‘Generalist genes’ and mathematics in 7-year-old twins
Introduction
It is hard to overestimate the importance of adequate mathematical ability in a society that requires a high degree of technical competence from its citizens. Continuous technological advances, workforce expectations, the competitive economic advantages that can be acquired from high levels of mathematical literacy, and simply the requirements of successful adult living, all drive the need to improve the standard of mathematical ability and to decrease the rate of mathematical underachievement. The importance of adequate mathematical ability is becoming increasingly recognized by society and is reflected in new government and commercial initiatives, such as Maths Year 2000 initiative and Maths@Work project, as well as reports on the importance of mathematics and assessments of current levels of numeracy (e.g. Smith, 2004).
Unfortunately, what is clear from a wide range of studies conducted in different countries is that a significant number of children demonstrate poor achievement in mathematics (Mazzocco & Myers, 2003). The prevalence of mathematical disability, defined as scoring at least 2 years below grade level in arithmetic in the presence of normal intelligence, is estimated as approximately 6% in school children (e.g. Gross-Tsur, Manor, & Shalev, 1996). This estimate is similar to the reported frequency of reading disability (Mazzocco & Myers, 2003). For this reason, the study of mathematical ability is worthy of a research effort similar in scope to that devoted to the study of reading ability. However, to date the body of research on reading ability by far exceeds that on mathematical ability.
As a result, the literature is only beginning to address the important question of how genes and environments influence mathematical ability and disability. The few twin and adoption studies of mathematics performance have reported a wide range of heritabilities from 0.20 to 0.90 (reviewed in Oliver et al., 2004). In a recent report based on the same dataset used in the present study, both mathematics ability and disability at 7 years assessed by teachers using UK National Curriculum criteria during the second year of elementary school showed genetic influence in between the extremes of previous estimates (0.65) (Oliver et al., 2004).
A ‘generalist genes’ theory of learning abilities and disabilities has recently been proposed which predicts that most genetic effects for scholastic achievement and cognitive abilities are general rather than specific (Plomin & Kovas, in press). That is, the genes that affect one area of learning, such as mathematics performance, are largely the same genes that affect other abilities, although there are some genetic effects that are specific to each ability. The main purpose of the present study is to test the ‘generalist genes’ theory in relation to mathematics performance. We used multivariate genetic analysis to assess the extent to which genetic effects on mathematics performance at 7 years of age overlap with genetic effects on reading performance and g. The same analysis indicates whether there are significant specific genetic effects on mathematics performance independent of reading and g.
Mathematics performance covaries phenotypically with reading and with g (Alarcón et al., 2000, Hecht et al., 2001, Jordan & Oettinger Montani, 1997, Knopik & DeFries, 1999), but the etiology of this covariation remains poorly understood. Even though individual differences in mathematics, reading and g are influenced by genes, it is possible that completely different sets of genes affect each of these three domains. Multivariate genetic analysis, which addresses the etiology of the covariance between traits rather than the variance of each trait considered on its own, can estimate the extent to which the genetic factors that influence individual differences in mathematics are also involved in shaping reading and g. Multivariate genetic analysis estimates the genetic correlation that represents the extent to which genetic effects on one trait are correlated with genetic effects on another trait independent of the heritability of traits (Plomin, DeFries, McClearn, & McGuffin, 2001). That is, the genetic correlation can be high when heritability is low and vice versa. The genetic correlation can be thought of as the probability that if a gene were found to be associated with one trait, the same gene would also be associated with the other trait.
Three multivariate genetic studies addressing the issue of genetic overlap between mathematics and reading suggest substantial overlap. The first study of genetic overlap between mathematics and reading included 146 MZ and 132 DZ twin pairs from 6 to 12 years of age assessed on the Metropolitan Achievement Tests of mathematics and reading (Thompson, Detterman, & Plomin, 1991). A genetic correlation of 0.98 was reported between mathematics and reading. However, wide confidence intervals surround genetic correlations, especially in modest sample sizes as in this study, although the data presented in this 1991 report do not permit an estimate of the confidence interval. In the only other twin study of the genetic overlap between mathematics and reading, a genetic correlation of 0.47 was found in a study of 220 MZ and 135 DZ twin pairs aged from 8 to 20 years (Knopik & DeFries, 1999). In an adoption study, the genetic correlation between reading and mathematical performance was 0.80 in a parent–offspring analysis (Wadsworth, DeFries, Fulker, & Plomin, 1995a) and 0.83 in a sibling analysis (Wadsworth, DeFries, Fulker, & Plomin, 1995b). One of these studies also explored the extent to which mathematics performance overlaps genetically with g. In a report based on 319 MZ and 251 DZ twin pairs aged from 8 to 20 years, the genetic correlation between latent factors of mathematics and g was 0.95 (Alarcón et al., 2000). The same estimate was obtained in a sample selected for learning deficits. Several studies indicate that reading and g also show substantial genetic correlations (Harlaar et al., 2005, Knopik & DeFries, 1999, Wainwright et al., 2004).
The only multivariate genetic study that simultaneously included mathematics, reading and a measure of g (verbal IQ only) also included phonological decoding in a study based on 196 MZ and 155 same-sex DZ twin pairs aged from 8 to 20 years (Light, DeFries, & Olson, 1998). A genetic correlation of 0.36 was found between mathematics and reading with approximately 82% of this correlation being due to genetic factors that also influence verbal IQ and phonological decoding ability. Some specific genetic influence was found for mathematics independent of reading, verbal IQ and phonological decoding.
The present study uses multivariate genetic analyses of data from a large sample of 7-year-old twins to test the ‘generalist genes’ hypothesis, which predicts that most genetic effects on mathematics performance overlap in their effects on reading and g. This is the first large multivariate genetic study to assess children of the same age when they just began their formal education in mathematics and to include g as measured by both verbal and non-verbal tests.
Section snippets
Participants and procedure
Participants were part of the Twins' Early Development Study (TEDS), a longitudinal study involving a representative sample of all twins born in England and Wales in 1994, 1995, and 1996. The twins' language, cognitive and behavior development have been assessed by parental questionnaires at 2, 3 and 4 years of age (Trouton, Spinath, & Plomin, 2002). Data from 4737 pairs of twins born between January 1994 and August 1995 were analyzed for this study. The following exclusion criteria were used:
Descriptive statistics and further exclusions
To allow for comparisons between the different measures, the three composites (mathematics, reading, and g) were separately standardized using the means and standard deviations of the entire sample (after medical and ethnic exclusions described in the method section) so that each test had zero mean and unit variance for the total sample of 8638 twins, although the means and standard deviations in the first column of Table 1 differ slightly from zero mean and unit variance after the exclusion of
Discussion
We investigated the extent to which genetic influences on mathematics performance also affect reading and g, as predicted by the generalist genes hypothesis. The results supported the generalist genes hypothesis in that the genetic correlations are 0.74 between mathematics and reading and 0.67 between mathematics and g. This finding implies that most of the genes that contribute to individual differences in mathematics ability also affect reading and g. Of course not all of the genetic effects
Acknowledgement
We gratefully acknowledge the ongoing contribution of the parents and children in the Twins' Early Development Study (TEDS). TEDS is supported by a programme grant (G9424799) from the UK Medical Research Council and our work on mathematics is supported in part by the US National Institute of Child Health and Human Development and the Office of Special Education and Rehabilitative Services (HD 46167).
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