D. Heron 
361 
Now these conclusions, if satisfactorily demonstrated, would obviously be of 
the highest importance, but they were immediately challenged by Professor Karl 
Pearson in a letter which appeared in Nature of November 21, 1912 (p. 334). 
Professor Pearson's letter is as follows : 
On an Apparent Fallacy in the Statistical Treatment of '"Antedating" in 
the Inheritance of Pathological Conditions. 
The problem of the antedating of family diseases is one of very great interest, and is likely 
to be more studied in the near future than ever it has been in the past. The idea of antedating, 
i.e. the appearance of an hereditary disease at an earlier age in the offspring than in the parent, 
has been referred to by Darwin and has no doubt been considered by others before him. Quite 
recently, studying the subject on insanity, Dr F. W. Mott speaks of antedating or anticipation 
as "Nature's method of eliminating unsound elements in a stock" ("Problems in Eugenics," 
papers communicated to the First International Eugenics Congress, 1912, p. 426). 
I am unable to follow Dr Mott's proof of the case for antedating in insanity. It appears to 
me to depend upon a statistical fallacy, but this apparent fallacy may not be real, and I should 
like more light on the matter. This is jjeculiarly desirable, because I understand further 
evidence in favour of antedating is soon forthcoming for other diseases, and will follow much the 
same lines of reasoning. Let us consider the whole of one generation of affected persons at any 
time in the community, and let tig represent the number who develop the disease at age s, 
then the generation is represented by 
«o, Hi, ••• «8)--- ''^100. say- 
Possibly some of these groups will not appear at all, l)ut that is of little importance for our 
present piirpose. 
Let us make the assumptions (1) that there is no antedating at all; (2) that there is no 
inheritance of age of onset; thus each individual reproduces the population of the affected 
reduced in the ratio oi p to 1. Then the family of any affected person, whatever the age at 
which he developed the disease, would represent on the average the distribution 
priQ, pn^, p7i2,... png, ... pnm- 
The sum of such families would give precisely the age distribution at onset of the preceding 
generation. 
Now let us suppose that for any reason certain of the groups of the first generation do not 
produce ofl^spring at all, or only in reduced numbers. Say that only of the are able 
to reproduce their kind ; then of the older generation, limited to parents, the distribution 
will be 
9o ''fi + 'Ji «i + ?2«2 + .■. + qs>h+ ... + qm'>hm, 
but the younger generation will be 
p {qo^Q + qi n^+q.,n2 + ...+qsns+ ... + qm^>m) («o + " i + •■ . + "« + ••. + '«ino), 
i.e. the relative proportions will remain absolutely the same. 
The avei'age age at onset and the frequency distribution of the older generation, that of the 
parents, will be entirely different from that of the offspring and will depend wholly on what values 
we give to the ^s. If frequency curves be formed of the two generations they will diflfer 
substantially from each other. This difference is not a result or a demonstration of any 
physiological principle of antedating but is solely due to the fact that those who develop the 
disease at different ages are not equally likely to marry and become parents. 
