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The previous chapter investigated the sources of individual differences throughout the normal distribution, which we refer to as learning abilities. In this chapter, we focus on the lower end of the distribution, learning disabilities. To what extent are learning disabilities etiologically distinct from the normal range of variation? Our hypothesis follows from Quantitative Trait Locus (QTL) theory, which posits that genetic influence on common disorders and complex traits is caused by many genes (loci) of small effect rather than by one gene or even by a few genes of large effect (Plomin, Owen, & McGuffin, 1994). Unlike single-gene effects, that are necessary and sufficient for the development of a disorder, QTLs contribute interchangeably and additively as probablilistic risk factors. If QTL theory is correct, common disorders such as learning disabilities are likely to be the quantitative extreme of the same genetic factors responsible for variation throughout the distribution. The QTL model refers to quantitative traits even in relation to disorders because if many genes affect a disorder, then it necessarily follows that there will be a quantitative distribution rather than a dichotomy. Stated more provocatively, there is no disability, just low ability—the abnormal is normal. The QTL model is discussed in greater detail in Chapter VII. The ultimate proof of the QTL model will come when QTLs identified for learning disabilities are found to be associated with the normal range of variation in abilities and vice versa.

With a large and representative twin sample like TEDS, it is possible to study disabilities in the context of abilities. We can compare estimates of genetic and environmental influence for abilities and for disabilities in the same sample. Finding that genetic or environmental estimates differ for abilities and disabilities indicates that there are etiological differences between abilities and disabilities. However, differences in the magnitude of genetic and environmental estimates for abilities and disabilities are merely quantitative differences, not qualitative differences. That is, even if heritability differed quantitatively for disabilities and abilities, the same genes could nonetheless be associated with disabilities and abilities. Conversely, heritabilities could be the same for disabilities and abilities and yet different genes could be associated with disabilities and abilities.

What we would most like to know is whether there are qualitative differences between disabilities and abilities. That is, are genes associated with learning disability different from the genes associated with normal variation in ability? As discussed in Chapter II, we believe that DF extremes analysis addresses this issue of qualitative differences directly. Finding group heritability implies genetic links between disabilities and abilities, and finding group shared environment implies shared environmental links between disabilities and abilities.

The structure of this chapter is similar to the previous chapter. However, instead of presenting twin correlations and ACE model fitting for the entire sample, this chapter focuses on twin concordances, twin “group” correlations, and DF extremes analyses for children with low scores. For reasons discussed in the previous chapter, we maximized power for these extremes analyses by combining boys and girls, same-sex, and opposite-sex DZ twins, and assessments by same and different teachers. Furthermore, because results presented in the previous chapter were so similar for components of each domain, the present chapter simplifies presentation of results by focusing on the composite scores for each domain at each age.

We selected twin pairs for whom at least one twin scored in the lowest 15% on the composite score. We have also conducted analyses using a 5% cut-off and generally find similar results. We have chosen to present results for the 15% cut-off for three reasons. First, performance one standard deviation below the mean, which corresponds to a 15.9% cut-off in a perfectly normal distribution, is often used as a cut-off for common disorders. Second, for the U.K. National Curriculum (NC), a 15% cut-off corresponds to children identified as performing below their grade expectation and failing items that are solved correctly by the majority of much younger children (Kovas, Haworth, Petrill, & Plomin, in press). Third, in TEDS, a 15% cut-off strikes a balance between extremity of scores and sample size needed to attain reasonable power in DF extremes analysis. The number of probands in the lowest 15% of the distribution for each measure and the number of MZ and DZ pairs with at least one proband are listed in the footnote to Table 12. In our individual differences analyses in the previous chapter, we excluded all twin pairs in which one or both twins scored 3 or more standard deviations below or above the mean so that our individual differences results would not be affected by very extreme scores. However, children with low extreme scores were restored for the present analyses because our focus here is on children with low scores and because DF extremes analysis is an analysis of means rather than variances and analyses of means are not inordinately affected by outliers.

Table 12. 
Twin group
DF estimates
MZDZMZDZh2g (SE)c2g (SE)
  1. Note.—7-year NC English: 1,170 families (1,632 probands) 392 MZ pairs, 778 DZ pairs.

  2. 7-year NC Math: 1,174 families (1,634 probands) 386 MZ pairs, 788 DZ pairs.

  3. 9-year NC English: 566 families (756 probands) 183 MZ pairs, 383 DZ pairs.

  4. 9-year NC Math: 554 families (732 probands) 198 MZ pairs, 356 DZ pairs.

  5. 9-year NC Science: 531 families (739 probands) 172 MZ pairs, 359 DZ pairs.

  6. 10-year NC English: 580 families (775 probands) 197 MZ pairs, 383 DZ pairs.

  7. 10-year NC Math: 571 families (769 probands) 193 MZ pairs, 378 DZ pairs.

  8. 10-year NC Science: 560 families (772 probands) 207 MZ pairs, 353 DZ pairs.

  9. 7-year TOWRE: 1,063 families (1,476 probands) 369 MZ pairs, 694 DZ pairs.

  10. 10-year PIAT: 470 families (589 probands) 176 MZ pairs, 294 DZ pairs.

  11. 10-year Web Math: 615 families (768 probands) 221 MZ pairs, 394 DZ pairs.

  12. 7-year g: 1,142 families (1,461 probands) 429 MZ pairs, 713 DZ pairs.

  13. 9-year g: 674 families (901 probands) 247 MZ pairs, 427 DZ pairs.

  14. 10-year g: 580 families (745 probands) 214 MZ pairs, 366 DZ pairs.

  15. MZ, monozygotic; DZ, dizygotic; h2g, group heritability; c2g, group shared environment.

7-year NC English. (.07).10 (.05)
7-year NC Math. (.08).11 (.06)
9-year NC English. (.09).00 (.07)
9-year NC Math. (.10).00 (.07)
9-year NC Science. (.10).04 (.07)
10-year NC English. (.09).00 (.07)
10-year NC Math. (.10).04 (.07)
10-year NC Science. (.11).17 (.08)
7-year TOWRE. (.06).23 (.05)
10-year PIAT. (.11).20 (.08)
10-year Web Math. (.10).16 (.07)
7-year g. (.07).26 (.05)
9-year g. (.08).37 (.06)
10-year g. (.09).20 (.07)

Table 12 summarizes the results in terms of MZ and DZ probandwise concordances, twin group correlations, and DF extremes estimates of group heritability and group shared environment. These results are examined in the following sections.


The concordances and twin group correlations (see Chapter II) yield similar results for all NC domains at all ages. For example, for the first row of results (7-year NC English), the much greater MZ concordance (76%) than DZ concordance (44%) suggests substantial heritability. The pattern of MZ and DZ concordances also suggests little influence of shared environment, especially when the base rate of 15% is taken into account. As explained in Chapter II, concordances are based on dichotomous data (affected or not), and cannot in themselves be used to estimate genetic and environmental parameters unless they are converted into liability correlations.

DF extremes analysis uses quantitative trait data to produce twin group correlations that indicate the extent to which co-twins of probands resemble the probands on a quantitative trait. For example, for 7-year NC English, the MZ group correlation of .85 indicates that the mean of the co-twins of MZ probands is 85% below the population mean as compared with the probands. That is, the mean standard score for both MZ and DZ probands for all measures is −1.6. The mean standard score of the MZ co-twins is −1.3, very similar to the proband mean. Doubling the difference between the MZ and DZ group correlations of .85 and .47 suggests a group heritability of .76. Group shared environment can be estimated as the extent to which group heritability does not explain MZ similarity: .85−.76=.09. These estimates are highly similar to those derived from DF extremes regression analysis shown in Table 12 (i.e., .75 for group heritability and .10 for group shared environment). Doubling the standard errors of these estimates (see Table 12) indicates that group heritabilities are statistically significant but that group shared environment is not.

Across the eight NC composite measures at 7, 9, and 10 years, the average group heritability estimate is .76 and the average group shared environment estimate is .06. As explained in Chapter II, it should be emphasized that these group statistics refer to group means, not to individual differences within the extreme group. For example, a group heritability of .76 means that 76% of the difference between the proband and population means can be attributed to genetic influences.


As compared with NC teacher ratings, the test scores yield lower estimates of group heritability and higher estimates of group shared environment. For the TOWRE at 7 years, group heritability is .65 and group shared environment is .23. Group heritabilities are also significantly lower than those for the NC teacher ratings for the web-based tests of reading and mathematics at 10 years (.43 and .47, respectively); group shared environments are .20 and .16.


The results for “g” at 7, 9, and 10 are similar to those for the web-based tests of reading and mathematics, despite the different modes of measurements of “g” at 7 (telephone), 9 (mailed booklets), and 10 (web-based tests). Group heritabilities range from .37 to .52 and group shared environments range from .20 to .37.


These results support the hypothesis that the abnormal is normal, both quantitatively and qualitatively. Evidence for the quantitative similarity of genetic and environmental estimates for the abnormal and normal can be seen in Figure 6, which summarizes visually the DF extremes results reported in this chapter and compares them with the individual differences results from the previous chapter. For example, in the previous chapter, the average model-fitting estimate of heritability across the NC composite scores and across age was .63, the average-shared environment was .14 and the average of non-shared environment was .22. In the present chapter, across the same NC composite scores and ages, DF extremes analyses yielded an average group heritability of .76, an average group shared environment of .06, and an average group nonshared environment of .18. The test measures of reading and mathematics and the measures of “g” at the three ages also yield similar results for disability and ability. The slight differences in results for the low extremes and the whole sample are well within their 95% confidence intervals. The similarity in results is especially remarkable because the analyses are so different. DF extremes analysis is based on means for the probands, the co-twins, and the population in which probands were selected from the lowest 15% of the distribution, whereas analyses from the previous chapter are based on individual differences throughout the distribution.

Figure 6.

—Comparison between genetic and environmental estimates for the lowest-performing 15% (DF extremes analyses from this chapter) and for individual differences throughout the entire distribution (Chapter III). The top panel compares extremes and the entire distribution for NC teacher assessments; the bottom panel summarizes results for the reading, mathematics and “g” test data.

If ACE estimates had differed for disabilities and abilities, this would indicate an etiological difference between them. However, as noted earlier and explained in Chapter II, such quantitative differences, for example in heritability, could be due to the same genes affecting disabilities and abilities but differing in the magnitude of their effect at the low end of the distribution. This could occur, for example, if shared environmental influences had a stronger effect at the low end of the distribution.

In the present situation in which similar quantitative ACE estimates were found for disabilities and abilities, it is possible that different genes are associated with disabilities and abilities even though the net effects of such genes are of a similar magnitude for disabilities and abilities. As mentioned earlier, what we would like to know is whether there are qualitative differences between disabilities and abilities; that is, whether different genes or different environmental factors affect disabilities and abilities. We suggest that DF extremes analysis itself, not the comparison between the results for DF extremes analysis and analysis of individual differences, speaks to qualitative differences between disabilities and abilities. Although this is a complicated issue (for details, see Plomin & Kovas, 2005), group heritability and group shared environment can be observed only to the extent that there are links between disability and ability. That is, if the measure of disability is unrelated to the measure of ability, there can be no group heritability or group shared environment—the co-twins' mean would regress back to the population mean in DF extremes analysis. However, finding genetic and environmental links between disability and ability does not imply that all effects are in common. Indeed it is likely that there are rare single-gene effects and rare environmental trauma that lead to learning disability but account for little variance in the population as a whole (Plomin & Kovas, 2005).

Thus, we conclude that the results presented in this chapter are consistent with the hypothesis that the abnormal is normal both quantitatively and qualitatively. The strongest test of the hypothesis that the abnormal is normal will come when genes are found that are associated with disabilities or abilities. Our prediction is that any gene associated with reading disability, for example, will also be associated with individual differences in reading ability throughout the distribution, including good readers. This hypothesis is consistent with QTL theory, which posits that common disorders are the quantitative extreme of the same genetic factors that create variation throughout the distribution.

It is possible that these conclusions do not apply to more severe forms of disability identified by different criteria and more severe cut-offs than the ones used in this study. However, as discussed earlier, the cut-off for disability used in this study selected children with very low performance, failing items that are successfully solved by the majority of younger children. Also, as discussed earlier, we repeated all analyses with a more severe cut-off of 5% of the whole sample, and obtained very similar results. Finally, it is possible that some rare variants of learning disabilities have a distinct etiology from that of most common disabilities, as discussed in the concluding chapter.

Although the results reported in this chapter have no immediate implications for teaching or for remediating disabilities, we believe that it is important for parents, teachers and policy makers to recognize that common learning disabilities are etiologically the low end of quantitative continua of ability, rather than being driven by unique genetic and environmental factors. This finding has far-reaching implications for defining learning disability as well as for research into factors that are responsible for learning disability, as discussed in Chapter VII.


ACE results for the lowest 15% of children at each age for all measures are remarkably similar to the individual differences results presented in the previous chapter for the entire distribution. That is, for disability as well as for ability, heritability for NC teacher ratings is very high (≈.70) and shared environment is very low (≈.10). For web-based measures of reading and mathematics at 10 years as well as for tests of “g” at all three ages, disability as well as ability shows less heritability (≈.40) and more shared environmental influence (≈.20).

The similarity of ACE results for disability and ability indicates that the quantitative etiologies of disability and ability are similar. The group heritability estimates suggest that the etiologies of disability and ability are also similar qualitatively.