficulties of psychiatric diagnosis at a phenotypic level, we have argued that, at an etiological level, such common disorders are quantitative traits reflecting multiple underlying dimensions of genetic (and environmental) risk (Plomin et al. 2009). To maximize our chances of identifying particular genetic variants, it is essential that we understand the genetic relationships among these traits by estimating and comparing the genetic correlations derived from genetically sensitive study designs (Plomin et al. 2008). In common with Cramer et al., we have found that one of the most effective ways to present and reason about such high-dimensional information is through graphical representation (Tufte 2001).

Accurate estimation of multivariate statistics such as genetic and environmental correlations requires large samples. We recently exploited widespread access to inexpensive and fast Internet connections in the United Kingdom to assess over 5,000 pairs of 12-year-old twins from the Twins Early Development Study (TEDS; Oliver & Plomin 2007) on four batteries: reading, mathematics, general cognitive ability (g), and, for the first time, language (Haworth et al. 2007). A multivariate structural equation model using latent factors showed that, as expected, genetic correlations among reading, mathematics, and g are high in late childhood and early adolescence (0.75–0.91), with language as highly correlated genetically with g as reading and mathematics (see our Fig. 1 here) (Davis et al. 2009).

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Figure 1

(Davis and Plomin). Latent factor twin model with genetic correlations highlighted: A, additive genetic effects; C, shared (common) environmental effects; and E, nonshared environmental effects. Squares represent measured traits, and circles represent latent factors. The lower tier of arrows represents factor loadings, and the second tier represents genetic and environmental path coefficients. The curved arrows at the top represent correlations between genetic (solid lines) and environmental (dotted lines) latent factors. Adapted from Davis et al. (2009).

However, as Cramer et al. demonstrate, there is another level of detail that cannot be investigated through analysis of latent factors. The batteries that index the latent constructs of reading, mathematics, g, and language can be broken down into their constituent tests, our “symptoms,” to better understand the complex relationships among cognitive components that result in high correlations at the level of latent factors. Our own approach to exploring these relationships used multidimensional scaling of genetic correlation matrices to produce interactive graphical representations of the underlying genetic architecture.

As shown in Figure 1, each latent construct was characterised by three or four subscales that assessed different aspects of the trait: 14 tests in total. These measures are described in detail in Davis et al. (2009). Multidimensional scaling can be used to reduce the high-dimensional relationships among the tests to two or three spatial dimensions.

Classical (metric) multidimensional scaling (Gower 1966; Young & Householder 1938) requires a matrix representing the pair-wise “distance” between every pair of traits. With a high-performance computing cluster we calculated the pair-wise genetic correlations among all the tests in the battery using maximum-likelihood structural equation model-fitting in Mx (Neale et al. 2006) to make a genetic correlation matrix. The genetic correlation matrix represents the genetic similarity among the tests. To represent the genetic dissimilarity, or distance, we subtracted the correlations in the matrix from 1. We performed multidimensional scaling on the resulting matrix using the R function cmdscale (R version 2.10.1; R Development Core Team, 2009) and checked whether three dimensions allowed an adequate representation of the true distance matrix using the criterion suggested by Mardia et al. (1979) and inspection of a Shepard diagram, which plots the distances obtained from multidimensional scaling against the values in the original distance matrix.

Figure 2 represents the well-fitting three-dimensional solution using the graphics library OpenGL, available in R through the rgl package. The screenshot shows genetically similar traits clustering together and genetically dissimilar traits more distant from one another in space. For a sense of scale, the closest relationship is between two measures of reading comprehension, GOAL and PIAT in the centre of the figure, with a genetic correlation of almost 1; the most distant relationship (a genetic correlation of 0.12) is between TOWRE on the far left, a measure of reading fluency, and Picture Completion on the far right, a measure of nonverbal ability. The image highlights subtle patterns of gene-sharing among the tests. For example, the mathematics tests cluster close together, while the comprehension and fluency components of reading ability are relatively separate in the centre and far left. Likewise, the g battery falls naturally into verbal (near the top) and nonverbal (far right) components. Meanwhile, reading comprehension, the verbal components of g, and language cluster at the top of the figure. Although most correlations are strong, the heterogeneity tells a more nuanced version of the generalist genes story than we saw at the level of latent factors.

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Figure 2

(Davis and Plomin). Screenshot of a three-dimensional representation of genetic similarities among the tests that form the latent factors in Figure 1. Each sphere represents a test, and tests are colored by corresponding latent factor from Figure 1: green for reading, blue for mathematics, red for g, and yellow for language. Tests with similar genetic influences are closer together in space.

This approach to visualizing the genetic relationship among traits at the symptom level complements Cramer et al.’s network approach to phenotypic comorbidity. When they call for scholars from a wide variety of disciplines to join together to fashion a new approach to psychometrics, they may certainly count geneticists among their allies.