Testing models for variation in intelligence

Abstract

A biometrical-genetical model for human variation adequately predicts observed correlations for measured intelligence. The estimation procedure is outlined.IN a recent review Jinks and Eaves (1974) stressed the close agreement between observed correlations between relatives for IQ and their expectations on the basis of a simple model. Their model involved five parameters: additive and dominant components of gene action (DR and HR); the marital correlation (a); the correlation (A) between spouses' additive genetical deviations; the component (Er) reflecting the environmental covariation of parent and offspring. The contribution of the environmental influences specific to individuals (E1) is a sixth parameter whose magnitude is fixed by the other five by the restraint that the total variance is unity.Jencks' (1973) application of path coefficients to the analysis of intelligence was partly questioned because of what was believed to be an upper limit upon the value of the path between the genotypes of parent and offspring. No such limit exists in fact so his conclusions cannot be discounted on this basis. More critical, however, was Jinks and Eaves' re-analysis of published correlations (Burt, 1966; Jencks, 1973) which demonstrated that any signficant heterogeneity of heritability estimates obtained from different degrees of relationship can be removed if the contribution of dominance is precisely specified and a weighted least squares procedure is adopted.The correlations analysed have already been tabulated (Jinks and Eaves, 1974), but details of the model and estimation procedure were necessarily omitted and are considered here. The model (table I) is that of Fisher (1918) for the correlations between relatives for a population in equilibrium under assortative mating with additions to specify the contribution of certain plausible environmental components. The model is a modification of that in the review because u has been reparameterised in terms of A and DR.This restriction is necessarily imposed if all the assumptions in Fisher's model are to be tested adequately. It will be seen that although the restraint alters the estimates somewhat the fundamental interpretation remains unaltered.In view of the fact that biometrical genetical models are usually linear and this model is substantially non-linear it is appropriate to outline the estimation procedure.The model for our vector of observed correlations x may be written x=f(4)-i-8where f() represents a vector of functions of the parameters , and g is a vector of deviations. We require to minimise the weighted sum of squared deviations(1)

The genetical analysis of covariance structure

“…Our maximum likelihood estimate of b is ft70l3 giving an estimate of A = 04958. This is somewhat higher than other estimates of A for IQ, (Eaves, 1973(Eaves, , 1975 probably reflecting once again the presence of a genuine common factor.…”

“…The model can be complicated in a variety of ways to include, for example, the contribution of non-additive genetical effects such as dominance, assortative mating, shared environmental effects (E2), genotype-environmental interaction and genotypeenvironmental covarianee (see e.g. Jinks and Fulker, 1970;Eaves, 1975;1976a, b;. However, before we attempt explanations in terms of more intricate effects we must satisfy ourselves by the appropriate sealing tests that a simpler model for individual differences is unacceptable.…”

“…(See e.g. Eaves, 1975). When this kind of model is fitted in the classical twin study the E2 estimate tends to be a conglomeration of certain other between-family effects which may be present.…”

“…Jinks and Fulker, 1970;Eaves, 1975;Eaves and Eysenek, 1975) have stressed the inadequacy of the ad hoc approach characteristic of behavioural genetics in the univariate ease, such remains the approach of most behavioural geneticists to their data. Unfortunately, all the problems of inefficient and misleading univariate methods are exacerbated by their importation into the domain of multivariate genetical analysis hecause crude methods of genetieal analysis have been combined with no less crude methods of factor analysis.…”

The advantages of analysing human variation using twins and twin half-sibs and cousins

“…Additionally, Eaves (1979) demonstrates that, if assortation is based solely on the basis of the measured phenotype, then the correlation between a twin and their co-twins spouse is expected to be the product of the twin correlation and the marital correlation, and the correlation between the two spouses of twins is expected to be the product of the twin correlation and the marital correlation squared. When assortation is based upon the measured phenotype, the basic model may be amended by the inclusion of the appropriate expectations (Fisher, 1918;Eaves, 1975).…”