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g as a consequence of shared genes.

1. Introduction

The nature of g continues to be a central question for research on human intelligence. Some theorists hypothesize that the g factor is an epiphenomenon that emerges because common cognitive tasks share a reliance on cultural knowledge and linguistic skills (Gardner, 1983; Gould, 1981). Other theorists posit that a shared subtest dependence on cognitive modules (Detterman, 1987), brain structures (Anderson, 1995), speed and efficiency of neural processing (Jensen, 1998), or a small number of major genes (Plomin, 1999) produces g and causally links g to a real world construct of general intelligence.

At a recent meeting, The Nature of Intelligence (Novartis Symposium, November/ December 1999, London, England), the discussion between psychometricians and evolutionary psychologists led to a collective suggestion that population genetics might explain g. In this paper, I present the logic of how a g factor can emerge naturally from uncontroversial assumptions about the genetic control of brain function. This account also explains the inverse relationship between the magnitude of cognitive task intercorrelations and overall ability levels (Detterman & Daniel, 1989), and establishes the necessary relationship between behavioral variance and ability that any nongenetic account would have to meet.

The logic behind the argument is presented mathematically; by demonstrating how behavioral test intercorrelation magnitudes are affected by dependence on shared genetic components and how this relationship is affected by the increased behavioral variance consequent to mutation. As g is a consequence of the computation of intercorrelations between abilities, argument by mathematical demonstration is legitimate and has been used previously to evaluate competing theories of human intelligence (Detterman, 1994). An important implication of the mutation theory of g is that a change of tactics will be necessary for determining the genetic, anatomical, and physiological correlates of human intelligence, and that there may be no "major" determinants of human intelligence.

2. Assumptions

(A) Cognitive tasks of the sort that comprise IQ tests are complex and depend for their successful performance on the coordinated, efficient function of distributed arrays of neurons in the brain (even an elementary cognitive task, such as simple reaction time, requires visual perception, accurate motor action, and sustained attention),

(B) A large number of genes are involved in the development and function of the brain,

(C) Most cognitive tasks show moderate heritabilities (Bouchard, Lykken, McGue, Segal, & Tellegen, 1990), and therefore,

(D) Any two cognitive tasks of the type used for IQ tests will share some fraction of their genetic determinants.

3. Demonstration

To see how this produces a positive correlation manifold for cognitive tests, consider the example of two cognitive metric Traits X and Y that are determined by three diallelic Loci A, B, and C. Loci A and B determine the phenotype of Trait X, and Loci B and C determine the phenotype of Trait Y. What is the correlation between Traits X and Y?

Corr {X, Y} = Cov{X,Y}/[square root of Var{X} * Var{Y}].

To begin simplifying the numerator note that,

Cov {X, Y} = Cov{A + B, B + C}.

As the covariance of a sum is the sum of the covariances,

Cov{A + B, B + C} = Cov{A, B} + Cov{A, C} + Cov{B, B} + Cov{B, C}.

If we assume that all the loci are independent, all of the above covariance terms are zero except the covariance of B with itself, which is the variance of B, thus,

Cov{X, Y} = Var{B}.

To simplify the denominator, recall that the variance of a sum of independent variables is equal to the sum of variances,

[square root of Var{X} * Var{Y}] = [square root of (Var{A} + Var{B}) * (Var{B} + Var{C})].

For simplicity, we assume that all the loci have equal variance, thus we can replace each loci variance term with the variance for B, which simplifies the denominator to,

[square root of Var{X} * Var{Y}] = 2Var{B},

and our correlation is simplified to,

Corr {X, Y) = Var{B}/2Var{B} = 1/2.

Following the same logic, the general equation for the correlation between two traits with numbers of Loci a and b, and a number of shared loci n is,

Corr{Trait 1, Trait 2} = n/[square root of a * b].

From this equation, we see that any two traits with shared components will have a positive correlation. While this example is based on shared genetic factors, the logic applies equally well to accounts based on shared cultural knowledge or cognitive modules. However, it is only the genetic account that definitely provides a plausible account of the Detterman and Daniel's data of increasing correlations at lower ability levels.

Genetic variance in populations is preserved through the balance of competing forces. For example, selection and genetic drift work to decrease variance and mutations increase genetic variance. Mutation is now believed to be a relatively common event. For example, it is calculated that each of us will experience a somatic gene mutation (Gillespie, 1998). While the odds that a particular gene will be subject to deleterious mutation is small, the aggregate probability is that at least one gene will. When we consider the large proportion of the human genome involved in the development and function of the human brain, it is probable that minor deleterious mutations in different genes affecting the brain are common.

With this in mind, we can return to our example. Assume that Locus B has mutated to B' and now has a variance equal to (1 + c)Var{B}, where c is any positive number. Thus, our new equation for the correlation between Traits X and Y is:

Corr {X, Y} = (1 + c)Var{B}/[square root of (Var{B} + [(1 + c) * Var{B}])([(1 + c) * Var{B}] + Var{B})].

This equation makes use of the assumed equal variance among all the nonmutated loci and the relation between the variances of B and B'. After expanding, canceling, and algebraic manipulation this equation can be rewritten as:

Corr{X,Y} = (1/2) (1 + c/1 + c/2).

Note that the numerator and denominator of the fraction to the right of the multiplication sign are the same except for the fact that the numerator has a c where the denominator has c/2. For any positive number c, the numerator will be greater than the denominator and the fraction will be greater than one. This factor when multiplied against our "unmutated" correlation increases its value. However, the effect of the deleterious mutation decreases the mean performance for each trait. Thus, a genetic account explains positive intercorrelations among cognitive tests and the increase in intercorrelation magnitude with decreasing ability levels.

4. Discussion

A number of assumptions were made in developing this argument. How likely are these assumptions to be violated in the "real world," and what are the implications of violations for the theory?

That the brain is a highly complex organ, produced through the effect of a large proportion of the genome is empirically established. That even simple cognitive tasks are sensitive to the interdependent function of a large amount of the brain is uncontroversial.

The genetic assumptions are definite simplifications. All genetic loci are not independent. However, a large proportion is and much of population genetics has advanced successfully on this simplifying assumption (Gillespie, 1998). The assumption of dependence would introduce additional complications into the calculation of the correlations between traits, but would not eliminate the positive manifold.

All genetic loci are unlikely to have equal effects on behavioral variance, though their assumption eased the demonstration. However, assuming unequal variances does not alter the basic pattern of increasing intercorrelations at decreasing ability levels through accumulated mutations (mutation load), though the magnitude of this relationship cannot be easily predicted.

Are all mutations deleterious; what about positive mutations? The fate of most advantageous mutations is elimination by genetic drift. Given the development of our genome over many millennia most spontaneous mutations are presumed to be harmful, though many are nearly recessive making their heterozygous phenotypes very much like "normal." Most of these mutations are also removed through the effects of drift and selection, however, the empirical demonstration of residual variation for traits like intelligence, that are assumed to be related to fitness, directly argues for a selection mutation balance.

The genetic account of g presented here has a plausibility and simplicity that is missing from many other accounts of g. However, environmental factors could still be compatible with the mathematical demonstration presented here if they had the effect of being like mutations. That is, they would be primarily "deleterious," thus negative in their effects on ability levels, but positive in their effect on behavioral variation.

The genetic account also has at least two additional implications. First, no specific or major genes exist for intelligence or g per se. g emerges from the interplay of all the genes important for brain function, the small probability that any individual gene will be mutated, and the large probability that some will be mutated. The process of mutation is common, not the genes effected. This predicts a failure for efforts to locate quantitative trait loci for g with large effect sizes (Plomin, 1999). Any genes found with metric effects on intelligence will be of small effect and pedestrian, but critical, for basic brain function.

The second conclusion is that the effort to correlate IQ with brain structure and function will need to change tactics. We will find correlations to IQ, for variables like brain size (Flashman, Andreasen, Flaum, & Swayze, 1997) and NAA levels (Jung et al., 1999) that are morphologic or physiological indices reliant on large numbers of genes and susceptible to the same statistical effects. However, the search for independent influences on intelligence will be the search for variables of small effect sizes, more akin to the needle in the haystack.

None of these argues against the concept of general intelligence. Rather, g and general intelligence can be regarded as measures of genetic quality for producing a brain. As such, it is unlikely that there are particular genetic, cognitive, structural, or physiological variables with privileged positions for determining general intelligence.


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Department of Neurology, University of Alabama at Birmingham, Neurology Service (127), Birmingham VA Medical Center, 700 South 19th Street, Birmingham, AL 35233, USA

Received 16 March 2000; accepted 20 March 2000

Britt Anderson, Current address: Brain Science Program, Brown University, Box 1953, Providence, RI 02912, USA. Tel.: +1-401-884-1685.

E-mail address: (B. Anderson).
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Author:Anderson, Britt
Geographic Code:4EUUK
Date:Nov 1, 2001
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