• Lancelot Hogben

Articles written in Journal of Genetics

• The genetic analysis of familial traits - I. Single gene substitutions

If familial trait is determined by a single recessive gene$$\frac{R}{{\Sigma \frac{{s. n_s }}{{1 - q^s }}}} = p$$ wherep is the probability that the offspring of two heterozygous parents will be recessive,R is the total number of recessives in observed families of at least one recessive,ns is the number of observed s-membered fraternities containing at least one recessive, and (p + q) = 1.

The standard deviation ofp determined in this way is$$\frac{{\sqrt {\Sigma n_s k_s } }}{{\Sigma n_s c_s }}$$.

Tables ofcs andks are given fors = 1 to 20,q being 3/4.

In general the proportion of recessives in recorded families showing either autosomal or sex-linked familial traits is significantly higher than 1/4. This may be due to the fact that cases showing a high familial incidence are recorded in medical journals more frequently than cases showing a low familial incidence.

If this is so, little progress will be made in genetical analysis of pathological traits by compilation of recorded data. This conclusion is supported by the fact that two cases showing comparatively insignificant discrepancies were based on unweighted observations of individual investigators, and the only case of completely satisfactory agreement is a disorder which is not rare.

• The genetic analysis of familial traits - II. Double gene substitutions, with special reference to hereditary dwarfism

The limits between which the expected ratios of affected offspring of parents of all possible phenotypes will lie, when a trait is determined by two complementary dominant genes on different chromosomes, or two independent recessive genes, have been investigated in this communication. The proportions expected vary with the incidence of the trait in the population. In the case of a trait determined by two independent complementary dominant genes the limiting value for matings of two normal parents is the same as that for a single recessive trait. When the two gene frequencies are of the same order this limit is reached rapidly.

Recorded data of various pathological conditions have been examined from this standpoint, and it has been shown that the extant observations on ateleiosis, and the Japanese cases of hereditary optic atrophy are interpretable on the assumption that this condition is significantly determined by two dominant genes. It is unlikely that this explanation will be found to apply to achondroplasia. It is possible that it applies to cleft palate, harelip and glioma retinae.

The foregoing analysis emphasises four prerequisites for the application of factorial analysis to clinical data. These are: first, exact information concerning the frequency of familial traits in the general population; second, the elimination of any bias due to neglect of families with a low familial incidence; third, the collection of random samples of matings involving one affected parent unbiassed by the possibility that such matings may or may not yield affected offspring; and finally, searching enquiry into the tendency to assortative mating.

One significant outcome of the present enquiry is the fact that the expected proportions of affected individuals calculated in such a way as to make allowance for the small size of the human family diverge at the lower limit much less rapidly than is at all obvious at first sight, as the number of genes determining a given trait increases.

• The genetic analysis of familial traits - III. Matings involving one parent exhibiting a trait determined by a single recessive gene substitution with special reference to sex-linked conditions

The present communication discusses the quantitative analysis of matings involving one affected parent, when a clinical condition is determined by a single recessive gene substitution.

The proportion of matings showing direct transmission is higher than would be calculated from the theory of random mating. One reason for this is that the application of a theory of random mating is limited by the geographical propinquity of the individuals concerned. There must, therefore, be a limit of dilution beyond which increasing rarity of the trait does not appreciably decrease the probability that an affected individual will mate with a carrier.

Matings of albinos with normal individuals having affected offspring satisfy the hypothesis that albinism is determined by a single recessive autosomal gene substitution. The discrepancy for matings of two normal parents with some albino offspring is not significant for large families, and may hence be attributed to biased selection of the small families recorded.

There are very few exceptions to the rule that all types of matings in stocks displaying red-green colour blindness conform to the requirements of the hypothesis that the condition is determined by a single recessive gene substitution on theX-chromosome.

As far as the extant evidence can be regarded as trustworthy, haemophilia must be interpreted as a recessive sex-linked condition which is alsosex limited.

There are two forms of Leber’s disease, both genetical types being found among Europeans and probably both among Japanese, though the majority of examples of the recessive sex-linked form are European and the majority of the Japanese cases are of the type which is apparently determined by two autosomal dominant genes.

• The factorial analysis of small families with parents of undetermined genotype

A method by which the standard deviation of the expectednumber of recessives may be calculated for human or other data derived from small families is given. This involves the same functions as previously tabulated for a method of comparing the hypothetical expectation of recessives with an“adjusted” proportion based on the observed data. It leads to precisely the same numerical results and is free from ana priori assumption implicit in the earlier statement.

• The limits of applicability of correlation technique in human genetics

Three main conclusions emerge from the foregoing discussion.

(1) The technique of correlation can be used to draw attention to the existence of genetic differences or of differences due to environment provided the selection of data is appropriate to the kind of differences we wish to detect.

(2) The belief that a comparison between observed correlations of relatives and correlations based upon purely genetical assumptions provides us with a measure of the influence of nurture is not justified, because of the close relationship between the distribution of gene differences and differences due to environment in populations of viviparous animals which live in families, especially when, as with human populations, the environment of different families may differ greatly.

(3) A balance sheet of nature and nurture, if it has any significance in the light of modern experimental concepts, does not entitle us to set limits to changes which might be produced by regulating the social or physical environment of a human population.

• A contribution to the relation of the gene loci involved in the isoagglutinin reaction, taste blindness, Friedreich’s ataxia and major brachydactyly of man

The following conclusions may now be stated:

Friedreich’s ataxia is determined by a single recessive gene substitution (f).

The locusF-f is not strongly linked toT-t (phenyl-thio-urea taste blindness) orA-B-R (isoagglutinin reaction). As far as the present evidence permits any inference it appears to segregate independently.

The locusBr-br (brachydactyly) is not strongly linked toT-t, neither isA-B-R. The data are insufficient to justify the statement thatA-B-R orBr-br segregates independently with respect toT-t.

The yield of relevant information obtained in linkage studies confined to a few genes is very small. In consequence the method of routine testing of hospital patients with a battery of tests would seem to be the most efficient way of advancing the mapping of human chromosomes.

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019