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The previous chapter moved beyond the basic nature–nurture question by investigating the causes of change and continuity in learning abilities. It began with a brief section on quantitative differences in which genetic and environmental parameter estimates were compared across age. However, its focus was on the etiology of continuity and change, which was addressed by the application of multivariate genetic analysis to longitudinal data. The present chapter uses the same multivariate genetic techniques to investigate common and unique causes within and between learning abilities at each age. For example, to what extent do the genes that affect one aspect of reading ability also affect others? To what extent do genes that affect reading ability also affect mathematics? To what extent do genes that affect reading and mathematics also affect general cognitive ability?

As in the two previous chapters, we have maximized power by combining boys and girls, same-sex and opposite-sex DZ twins, and assessments by same and different teachers. Also, as in the previous chapter, the present chapter primarily reports analyses on individual differences for the entire sample, again for reasons of power. However, similar to the previous chapter, we present an example of a multivariate extremes analysis, in this case for web-based assessments of reading and mathematics at 10 years.

PHENOTYPIC CORRELATIONS

  1. Top of page
  2. PHENOTYPIC CORRELATIONS
  3. MULTIVARIATE GENETIC MODEL-FITTING ANALYSIS
  4. BIVARIATE ACE ESTIMATES
  5. ACE CORRELATIONS
  6. CHOLESKY ANALYSES OF “g” AND NC TEACHER ASSESSMENTS
  7. MULTIVARIATE DF EXTREMES ANALYSIS
  8. SUMMARY

If there were no phenotypic correlation between traits, no multivariate genetic analysis would be needed to conclude that different genetic and environmental factors affect the two traits. If traits are correlated phenotypically, as found in decades of research on cognitive and academic abilities, multivariate genetic analysis is essential to determine the extent to which their phenotypic correlation is mediated genetically or environmentally.

Table 15 lists phenotypic correlations within domains at each age. (Appendix E is a complete intercorrelation matrix within and between ages.) The average correlation for the three components within each domain across ages is .69 for NC English, .85 for NC mathematics, and .85 for NC science. These substantial intercorrelations were not limited to teacher NC ratings. Despite the different cognitive processes assumed to underlie reading words and nonwords, these two components on the TOWRE test at 7 years correlate .83. The average correlation between the three components of our web-based battery of mathematics at 10 years was somewhat lower, .59. Even when very different methods were employed, phenotypic correlations could be substantial: At 7 years, NC reading correlated .67 with the TOWRE composite. The correlations between NC ratings and our web-based tests at 10 years were less substantial: .44 for reading and .49 for mathematics.

Table 15.  PHENOTYPIC CORRELATIONS WITHIN DOMAIN AT EACH AGE FOR ONE RANDOMLY SELECTED MEMBER OF EACH TWIN PAIR
 123
  1. Note.—NC, National Curriculum; TOWRE, Test of Word Reading Efficiency; PIAT, Peabody Individual Achievement Test.

  2. **Indicates significance at .01 alpha level.

7-year NC English:
 1. Speaking1  
 2. Reading.64**1 
 3. Writing.56**.66**1
7-year NC mathematics:
 1. Using1  
 2. Numbers.81**1 
 3. Shapes.80**.84**1
9-years NC English:
 1. Speaking1  
 2. Reading.69**1 
 3. Writing.67**.77**1
9-year NC mathematics:
 1. Using1  
 2. Numbers.87**1 
 3. Shapes.84**.86**1
9-year NC science:
 1. Enquiry1  
 2. Life.80**1 
 3. Physical.83**.88**1
10-year NC English:
 1. Speaking1  
 2. Reading.71**1 
 3. Writing.71**.77**1
10-year NC mathematics:
 1. Using1  
 2. Numbers.88**1 
 3. Shapes.87**.90**1
10-year NC science:
 1. Enquiry1  
 2. Life.83**1 
 3. Physical.85**.91**1
7-year TOWRE
 1. Word1 
 2. Nonword.83**1
1. 7-year TOWRE composite1 
2. 7-year NC reading.67**1
1. 10-year PIAT1 
2. 10-year NC reading.44**1
10-year web mathematics:
 1. Understanding Number1  
 2. Nonnumerical Processes.61**1 
 3. Computation and Knowledge.64**.51**1
1. 10-year web mathematics1 
2. 10-year NC mathematics.49**1

Correlations were also substantial between domains, as shown in Table 16. The average correlation across the NC composites for the three ages was .75. Web-based tests of reading and mathematics at 10 years correlated .50.

Table 16.  PHENOTYPIC CORRELATIONS BETWEEN DOMAINS AT EACH AGE FOR ONE RANDOMLY SELECTED MEMBER OF EACH TWIN PAIR
 1234
  1. Note.—NC, National Curriculum; TOWRE, Test of Word Reading Efficiency; PIAT, Peabody Individual Achievement Test.

  2. **Indicates significance at .01 alpha level.

7 years
 1. g1  
 2. NC English.41**1 
 3. NC mathematics.39**.74**1
9 years
 1. g1   
 2. NC English.40**1  
 3. NC mathematics.41**.74**1 
 4. NC science.37**.74**.75**1
10 years
 1. g1   
 2. NC English.41**1  
 3. NC mathematics.38**.76**1 
 4. NC science.37**.78**.77**1
7 years
 1. g1 
 2. TOWRE.41**1
10 years
 1. g1  
 2. PIAT.55**1 
 3. web mathematics.61**.50**1

Also shown in Table 16 are correlations with “g”: On average across the ages, “g” correlated .41 with NC English, .39 with NC mathematics, and .37 with NC science. With the other test scores, “g” correlated .41 with 7-year TOWRE, .55 with 10-year PIAT, and .61 with 10-year mathematics.

In summary, there are substantial phenotypic correlations within and between these domains. In this chapter, we use multivariate genetic analysis to assess genetic and environmental mediation of these phenotypic correlations.

MULTIVARIATE GENETIC MODEL-FITTING ANALYSIS

  1. Top of page
  2. PHENOTYPIC CORRELATIONS
  3. MULTIVARIATE GENETIC MODEL-FITTING ANALYSIS
  4. BIVARIATE ACE ESTIMATES
  5. ACE CORRELATIONS
  6. CHOLESKY ANALYSES OF “g” AND NC TEACHER ASSESSMENTS
  7. MULTIVARIATE DF EXTREMES ANALYSIS
  8. SUMMARY

As described in the previous chapter in relation to longitudinal analysis and more generally in Chapter II, multivariate genetics can be used to analyze the covariance between traits rather than the variance of each trait separately in order to estimate the extent to which the same (common) or different (unique) genetic and environmental factors affect the traits. We will not repeat here the description of the two basic sets of statistics of multivariate genetic analysis: bivariate ACE statistics that specify the extent to which the phenotypic correlation is mediated by genetic and environmental factors, and ACE correlations that index the extent to which the same genetic and environmental factors affect the traits regardless of their effect on the phenotype.

The only difference in approach is that the model used in most of the analyses in this chapter is a correlated factors model rather than a Cholesky model. The Cholesky model is most suited to variables that can be ordered, as was the case for the longitudinal analyses presented in the previous chapter in which the variables can be ordered by age. The correlated factors model is more appropriate for most of the multivariate genetic analyses in this chapter because it is not dependent on the order in which the variables are included and it also has the advantage of focusing on ACE correlations. We do use the Cholesky model in the final set of analyses in which we enter “g” first in order to investigate the multivariate ACE structure of academic performance in reference to “g.” Despite these presentational issues, it should be kept in mind that the correlated factors model and the Cholesky model are algebraic transformations of each other and thus the same bivariate ACE estimates and ACE correlations can be obtained from the two models, as illustrated in the previous chapter.

In Figure 9, the three components of NC English at 7 years are used as an example of a correlated factor model-fitting analysis, with results depicted as a path diagram. In the first panel, the coefficients from the latent A variables to the measured traits (shown in rectangles) are heritability estimates (the path coefficient itself is the square root of this heritability). The analogous coefficients in the other panels are shared (C) and nonshared (E) environment contributions to variance. Heritabilities are substantial (61% on average), shared environment is modest (12%) and nonshared environment is moderate (27%). These heritability estimates are similar but not identical to those presented in Chapter III because a univariate full sex-limitation model was used in Chapter III, whereas the present analyses are based on a multivariate model with sexes combined.

image

Figure 9. —Trivariate genetic model-fitting results at 7 years for three domains of NC English.

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As seen in Figure 9, the common factor model directly displays the ACE correlations, which are substantial for A (genetic correlation of .70 on average), unity for C (shared environment correlation of 1.0 on average), and modest for E (nonshared environment correlation of .28 on average). Bivariate heritability is a function of these heritabilities and genetic correlations. For example, multiplying the chain of paths between speaking and reading in the top panel of Figure 9 indicates that the genetic contribution to the phenotypic correlation between speaking and reading is .41 (i.e.,√.60 × .67 ×√.63=.41). The C and E contributions to the phenotypic correlation are .14 and .06. Thus, the model-fitting estimate of the phenotypic correlation is .61 (i.e., .41+.14+.06=.61), which is close to the correlation of .64 shown in Table 15. The bivariate heritability is the proportion of the phenotypic correlation that is mediated genetically, which is 67% (i.e., .41÷.61=.67). The bivariate C and E estimates are 23% and 10%.

BIVARIATE ACE ESTIMATES

  1. Top of page
  2. PHENOTYPIC CORRELATIONS
  3. MULTIVARIATE GENETIC MODEL-FITTING ANALYSIS
  4. BIVARIATE ACE ESTIMATES
  5. ACE CORRELATIONS
  6. CHOLESKY ANALYSES OF “g” AND NC TEACHER ASSESSMENTS
  7. MULTIVARIATE DF EXTREMES ANALYSIS
  8. SUMMARY

Rather than showing path diagrams like Figure 9 for all of the multivariate genetic analyses, Table 17 summarizes the bivariate ACE estimates and the ACE correlations within domains. The first row shows a model-fitting estimate of 67% for bivariate heritability for NC speaking and NC reading at 7 years, which is the same as the estimate calculated above. The bivariate ACE estimates indicate that the phenotypic correlations within domains are largely mediated genetically. Bivariate heritabilities are substantial for NC ratings at 7 and 9 years—the average is 72%, meaning that 72% of the phenotypic correlations within domains are mediated genetically. At 10 years, bivariate heritabilities are somewhat (but not nearly significantly) lower—64% on average for English and mathematics and 51% for science. Similar results indicating substantial genetic mediation emerged for Word and Nonword components of the TOWRE at 7 years (73%) and for the three components of the web-based battery of mathematics tests (58%). Bivariate heritabilities were also substantial in comparisons between NC teacher assessments and tests: 83% for NC reading and TOWRE at 7 years, 79% for NC reading and PIAT at 10 years, and 85% for NC mathematics and the composite of the three mathematics components at 10 years.

Table 17.  WITHIN-DOMAIN MULTIVARIATE GENETIC ANALYSES: BIVARIATE GENETIC (A), SHARED ENVIRONMENT (C), AND NONSHARED ENVIRONMENT (E) ESTIMATES AND BIVARIATE A, C, AND E CORRELATIONS (95% CIS IN PARENTHESES)
 A (axayrA/rP)C (cxcyrC/rP)E (exeyrE/rP)rArCrE
  1. Note.—NC, National Curriculum; TOWRE, Test of Word Reading Efficiency; PIAT, Peabody Individual Achievement Test.

7-year NC English
 1. Speaking and listeningBiv a21–2: .67 (.60–.74)Biv c212: .23 (.16–.29)Biv e212: .10 (.08–.12)rA1–rA2: .67 (.64–.70)rC1–rC2: 1.00 (.94–1.00)rE1–rE2: .26 (.22–.30)
 2. ReadingBiv a213: .67 (.60–.75)Biv c213: .21 (.14–.27)Biv e213: .12 (.10–.14)rA1–rA3: .64 (.60–.68)rC1–rC3: 1.00 (.91–1.00)rE1–rE3: .25 (.21–.29)
 3. WritingBiv a223: .72 (.66–.78)Biv c223: .14 (.09–.19)Biv e223: .14 (.12–.17)rA2–rA3: .78 (.75–.81)rC2–rC3: 1.00 (.83–1.00)rE2–rE3: .32 (.28–.35)
7-year NC mathematics
 1. Using and applyingBiv a212: .72 (.65–.78)Biv c212: .08 (.03–.14)Biv e212: .20 (.18–.22)rA1–rA2: .89 (.88–.92)rC1–rC2: 1.00 (.79–1.00)rE1–rE2: .55 (.52–.58)
 2. NumbersBiv a213: .71 (.64–.78)Biv c213: .10 (.04–.16)Biv e213: .19 (.17–.21)rA1–rA3: .87 (.85–.89)rC1–rC3: 1.00 (.85–1.00)rE1–rE3: .55 (.52–.58)
 3. ShapesBiv a223: .70 (.64–.77)Biv c223: .09 (.03–.15)Biv e223: .21 (.19–.23)rA2–rA3: .91 (.89–.92)rC2–rC3: 1.00 (.89–1.00)rE2–rE3: .62 (.60–.65)
9-Year NC English
 1. Speaking and listeningBiv a212: .75 (.64–.85)Biv c212: .11 (.01–.21)Biv e212: .14 (.12–.17)rA1–rA2: .81 (.76–.87)rC1–rC2: .94 (.39–1.00)rE1–rE2: .36 (.31–.42)
 2. ReadingBiv a213: .72 (.62–.83)Biv c213: .13 (.04–.22)Biv e213: .15 (.12–.18)rA1–rA3: .78 (.73–.83)rC1–rC3: .99 (.72–1.00)rE1–rE3: .33 (.28–.39)
 3. WritingBiv a223: .80 (.71–.87)Biv c223: .07 (.01–.15)Biv e223: .13 (.11–.16)rA2–rA3: .89 (.86–.92)rC2–rC3: .98 (.46–1.00)rE2–rE3: .37 (.31–.42)
9-year NC mathematics
 1. Using and applyingBiv a212: .76 (.67–.82)Biv c212: .04 (.00–.12)Biv e212: .20 (.17–.23)rA1–rA2: .95 (.94–.98)rC1–rC2: .88 (.00–1.00)rE1–rE2: .62 (.58–.66)
 2. NumbersBiv a213: .73 (.64–.81)Biv c21–3: .07 (.00–.16)Biv e213: .20 (.18–.23)rA1–rA3: .91 (.89–.94)rC1–rC3: .99 (.65–1.00)rE1–rE3: .62 (.58–.66)
 3. ShapesBiv a223: .74 (.64–.82)Biv c223: .06 (.00–.14)Biv e223: .21 (.18–.23)rA2–rA3: .97 (.94–1.00)rC2–rC3: .82 (.00–1.00)rE2–rE3: .65 (.61–.68)
9-year NC science
 1. Scientific enquiryBiv a212: .69 (.59–.79)Biv c212: .11 (.02–.20)Biv e212: .20 (.17–.23)rA1–rA2: .88 (.84–.93)rC1–rC2: .90 (.51–1.00)rE1–rE2: .55 (.50–.59)
 2. Life processesBiv a213: .67 (.57–.77)Biv c213: .11 (.02–.20)Biv e213: .22 (.19–.25)rA1–rA3: .89 (.86–.93)rC1–rC3: .97 (.66–1.00)rE1–rE3: .62 (.58–.66)
 3. Physical processesBiv a223: .70 (.61–.78)Biv c223: .07 (.00–.16)Biv e223: .23 (.20–.25)rA2–rA3: .93 (.90–.95)rC2–rC3: .90 (.17–1.00)rE2–rE3: .74 (.71–.77)
10–year NC English
 1. Speaking and listeningBiv a212: .58 (.48–.68)Biv c212: .25 (.16–.33)Biv e212: .17 (.15–.20)rA1–rA2: .77 (.72–.83)rC1–rC2: .98 (.83–1.00)rE1–rE2: .43 (.38–.48)
 2. ReadingBiv a213: .63 (.54–.73)Biv c213: .22 (.12–.30)Biv e213: .15 (.12–.18)rA1–rA3: .79 (.75–.83)rC1–rC3: 1.00 (.91–1.00)rE1–rE3: .38 (.32–.43)
 3. WritingBiv a223: .61 (.52–.70)Biv c223: .22 (.13–.30)Biv e223: .17 (.15–.20)rA2–rA3: .86 (.82–.92)rC2–rC3: .99 (.86–1.00)rE2–rE3: .45 (.40–.50)
10-year NC mathematics
 1. Using and applyingBiv a212: .69 (.60–.78)Biv c212: .09 (.01–.18)Biv e212: .22 (.19–.25)rA1–rA2: .96 (.93–.99)rC1–rC2: .85 (.35–.99)rE1–rE2: .68 (.64–.71)
 2. NumbersBiv a213: .64 (.55–.74)Biv c213: .13 (.04–.21)Biv e213: .23 (.20–.26)rA1–rA3: .92 (.90–.95)rC1–rC3: .98 (.81–1.00)rE1–rE3: .70 (.67–.73)
 3. ShapesBiv a223: .67 (.58–.76)Biv c223: .11 (.02–.19)Biv e223: .22 (.20–.25)rA2–rA3: .98 (.95–1.00)rC2–rC3: .90 (.62–1.00)rE2–rE3: .71 (.68–.74)
10-year NC science
 1. Scientific enquiryBiv a212: .53 (.44–.63)Biv c212: .26 (.18–.34)Biv e212: .20 (.18–.23)rA1–rA2: .93 (.88–.99)rC1–rC2: .90 (.81–.98)rE1–rE2: .59 (.54–.63)
 2. Life processesBiv a213: .50 (.42–.60)Biv c213: .27 (.19–.35)Biv e213: .22 (.20–.25)rA1–rA3: .93 (.88–.98)rC1–rC3: .94 (.86–1.00)rE1–rE3: .65 (.62–.69)
 3. Physical processesBiv a223: .49 (.41–.58)Biv c223: .26 (.19–.34)Biv e223: .24 (.22–.27)rA2–rA3: .95 (.92–.98)rC2–rC3: .98 (.94–1.00)rE2–rE3: .78 (.75–.80)
7-year TOWRE
 1. WordBiv a212: .73 (.67–.79)Biv c212: .16 (.10–.21)Biv e212: .11 (.10–.12)rA1–rA2: .88 (.87–.90)rC1–rC2: 1.00 (.90–1.00)rE1–rE2: .50 (.47–.53)
 2. Nonword
7-year reading
 1. TOWREBiv a212: .83 (.75–.91)Biv c212: .09 (.01–.17)Biv e212: .08 (.06–.10)rA1–rA2: .78 (.73–.82)rC1–rC2: .77 (.23–1.00)rE1–rE2: .28 (.23–.33)
 2. NC reading
10–year web mathematics
 1. Understanding NumberBiv a212: .57 (.44–.70)Biv c212: .26 (.15–.37)Biv e212: .17 (.12–.21)rA1–rA2: .95 (.80–1.00)rC1–rC2: .81 (.65–1.00)rE2–rE3: .23 (.18–.29)
 2. Nonnumerical ProcessesBiv a213: .59 (.45–.72)Biv c213: .18 (.08–.29)Biv e213: .23 (.18–.28)rA1–rA3: .90 (.81–.99)rC1–rC2: .95 (.63–1.00)rE1–rE3: .31 (.26–.36)
 3. Computation and KnowledgeBiv a223: .57 (.42–.74)Biv c223: .24 (.11–.37)Biv e223: .18 (.13–.24)rA2–rA3: .76 (.64–.93)rC1–rC3: .95 (.63–1.00)rE2–rE3: .20 (.14–.25)
10–year reading
 1. PIATBiv a212: .79 (.62–.97)Biv c212: .18 (.02–.33)Biv e212: .03 (.00–.08)rA1–rA2: .78 (.62–.96)rC1–rC2: .39 (.06–.65)rE1–rE2: .04 (.00–.11)
 2. NC reading
10-year mathematics
 1. Web mathematicsBiv a212: .85 (.67–1.00)Biv c212: .04 (.00–.19)Biv e212: .11 (.07–.16)rA1–rA2: .74 (.63–.86)rC1–rC2: .14 (.00–.52)rE1–rE2: .19 (.12–.26)
 2. NC mathematics

Bivariate heritabilities were also substantial between domains, as shown in Table 18. The average bivariate heritability across the NC composites for the three ages was 64%. Bivariate heritability was 49% for web-based assessments of reading and mathematics at 10 years. Bivariate heritabilities with “g” were 76% on average for NC English, NC mathematics, and NC science composites at 7, 9, and 10 years. Bivariate heritabilities between “g” and test scores were 62% with 7-year TOWRE, 51% with 10-year PIAT, and 59% with 10-year mathematics (see Table 19).

Table 18.  BETWEEN-DOMAIN MULTIVARIATE GENETIC ANALYSES: BIVARIATE GENETIC (A), SHARED ENVIRONMENT (C), AND NONSHARED ENVIRONMENT (E) ESTIMATES AND BIVARIATE A, C, AND E CORRELATIONS (95% CIS IN PARENTHESES)
 A (axayrA/rP)C (cxcyrC/rP)E (exeyrE/rP)rArCrE
  1. Note.—NC, National Curriculum; TOWRE, Test of Word Reading Efficiency; PIAT, Peabody Individual Achievement Test.

7-year tests
 1. gBiv a21–2: .62 (.52.73)Biv c21–2: .30 (.20.39)Biv e21–2: .08 (.06.11)rA1–rA2: . .47 (.40.55)rC1–rC2: .63 (.45.85)rE1–rE2: .14 (.10.19)
 2. TOWRE
7-year NC
 1. EnglishBiv a21–2: .69 (.63.75)Biv c21–2: .20 (.14.26)Biv e21–2: .11 (.10.13)rA1–rA2: .78 (.76.80)rC1–rC2: 1.00 (.971.00)rE1–rE2: .40 (.36.43)
 2. Mathematics
9-year NC
 1. EnglishBiv a21–2: .73 (.64.82)Biv c21–2: .14 (.06.23)Biv e21–2: .13 (.11.15)rA1–rA2: .79 (.76.83)rC1–rC2: 1.00 (.811.00)rE1–rE2: .40 (.35.46)
 2. MathematicsBiv a21–3: .69 (.60.79)Biv c21–3: .17 (.08.26)Biv e21–3: .14 (.12.16)rA1–rA3: .78 (.74.83)rC1–rC3: 1.00 (.781.00)rE1–rE3: .46 (.41.51)
 3. ScienceBiv a22–3: .72 (.62.81)Biv c22–3: .15 (.06.23)Biv e22–3: .14 (.11.16)rA2–rA3: .82 (.79.86)rC2–rC3: 1.00 (.851.00)rE2–rE3: .41 (.36.46)
10-year tests
 1. gBiv a21–2: .51 (.38.63)Biv c21–2: .39 (.28.50)Biv e21–2: .10 (.06.14)rA1–rA2: .63 (.52.76)rC1–rC2: .85 (.68.99)rE1–rE2: .17 (.11.23)
 2. PIATBiv a21–3: .59 (.48.70)Biv c21–3: .30 (.20.40)Biv e21–3: .11 (.08.14)rA1–rA3: .76 (.66.86)rC1–rC3: .84 (.66.99)rE1–rE3: .22 (.16.28
 3. Web mathematicsBiv a22–3: .49 (.36.63)Biv c22–3: .41 (.29.51)Biv e22–3: .10 (.06.15)rA2–rA3: .52 (.43.64)rC2–rC3: 1.00 (.771.00)rE2–rE3: .16 (.09.21)
10-year NC
 1. EnglishBiv a21–2: .60 (.52.69)Biv c21–2: .26 (.18.33)Biv e21–2: .14 (.12.16)rA1–rA2: .79 (.75.82)rC1–rC2: 1.00 (.941.00)rE1–rE2: .45 (.40.50)
 2. MathematicsBiv a21–3: .52 (.44.61)Biv c21–3: .33 (.25.40)Biv e21–3: .15 (.13.18)rA1–rA3: .78 (.74.82)rC1–rC3: 1.00 (.951.00)rE1–rE3: .51 (.46.56)
 3. ScienceBiv a22–3: .55 (.47.64)Biv c22–3: .29 (.20.36)Biv e22–3: .16 (.14.19)rA2–rA3: .80 (.76.84)rC2–rC3: 1.00 (.951.00)rE2–rE3: .49 (.44.54)
Table 19. g” VERSUS NC COMPOSITES: BIVARIATE GENETIC (A), SHARED ENVIRONMENT (C), AND NONSHARED ENVIRONMENT (E) ESTIMATES AND BIVARIATE A, C, AND E CORRELATIONS (95% CIS IN PARENTHESES)
 A (axayrA/rP)C (cxcyrC/rP)E (exeyrE/rP)rArCrE
  1. Note.—NC, National Curriculum.

7 years
 1. gBiv a21–2: .73 (.60.87)Biv c21–2: .21 (.09.32)Biv e21–2: .06 (.03.10)rA1–rA2: .59 (.50.70)rC1–rC2: .38 (.17.56)rE1–rE2: .10 (.04.15)
 2. NC EnglishBiv a21–3: .73 (.59.88)Biv c21–3: .19 (.06.31)Biv e21–3: .08 (.04.12)rA1–rA3: .54 (.45.65)rC1–rC3: .38 (.13.61)rE1–rE3: .10 (.05.16)
 3. NC mathematics
9 years
 1. gBiv a21–2: .68 (.52.86)Biv c21–2: .27 (.11.41)Biv e21–2: .05 (.01.10)rA1–rA2: .58 (.45.71)rC1–rC2: .42 (.19.65)rE1–rE2: .09 (.01.16)
 2. NC EnglishBiv a21–3: .70 (.54.86)Biv c21–3: .22 (.07.36)Biv e21–3: .08 (.03.13)rA1–rA3: .62 (.49.75)rC1–rC3: .44 (.20.71)rE1–rE3: .13 (.05.20)
 3. NC mathematicsBiv a21–4: .63 (.45.81)Biv c21–4: .32 (.15.47)Biv e21–4: .06 (.01.11)rA1–rA4: .50 (.37.64)rC1–rC4: .48 (.25.75)rE1–rE4: .09 (.01.16)
 4. NC science
10 years
 1. gBiv a21–2: .83 (.631.00)Biv c21–2: .12 (.00.29)Biv e21–2: .05 (.00.11)rA1–rA2: .65 (.52.80)rC1–rC2: .21 (.00.47)rE1–rE2: .08 (.00.16)
 2. NC EnglishBiv a21–3: .91 (.691.00)Biv c21–3: .04 (.00.23)Biv e21–3: .05 (.00.12)rA1–rA3: .67 (.52.83)rC1–rC3: .08 (.00.40)rE1–rE3: .06 (.00.14)
 3. NC mathematicsBiv a21–4: .89 (.661.00)Biv c21–4: .08 (.00.27)Biv e21–4: .04 (.00.11)rA1–rA4: .69 (.53.88)rC1–rC4: .10 (.00.35)rE1–rE4: .04 (.00.12)
 4. NC science

In summary, bivariate heritabilities were substantial within and between domains. Both shared and nonshared environment account for significant portions of the remainder of the phenotypic correlations not mediated by genetics. Across all of the comparisons in Tables 16 and 17, the average bivariate estimates were 18% for shared environment and 16% for nonshared environment. Relatively greater bivariate shared environment estimates were found for correlations involving test scores: “g” and TOWRE at 7 years (30%), “g” and PIAT at 10 years (39%), “g” and the mathematics composite at 10 years (30%) and between the PIAT and the mathematics composite at 10 years (41%). This might reflect test-taking skills.

ACE CORRELATIONS

  1. Top of page
  2. PHENOTYPIC CORRELATIONS
  3. MULTIVARIATE GENETIC MODEL-FITTING ANALYSIS
  4. BIVARIATE ACE ESTIMATES
  5. ACE CORRELATIONS
  6. CHOLESKY ANALYSES OF “g” AND NC TEACHER ASSESSMENTS
  7. MULTIVARIATE DF EXTREMES ANALYSIS
  8. SUMMARY

Tables 17 and 18 also include ACE correlations. To reiterate, ACE correlations index the extent to which the same genetic and environmental factors affect traits regardless of the magnitude of their effects on the phenotypes. A genetic correlation can be viewed as the probability that a DNA marker found to be associated with one trait will also be associated with the other trait. The first row in Table 17 shows a genetic correlation (rA) of .67 between NC speaking and reading at 7 years, which is the source of the genetic correlation shown in the path model in Figure 9.

The genetic correlations within all of the domains (Table 17) are strikingly high: The average of the 31 genetic correlations in Table 17 is .86. For NC teacher ratings at all three ages, genetic correlations within the English domain are somewhat higher between reading and writing (.84) than between speaking/listening versus reading or writing (.74), although the main point is that both sets of genetic correlations are exceptionally high. High genetic correlations are found for tests as well as teacher ratings. The word and nonword subtests of the TOWRE at 7 years yielded a genetic correlation of .88, and the average genetic correlation among the mathematics subtests at 10 years was .87. Even when different measurement methods were compared, genetic correlations within domains are high: .78 for NC teacher-rated reading versus PIAT web-based test scores at 10 years and .74 between NC teacher-rated mathematics versus web-based mathematics tests scores at 10 years.

Genetic correlations were also substantial between domains (Table 18). The average genetic correlation across the NC composites for the three ages was .79. The genetic correlation was .52 between web-based assessments of reading and mathematics at 10 years. The genetic correlation between “g” and test scores was .47 with 7-year TOWRE, .63 with 10-year PIAT, and .76 with 10-year mathematics.

In summary, genetic correlations were very high within and between domains. Because bivariate ACE estimates sum to 100%, if bivariate genetic estimates are high, as they are in our analyses, bivariate shared (C), and nonshared (E) environmental estimates must be low. In contrast, ACE correlations can all be high or low. As shown in Tables 17 and 18, C correlations are extremely high—near unity both within and between domains—with just two striking exceptions. For NC reading and PIAT at 10 years, the C correlation is only .39, although the C correlation is .77 for NC reading and TOWRE at 7 years. The second exception is NC mathematics and web-based mathematics at 10 years, which yielded a C correlation of .14. It is interesting that these exceptions involve comparisons between NC teacher ratings and web-based tests, suggesting that different shared environmental influences affect NC teacher ratings and web-based tests at 10 years.

E correlations are on average half the magnitude of the genetic correlations. Across Tables 17 and 18, the average E correlation is .42, suggesting that different nonshared environmental factors are at work within and between learning abilities. However, E correlations vary considerably across domains. They are consistently lower for the three components of NC English at all ages (.35 on average) than for NC mathematics (.63) and NC science (.66). Similar to the pattern of results for C correlations, E correlations were extremely low for NC reading versus PIAT at 10 years (.04) and for NC mathematics versus web-based mathematics at 10 years (.19).

CHOLESKY ANALYSES OF “g” AND NC TEACHER ASSESSMENTS

  1. Top of page
  2. PHENOTYPIC CORRELATIONS
  3. MULTIVARIATE GENETIC MODEL-FITTING ANALYSIS
  4. BIVARIATE ACE ESTIMATES
  5. ACE CORRELATIONS
  6. CHOLESKY ANALYSES OF “g” AND NC TEACHER ASSESSMENTS
  7. MULTIVARIATE DF EXTREMES ANALYSIS
  8. SUMMARY

These substantial genetic correlations suggest that the same genes largely affect performance in different academic subjects. Some of these genetic effects are even more general in that they also affect “g.” To what extent is it all “g”? We incorporated “g” and NC ratings of English, mathematics and science in a multivariate genetic analysis that explored the genetic structure of academic performance in relation to “g.” As mentioned earlier, a Cholesky model, similar to the model used in the previous chapter, is best suited to address this issue. Separate Cholesky analyses were conducted at 7, 9, and 10 years, with the results shown as path diagrams in Figures 10–12, respectively.

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Figure 10. —Seven years: Multivariate genetic model-fitting results for “g,” NC English, and NC mathematics (95% confidence intervals shown in parentheses).

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Figure 11. —Nine years: Multivariate genetic model-fitting results for “g,” NC English, NC mathematics, and NC science.

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Figure 12. —Ten years: Multivariate genetic model-fitting results for “g,” NC English, NC mathematics, and NC science (95% confidence intervals shown in parentheses).

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The A1 latent variable extracts genetic variance that is in common between “g” and academic performance. For example, in Figure 10 (7 years), .37 is the heritability of “g.” The A1 loadings of .23 for English and .19 for mathematics indicate that a significant and substantial amount of the genetic variance on English and mathematics is shared in common with “g.” However, English and mathematics are more highly heritable than “g,” as shown in Chapter III. The heritability estimates from the Cholesky model are .65 for English (i.e., .23+.42=.65) and .65 for mathematics (.19+.21+.25=.65). Thus, only a third of the genetic variance on English is shared in common with “g” (.23÷.65=.35). Similarly, only a third of the genetic variance on mathematics is shared in common with “g” (.19÷.65=.29).

An important feature of the Cholesky model is that it can be used to estimate genetic variance shared by English and mathematics that is independent of “g.” This analysis is captured by the A2 latent variable. The significant and substantial loadings of English and mathematics on the A2 latent variable indicate that English and mathematics share genetic variance independent of “g.” For mathematics, about a third of its genetic variance is shared with English independent of “g” (.21÷.65=.32). The A3 latent variable indexes genetic variance that is unique to mathematics, that is, not shared with either “g” or English. Focusing on mathematics, the results suggest that about a third of its genetic variance is in common with both “g” and English, about a third is in common with English independent of “g,” and the remaining third is unique to mathematics. A similar conclusion would be reached for English if it were the last variable in the Cholesky analysis.

At 9 and 10 years (Figures 11 and 12), NC science is also included in the Cholesky analyses. Focusing on science, which is the last variable in the Cholesky analysis, a similar conclusion emerges at 9 years (Figure 11). The heritability of science at 9 years is estimated in this model as .61 (.15+.21+.07+.18=.61). Of the genetic variance on science, 25% is in common with “g,” English, and mathematics (.15÷.61=.25); 34% is independent of “g” but in common with English and mathematics (.21÷.61=.34); 11% is independent of “g” and English but in common with mathematics; and 30% is unique to science.

At 10 years (Figure 12), the heritability of science is estimated as .48; this lower estimate at 10 years is the same as the model-fitting estimate presented earlier in Table 11. Of this genetic variance, 48% is in common with “g,” English, and mathematics; 17% is independent of “g” but in common with English and mathematics; 6% is independent of “g” and English but in common with mathematics; and 29% is unique to science. This suggests that science at 10 years may have more to do with “g” genetically. However, the results for English and mathematics are similar at 10 years in suggesting that only about a third of their genetic variance is shared in common with “g.”

The main point of these genetic analyses is that academic performance is not just “g.” That is, although about a third of the genetic variance of English and mathematics is in common with “g,” about a third of the genetic variance is general to academic performance but not “g,” and about a third is specific to each domain.

The results for shared environment suggest that shared environment effects on “g” are different from shared environment effects on academic performance. However, the same shared environment factors affect performance in English, mathematics, and science. Nonshared environment is largely unique to “g” and unique to each domain of academic performance.

The bivariate ACE estimates and the ACE correlations between “g” and NC composites are listed in Table 19 based on the Cholesky model-fitting analyses summarized in Figures 10–12. The bivariate ACE estimates follow directly from the figures: Most (76%) of the phenotypic correlations between “g” and NC composites is mediated genetically, and the remainder of the phenotypic correlations are due primarily to shared environment (18%). Nonshared environment accounts for a negligible amount of overlap between “g” and NC composites (6%).

The ACE correlations in Table 19 underline the conclusions drawn from the Cholesky analyses. Although the genetic correlations between “g” and NC composites are substantial (.61 on average), they are lower, often significantly lower, than the genetic correlations between NC composites, which are about .80 on average (see Table 18). In other words, the general effects of genes on learning abilities is not all “g”—learning abilities are more highly correlated genetically with each other than they are with “g.” The C correlations between “g” and NC composites are moderate (.31 on average) and the E correlations are modest (.08 on average), suggesting again that environmental influences, especially nonshared environmental influences, contribute to differences between learning abilities.

MULTIVARIATE DF EXTREMES ANALYSIS

  1. Top of page
  2. PHENOTYPIC CORRELATIONS
  3. MULTIVARIATE GENETIC MODEL-FITTING ANALYSIS
  4. BIVARIATE ACE ESTIMATES
  5. ACE CORRELATIONS
  6. CHOLESKY ANALYSES OF “g” AND NC TEACHER ASSESSMENTS
  7. MULTIVARIATE DF EXTREMES ANALYSIS
  8. SUMMARY

In this chapter, we have focused on multivariate genetic analyses based on individual differences for the entire sample (abilities) rather than extremes (disabilities) for two reasons. First, power is much greater for the entire sample and power is especially critical for multivariate genetic analyses. Second, our univariate analyses of extremes in Chapter III indicate that the results for the extremes are highly similar to results for the entire sample; this is the basis for the conclusion that the abnormal is normal. However, multivariate genetic results could be different for extremes and the entire sample and there are very few examples of multivariate extremes analyses. For these reasons, an example of a bivariate DF extremes analysis is presented in this section, based on two tests administered via the internet at 10 years of age: PIAT reading comprehension and mathematics.

We will not repeat here the description of bivariate DF extremes analysis from the previous chapter, which applied extremes analysis to longitudinal data on reading from 7 years (TOWRE) to 10 years (PIAT). In summary review, bivariate group heritability in our example addresses the genetic contribution to the phenotypic difference between the proband mean on reading and the population mean on mathematics (see Kovas, Haworth, Harlaar, Petrill, Dale, & Plomin, in press). Because bivariate DF extremes analysis is directional, two analyses need to be conducted that could yield different results: Selecting probands for poor reading performance and comparing co-twin quantitative trait scores on mathematics (reading [RIGHTWARDS ARROW] mathematics) and vice versa (mathematics [RIGHTWARDS ARROW] reading). From these two analyses, a bivariate extremes genetic correlation can be derived. Similar bivariate extreme estimates can be obtained for shared and nonshared environment but in this example we focus on genetic factors in order to simplify the presentation.

As in previous analyses of extremes, we selected probands for scores in the lowest 15% of reading and mathematics. For the reading[RIGHTWARDS ARROW]mathematics analysis, the phenotypic group correlation was .60 indicating that children with the lowest reading scores also had low mathematics scores. More specifically, the reading probands had reading scores that were 1.6 SD below the population mean on reading and .96 SD below the population mean on mathematics (−.96÷−1.6=.60). Bivariate group heritability was .38. That is, genetic factors explained 38% of the difference between the mean reading score of probands and the population mean on mathematics.

Results for the mathematics[RIGHTWARDS ARROW]reading analysis were similar. The phenotypic group correlation was .46 and bivariate group heritability was .24. Although the bivariate group heritabilities at the extremes were lower than the bivariate heritabilities described earlier, combining the results for the reading[RIGHTWARDS ARROW]mathematics analysis and the mathematics [RIGHTWARDS ARROW] reading analysis yielded a genetic correlation of .67. That is, two-thirds of the genetic effects on low reading and low mathematics are in common.

Table 20 compares the bivariate extremes results to bivariate results for the entire sample. The results are roughly similar, suggesting general genetic effects that encompass not only reading and mathematics abilities but also disabilities.

Table 20.  COMPARISON BETWEEN BIVARIATE GENETIC RESULTS FOR THE LOW EXTREMES AND FOR THE ENTIRE SAMPLE FOR READING AND MATHEMATICS TEST SCORES AT 10 YEARS
 Individual DifferencesDF Extremes
PIAT[RIGHTWARDS ARROW] MathematicsMathematics[RIGHTWARDS ARROW] PIAT
  1. Note.—PIAT, Peabody Individual Achievement Test

Phenotypic correlation.50.60.46
Bivariate heritability.49.38.24
Genetic correlation.52.67

SUMMARY

  1. Top of page
  2. PHENOTYPIC CORRELATIONS
  3. MULTIVARIATE GENETIC MODEL-FITTING ANALYSIS
  4. BIVARIATE ACE ESTIMATES
  5. ACE CORRELATIONS
  6. CHOLESKY ANALYSES OF “g” AND NC TEACHER ASSESSMENTS
  7. MULTIVARIATE DF EXTREMES ANALYSIS
  8. SUMMARY

Generalist Genes

These multivariate genetic results are consistent with other research (Plomin & Kovas, 2005) in yielding high genetic correlations within and between learning abilities. Within domains, the average of the 31 genetic correlations reported in Table 17 was .86. High average genetic correlations within domains emerged not just for NC teacher ratings (.87) but also for subtests of the TOWRE (.88) and the mathematics battery (.87). Even across methods (NC teacher ratings of reading and mathematics versus tests of reading and mathematics), genetic correlations within domains were high (.76). Finding such high genetic correlations within domains is striking because most of the components within domains seem to require quite different cognitive processes (e.g., reading words and nonwords in the TOWRE test for which the genetic correlation was .88). As another example, the three mathematics subtests represent three very different aspects of mathematics—straightforward computations, nonnumerical mathematical processes including concepts such as rotational or reflective symmetry, and understanding the numerical and algebraic processes that need to be applied to solve particular problems—and yet their average genetic correlation was .87.

Even more surprising are the high genetic correlations among the NC composites of English, mathematics, and science, where the average genetic correlation at 7, 9, and 10 years was .79. The web-based tests of reading and mathematics at 10 years yielded a genetic correlation of .52. Although the multivariate genetic analyses in this chapter are primarily based on the entire sample, a bivariate extremes analysis yielded results similar to those based on the entire sample. We emphasize genetic correlations because they indicate the extent to which the same genes affect different traits regardless of the heritability of the traits. However, bivariate heritabilities, which specify the extent to which genetic factors mediate the phenotypic correlation between traits, were also substantial. For example, the average bivariate heritability for NC ratings at 7, 9, and 10 years was 67% within domains (Table 17) and 64% between domains (Table 18).

These results lead us to conclude that the same set of genes is largely responsible for genetic influence on these diverse areas of learning abilities and disabilities. In order to highlight this general effect of genes, we refer to them as “generalist genes” (Plomin & Kovas, 2005). When DNA research identifies any of the many genes responsible, for example, for the high heritability of reading ability and disability, we predict that most (but not all) of these genes will also be associated with mathematics ability and disability. The notion of generalist genes has far-reaching implications for diagnosis and treatment of learning disabilities and for understanding the cognitive and brain mechanisms that mediate the effects of generalist genes on behavior. These implications of generalist genes are discussed in the following final chapter.

Our multivariate genetic analyses between learning abilities and general cognitive ability (“g”) suggest that some generalist genes that affect learning abilities are even more general in that they also affect other sorts of cognitive abilities included in “g.” However, generalist genes are not just “g” because learning abilities are more strongly correlated genetically with each other than they are with “g.” About a third of the genetic variance of English and mathematics is in common with “g,” about a third of the genetic variance is general to academic performance independent of “g,” and about a third is specific to each domain. Science at 10 years is more genetically related to “g” than are English and mathematics. One possible explanation is that the general environment (TV, newspapers, etc.) may play more of a role in science than in English and mathematics, which are more formally taught. The hallmark of “g” is the ability to pick up knowledge from a relatively unstructured environment.

As with longitudinal analyses, the mechanisms through which generalist genes have their effects on covariation between different traits are as yet to be discovered. Existing cognitive theories that attempt to explain the positive manifold among cognitive tasks propose different mechanisms for this phenomenon (see Van der Maas et al., 2006, for review). When the DNA polymorphisms involved in individual differences in each ability are discovered, the generalist genes hypothesis, and its relation to various cognitive theories, can be definitively tested.

Specialist Environments

Like the genetic correlations, the shared environmental correlations are very high. Thus, what differentiates learning abilities is largely nonshared environmental factors that make children growing up in the same family different from one another. Nonshared environment correlations are on average about .40, in contrast to the average genetic correlation of about .80. In other words, the nonshared environmental factors that affect one domain are mostly different from those that affect another domain. Bivariate nonshared environment estimates are 16% on average, indicating that nonshared environmental factors do not contribute much to the substantial correlations among learning abilities.

Unlike shared environment, for which it is easy to point to possible influences with general effects such as socioeconomic status or school quality, it is more difficult to imagine nonshared environmental influences that might affect siblings differently—in this case, even clones (MZ twins) growing up in the same family, attending the same schools, and sitting in the same classrooms. Even though we have a long way to go to understand such nonshared environmental influences, we now have another reason to promote research in this area: These influences are the source of specialist environments contributing to perturbations in children's profiles of performance across academic subjects. One implication is that educational programs might have their greatest impact on remediating discrepant performances between learning abilities (such as differences in reading and mathematics). That is, if the environment contributes most to differences in performance in reading and mathematics, it seems reasonable to expect that such performance profile differences might be most susceptible to intervention. The same speculation might apply to discrepancies between learning abilities and cognitive abilities, which is one way to view over-achievement and under-achievement.

We hypothesize that the effects of nonshared environments will be similar to those of genes: There will be many environments, each having only a small effect on a particular phenotype. Finding such influences will be a difficult task and will require innovative methods, such as focusing on perceptions rather than “objective measures” and using genetically sensitive designs, such as studying discordant monozygotic twins. We predict that once specific measured genes and environments are available, this information will be widely utilized to predict and prevent learning disabilities, to evaluate interventions, and to study gene–environment interplay.