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Reading performance and general cognitive ability in twins with reading difficulties and control pairs
Pergamon PII:
Person. indiuid. Dijf Vol. 22, No. 6, pp. 793-803, 1997 Q 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0191-8869197 $17.00+0.00 SO191-8869(96)00267-X
READING PERFORMANCE AND GENERAL COGNITIVE ABILITY IN TWINS WITH READING DIFFICULTIES AND CONTROL PAIRS Maricela ‘Institute
for Behavioral
Alarcon’.‘*
and J. C. DeFries’,’
Genetics, Campus Box 447 and ‘Department Colorado, Boulder, CO 80309, U.S.A.
of Psychology,
University
of
CReceired 22 Ocroher 1996) Summary-The etiology of the observed relationship betwaeen general cognitive ability and reading performance was investigated by analyzing data from samples of twin pairs tested in the Colorado Learning Disabilities Research Center. Bivariate phenotypic and genetic structural equation models were fitted to data from 486 twin pairs selected for reading deficits (276 identical and 210 same-sex fraternal) and 3 14 control pairs (195 identical and 119 same-sex fraternal). Subtests of the Peabody Individual Achievement test (Reading Recognition. Reading Comprehension, and Spelling) were used as measures of reading performance, and verbal and performance IQ scores from the Wechsler Intelligence Scale for ChildrenRevised (WISC-R) or Wechsler Adult Intelligence Scale-Revised (WAIS-R) were used as indices of general cognitive ability. The results of these confirmatory factor analyses indicate that shared environmental influences do not contribute significantly to covariation between general cognitive ability and reading performance. In contrast, genetic influences contribute substantially to the relationship between the two latent factors. Moreover, the genetic and phenotypic variances of reading performance in the proband group are larger than those in controls, whereas both the genetic and phenotypic correlations between reading performance and general cognitive ability are lower in probands. These results are consistent with recent reports that reading disability may be caused by one or more genes with major effects. CJ 1997 Elsevier Science Ltd
INTRODUCTION
Individual differences in general cognitive ability are highly correlated with measures of language processes and academic achievement (Lyon, 1989). For example, Kaufman (1973) obtained significant correlations between the reading subtest of the Metropolitan Achievement Test and the Stanford-Binet IQ, the WPPSI full-scale IQ and the General Cognitive Index of the McCarthy Scales of Children’s Abilities (0.51,0.36 and 0.44, respectively). Subsequently, Covin and Lubimiv (1976) reported that the reading subtest of the Wide Range Achievement Test is significantly correlated with the Wechsler Intelligence Scale for Children-Revised (WISC-R) verbal (0.68) performance (0.35) and full-scale (0.58) IQs (Covin & Lubimiv, 1976). Tramill and Tramill (1981) also reported significant correlations between the reading comprehension subtest of the Peabody Individual Achievement Test (PIAT) and the WISC-R verbal (0.56), performance (0.38) and fullscale (0.52) scores. More recently, Wiese, Lamb and Piersel(l988) obtained substantial correlations between the reading cluster of the Woodcock-Johnson Psycho-Educational Battery Tests of Achievement and the WISC-R verbal, performance and full-scale IQ tests (0.72,0.33, and 0.62, respectively). In addition, when Hartlage and Steele (1977) used school grades as indicators of academic achievement, the WISC-R verbal and full-scale IQ scores correlated with grade 1 reading (0.46) and writing (0.59), and with grade 2 reading/spelling (0.77) and writing (0.44). Thus, across a variety of measures, the phenotypic relationship between general cognitive ability and reading performance has been well established; however, relatively few studies have attempted to assess the etiology of this relationship. Brooks, Fulker and DeFries (1990) first investigated the etiology of the relationship between reading performance and general cognitive ability in a control sample tested in the Colorado Twin Study of Reading Disability. Data from three subtests of the PIAT (Reading Recognition, Reading Comprehension and Spelling) and WISC-R full-scale IQ were subjected to confirmatory factor
*To whom all correspondence
should be addressed. 793
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Maricela Alar&n and J. C. DeFries
analysis. Results of a multivariate genetic analysis indicated that the three reading measures covaried independently of IQ and that the phenotypic relationship between the latent reading and IQ factors was largely genetic in origin. In a subsequent analysis of parent-offspring data from the Colorado Adoption Project, Cardon et al. (1990) fitted general cognitive ability data and Reading Recognition subtest scores to a multivariate conditional path model and found that almost 80% of the phenotypic correlation between Reading Recognition and WISC-R full-scale IQ was due to hereditary influences. The nature of the relationship between measures of specific cognitive abilities and academic achievement has also been previously assessed (Petri11 & Thompson, 1993; Thompson, Detterman & Plomin, 1991; Wadsworth et al., 1995a, 1995b). For example, Thompson et al. (1991) conducted a multivariate genetic analysis of specific cognitive abilities (verbal, spatial, perceptual speed and memory) and scholastic achievement data from the Western Reserve Twin Project. Although the phenotypic correlations among the various measures were relatively low, results of their analyses indicated that the phenotypic relationships between specific cognitive abilities and scholastic achievement are due substantially to genetic factors. The primary objective of the present report was to assess the etiology of the relationship between general cognitive ability and reading performance in a sample of twins selected for reading deficits and in an updated sample of control twins previously analyzed by Brooks et al. (1990). By fitting a bivariate (two-factor) structural equation model (Neale & Cardon, 1992) to the twin data, the proportions of the phenotypic variance due to additive genetic, shared environmental and nonshared environmental influences were estimated for cognitive ability and reading performance in both samples. In addition, the phenotypic correlation between the two factors was partitioned into components due to genetic, shared environmental and non-shared environmental influences. Differences between groups in the magnitude of genetic and phenotypic variances for reading performance, as well as group differences in the genetic and phenotypic correlations between reading performance and general cognitive ability, support previously obtained evidence that reading disability may be caused by one or more genes with major effects (Alarcon & DeFries, 1995; Cardon et al., 1994, 1995; Grigorenko et al., 1996).
METHODS
Participants The data for this analysis were collected from twin pairs tested through May 3 1, 1996, in the ongoing Colorado Learning Disabilities Research Center. The twin pairs were systematically ascertained through 27 co-operating school districts in the state of Colorado (DeFries & Gillis, 1991). School administrators identified all twin pairs in a school, regardless of their reading status, and permission was then requested from the twins’ parents to examine the children’s records for evidence of reading problems (e.g. low achievement test scores, teacher referrals to a reading therapist or special program, etc). If at least one member of a twin pair had a positive school history of reading problems, both children were invited to participate in the study. Where possible, control twins in which neither member of the pair had a positive history of reading difficulties were matched to the proband sample on the basis of age, sex and school district. Informed consent was obtained from the parents and the twins prior to testing. Zygosity of the twin pairs was determined using selected items from the Nichols and Bilbro (1966) questionnaire, which has a reported accuracy of 95%. In cases where zygosity was doubtful, blood samples were drawn and genotyped. For the purposes of this analysis, those pairs in which at least one member had a positive school history of reading problems were included in the proband group. In addition, the probands had no uncorrected visual acuity or auditory deficits, or neurological problems. The control group included twin pairs in which neither member had a school history of reading problems. A total of 800 twin pairs were tested: 486 pairs were in the proband group and 314 pairs were controls. The proband group included 276 monozygotic (MZ) twin pairs and 2 10 same-sex &zygotic (DZ) pairs, while the control group included 195 MZ pairs and 119 same-sex DZ pairs.The twins' ages ranged from 8 to 20 years at the time of testing with an average age of 12 years.
Bivariate model
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Measures
At the Institute for Behavioral Genetics, the children were administered an extensive psychometric test battery including the Wechsler Intelligence Scale for Children-Revised (Wechsler, 1974) or the Wechsler Adult Intelligence Scale-Revised (WAIS-R; Wechsler, 1981) and the Peabody Individual Achievement Test (Dunn and Markwardt, 1970). Scores for each of these variables were age-adjusted using regression deviation scores. The PIAT Reading Recognition (REC), Reading Comprehension (COMP) and Spelling (SPELL) subtests were used as measures of reading performance, whereas performance IQ (PIQ) and verbal IQ (VIQ) scores were used as measures of general cognitive ability. In theory, structural equation models should only be fitted to data from random samples. Although our samples were not randomly ascertained, strict selection criteria were not employed. Individuals were only required to have a positive school history of reading problems to be included in the proband group and no positive school history to be in the control group. Consequently, their frequency distributions do not deviate significantly from normality. However, scatterplots indicated the existence of possible outliers in the proband sample. Therefore, the standardized scores for the measured variables were rank-normalized (Blom, 1958). The rank-normalizing procedure was performed on the data from both groups simultaneously, to preserve mean differences between the groups. A Kolmogorov-Smirnov Z-test, which compares a variable’s distribution with the distribution of a normal curve, was performed separately on each of the transformed variables from the proband and control samples. Results from these analyses indicated that the distributions of the transformed Reading Recognition, Reading Comprehension and Spelling scores for the proband (Z = 0.73, P = 0.66; Z = 0.69, P = 0.74; and Z = 0.40, P = 1.00, respectively) and control (Z = 1.00, P = 0.27; Z = 0.70, P = 0.70; and Z = 0.74, P = 0.65) groups did not deviate significantly from normality, nor did those of the transformed verbal and performance IQ scores for the probands (Z = 0.89, P = 0.41; and Z = 0.89, P = 0.41, respectively) and controls (Z = 0.80, P = 0.55; Z = 0.88, P = 0.42). Therefore, the data were deemed to be adequate for structural equation model-fitting. Analyses
The bivariate phenotypic and genetic structural equation models, along with their corresponding submodels, were fitted to the twin data using h4X (Neale, 1991). The overall fit of the models to the data was evaluated using the x2 statistic as well as several other goodness-of-fit indices (Bollen, 1989). Despite the influence of sample size on the x2 statistic (Bollen, 1989; Hayduk, 1987; Neale & Cardon, 1992), it was employed to obtain x2 difference tests to assess the fit of various submodels. The Tucker-Lewis (1973) index was also used because of its relative independence of sample size (Marsh, Balla & McDonald, 1988). In addition, a modified version of the Bentler and Bonett normed fit index (Bollen, 1989) was also used, since it is adjusted according to the degrees of freedom of the model of interest. Both the Tucker-Lewis (TL) and the modified normed fit (NF) indices are measures of the extent to which a model-of-interest fits the data relative to a baseline or null model. The closer the indices are to 1, the better the fit of the model. A baseline model appropriate for factor analysis is one in which covariances do not exist among the variables (i.e. the expected variance-covariance matrices only include diagonal elements). Covariances among the rank-normalized variables were computed using the SPSS (1988) statistical package. For the phenotypic analysis, four 5 x 5 covariance matrices (REC, COMP, SPELL, VIQ, and PIQ) were obtained: one for MZ and one for DZ pairs for each of the two samples. To fit the genetic model to data from twin pairs, four corresponding 10 x 10 covariance matrices were obtained. In each of the twin models, the additive genetic correlation between members of the pairs was 1 for MZ twins and 0.5 for DZ twins; the shared environmental correlation was 1 for both MZ and DZ twins; and the non-shared environmental influences were uncorrelated between members of twin pairs. Phenotypic models
A phenotypic model with two correlated factors was fitted simultaneously to the four 5 x 5 covariance matrices to provide parameter estimates for the proband and control groups. The reading
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Maricela Alar&n and J. C. DeFries
Fig.
1,Path diagram for bivariate phenotypic
model of data from individuals.
factor loaded on the three PIAT subtests and the general cognitive factor loaded on the VIQ and PIQ subtests of the WISC-R or WAIS-R. In addition, one residual for each of the measured variables was included to account for specific influences not shared with the factors. The model, depicted in Fig. 1, includes the phenotypic correlation between the two latent variables as well as loadings of each of the measures on the corresponding reading or cognitive factors. In order to test for homogeneity of variances and covariances across the two samples, the xz estimate for the full phenotypic model was compared to the x2 obtained after equating the parameters for the proband and control groups. Genetic models As depicted in Fig. 2, the bivariate twin model partitions the phenotypic variances and covariances into genetic and environmental components. For a given variable (e.g. READ), the phenotypic correlation between members of MZ twin pairs is due to both additive genetic (a’) and shared environmental (c’) influences. Since DZ twins share only half of their segregating genes, but all of the shared environmental influences, their corresponding phenotypic correlation estimates 1/2a2 + c2. Thus, twice the difference between the MZ and DZ observed correlations estimates heritability (a’). Subtracting the heritability estimate from the MZ correlation provides an estimate of the proportion of the total variance due to shared environmental effects (c’), and subtracting the MZ correlation from 1 provides an estimate of the proportion of the variance due to non-shared environmental effects (e’). The bivariate model simply extends these basic principles and provides estimates of univariate parameters (i.e. u2, c2 and e2 for each of the traits) in addition to cross-trait correlations, which can also be partitioned into genetic and environmental components. In the bivariate twin model (Fig. 2), the additive genetic, shared environmental and non-shared environmental influences on reading performance are represented by A,, CR, and ER, respectively. A,, Cc, and E, are the corresponding additive genetic, shared environmental and non-shared environmental influences on the general cognitive factor. The path coefficients for additive genetic, shared environmental and non-shared environmental influences on the reading variables are symbolized by a, c and e, respectively. The corresponding coefficients for the cognitive variables are a’, c’ and e’, respectively. The cross-trait genetic (r,& shared environmental (rC) and non-shared environmental (rE) correlations are also depicted in Fig. 2, as are the residuals for each measure partitioned into specific additive genetic (A), specific shared environmental (C) and specific nonshared environmental (E) components. Each of the full models was compared to corresponding nested submodels using x2 difference tests. The following submodels were examined: (1) submodels in which various proband and control parameter estimates are constrained to be equal; (2) an environmental model in which rA, a and a’
Bivariate model
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Maricela Alar&n and J. C. DeFries
are constrained to be zero; (3) a genetic model in which rc, c and c’ are constrained to be zero; and (4) submodels that test whether specific genetic and environmental effects, independent of those that contribute to the covariance of the factors, significantly influence the reading and cognition variables. RESULTS Phenotypic analysis
The parameter estimates resulting from the fit of the full phenotypic model to the data are presented in Fig. 3, and the goodness-of-fit indices for the full and corresponding submodels are shown in Table 1. The full model yielded separate parameter estimates for the proband and control groups. Due to the large sample size (1600 individuals), the x2 value for the full model is very high (x2 = 226.25, d.f. = 38, P < 0.001). However, the Tucker-Lewis index (0.90) and the normed fit index (0.92) which do not depend on sample size, both indicate an acceptable fit of the full model. As shown, the phenotypic correlation between the reading performance and general cognitive ability factors was 0.41 in the proband group and 0.76 in the control group, suggesting a moderate to strong relationship between the latent variables in both samples. As shown in Table 1, the factor structure for the cognitive variables was similar in the proband and control groups. When the parameter estimates for the cognitive variables were equated across groups, the reduced model did not significantly increase the x2 estimate (model II, xifl= 8.88, d.f. = 4, P > O.OSO).Thus, the factor structure of general cognitive ability does not differ significantly between samples selected for reading deficits and controls. In contrast, the factor structure for reading performance (model III) and the correlation between reading and cognition (model 1V) significantly differed (P < 0.005) between the proband and control samples. Post hoc analyses revealed that the variances and covariances of the reading variables in the proband group were significantly larger than those of the control group. These phenotypic .41 t.76)
Fig. 3. Parameter estimates for the full bivariate phenotypic model of data from individuals in the Colorado Learning Disabilities Research Center. Estimates for the control group are shown in parentheses.
Table 1. Goodness-of-fit
I. Il. Ill. IV.
comparisons Learning
of phenotypic models for twin data from the Colorado Disabilities Research Center
Model*
NPAR
vs
x2
d.f.
P
TL
NF
Full cog,,,, = CO&,“, read,,,, = read,,,, rprob= ra.,
22 18 12 17
I II II
226.25 8.88 240.13 34.18
38 4 6
< 0.001 a 0.050 < 0.005
0.90 0.91 0.83 0.90
0.92 0.92 0.82 0.90
I
Q0.005
“cog = cognitive variables; read = reading variables;prob = probands; cant = controls NPAR = number of parameters; TL = Tucker-Lewis index; NF = normed fit index.
Bivariate model
799
Table 2. Phenotypic variances and covariances for reading performance variables in proband and control groups” Members of monozygotic Rec.
pairs
Camp.
Spell.
Comp.
Spell.
Members of dizygotic pairs Rec.
Comp.
Comp.
“Parameter estimates for proband and control groups above and below diagonal, respectively. Rec. = reading recognition; Comp. = reading comprehension; Spell. = spelling.
variances and covariances of the reading measures for members of MZ and DZ pairs are presented in Table 2. As may be noted from Table 2, the proband variances and covariances are substantially larger than those for the control sample. Thus, the proband sample is not attenuated relative to the controls. The larger variances for reading performance measures in the proband group may be due to a major quantitative trait locus (QTL) for reading disability in individuals selected for reading deficits (Alarcon & DeFries, 1995). The fact that the phenotypic correlation between the reading and cognitive factors in the proband sample is less than that in the controls suggests that this putative QTL may be highly specific to measures of reading performance. Twin analyses
The proportions of variance due to additive genetic, shared environmental and non-shared environmental sources obtained from the full bivariate twin model are presented in Table 3. The parameter estimates were standardized separately for each factor, i.e. a*+ c2+e2 = 1 and u’*+c’*+e’* = 1. Reading performance is highly heritable in both the proband (0.82) and control (0.66) groups. In contrast, shared environmental influences on reading performance account for only small proportions of the variance in the proband (0.01) and control (0.18) groups. These a2 and c2 estimates agree closely with those obtained from a recent regression analysis of a composite measure of reading performance in subsets of these two samples (DeFries & Alarcon, 1996). General cognitive ability is also substantially heritable in both the proband and control groups (0.68 and 0.62, respectively), indicating that over 60% of the phenotypic variance of cognition is due to genetic influences. In contrast, shared environmental influences account for relatively little variance in general cognitive ability in the proband (0.14) and control (0.28) groups. The parameter estimates for the full bivariate twin model are shown in Fig. 4. In the proband and control samples, the genetic correlations (Ye)between reading and cognition are 0.52 and 0.8 1,
Maricela Alarcon and J. C. DeFries
800
.52(.81) 1.oo(1.OO) .59(.25)
\
Fig. 4. Parameter
estimates
for the full bivariate twin model (one twin only). Estimates group are shown in parentheses.
.46 (.43)
for the control
respectively. Moreover, 87% of the phenotypic correlation (r = 0.45 in the full genetic model) between reading performance and cognition in the proband sample is due to genetic influences, i.e. arAa’/rp = (0.91) (0.52) (0.83)/0.45 = 0.87, in which a and a’ represent the standardized genetic parameter estimates. In the control sample, 67% of the phenotypic relationship (r = 0.77 in the full genetic model) between reading and cognition is due to genetic influences. Although the estimates of rc in both groups are 1, they are not significant because shared environmental influences account for relatively little variance (Table 3). Although the within-family environmental influences appear to be more variable specific in the controls (rE = 0.25) than in the probands (r, = 0.59) they are not significantly different. The results of goodness-of-fit tests for the various twin model comparisons are presented in Table 4. Based on the results obtained from fitting the phenotypic model to the data, we equated the genetic and environmental parameter estimates for the cognitive variables between groups (model II). As expected, model II did not significantly reduce the model fit (x& = 18.81, d.f. = 11, P 2 0.050). Model III tested whether the genetic and environmental parameter estimates for the Table 3. Proportions of variance estimated from the general bivariate twin model Proband source of variance
e2
Controlb
Reading
Cognition
Reading
Cognition
0.82 0.01 0.16
0.68 0.14 0.17
0.66 0.18 0.16
0.62 0.28 0.10
BT”= 0.52, Tc = 1.00; TE= 0.59. brA = 0.81, rc = 1.00; TE= 0.25.
801
Bivariate model Table 4. Goodness-of-fit
comparisons
Model” I II II1 IV V VI VII VIII
cog,,,, read,,,,
Full = co&,., = read,.,
rAO,“b = rl.“n, r,=a=a’=O r,=c=c’=O specific A = 0 specific C = 0
of twin models for data from the Colorado Research Center NPAR 58 47 32 46 42 42 34 34
vs
I II II II II VI VI
x2
d.f.
360.96 18.81 59.53 6.71 161.18 3.61 33.13 15.27
162 11 15 1 16 16 8 8
Learning Disabilities
P 4 > < Q Q 2 < >
0.005 0.050 0.005 0.005 0.005 0.995 0.005 0.050
TL
NF
0.90 0.90 0.89 0.90 0.84 0.90 0.90 0.91
0.91 0.90 0.88 0.90 0.83 0.90 0.89 0.90
‘cog = cognitive variables; read = reading variables; prob = probands; cant = controls. NPAR = number of parameters; TL = Tucker-Lewis index; NF = normed fit index.
reading variables differed between groups. Also as expected, the genetic and environmental variances and covariances for reading variables significantly differ between samples (x& = 59.53, d.f. = 15, P d 0.005). In addition, genetic correlations between the reading and cognitive factors differ in the proband and control groups (model IV, x& = 6.71, d.f. = 1, P < 0.005). Also, genetic variances and covariances could not be dropped from the model (model V, x& = 161.18, d.f. = 16, P < O.OOS), confirming that the relationship between reading and cognition is due significantly to genetic factors. In contrast, the shared environmental influences (model VI) could be dropped from the twin model without a significant loss of fit (x&, = 3.67, d.f. = 16, P 2 0.995). In order to determine whether genetic influences independent of those shared by the two factors significantly influence the measured variables, the specific additive genetic effects were dropped from the model. Model VII fits the data significantly worse than model VI (& = 33.13, d.f. = 8, P < O.OOS),indicating that genetic influences independent of those shared by the factors contribute to the measures of reading and cognition. Finally, when we dropped the specific shared environmental influences from the model (model VIII), the change in x2 was not significant (& = 15.27, d.f. = 8, P 3 0.05); thus, shared environmental effects neither contribute significantly to the covariation between the traits, nor account for significant independent variation in the reading and cognition variables. DISCUSSION
The nature of the relationship between general cognitive ability (measured by VIQ and PIQ) and reading performance (measured by REC, COMP and SPELL) was examined by fitting structural equation models to twin data from the Colorado Learning Disabilities Research Center. In the proband sample, at least one member of each twin pair (276 MZ and 210 same-sex DZ) had a positive school history of reading problems. In contrast, neither member of each pair in the control sample (195 MZ and 119 same-sex DZ) had a school history of reading deficits. The proportions of the observed variance due to genetic and environmental influences were estimated for the various measures, and the phenotypic correlation between reading performance and general cognitive ability was partitioned into components due to genetic, shared and non-shared environmental influences in both groups. Specific genetic and environmental influences, independent of the covariation between the two factors, were also estimated. In general, there were no fundamental differences between the proband and control groups in the genetic and environmental etiologies of general cognitive ability or in its factor structure: in both groups, over 60% of the variability in cognitive ability was due to genetic influences and the shared environmental effect was small. However, the genetic and phenotypic variances and covariances for the reading measures were significantly larger in the proband group than in the controls. These results support the hypothesis that a QTL for reading disability is more prevalent in the group selected for reading deficits (Alar&n & DeFries, 1995; Cardon et al., 1994, 1995; Grigorenko et al., 1996). If there is an allele at a single locus that has a substantial deleterious effect on reading performance, its frequency should be higher in a sample of children selected for reading deficits than in a sample of control children (Alar&n & DeFries, 1995). Thus, because genetic variance is a function of allele frequency (Falconer, 1989), the genetic and phenotypic variances should be
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higher in the proband group than in the control group if there is a major QTL for reading performance. As predicted by this hypothesis, the heritability of reading performance was higher in the proband group (0.82) than in the controls (0.66). If the increased variance in the proband group is specific to reading performance, the correlation between the reading and cognitive factors in the probands should be attenuated. Although the phenotypic correlations between reading performance and general cognitive ability in the proband (Y, = 0.41) and control (rP = 0.76) groups are both substantial, the difference in their magnitude is significant (P < 0.005). Finally, when the full twin model was fitted to the data, resulting estimates of the genetic correlation between reading performance and general cognitive ability were 0.52 and 0.81 for the probands and controls, respectively. Thus, our findings of greater phenotypic and genetic variances for reading performance and lower phenotypic and genetic correlations between reading performance and general cognitive ability in the proband sample provide additional evidence that reading disability may be caused by one or more genes with major effects. Ackno~~led~rmpnts~This work was supported in part by program project and center grants from the National Institute of Child Health and Human Development (HD-I 1681 and HD-27802) to J. C. DeFries. The report was prepared while M. Alarcon was supported by funds from the Graduate School, University of Colorado. The invaluable contributions of staff members of the many Colorado school districts and of the families who participated in this study, are gratefully acknowledged.
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803 ability and academic achievement in the and sibling data. Behavior Genetics, 25,
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Wadsworth, S. J., DeFries, J. C., Fulker, D. W. & Plomin, R. (1995b). Covariation among measures of cognitive ability and academic achievement in the Colorado Adoption Project: Sibling data. Personality and Individual Differences, 18. 63-73. Wechsler, D. (1974). Examiner’s manual: Wechsler intelligence scale ,for children-revised. New York: The Psychological Corporation. Wechsler, D. (198 1). Examiner’s manual: Wechsler adult intelligence scale-revised. New York: The Psychological Corporation. Wiese, M. J., Lamb, C. & Piersel, W. C. (1988). WISC-R factor scores and student self-ratings of behavior as predictors of academic achievement. Psychology in the Schools, 25, 3541.
Person. indiuid. Dijf Vol. 22, No. 6, pp. 793-803, 1997 Q 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0191-8869197 $17.00+0.00 SO191-8869(96)00267-X
READING PERFORMANCE AND GENERAL COGNITIVE ABILITY IN TWINS WITH READING DIFFICULTIES AND CONTROL PAIRS Maricela ‘Institute
for Behavioral
Alarcon’.‘*
and J. C. DeFries’,’
Genetics, Campus Box 447 and ‘Department Colorado, Boulder, CO 80309, U.S.A.
of Psychology,
University
of
CReceired 22 Ocroher 1996) Summary-The etiology of the observed relationship betwaeen general cognitive ability and reading performance was investigated by analyzing data from samples of twin pairs tested in the Colorado Learning Disabilities Research Center. Bivariate phenotypic and genetic structural equation models were fitted to data from 486 twin pairs selected for reading deficits (276 identical and 210 same-sex fraternal) and 3 14 control pairs (195 identical and 119 same-sex fraternal). Subtests of the Peabody Individual Achievement test (Reading Recognition. Reading Comprehension, and Spelling) were used as measures of reading performance, and verbal and performance IQ scores from the Wechsler Intelligence Scale for ChildrenRevised (WISC-R) or Wechsler Adult Intelligence Scale-Revised (WAIS-R) were used as indices of general cognitive ability. The results of these confirmatory factor analyses indicate that shared environmental influences do not contribute significantly to covariation between general cognitive ability and reading performance. In contrast, genetic influences contribute substantially to the relationship between the two latent factors. Moreover, the genetic and phenotypic variances of reading performance in the proband group are larger than those in controls, whereas both the genetic and phenotypic correlations between reading performance and general cognitive ability are lower in probands. These results are consistent with recent reports that reading disability may be caused by one or more genes with major effects. CJ 1997 Elsevier Science Ltd
INTRODUCTION
Individual differences in general cognitive ability are highly correlated with measures of language processes and academic achievement (Lyon, 1989). For example, Kaufman (1973) obtained significant correlations between the reading subtest of the Metropolitan Achievement Test and the Stanford-Binet IQ, the WPPSI full-scale IQ and the General Cognitive Index of the McCarthy Scales of Children’s Abilities (0.51,0.36 and 0.44, respectively). Subsequently, Covin and Lubimiv (1976) reported that the reading subtest of the Wide Range Achievement Test is significantly correlated with the Wechsler Intelligence Scale for Children-Revised (WISC-R) verbal (0.68) performance (0.35) and full-scale (0.58) IQs (Covin & Lubimiv, 1976). Tramill and Tramill (1981) also reported significant correlations between the reading comprehension subtest of the Peabody Individual Achievement Test (PIAT) and the WISC-R verbal (0.56), performance (0.38) and fullscale (0.52) scores. More recently, Wiese, Lamb and Piersel(l988) obtained substantial correlations between the reading cluster of the Woodcock-Johnson Psycho-Educational Battery Tests of Achievement and the WISC-R verbal, performance and full-scale IQ tests (0.72,0.33, and 0.62, respectively). In addition, when Hartlage and Steele (1977) used school grades as indicators of academic achievement, the WISC-R verbal and full-scale IQ scores correlated with grade 1 reading (0.46) and writing (0.59), and with grade 2 reading/spelling (0.77) and writing (0.44). Thus, across a variety of measures, the phenotypic relationship between general cognitive ability and reading performance has been well established; however, relatively few studies have attempted to assess the etiology of this relationship. Brooks, Fulker and DeFries (1990) first investigated the etiology of the relationship between reading performance and general cognitive ability in a control sample tested in the Colorado Twin Study of Reading Disability. Data from three subtests of the PIAT (Reading Recognition, Reading Comprehension and Spelling) and WISC-R full-scale IQ were subjected to confirmatory factor
*To whom all correspondence
should be addressed. 793
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Maricela Alar&n and J. C. DeFries
analysis. Results of a multivariate genetic analysis indicated that the three reading measures covaried independently of IQ and that the phenotypic relationship between the latent reading and IQ factors was largely genetic in origin. In a subsequent analysis of parent-offspring data from the Colorado Adoption Project, Cardon et al. (1990) fitted general cognitive ability data and Reading Recognition subtest scores to a multivariate conditional path model and found that almost 80% of the phenotypic correlation between Reading Recognition and WISC-R full-scale IQ was due to hereditary influences. The nature of the relationship between measures of specific cognitive abilities and academic achievement has also been previously assessed (Petri11 & Thompson, 1993; Thompson, Detterman & Plomin, 1991; Wadsworth et al., 1995a, 1995b). For example, Thompson et al. (1991) conducted a multivariate genetic analysis of specific cognitive abilities (verbal, spatial, perceptual speed and memory) and scholastic achievement data from the Western Reserve Twin Project. Although the phenotypic correlations among the various measures were relatively low, results of their analyses indicated that the phenotypic relationships between specific cognitive abilities and scholastic achievement are due substantially to genetic factors. The primary objective of the present report was to assess the etiology of the relationship between general cognitive ability and reading performance in a sample of twins selected for reading deficits and in an updated sample of control twins previously analyzed by Brooks et al. (1990). By fitting a bivariate (two-factor) structural equation model (Neale & Cardon, 1992) to the twin data, the proportions of the phenotypic variance due to additive genetic, shared environmental and nonshared environmental influences were estimated for cognitive ability and reading performance in both samples. In addition, the phenotypic correlation between the two factors was partitioned into components due to genetic, shared environmental and non-shared environmental influences. Differences between groups in the magnitude of genetic and phenotypic variances for reading performance, as well as group differences in the genetic and phenotypic correlations between reading performance and general cognitive ability, support previously obtained evidence that reading disability may be caused by one or more genes with major effects (Alarcon & DeFries, 1995; Cardon et al., 1994, 1995; Grigorenko et al., 1996).
METHODS
Participants The data for this analysis were collected from twin pairs tested through May 3 1, 1996, in the ongoing Colorado Learning Disabilities Research Center. The twin pairs were systematically ascertained through 27 co-operating school districts in the state of Colorado (DeFries & Gillis, 1991). School administrators identified all twin pairs in a school, regardless of their reading status, and permission was then requested from the twins’ parents to examine the children’s records for evidence of reading problems (e.g. low achievement test scores, teacher referrals to a reading therapist or special program, etc). If at least one member of a twin pair had a positive school history of reading problems, both children were invited to participate in the study. Where possible, control twins in which neither member of the pair had a positive history of reading difficulties were matched to the proband sample on the basis of age, sex and school district. Informed consent was obtained from the parents and the twins prior to testing. Zygosity of the twin pairs was determined using selected items from the Nichols and Bilbro (1966) questionnaire, which has a reported accuracy of 95%. In cases where zygosity was doubtful, blood samples were drawn and genotyped. For the purposes of this analysis, those pairs in which at least one member had a positive school history of reading problems were included in the proband group. In addition, the probands had no uncorrected visual acuity or auditory deficits, or neurological problems. The control group included twin pairs in which neither member had a school history of reading problems. A total of 800 twin pairs were tested: 486 pairs were in the proband group and 314 pairs were controls. The proband group included 276 monozygotic (MZ) twin pairs and 2 10 same-sex &zygotic (DZ) pairs, while the control group included 195 MZ pairs and 119 same-sex DZ pairs.The twins' ages ranged from 8 to 20 years at the time of testing with an average age of 12 years.
Bivariate model
795
Measures
At the Institute for Behavioral Genetics, the children were administered an extensive psychometric test battery including the Wechsler Intelligence Scale for Children-Revised (Wechsler, 1974) or the Wechsler Adult Intelligence Scale-Revised (WAIS-R; Wechsler, 1981) and the Peabody Individual Achievement Test (Dunn and Markwardt, 1970). Scores for each of these variables were age-adjusted using regression deviation scores. The PIAT Reading Recognition (REC), Reading Comprehension (COMP) and Spelling (SPELL) subtests were used as measures of reading performance, whereas performance IQ (PIQ) and verbal IQ (VIQ) scores were used as measures of general cognitive ability. In theory, structural equation models should only be fitted to data from random samples. Although our samples were not randomly ascertained, strict selection criteria were not employed. Individuals were only required to have a positive school history of reading problems to be included in the proband group and no positive school history to be in the control group. Consequently, their frequency distributions do not deviate significantly from normality. However, scatterplots indicated the existence of possible outliers in the proband sample. Therefore, the standardized scores for the measured variables were rank-normalized (Blom, 1958). The rank-normalizing procedure was performed on the data from both groups simultaneously, to preserve mean differences between the groups. A Kolmogorov-Smirnov Z-test, which compares a variable’s distribution with the distribution of a normal curve, was performed separately on each of the transformed variables from the proband and control samples. Results from these analyses indicated that the distributions of the transformed Reading Recognition, Reading Comprehension and Spelling scores for the proband (Z = 0.73, P = 0.66; Z = 0.69, P = 0.74; and Z = 0.40, P = 1.00, respectively) and control (Z = 1.00, P = 0.27; Z = 0.70, P = 0.70; and Z = 0.74, P = 0.65) groups did not deviate significantly from normality, nor did those of the transformed verbal and performance IQ scores for the probands (Z = 0.89, P = 0.41; and Z = 0.89, P = 0.41, respectively) and controls (Z = 0.80, P = 0.55; Z = 0.88, P = 0.42). Therefore, the data were deemed to be adequate for structural equation model-fitting. Analyses
The bivariate phenotypic and genetic structural equation models, along with their corresponding submodels, were fitted to the twin data using h4X (Neale, 1991). The overall fit of the models to the data was evaluated using the x2 statistic as well as several other goodness-of-fit indices (Bollen, 1989). Despite the influence of sample size on the x2 statistic (Bollen, 1989; Hayduk, 1987; Neale & Cardon, 1992), it was employed to obtain x2 difference tests to assess the fit of various submodels. The Tucker-Lewis (1973) index was also used because of its relative independence of sample size (Marsh, Balla & McDonald, 1988). In addition, a modified version of the Bentler and Bonett normed fit index (Bollen, 1989) was also used, since it is adjusted according to the degrees of freedom of the model of interest. Both the Tucker-Lewis (TL) and the modified normed fit (NF) indices are measures of the extent to which a model-of-interest fits the data relative to a baseline or null model. The closer the indices are to 1, the better the fit of the model. A baseline model appropriate for factor analysis is one in which covariances do not exist among the variables (i.e. the expected variance-covariance matrices only include diagonal elements). Covariances among the rank-normalized variables were computed using the SPSS (1988) statistical package. For the phenotypic analysis, four 5 x 5 covariance matrices (REC, COMP, SPELL, VIQ, and PIQ) were obtained: one for MZ and one for DZ pairs for each of the two samples. To fit the genetic model to data from twin pairs, four corresponding 10 x 10 covariance matrices were obtained. In each of the twin models, the additive genetic correlation between members of the pairs was 1 for MZ twins and 0.5 for DZ twins; the shared environmental correlation was 1 for both MZ and DZ twins; and the non-shared environmental influences were uncorrelated between members of twin pairs. Phenotypic models
A phenotypic model with two correlated factors was fitted simultaneously to the four 5 x 5 covariance matrices to provide parameter estimates for the proband and control groups. The reading
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Maricela Alar&n and J. C. DeFries
Fig.
1,Path diagram for bivariate phenotypic
model of data from individuals.
factor loaded on the three PIAT subtests and the general cognitive factor loaded on the VIQ and PIQ subtests of the WISC-R or WAIS-R. In addition, one residual for each of the measured variables was included to account for specific influences not shared with the factors. The model, depicted in Fig. 1, includes the phenotypic correlation between the two latent variables as well as loadings of each of the measures on the corresponding reading or cognitive factors. In order to test for homogeneity of variances and covariances across the two samples, the xz estimate for the full phenotypic model was compared to the x2 obtained after equating the parameters for the proband and control groups. Genetic models As depicted in Fig. 2, the bivariate twin model partitions the phenotypic variances and covariances into genetic and environmental components. For a given variable (e.g. READ), the phenotypic correlation between members of MZ twin pairs is due to both additive genetic (a’) and shared environmental (c’) influences. Since DZ twins share only half of their segregating genes, but all of the shared environmental influences, their corresponding phenotypic correlation estimates 1/2a2 + c2. Thus, twice the difference between the MZ and DZ observed correlations estimates heritability (a’). Subtracting the heritability estimate from the MZ correlation provides an estimate of the proportion of the total variance due to shared environmental effects (c’), and subtracting the MZ correlation from 1 provides an estimate of the proportion of the variance due to non-shared environmental effects (e’). The bivariate model simply extends these basic principles and provides estimates of univariate parameters (i.e. u2, c2 and e2 for each of the traits) in addition to cross-trait correlations, which can also be partitioned into genetic and environmental components. In the bivariate twin model (Fig. 2), the additive genetic, shared environmental and non-shared environmental influences on reading performance are represented by A,, CR, and ER, respectively. A,, Cc, and E, are the corresponding additive genetic, shared environmental and non-shared environmental influences on the general cognitive factor. The path coefficients for additive genetic, shared environmental and non-shared environmental influences on the reading variables are symbolized by a, c and e, respectively. The corresponding coefficients for the cognitive variables are a’, c’ and e’, respectively. The cross-trait genetic (r,& shared environmental (rC) and non-shared environmental (rE) correlations are also depicted in Fig. 2, as are the residuals for each measure partitioned into specific additive genetic (A), specific shared environmental (C) and specific nonshared environmental (E) components. Each of the full models was compared to corresponding nested submodels using x2 difference tests. The following submodels were examined: (1) submodels in which various proband and control parameter estimates are constrained to be equal; (2) an environmental model in which rA, a and a’
Bivariate model
191
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Maricela Alar&n and J. C. DeFries
are constrained to be zero; (3) a genetic model in which rc, c and c’ are constrained to be zero; and (4) submodels that test whether specific genetic and environmental effects, independent of those that contribute to the covariance of the factors, significantly influence the reading and cognition variables. RESULTS Phenotypic analysis
The parameter estimates resulting from the fit of the full phenotypic model to the data are presented in Fig. 3, and the goodness-of-fit indices for the full and corresponding submodels are shown in Table 1. The full model yielded separate parameter estimates for the proband and control groups. Due to the large sample size (1600 individuals), the x2 value for the full model is very high (x2 = 226.25, d.f. = 38, P < 0.001). However, the Tucker-Lewis index (0.90) and the normed fit index (0.92) which do not depend on sample size, both indicate an acceptable fit of the full model. As shown, the phenotypic correlation between the reading performance and general cognitive ability factors was 0.41 in the proband group and 0.76 in the control group, suggesting a moderate to strong relationship between the latent variables in both samples. As shown in Table 1, the factor structure for the cognitive variables was similar in the proband and control groups. When the parameter estimates for the cognitive variables were equated across groups, the reduced model did not significantly increase the x2 estimate (model II, xifl= 8.88, d.f. = 4, P > O.OSO).Thus, the factor structure of general cognitive ability does not differ significantly between samples selected for reading deficits and controls. In contrast, the factor structure for reading performance (model III) and the correlation between reading and cognition (model 1V) significantly differed (P < 0.005) between the proband and control samples. Post hoc analyses revealed that the variances and covariances of the reading variables in the proband group were significantly larger than those of the control group. These phenotypic .41 t.76)
Fig. 3. Parameter estimates for the full bivariate phenotypic model of data from individuals in the Colorado Learning Disabilities Research Center. Estimates for the control group are shown in parentheses.
Table 1. Goodness-of-fit
I. Il. Ill. IV.
comparisons Learning
of phenotypic models for twin data from the Colorado Disabilities Research Center
Model*
NPAR
vs
x2
d.f.
P
TL
NF
Full cog,,,, = CO&,“, read,,,, = read,,,, rprob= ra.,
22 18 12 17
I II II
226.25 8.88 240.13 34.18
38 4 6
< 0.001 a 0.050 < 0.005
0.90 0.91 0.83 0.90
0.92 0.92 0.82 0.90
I
Q0.005
“cog = cognitive variables; read = reading variables;prob = probands; cant = controls NPAR = number of parameters; TL = Tucker-Lewis index; NF = normed fit index.
Bivariate model
799
Table 2. Phenotypic variances and covariances for reading performance variables in proband and control groups” Members of monozygotic Rec.
pairs
Camp.
Spell.
Comp.
Spell.
Members of dizygotic pairs Rec.
Comp.
Comp.
“Parameter estimates for proband and control groups above and below diagonal, respectively. Rec. = reading recognition; Comp. = reading comprehension; Spell. = spelling.
variances and covariances of the reading measures for members of MZ and DZ pairs are presented in Table 2. As may be noted from Table 2, the proband variances and covariances are substantially larger than those for the control sample. Thus, the proband sample is not attenuated relative to the controls. The larger variances for reading performance measures in the proband group may be due to a major quantitative trait locus (QTL) for reading disability in individuals selected for reading deficits (Alarcon & DeFries, 1995). The fact that the phenotypic correlation between the reading and cognitive factors in the proband sample is less than that in the controls suggests that this putative QTL may be highly specific to measures of reading performance. Twin analyses
The proportions of variance due to additive genetic, shared environmental and non-shared environmental sources obtained from the full bivariate twin model are presented in Table 3. The parameter estimates were standardized separately for each factor, i.e. a*+ c2+e2 = 1 and u’*+c’*+e’* = 1. Reading performance is highly heritable in both the proband (0.82) and control (0.66) groups. In contrast, shared environmental influences on reading performance account for only small proportions of the variance in the proband (0.01) and control (0.18) groups. These a2 and c2 estimates agree closely with those obtained from a recent regression analysis of a composite measure of reading performance in subsets of these two samples (DeFries & Alarcon, 1996). General cognitive ability is also substantially heritable in both the proband and control groups (0.68 and 0.62, respectively), indicating that over 60% of the phenotypic variance of cognition is due to genetic influences. In contrast, shared environmental influences account for relatively little variance in general cognitive ability in the proband (0.14) and control (0.28) groups. The parameter estimates for the full bivariate twin model are shown in Fig. 4. In the proband and control samples, the genetic correlations (Ye)between reading and cognition are 0.52 and 0.8 1,
Maricela Alarcon and J. C. DeFries
800
.52(.81) 1.oo(1.OO) .59(.25)
\
Fig. 4. Parameter
estimates
for the full bivariate twin model (one twin only). Estimates group are shown in parentheses.
.46 (.43)
for the control
respectively. Moreover, 87% of the phenotypic correlation (r = 0.45 in the full genetic model) between reading performance and cognition in the proband sample is due to genetic influences, i.e. arAa’/rp = (0.91) (0.52) (0.83)/0.45 = 0.87, in which a and a’ represent the standardized genetic parameter estimates. In the control sample, 67% of the phenotypic relationship (r = 0.77 in the full genetic model) between reading and cognition is due to genetic influences. Although the estimates of rc in both groups are 1, they are not significant because shared environmental influences account for relatively little variance (Table 3). Although the within-family environmental influences appear to be more variable specific in the controls (rE = 0.25) than in the probands (r, = 0.59) they are not significantly different. The results of goodness-of-fit tests for the various twin model comparisons are presented in Table 4. Based on the results obtained from fitting the phenotypic model to the data, we equated the genetic and environmental parameter estimates for the cognitive variables between groups (model II). As expected, model II did not significantly reduce the model fit (x& = 18.81, d.f. = 11, P 2 0.050). Model III tested whether the genetic and environmental parameter estimates for the Table 3. Proportions of variance estimated from the general bivariate twin model Proband source of variance
e2
Controlb
Reading
Cognition
Reading
Cognition
0.82 0.01 0.16
0.68 0.14 0.17
0.66 0.18 0.16
0.62 0.28 0.10
BT”= 0.52, Tc = 1.00; TE= 0.59. brA = 0.81, rc = 1.00; TE= 0.25.
801
Bivariate model Table 4. Goodness-of-fit
comparisons
Model” I II II1 IV V VI VII VIII
cog,,,, read,,,,
Full = co&,., = read,.,
rAO,“b = rl.“n, r,=a=a’=O r,=c=c’=O specific A = 0 specific C = 0
of twin models for data from the Colorado Research Center NPAR 58 47 32 46 42 42 34 34
vs
I II II II II VI VI
x2
d.f.
360.96 18.81 59.53 6.71 161.18 3.61 33.13 15.27
162 11 15 1 16 16 8 8
Learning Disabilities
P 4 > < Q Q 2 < >
0.005 0.050 0.005 0.005 0.005 0.995 0.005 0.050
TL
NF
0.90 0.90 0.89 0.90 0.84 0.90 0.90 0.91
0.91 0.90 0.88 0.90 0.83 0.90 0.89 0.90
‘cog = cognitive variables; read = reading variables; prob = probands; cant = controls. NPAR = number of parameters; TL = Tucker-Lewis index; NF = normed fit index.
reading variables differed between groups. Also as expected, the genetic and environmental variances and covariances for reading variables significantly differ between samples (x& = 59.53, d.f. = 15, P d 0.005). In addition, genetic correlations between the reading and cognitive factors differ in the proband and control groups (model IV, x& = 6.71, d.f. = 1, P < 0.005). Also, genetic variances and covariances could not be dropped from the model (model V, x& = 161.18, d.f. = 16, P < O.OOS), confirming that the relationship between reading and cognition is due significantly to genetic factors. In contrast, the shared environmental influences (model VI) could be dropped from the twin model without a significant loss of fit (x&, = 3.67, d.f. = 16, P 2 0.995). In order to determine whether genetic influences independent of those shared by the two factors significantly influence the measured variables, the specific additive genetic effects were dropped from the model. Model VII fits the data significantly worse than model VI (& = 33.13, d.f. = 8, P < O.OOS),indicating that genetic influences independent of those shared by the factors contribute to the measures of reading and cognition. Finally, when we dropped the specific shared environmental influences from the model (model VIII), the change in x2 was not significant (& = 15.27, d.f. = 8, P 3 0.05); thus, shared environmental effects neither contribute significantly to the covariation between the traits, nor account for significant independent variation in the reading and cognition variables. DISCUSSION
The nature of the relationship between general cognitive ability (measured by VIQ and PIQ) and reading performance (measured by REC, COMP and SPELL) was examined by fitting structural equation models to twin data from the Colorado Learning Disabilities Research Center. In the proband sample, at least one member of each twin pair (276 MZ and 210 same-sex DZ) had a positive school history of reading problems. In contrast, neither member of each pair in the control sample (195 MZ and 119 same-sex DZ) had a school history of reading deficits. The proportions of the observed variance due to genetic and environmental influences were estimated for the various measures, and the phenotypic correlation between reading performance and general cognitive ability was partitioned into components due to genetic, shared and non-shared environmental influences in both groups. Specific genetic and environmental influences, independent of the covariation between the two factors, were also estimated. In general, there were no fundamental differences between the proband and control groups in the genetic and environmental etiologies of general cognitive ability or in its factor structure: in both groups, over 60% of the variability in cognitive ability was due to genetic influences and the shared environmental effect was small. However, the genetic and phenotypic variances and covariances for the reading measures were significantly larger in the proband group than in the controls. These results support the hypothesis that a QTL for reading disability is more prevalent in the group selected for reading deficits (Alar&n & DeFries, 1995; Cardon et al., 1994, 1995; Grigorenko et al., 1996). If there is an allele at a single locus that has a substantial deleterious effect on reading performance, its frequency should be higher in a sample of children selected for reading deficits than in a sample of control children (Alar&n & DeFries, 1995). Thus, because genetic variance is a function of allele frequency (Falconer, 1989), the genetic and phenotypic variances should be
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Maricela Alarcon and J. C. DeFries
higher in the proband group than in the control group if there is a major QTL for reading performance. As predicted by this hypothesis, the heritability of reading performance was higher in the proband group (0.82) than in the controls (0.66). If the increased variance in the proband group is specific to reading performance, the correlation between the reading and cognitive factors in the probands should be attenuated. Although the phenotypic correlations between reading performance and general cognitive ability in the proband (Y, = 0.41) and control (rP = 0.76) groups are both substantial, the difference in their magnitude is significant (P < 0.005). Finally, when the full twin model was fitted to the data, resulting estimates of the genetic correlation between reading performance and general cognitive ability were 0.52 and 0.81 for the probands and controls, respectively. Thus, our findings of greater phenotypic and genetic variances for reading performance and lower phenotypic and genetic correlations between reading performance and general cognitive ability in the proband sample provide additional evidence that reading disability may be caused by one or more genes with major effects. Ackno~~led~rmpnts~This work was supported in part by program project and center grants from the National Institute of Child Health and Human Development (HD-I 1681 and HD-27802) to J. C. DeFries. The report was prepared while M. Alarcon was supported by funds from the Graduate School, University of Colorado. The invaluable contributions of staff members of the many Colorado school districts and of the families who participated in this study, are gratefully acknowledged.
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