## The Monogenic Theory of Schizophrenia

*Acta Genetica et Statistica Medica *(Basel) 8: 50‑56 (1958).

Despite the researches of thirty years, the genetic basis of schizophrenia still remains a matter of doubt. Some of the available observations suggest a recessive mode of inheritance, while others are more easily reconciled with dominance. To explain the discrepancies it has been suggested that schizophrenia is genetically heterogeneous; but even this attempt to make the best of both worlds encounters difficulties.

In his important paper on a North Swedish population, Böök (1953) proposed the hypothesis that, in this population isolate, schizophrenia was due to a recessive gene which manifested itself in all homozygotes and in about one in every five heterozygotes. This was, in fact, the hypothesis which provided the best fit for his data. It is one which involves features both of dominance and recessivity; and it is desirable to see whether hypotheses of this form might be compatible with the data obtained from other populations, whether, in fact, the monogenic theory of Böök could be applied more universally.

Böök's calculations of the frequencies of genotypes and matings are not very easy to follow; and as an alternative approach the following simple formulation is offered. We shall write A = the dominant (normal) gene, with frequency of (1‑*p*) in the population, and *a* = the schizophrenic gene, with frequency *p*. Then among the relatives of particular genotypes, other named genotypes will appear with frequencies which will be functions of p, as shown in Table 10.1.

The frequency of schizophrenia in the general population (*s*) is given by the formula *s* = 2*mp*(1-*p*)+*p*2, where *m* is the frequency of manifestation of the schizophrenic gene in the heterozygote. We can take 0.008 as a fairly reliable estimate of the frequency of schizophrenia in most European countries. Using this formula, we can calculate the value of *p* corresponding to every value of m between its limits of 0 and 1, or, more conveniently, calculate the value of m corresponding to various values of p. It is also interesting to note at the same time the corresponding values of h, where *h* = *p*^{2}/0.008, and represents the proportion of all schizophrenics who are homozygotes. This is a convenient measure of the degree to which the mode of inheritance approaches to recessivity, and varies between 1 and a very small value.

To every value of *p*, and of *m*, there will also correspond values for the expectation of schizophrenia among the various classes of relatives of schizophrenics, or in given types of matings. There are available the results of adequate investigations of the frequency of schizophrenia in the children of schizophrenics, in their sibs, and in the children of two schizophrenic consorts. Furthermore, Nixon and Slater (1957) have made one estimate of the frequency of schizophrenia in the children of first cousins. The theoretical expectations, calculated by the use of Table 10.1, are as follows:

Frequency of schizophrenia in the children of schizophrenics = ½ (1+h) (*m*+*p*)‑*hmp*;

Frequency of schizophrenia in the sibs of schizophrenics= 1/4 {2*m*+*h*+*p* (2*m*+*h*+1 2*mh*)+p2 (1‑ 2*m*)};

Frequency of schizophrenia in the children of two schizophrenics= ¼ (1+*h*){2*m*(1-*h*)+1+*h*};

Frequency of schizophrenia in the children of first cousins = 1/16 (15*s*+*p*).

Values of these expectations have been calculated for eleven points of the entire range of possibilities, and are given in Table 10.2.

The relationships between *p*, *m* and *h* and the corresponding expectations of schizophrenia in the various classes of relative are also shown in Figure 10.1.

This makes very evident the extent to which the expectation in the sibs drops between the extremes of recessivity and dominance, instead of taking, as one might have expected, intermediate values; the minimum is seen in the neighborhood of the point where there is a 12 per cent rate of manifestation in the heterozygote. Something similar is seen in the behaviour of the figures for the children of one schizophrenic, where the minimum is found at a 6 per cent rate of manifestation; but there is very little change between the 12 per cent point and the extreme of absolute reeessivity. At low gene frequencies, when *m* exceeds 0.2, there is practically no difference between the expectations in sibs and in children. It is also noteworthy that the expectation of schizophrenia in the children of two schizophrenics varies in a remarkable way between the extremes of dominance and recessivity, so that observational estimates are clearly capable of providing valuable information. The expectation of schizophrenia in the children of cousins, on the other hand, varies very little and shows itself to be an insensitive measure of dominance-recessivity.

We may now compare the expectations with the frequencies that have been actually observed. The frequency of schizophrenia in the sibs of schizophrenics has been estimated by Kallmann (1953) as 0.142; other workers have found a slightly lower figure. This expectation is found on the curve for sibs both at gene frequency 0.015 and again at 0.055. If the frequency were lower than 0.142, a corresponding expectation could be found with a p value between these limits. Kallmann, again, has found the frequency of schizophrenia in the children of schizophrenics to be 0.164; this point is found on the curve for children at gene frequency 0.013. The estimate of Elsässer (1952) for the frequency of schizophrenia in the children of two schizophrenic consorts is 0.392. This point is found on the corresponding curve at values of *p* of 0.015 and 0.038. Finally, Nixon and Slater estimated that the frequency of schizophrenia in the children of cousins was 57/40 of the frequency in the general population = 0.011, which corresponds with a gene frequency of 0.055.

When one takes into account the magnitude of the statistical errors to which all these estimates are liable, it is seen that they are all readily compatible with a gene frequency of about 0.015, and a manifestation rate in the heterozygote of about 0.26. At this point, all but 3 per cent of schizophrenics are heterozygous.

There is one important group of observations of which so far no mention has been made, i.e. the data relating to the incidence of schizophrenia in the MZ twins of schizophrenics. The concordance rate within MZ pairs has been estimated as lying between 76 per cent (Slater, 63) and 86 per cent (Kallmann, 1953). If we merely thought of the MZ co‑twins of schizophrenics as a group of persons of whom 3 per cent were homozygous and 97 per cent were heterozygous, then we might conclude that the concordance rate should be 28 per cent. However, the MZ co‑twins of schizophrenics are identical with their partners, not only in respect of the hypothetical specific schizophrenic gene, but also in respect of the total genetic equipment. If a much higher concordance rate than 28 per cent is actually found, this is a matter for no surprise. But the fact that the genotypic milieu should play such a part deprives the data obtained from twins of any value for the testing of the monogenic hypothesis.

If it were desired, it would be a simple though slightly laborious task to calculate expectations for other classes of relatives than those discussed above. It seems improbable, however, that information of much critical value would be thereby obtained. Furthermore, the observational data for comparison would be less reliable. In the case of one class, that of parents, the observed frequency of schizophrenia could not be safely used for such a purpose, since parents are a group of persons who have been selected for survival and for health.

Taking the material we have, it would seem that some at least of our knowledge of the incidence of schizophrenia in the relatives of schizophrenics could be adequately explained by the hypothesis of a single partially dominant gene, such as Böök proposed for the special circumstances of a North Swedish isolate; and that this hypothesis therefore merits further investigation.

SUMMARY

The consequences are examined of a hypothesis which proposes a single partially dominant gene as the genetical basis of schizophrenia. It is shown that a simple relationship connects gene frequency and rate of manifestation in the heterozygote, if the frequency of schizophrenia in the general population is held constant; a series of values for these two variables has been calculated, when the frequency of schizophrenia is taken as 0.008. The expectation of schizophrenia in certain classes of relatives of schizophrenics also varies with the gene frequency and with the manifestation rate, but in a complex way such that, between high values at the extremes of complete dominance and complete recessivity, not intermediate values but minima are found. The observed frequencies of schizophrenia in the sibs of schizophrenics, in the children of one schizophrenic parent, and in the children of two schizophrenic parents, are compatible with this theory, and would correspond with a manifestation rate in the heterozygote of about 0.26 and a gene frequency of about 0.015.

Acknowledgment. I am much indebted to Mr. W. L. B. Nixon for valuable help.