Miscellanea 
405 
Again Exp. 726 in Table E, is said to be a mating of non-crested birds and thus ought to be 
included in Table I, while the father of Bird No. 142 used in Exp. 723 is crested, not non -crested 
as stated. 
Davenport states that out of 102 offspring of non-crested parents, all were non-crested. It 
is true that in this conclusion he is supported by Galloway but the point to be insisted on here 
is that this conclusion cannot be reached from his own data since, according to Table E, Birds 
Nos. 39, 40, and 71, were crested birds and came from non-crested parents. 
Turning now to Table II, we find agciin an extraordinary number of blunders. 
For Exp. 710a, read Exp. 711 ; for Exp. 713, read 714; for Exp. 515, read 513 ; for Exp. 625, 
read 624; for Exp. 712, read 713. 
Further, the results of Exps. 703, 604, 704 and 720, are not in accordance with the results of 
those experiments given in Table E. 
In Exp. 703, instead of the proportion of non-crested to crested birds, 3 : 7, read 3:6; in 
Exp. 604, instead of 7 : 1, read 7:2; in Exp. 704, instead of 0 : 7, read 0:5; and in Exp. 720 
instead of 0 : 1, read 0 : 2. 
In Exp. 714 (not 713 as stated), Bird No. 240 is said to come from two crested parents. 
According to Table E, however, No. 240 is one of the "original stock of whose ancestry, con- 
sequently, nothing is known directly." Similarly in Exps. 503 and 511, Bird No. 3 is said 
to come from a mating of crest and non-crest, while on p. 11 and in Table E it is said to be 
"original stock." 
Davenport's method of dealing with those tables is equally faulty. 
In part 1 of Table II he deals with matings between crested birds. Now crested birds, on 
the assumption made by Davenport, that crest is dominant over absence of crest, may be either 
DD or DR, and if DD be mated with DD or DR all the offspring should be crested, while if DR 
be mated with DR, three-fourths of the offspring should be crested. 
It is important therefore that DD's should be distinguished from DR's. If any of the off- 
spring of a pair of crested birds are non-crested then both parents must be heterozygous ; but if 
all the offspring are crested, it by no means follows that one or both of the parents is homo- 
zygous. So long as only crested birds are produced we cannot distinguish between DD's and 
DR's. All we can do is to appeal to the laws of probability and estimate the chance that all the 
offspring of a pair of crested birds, which are really heterozygous, shall be crested. 
Now Davenport, as the author of a book on Statistical Methods, must be familiar with the 
various probabilities involved in those cases. He says that " at least two birds are homozygous 
in crest. No. 12 which has produced nine young all crested and No. 79 which has produced 
11 young all crested." One is not surprised to find that according to Table E, No. 79 has pro- 
duced only nine young all crested and this correction must first be applied. Further he says 
that No. 126 which has produced four young all crested is "possibly homozygous" ; and that 
No. 9 has produced 16 crested birds and one non-crested. 
Let us consider the probabilities involved in those cases. What is the chance that a pair of 
DR's, i.e. crested but heterozygous birds, will produce " n " young all crested 1 In the long run 
they will produce three crested birds to one non-crested bird, and thus the chances that 
n, n-1, w-2, etc. out of n will be crested are the successive terms of (3-^-1)" out of 4". 
Thus the chance that all out of nine shall be crested is (!)'■' = 1 in 13. 
Now he actually gets in his experiments the proportion 16 : 1. What is the probability of 
such a combination arising ? It is 
310 
17 — =1 in 23. 
^' • 417 
Biometrika vii 52 
