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Correlation and Application of Statistics to Problems of Heredity 37 Constitution and Ancestry of Hazel-Eyed Sibships.

 

Generations

Total cases

observed in

168 families

 

Percentages

 

Light Eyed

Hazel Eyed

Dark Eyed

I. Siblings   ...

II. Parents   ...

III. Grandparents

948

336

449

45

49

60

32

25

13

23

26

27

General Population

4490

61.2

12.7

26.1

the general population percentage. The distribution of the grandparents of a hazel-eyed person is practically the same as that of the general population. From these data Galton concludes as follows


"The total result in passing from Generation III to I, is that the percentage of the light eyes is diminished from 60 or 61 to 45, therefore by one quarter of its original amount, and that the percentage of the dark eyes is diminished from 26 or 27 to 23, that is to about [I by about] oneeighth of its original amount, the hazel element in either case absorbing the difference. It follows that the chance of a light-eyed parent having hazel offspring is about twice as great as that of a dark-eyed parent. Consequently since hazel is twice as likely to be met with in any given light-eyed family as in a given dark-eyed one, we may look upon two-thirds of the hazel eyes as being fundamentally light and one-third of them as fundamentally dark. I shall allot them rateably in that proportion between light and dark and so get rid of them. M. Alphonse de Candolle has also shown from his data that yeux gris (which I take to be equivalent to my hazel) are referable to a light ancestry rather than to a dark one, but his data are numerically insufficient to warrant a precise estimate of the relative frequency of their derivation from each of these two sources." (pp. 407-8.)

I find it very difficult to follow this reasoning, or to see from the table above its validity. It would seem to be essential to follow up the particular ancestry of each hazel-eyed individual, before we can draw the conclusions that Galton does from the massed numbers of children, parents and grandparents. Galton and de Candolle at least admit the difficulty of the hazel eyes; many Mendelian writers speak only of "brown" and "blue" eyes; others speak of hazel-eyed persons as heterozygotes*.

Galton having thus disposed of his yeux gris, now turns to the same multiple regression formula as he has used for stature, namely he makes the regression coefficient I for a parent, 11C for a grandparent and so on to higher ancestry. He also makes use of what is, I believe, an erroneous hypothesis, at any rate one inconsistent with his multiple regression coefficients,


* Sometimes a definition is given of pure blue eyes as being those without anterior pigment. According to one ardent Mendelian this can always and only be tested with a lens; another accepted relatives' statements, and came to the same conclusion without a lens. From twelve cases in which both eyes were carefully examined with a lens and thus found to be without anterior pigment, the excised eye when sectioned and examined microscopically showed quite clearly anterior pigment. Hitherto I have failed to come across any eye, however blue, which is without some anterior pigment when sectioned. At what degree of pigmentation does the recessive character cease?


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