Biometrika, 2: 388-390 (1903)

Intermittent Prepotency
K. Pearson and A. Lee

*R. S. Proc. Vol. 71, pp. 290-4.
**Phil. Trans. Vol. 195, A, p. 106.
See also F. Lutz, Biometrika, Vol. ii. p. 236.
Proc. Vol. 66, p. 157.

I now turn to what personally I consider one of the most obscure points in the quantitative determination of inheritance, namely: the manner in which fraternal resemblance varies from species to species, while paternal inheritance remains fairly constant. If we look at Table V. we see that within moderate limits parental influence approximates to the same value for very different species and very diverse characters. This cannot be asserted with the same accuracy of fraternal correlation. I have found values of it ranging from .4 to .7 for large and apparently very trustworthy data for different species. I attribute this, although I have not been able at present to verify it, to prepotency*. In dealing with prepotency I think it important to distinguish ab initia between three kinds: sex-prepotency, unit prepotency, and intermittent prepotency. By sex-prepotency I understand that the offspring of one or other sex or of both sexes are more like the male or the female parent as the case may be. Its existence is demonstrated by showing that the correlation for one parent with all the offspring or with one class of offspring is greater than for the other parent. An examination of Table IV. seems to prove that in man for stature, span and forearm there exists no sex-prepotency. On the other hand in eye-colour in man, there does appear to be a differential sex-prepotency, fathers are prepotent over mothers for eye-colour in sons, and mothers are prepotent over fathers for the same character in daughters**. If the paternal record were trustworthy in the case of Basset Hounds—which I am very doubtful about—then there would be a large sex-prepotency for all offspring of the dam over sire in coat-colour†. From this sex-prepotency must be distinguished an individual prepotency which I term unit prepotency, and which is independent of sex. In unit prepotency one or other unit in a mating is prepotent owing to the possession of some physical character, other than a sexual character. This physical character may or may not be that in which the prepotency shows itself in the offspring. Thus it is conceivable that a dark-eyed parent of either sex might have a unit prepotency over a light-eyed parent, not necessarily in eye-colour or in eye-colour only, but possibly in hair-colour, or stature or mental characters. The unit prepotency may, however, in no way depend upon a simple observable character like this, but on a subtle combination of physical factors producing individual prepotency in one unit of the pair. To demonstrate the latter form of unit prepotency will always be a difficult problem; it could possibly be attacked by considering the reduction of variability in the array of offspring of supposed unit prepotent matings below the average variability of arrays in which such prepotency is supposed not to exist. This method would hardly be possible in the case of man where the number of offspring is too small to get the variability of an array free from a very large probable error. It might be effective in the case of snails, moths, many insects and plants with numerous offspring. When unit prepotency is supposed to be associated with the possession of a definite physical character, it is perfectly possible to attack the problem by the method of association, i.e., investigating the association between the presence (or absence) of this character in a parent and the ratio to total offspring of offspring in the array who do (or do not) possess this character, or some other character of the parent in question. If unit prepotency were absolute we should have the case of "dominance" as originally propounded by Mendel.

*R. S. Proc. Vol. 66, p. 141, etc. and
Phil. Trans.
Vol. 195, A, p. 89 et seq.

While we suppose unit prepotency,—the tendency of one individual out of a pair to be prepotent,—to be chronic, there is another form of prepotency which we may describe as intermittent. One or other parent may at a particular mating, or may in certain individual offspring of one and the same mating, be prepotent. On another occasion, or in other offspring of one and the same mating, it may not be prepotent or even the other parent may be prepotent. Such prepotency might exhibit itself in "alternative" or "exclusive" inheritance*, and is distinct from any unit prepotency or absolute or partial dominance. It does not depend on the possession by one mate of certain characters, but on the condition of the parents and other circumstances peculiar to a special mating.

R. S. Proc. Vol. 66, p. 152, and
Phil. Trans.
Vol. 195, A, p. 101.

Now the fundamental point to be borne in mind is this, that apart from sex-prepotency, neither unit prepotency nor intermittent prepotency need in any way influence the parental correlations. The average resemblances of offspring to either parent will not be affected if in some matings the mother, in other the father is prepotent. Nor again will it be affected, if occasionally the two parents are intermittently prepotent. But such types of prepotency will largely influence the degree of resemblance between brethren. If, either invariably or intermittently, one parent is prepotent, the offspring of all matings of these parents or the offspring of one litter will be more alike, than the offspring of another species in which such prepotency does not exist. When therefore we find parental correlation the same for a number of species and fraternal correlation different, I am strongly of opinion that this will be found to be due to differing amounts of unit prepotency or of intermittent prepotency or of both combined in diverse species. I have already insisted on this effect of prepotency in disturbing fraternal correlation†, but it seemed necessary again to refer to it as the probable explanation of the great differences observable in the fraternal correlations given below in Table XI.

TABLE XI. Fraternal Correlation in Different Species.

Species Characters Brother and Brother Sister and Brother Sister and Brother All siblings
Man Family Records. Mean of three characters .517 .533 .506 .519
Eye Colour .517 .446 .462 .475
School Records. Mean of sixteen characters .520 .519 .518 .519
Basset Hound Coat Colour for same litter -- -- -- .508
Greyhound‡ Amount of Red in Coat, same litter .683 .710 .707 .700
Amount of Black in Coat, same litter .642 .680 .659 .660
Thoroughbred Horse Coat Colour .623 .693 .583 .633
Daphnia (Magna) Ratio of Protopodite to Body Length -- -- -- .693
Aphis (Hyalopterus
Trirhodius
)
Ratio of Right Antenna to Frontal Breadth -- -- -- .589

‡Unpublished results, tabled by Miss A. Barrington from Mr. Howard Collins’ data, reduced by Dr. A. Lee.

*Biometrika, Vol. II. p. 81.
†In the case of these insects differential environment may, of course, have emphasised the resemblance.

I have not placed in this table the results for stature as found from Mr. Galton's Family Data, nor those for Cephalic Index for North American Indians, because I consider that the results for both these characters are replaced by the larger series we have now at our disposal, and which are included under "man" in the above list. Otherwise it embraces nearly all the data we have as yet at our disposal. Now it is clear that the value for man is about .5 and agrees well with the value found for Basset Hounds, and indeed with that for the Shirley Poppy, assuming complete cross fertilisation*. On the other hand the horses and greyhounds, while agreeing well with man for the parental correlations (see Table V. p. 23), show a much increased fraternal correlation of the same order as that between the parthenogenetic offspring of Daphnia and Aphis†. Now how far is this due to such factors as unit prepotency or intermittent prepotency? All we can do at present is to suspend our judgment on this point. In the case of dogs, intermittent prepotency might manifest itself by the offspring of the same parents for the same litter being more alike than for different litters. Now will this account for the high values of the greyhound results? Unfortunately our records contain only greyhounds of the same litter, all members being recorded, while the volumes of the greyhound stud-book contain only a selection of all dogs born, colour undoubtedly being a selected character. Further it is very difficult from those volumes to extract a sufficient number of brethren of full blood from different litters. Still we hope to be able to throw some light on the problem of at least intermittent prepotency in the case of greyhounds. It is remarkable that the fraternal correlation in the Basset Hounds, while according closely with that in man, is the same sensibly in intensity for siblings from the same and from different litters. The case of the thoroughbred horses is somewhat different, but here we propose to draw up separate tables for twin foals and foals from the same parents in different years, and thus if possible differentiate intermittent prepotency, if it really exists. The high values, however, found for half-siblings in the case of the thoroughbreds seem to indicate that we must look rather to unit prepotency than intermittent prepotency for the source of the high value of fraternal as compared with parental correlation in the case of the horse.

What is quite clear is that we badly want the measurement of further characters for siblings in both mammals and insects. The present results show that while the value .5 has overwhelming evidence for it in the case of both measurable and unmeasurable characters in man, we are yet without like data for the measurable characters in horse, dog or any other mammal. Should these ultimately be found to agree with the results given above for the quantitatively unmeasurable characters, I personally hold at present, that the solution for equal parental and unequal fraternal correlations in these different species should first be sought in a fuller study of unit and intermittent prepotency.

CybeRose note: Intermittent prepotency comes very close to what I have called elective expression.