In this chapter, we go beyond estimating heritability by investigating the causes of change and continuity in the development of individual differences in learning abilities during middle childhood. There are two types of questions that can be asked using the twin method: quantitative differences in genetic and environmental influences on a trait, and qualitative changes in those influences. In the former, we ask whether the magnitude of genetic and environmental effects differs from age to age. This question can be addressed to a limited extent using cross-sectional data, although longitudinal data are better because the same sample is assessed across ages and therefore cohort differences are eliminated. The question of qualitative changes is the extent to which the same genetic and environmental effects operate across ages. Such analyses of age-to-age change and continuity require longitudinal data.

As in the previous chapter, we have maximized power by combining boys and girls, same-sex and opposite-sex DZ twins, and assessments by same and different teachers. We have also, for reasons of length and clarity of interpretation, reported results only for composite scores at each age. Unlike the previous chapter, which focused on the lower 15% of the distribution, the present chapter primarily reports analyses for the entire sample, again for reasons of power. However, we also present an example of a longitudinal extremes analysis of genetic and environmental contributions to change and continuity for reading disability at 7 and 10 years.

QUANTITATIVE AGE DIFFERENCES IN ETIOLOGY

Chapter III included estimates of genetic and environmental influence at 7, 9, and 10 years. Figure 7 presents the main results, organized to facilitate comparisons across age for each composite measure. For example, for the NC English composite, heritabilities were similar at 7 (.65), 9 (.67), and 10 (.60) years. Shared environment estimates were also similar across the ages (.17, .11, and .20). Comparably stable estimates can be seen for the NC mathematics composite at 7, 9, and 10 years. NC Science between 9 and 10 years showed some difference in heritability (.64 vs. .50) and shared environment (.12 vs. .26), although these differences were not significant as indicated by their overlapping 95% confidence intervals (see Table 11).

ACE estimates were also stable for “g.” The only significant difference for age in Figure 7 is the difference in heritability between TOWRE at 7 years (.70) and PIAT at 10 years (.39). However, these two tests are very different: TOWRE at 7 years is a brief telephone-administered test of word recognition, whereas the PIAT at 10 years is a web-based test of reading comprehension. Thus, the ACE differences between these two measures might be due to measurement differences in content or method rather than age differences.

We were surprised to find such similar ACE results for learning abilities across ages despite major changes in content and complexity of the curriculum from 7 to 10 years (a transition between the two key stages on U.K. National Curriculum). Although 3 years represents a third of these children's life span, it may be too short a time to assess quantitative changes. For example, it is well documented that the heritability of “g” increases almost linearly during development—about 20% in infancy, 30% in middle childhood, 40% in adolescence, 50% in young adulthood, 60% in middle adulthood, and 70% in late adulthood (Boomsma, 1993; McGue, Bouchard, Jr., Iacono, & Lykken, 1993; Plomin, 1986). In our study, heritability of “g” was .36 at 7, .36, and 9 and .41 at 10, remarkably similar results despite the very different methodologies used to assess “g” at 7 (telephone), 9 (booklets), and 10 (internet) (Davis, Arden, & Plomin, 2007). Taking a longer view of development, we find the expected increase in heritability from early childhood to middle childhood. At 2–4 years, the average heritability of “g” was .26 (Spinath, Ronald, Harlaar, Price, & Plomin, 2003) as compared with the present average heritability of .38 at 7, 9, and 10 years. However, the TEDS measures of “g” in early childhood are very different from the measures used in middle childhood; for this reason, the apparent age difference could be due to the difference in measures.

These results indicating little age difference in ACE estimates raise the problem of power in detecting age differences in genetic and environmental parameter estimates. As mentioned earlier, for NC Science, heritability estimates and 95% confidence intervals are .63 (.55–.72) at 9 years and .48 (.41–.56) at 10 years. For shared environment, the estimates are .12 (.04–.20) and .27 (.19–.34). Even these relatively large differences in genetic and environmental parameter estimates are not quite statistically significant despite the relatively large sample size. Only heritability estimates that differ by as much as .20 (e.g., .65 vs. .45) would be detected as significantly different with these sample sizes. The only significant difference in Table 11 is between the heritability estimates for TOWRE at 7 years and PIAT at 10 years; these heritability estimates differ by .31. Moreover, significance only represents 50% power, which means that a difference of this magnitude would not be detected as significant half of the time.

QUALITATIVE AGE CHANGES IN ETIOLOGY

The longitudinal design of TEDS makes it possible to go beyond these essentially cross-sectional comparisons in ACE parameter estimates to investigate genetic and environmental influences on age-to-age change and continuity. As explained in Chapter II, longitudinal genetic analysis is a special case of multivariate genetic analysis, a technique that analyzes the covariance between traits rather than the variance of each trait separately. Longitudinal genetic analysis addresses the covariance across age for the same trait and decomposes the covariance (which indexes continuity) as well as the variance that does not covary (which indexes change) into genetic and environmental sources. In other words, longitudinal genetic analysis asks the extent to which genetic and environmental factors mediate phenotypic continuity and change from age to age. The statistic bivariate heritability describes the extent to which genetic factors account for the phenotypic correlation between two traits in multivariate genetic analysis or between the same trait at two ages in longitudinal genetic analysis.

A second question that longitudinal and multivariate genetic analyses address is the extent to which the same genetic and environmental factors operate across age, independent of the magnitude of their effect on the phenotype. For example, regardless of the heritability of a trait at two ages, to what extent do the genes that affect that trait at one age also affect the trait at another age? This second statistic is the genetic correlation. Comparable longitudinal correlations can be derived for shared and nonshared environment.

Longitudinal genetic analysis begins with phenotypic stability. If there is no phenotypic stability, genetic, and environmental influences at one age are independent of those at a second age. If there were no phenotypic stability, all genetic and environmental influences would contribute to change and the analysis reduces to separate analyses of genetic and environmental influences at each age. For learning abilities, age-to-age phenotypic correlations are substantial from 7 to 9, from 9 to 10, and even from 7 to 10. For NC English, the correlations are .63, .68, and .62, respectively; for NC mathematics, the correlations are .58, .63, and .55; for NC science from 9 to 10, the correlation is .49. Stability between the TOWRE word recognition test at 7 years and the PIAT reading comprehension test at 10 years is .44, but this lower stability might reflect differences in the measures. Similarly moderate stability is seen for “g” (.42 from 7 to 9, .55 from 9 to 10, and .40 from 7 to 10) despite the differences in measurement at 7 (telephone), 9 (booklet), and 10 (internet). A full phenotypic matrix across measures and across ages is included as Appendix E.

Longitudinal Model-Fitting Results

Longitudinal genetic analysis is based on cross-age twin correlations in which, for example, one twin's English score at 7 years is correlated with the co-twin's English score at 9 years. Genetic mediation of stability is indicated to the extent that cross-age twin correlations are greater for MZ than DZ twins. Rather than presenting the cross-age twin correlations, we have summarized the results visually, as derived from fitting a longitudinal model called Cholesky decomposition, which is described and illustrated in Chapter II.

The model-fitting results for our longitudinal genetic analyses are shown in Figure 8, for genetic (A), shared environmental (C), and nonshared environmental (E) influences. The first factor A_{1} captures genetic influences in common across 7, 9, and 10 years. The loadings (95% confidence intervals in parentheses) indicate the variance of each variable that is accounted for by that factor. For the NC English composite, all of the genetic variance at 7 years is assigned to the first genetic factor −.67 is the heritability of English at 7 years in this longitudinal analysis, which is similar to the cross-sectional estimate of .65 shown in Table 11. (The square root sign is shown before .67 because the path coefficient itself, which is a standardized partial regression, is actually the square root of .67, i.e., .82. As seen below, it is easier to interpret the results using these squared path coefficients.) The significant and substantial loadings of English at 9 and 10 years on this general factor (A_{1}) indicate strong genetic continuity. Of the genetic variance at 9 years (.32+.33=.65), about half (.32÷.65=49%) is shared with genetic variance at 7 years. Of the genetic variance at 10 years (.26+.07+.24=.57), almost half (.26÷.57=46%) is shared with genetic variance at 7 years.

Beyond this strong general genetic factor (A_{1}), most of the remaining genetic variance is unique to each age, signaling genetic change. However, the second genetic factor (A_{2}) indicates that some of the new genetic variance that emerges at 9 years contributes to continuity at 10 years. That is, 12% (i.e., .07÷.57) of the genetic variance at 10 years is shared with genetic variance at 9 years, independent of genetic variance shared across all three ages. NC mathematics at 7, 9, and 10 years also suggests genetic continuity and change in almost equal measure. NC science at 9 and 10 years, however, suggests more change than continuity, as do the reading tests at 7 years (word recognition) and 10 years (reading comprehension). “g,” however, shows as much genetic continuity as change.

The shared environmental (C) results in Figure 8 can be interpreted similarly but with one caveat. The effect of shared environment (that is, shared by the twins) is modest; the average estimate of C for NC composite scores across age is only .14. Because the variance of C is modest, attempts to decompose its covariance across age entail large confidence intervals as indicated in Figure 8. Despite this limitation, the general picture that emerges for C in Figure 8 is similar to A: C contributes to continuity and change. For example, the total C contribution to the variance of English at 10 years is .20 (.10+.04+.06) in this longitudinal analysis, which is the same estimate as in our cross-sectional analysis (Table 11). Half (.10÷.20) of the C variance at 10 years is shared in common with 7 and 9 years, one-fifth (.04÷.20) of the C variance at 10 years is shared with 9 years independent of 7 years, and one-third (.06÷.20) of the C variance at 10 years is independent of C variance at 7 and 9 years. The C contribution to continuity is a little less for mathematics, for the tests of reading, and for “g.” For science, C contributes entirely to continuity (there is no new C variance at 10 years).

The nonshared environmental (E) results in Figure 8 yield a very different result: E contributes entirely to change for all measures. One caution, however, is that estimates of E include error of measurement which looks like change.

Bivariate ACE

The results of the Cholesky model-fitting analyses shown in Figure 8 generally indicate that genetic influences contribute to continuity and change in about equal measure. However, this interpretation focuses on the heritability at each age and the extent to which these genetic influences are shared across ages. Two additional statistics which can be derived from these Cholesky analyses address somewhat different questions, and they indicate even greater genetic stability. As described in Chapter II, bivariate heritability indexes the extent to which the phenotypic correlation between ages is mediated genetically. The rest of the phenotypic correlation is explained by bivariate shared environment and bivariate nonshared environment.

As shown in Table 13, bivariate heritabilities across 7, 9, and 10 for NC English and NC mathematics range from .70 to .79, indicating that genetic factors largely account for the age-to-age phenotypic correlations, which are about .60 to .70. Even from 7 to 10 years, the bivariate heritabilities are .71 for NC English and .78 for NC mathematics. For NC science from 9 to 10 years, bivariate heritability is .54, suggesting that only about half of the phenotypic correlation of .52 from 9 to 10 years is genetically mediated. Although the reading tests at 7 and 10 years showed only modest phenotypic stability (.44) and significant differences in heritability, 83% of their stability can be attributed to genetic mediation. The longitudinal correlations for “g” are also largely mediated genetically. Because bivariate heritabilities indicate that genetic influence largely accounts for phenotypic stability, C and E bivariate stability estimates must be smaller, and Table 13 shows that they are.

Table 13. LONGITUDINAL ANALYSIS: PROPORTION OF PHENOTYPIC CORRELATION (r_{P}) BETWEEN AGES MEDIATED BY A (a_{x}a_{y}r_{A}/r_{P}), C (c_{x}c_{y}r_{C}/r_{P}), AND E (e_{x}e_{y}r_{E}/r_{P}), AND A (r_{A}), C (r_{C}), AND E (r_{E}) CORRELATIONS (95% CIS IN PARENTHESES)

A (a_{x}a_{y}r_{A}/r_{P})

C (c_{x}c_{y}r_{C}/r_{P})

E (e_{x}e_{y}r_{E}/r_{P})

r_{A}

r_{C}

r_{E}

Note.—CI, confidence interval.

NC English: 7, 9, 10

1. English at 7

Biv a^{2}1–2: .79 (.65–.95)

Biv c^{2}1–2: .12 (.00–.25)

Biv e^{2}1–2: .09 (.06–.12)

r_{A1}–r_{A2}: .70 (.61–.79)

r_{C1}–r_{C2}: .54 (.00–.91)

r_{E1}–r_{E2}: .25 (.16–.34)

2. English at 9

Biv a^{2}1–3: .71 (.57–.86)

Biv c^{2}1–3: .20 (.06–.33)

Biv e^{2}1–3: .09 (.06–.13)

r_{A1}–r_{A3}: .67 (.58–.77)

r_{C1}–r_{C3}: .71 (.32–1.00)

r_{E1}–r_{E3}: .26 (.17–.34)

3. English at 10

Biv a^{2}2–3: .70 (.56–.85)

Biv c^{2}2–3: .19 (.05–.31)

Biv e^{2}2–3: .11 (.08–.15)

r_{A2}–r_{A3}: .73 (.64–.81)

r_{C2}–r_{C3}: .74 (.36–1.00)

r_{E2}–r_{E3}: .33 (.24–.41)

NC mathematics: 7, 9, 10

1. Mathematics at 7

Biv a^{2}1–2: .76 (.59–.93)

Biv c^{2}1–2: .17 (.01–.32)

Biv e^{2}1–2: .07 (.03–.12)

r_{A1}–r_{A2}: .62 (.53–.73)

r_{C1}–r_{C2}: .80 (.10–1.00)

r_{E1}–r_{E2}: .16 (.07–.25)

2. Mathematics at 9

Biv a^{2}1–3: .78 (.61–.96)

Biv c^{2}1–3: 13 (.00–.28)

Biv e^{2}1–3: .09 (.05–.14)

r_{A1}–r_{A3}: .68 (.56–.79)

r_{C1}–r_{C3}: .52 (.00–.95)

r_{E1}–r_{E3}: .20 (.11–.28)

3. Mathematics at 10

Biv a^{2}2–3: .75 (.59–.92)

Biv c^{2}2–3: .13 (.00–.27)

Biv e^{2}2–3: .12 (.08–.16)

r_{A2}–r_{A3}: .73 (.63–.84)

r_{C2}–r_{C3}: .55 (.00–.96)

r_{E2}–r_{E3}: .27 (.19–.36)

NC science: 9, 10

1. Science at 9

Biv a^{2}1–2: .54 (.39–.71)

Biv c^{2}1–2: .36 (.21–.49)

Biv e^{2}1–2: .10 (.06–.14)

r_{A1}–r_{A2}: .49 (.39–.61)

r_{C1}–r_{C2}: 1.00 (.69–1.00)

r_{E1}–r_{E2}: .19 (.11–.27)

2. Science at 10

Reading: 7, 10

1. Reading at 7

Biv a^{2}1–2: .83 (.68–.99)

Biv c^{2}1–2: .11 (.00–.25)

Biv e^{2}1–2: .06 (.02–.10)

r_{A1}–r_{A2}: .60 (.51–.71)

r_{C1}–r_{C2}: .45 (.00–1.00)

r_{E1}–r_{E2}: .11 (.04–.17)

2. Reading at 10

g: 7, 9, 10

1. g at 7

Biv a^{2}1–2: .71 (.53–.89)

Biv c^{2}1–2: .27 (.11–.42)

Biv e^{2}1–2: .02 (.00–.07)

r_{A1}–r_{A2}: .70 (.54–.87)

r_{C1}–r_{C2}: .37 (.16–.57)

r_{E1}–r_{E2}: .03 (.00–.10)

2. g at 9

Biv a^{2}1–3: .80 (.61–1.00)

Biv c^{2}1–3: .18 (.00–.34)

Biv e^{2}1–3: .02 (.00–.08)

r_{A1}–r_{A3}: .72 (.57–.90)

r_{C1}–r_{C3}: .30 (.01–.54)

r_{E1}–r_{E3}: .03 (.00–.10)

3. g at 10

Biv a^{2}2–3: .55 (.42–.69)

Biv c^{2}2–3: .38 (.26–.49)

Biv e^{2}2–3: .07 (.04–.11)

r_{A2}–r_{A3}: .74 (.60–.89)

r_{C2}–r_{C3}: .66 (.50−.82)

r_{E2}–r_{E3}: .15 (.08–.22)

Why do the Cholesky analyses shown in Figure 8 suggest genetic continuity and change in equal amounts, whereas the bivariate heritabilities shown in Table 13 suggest substantial genetic stability? There can be no conflict here because the bivariate heritabilities are derived directly from the Cholesky analyses, as illustrated below. As mentioned earlier, these analyses focus on different issues. The Cholesky analysis of genetic influence (first part of Figure 8) is focused exclusively on genetic variance (heritability) in the sense that it refers to the extent to which heritability at one age is shared with heritability at another age. In contrast, bivariate heritability focuses on the phenotypic correlation and the extent to which it is mediated by genetic factors.

This contrast can be seen more clearly if we work out an example of the A, C, and E contributions to the phenotypic correlation as derived from the Cholesky analysis in Figure 8 by the chain of paths connecting ages. For example, for English at 7 and 9 years, the A contribution to the phenotypic correlation is .46, as estimated by the product of the path coefficients (√.67 ×√.32=.46). The C contribution is .07 (√.14 ×√.04=.07). The E contribution is .04 (√.19 ×√.01=.04). These A, C, and E contributions sum to .57 which is reasonably similar to the phenotypic correlation of .63 estimated for all individuals without taking into account the paired (twin) structure of the data. Bivariate heritability, the genetic contribution to the phenotypic correlation, is .81 (.46÷.57=.81), which is also similar to the bivariate heritability estimate of .79 shown in Table 13. In other words, 81% of the phenotypic correlation is genetically mediated. In contrast, the Cholesky analysis described above indicates that, of the genetic variance at 9 years (.32+.33=.65), only 49% is shared with genetic variance at 7 years (.32÷.65=.49).

ACE Correlations

The second statistic that aids interpretation of longitudinal or multivariate genetic results is the genetic correlation. Bivariate heritability indexes the genetic contribution to the phenotypic correlation; the genetic correlation represents the extent to which genetic influences at one age correlate with genetic influences at the other age regardless of their heritability. Genetic correlations are particularly useful in relation to molecular genetics because they can be thought about as the probability that a gene associated with one trait or age will also be associated with the other trait or age. Shared environment correlations and nonshared environment correlations can be conceptualized similarly, and the full set of correlations are called ACE correlations (see Chapter II for details).

A, C, and E correlations are shown in Table 13. These correlations can be derived from the bivariate ACE estimates. For example, the genetic correlation between NC English at 7 and 9 years is shown in Table 13 as .70, which was obtained from the model-fitting analysis. The origin of this genetic correlation can be seen in Figure 8. The genetic contribution to the correlation between NC English at 7 and 9 years is .46, the product of √.67 and √.32. From the basic multivariate genetic model, this genetic contribution to the phenotypic correlation can be shown to be equivalent to the product of the square roots of the heritabilities of the two variables and their genetic correlation (Plomin & DeFries, 1979). Knowing the heritabilities of the two variables, we can solve for the genetic correlation simply by dividing by the product of the square roots of the heritabilities. For example, the heritabilities for NC English are .67 at 7 years and .65 at 9 years. Dividing .46 (the genetic contribution to the phenotypic correlation) by the product of the square roots of their heritabilities estimates the genetic correlation as .70 [.46÷(√.67 ×√.65)=.70], which is exactly the same as the model-fitting estimate of the genetic correlation shown in Table 13.

The genetic correlations in Table 13 are substantial. Even between 7 and 10 years, the genetic correlations are .67 for NC English, .68 for NC mathematics, and .72 for “g.” Even TOWRE at 7 years and PIAT at 10 years yield a high genetic correlation of .60 despite their significant differences in heritability and their modest phenotypic correlation. In what is becoming a familiar pattern, NC science is the odd one out; in this case, it shows the lowest genetic correlation in Table 13, indicating greater qualitative differences in genetic influences from 9 to 10 years.

Unlike bivariate ACE estimates which sum to the phenotypic correlation, ACE correlations are independent; they could all be zero or they could all be unity. In Table 13, the C correlations are in fact quite similar to the A correlations for NC English and mathematics: Between 7 and 10 years, the C correlations are .71 for NC English and .52 for NC mathematics. For “g” between 7 and 10 years, the C correlation is more modest, 30. NC science yields the highest C correlation: 1.0 between 9 and 10 years. TOWRE reading at 7 years and PIAT reading at 10 years yield a C correlation of .45. The significant but modest E correlations for all measures (except “g”) suggest that nonshared environment is not completely due to error of measurement, which would not be expected to be stable longitudinally.

Longitudinal DF Extremes Analysis

In the previous chapter, DF extremes analyses indicated that the abnormal is normal. As described in Chapter II and illustrated in Chapter IV, univariate DF extremes analysis begins with probands selected for extreme scores (or diagnoses) and analyzes how similar the mean of their co-twins is to the mean of the probands on a quantitative measure. By comparing MZ and DZ co-twin means, “group” heritability can be estimated indicating the extent to which the mean quantitative trait score difference between the probands and the population can be attributed to genetic influence.

Univariate DF extremes analysis can be extended to bivariate analysis (Light & DeFries, 1995; Plomin & Kovas, 2005). Although not discussed previously, the same considerations apply to the application of DF extremes analysis to longitudinal data—rather than analyzing two traits at the same measurement occasion, we can analyze the same trait at two measurement occasions. Longitudinal DF extremes analysis can address the issue of genetic mediation of continuity and change for learning disabilities rather than for learning abilities—that is, for the low-performing extremes rather than for individual differences throughout the entire distribution. This form of analysis is especially relevant for the goal of understanding both the antecedents and the long-term consequences of early disability, an issue with theoretical and applied significance.

A brief description of bivariate DF extremes analysis follows. In contrast to univariate DF extremes analysis which selects probands as extreme on X and compares the quantitative scores of their MZ and DZ co-twins on X, bivariate DF extremes analysis selects probands on X and compares the quantitative scores of their co-twins on Y, a cross-trait twin group correlation. The genetic contribution to the phenotypic difference between the means of the probands on trait X and the population on Y can be estimated by doubling the difference between the cross-trait twin group correlations for MZ and DZ twins. Bivariate group heritability is the ratio between this genetic estimate and the phenotypic difference between the probands on trait X and the population on Y. Unlike bivariate analysis of individual differences in unselected samples, such as those done earlier in this chapter, bivariate DF extremes analysis is directional in the sense that selecting probands on X and examining quantitative scores of co-twins on Y could yield different results as compared with selecting probands on Y and examining quantitative scores of co-twins on X. A group genetic correlation can be derived from four group parameter estimates: bivariate group heritability estimated by selecting probands for X and assessing co-twins on Y, bivariate group heritability estimated by selecting probands for Y and assessing co-twins on X, and univariate group heritability estimates for X and for Y (see Knopik, Alarcón, & DeFries, 1997). The group genetic correlation is the most informative summative index of genetic effects on low extremes in a longitudinal context. Although it is possible to conduct similar analyses of environmental influences, in this example of a longitudinal DF extremes analysis we will focus on genetic influences.

As an example of bivariate DF extremes analysis applied for the first time to longitudinal data, we analyzed the relationship between 7-year TOWRE scores and 10-year PIAT scores. Because bivariate DF extremes analyses are bidirectional, we conducted two separate analyses: (1) selecting children in the lowest 15% of 7-year TOWRE and analyzing their co-twins' scores on the 10-year PIAT (TOWRE → PIAT), and (2) selecting children in the lowest 15% of 10-year PIAT and analyzing their co-twins' scores on the 7-year TOWRE (PIAT→TOWRE).

For the TOWRE→PIAT longitudinal analysis, the phenotypic group correlation was .58, indicating that children with low scores on the TOWRE at 7 also had low scores on the PIAT at 10–they were 1.5 SD below the mean on the TOWRE at 7 and .87 SD below the mean on the PIAT at 10. Bivariate group heritability was .61; that is, most of the phenotypic group correlation between the TOWRE and PIAT is mediated genetically. In other words, genetic factors explain 61% of the difference between the mean TOWRE score of probands at 7 years and the population mean on the PIAT at 10 years. That is, to the extent the low scores (lowest 15%) on the TOWRE predict below average scores on the PIAT 3 years later, this is due in large part to common genetic factors.

As noted earlier, the results of bi-directional bivariate extremes analyses need not be symmetrical, as is the case for the analysis of PIAT→TOWRE. The phenotypic group correlation was .39 and bivariate group heritability was only .37, which indicates that genetic factors explain 37% of the difference between the mean PIAT score of probands at 10 years and the population mean on the TOWRE at 7 years. Nonetheless, combining the results for the TOWRE→PIAT and the PIAT→TOWRE analyses yielded a genetic correlation of .90. This suggests that despite the differences in bivariate group heritability for the two analyses, the genetic correlation is substantial between the extremes of TOWRE at 7 years and PIAT at 10 years.

Table 14 compares these results from our longitudinal analyses at the extreme to those presented earlier in this chapter for the entire distribution. Although it is noteworthy that there is lower bivariate heritability at the extremes than across the full distribution, the key result is the genetic correlation, which provides the strongest evidence for genetic links between low scores on the TOWRE at 7 years and low scores on the PIAT at 10 years. Because the TOWRE and PIAT are so different (word recognition versus reading comprehension), this analysis could be viewed as a multivariate analysis as well as a longitudinal analysis. Indeed, it could be argued that all longitudinal analyses are also multivariate analyses because it cannot be assumed that the “same” measure assessed at two ages involves the same cognitive processes at the two ages. In the next chapter, which focuses on multivariate genetic analysis, we include an example of a bivariate extremes analysis between poor performance on reading and on mathematics that is clearly bivariate and not longitudinal.

Table 14. COMPARISON OF GENETIC RESULTS FROM LONGITUDINAL GENETIC ANALYSES OF THE TOWRE AT 7 YEARS AND PIAT AT 10 YEARS FOR THE ENTIRE DISTRIBUTION (INDIVIDUAL DIFFERENCES) VERSUS THE LOWEST 15% EXTREMES

Individual differences

DF extremes

TOWRE→PIAT

PIAT→TOWRE

Phenotypic correlation

.44

.58

.39

Bivariate heritability

.83

.61

.37

Genetic correlation

.60

.90

SUMMARY

Genetic Stability

These developmental analyses lead to the conclusion that genetic influences on learning abilities and disabilities primarily contribute to stability. Genetic correlations from age to age are substantial, about .70, even from 7 to 10 years for NC English, NC mathematics, and “g.” Even TOWRE at 7 years and PIAT at 10 years yield a substantial genetic correlation of .60 despite the differences in these measures. In the first application of bivariate DF extremes analysis to longitudinal data, we showed that an even higher genetic correlation of .90 was obtained for the low extremes of the TOWRE and PIAT.

These substantial genetic correlations suggest that genes found to be associated with learning abilities and disabilities at one age are also likely to yield associations at other ages. However, the fact that the genetic correlations are not unity indicates that some gene associations will differ from age to age. Molecular genetic studies that assess learning abilities and disabilities longitudinally are needed to detect all of the genes responsible for their substantial heritability.

ACE correlations are useful in understanding the nature of genetic stability and change regardless of their contribution to phenotypic variance. Bivariate ACE estimates are useful in the more practical sense of understanding genetic and environmental contributions to phenotypic stability and change from age to age. These statistics also indicate genetic stability and environmental change. For NC English, NC mathematics, TOWRE and PIAT reading, and “g” from 7 years to 10 years, bivariate heritabilities are .71, .78, .83, and .80, respectively. In other words, about 80% of the phenotypic correlations from 7 to 10 years are mediated genetically.

We know very little about the mechanisms by which genes have their effects on individual differences on cognition and we know even less about how genes affect change and continuity. Many hypothetical mechanisms can be proposed. For example, any DNA variation that contributes to the whole brain efficiency (e.g., myelination) would continue to have its effects across ages. However, until the actual polymorphisms are discovered, these hypotheses will remain speculative.

Environmental Change

In contrast to genetic stability, environmental influences, especially nonshared environment, involve change. Shared environment correlations between 7 and 10 years are also high for NC English (.71) but lower for NC mathematics (.52) and for TOWRE and PIAT reading (.45), and much lower for “g” (.30). It is not difficult to think of shared environmental factors such as socioeconomic status or school quality that might make twins growing up in the same family and attending the same schools stable longitudinally in their learning abilities. However, these results suggest that shared environmental factors are as much involved in change as continuity; shared environmental factors that make change in a similar way such as changing neighborhoods or schools. However, it should be noted that shared environment accounts for only a modest amount of variance, .14 on average for NC composite scores.

Nonshared environment correlations are lower still: .26, .20, .11, and .03, respectively. Although progress has been slow in identifying specific nonshared environmental factors that make twins different from one another, whatever these factors may be they also largely change from age to age. The remaining 20% of the phenotypic correlation is explained primarily by shared environment.

ACE correlations and bivariate ACE estimates are based on longitudinal analyses of qualitative age changes using multivariate genetic models. The chapter began with an analysis of quantitative age differences in ACE parameter estimates at each age. These analyses indicate stability of both genetic and environmental influences in that ACE parameter estimates are remarkably similar at 7, 9, and 10 years. However, such quantitative age comparisons are much less informative than analyses of qualitative age changes.

The following chapter uses the same multivariate genetic techniques to investigate the causes of relationships within components of learning abilities and between different domains at each age.