164 
or „selective elimination" of the Heeg er i homozygotes, would 
produce the observed results. Of these two sources of modified 
ratios, „selective elimination" seems to be the more promising, 
because there appears to be at present no satisfactory evidence that 
„selective fertilization" occurs in any other organism, while „selec- 
tive elimination" has been clearly demonstrated in Antirrhinum ^) 
and in yellow mice.^) In both of these, the one class of homozy- 
gotes is entirely eliminated, so that the normal ratio 3:1(1 + 2:1) 
becomes 2:1. If „selective elimination" is the source of the 
discrepancies between the theoretical and observed ratios in 
the capsule-characters of Bursa, its operaton must diflfer from that 
in Antirrhinum and in yellow mice in two particulars, namely, 
there must be only a partial elimination of one homozygous class 
in Bursa, and this elimination must affect the negative, instead 
of the positive, homozygotes. 
The ratios for the rosette - characters in several of the 
families also deviate considerably from the expected ratio 3:1, 
and it is a pertinent question whether any of these deviations 
is significant, or whether they may be accounted for by the 
errors of random sampling, due to the small size of the families. 
The fact that several of the ratios lie above 3 : 1 and others 
below, suggests that at least a considerable part of the Variation 
in the ratios is due to purely chance causes of this kind. The 
ratio 3:1 is the ideal, but can be absolutely expected only 
when the number of offspring is infinite. 
Too little attention is paid by students of genetics perhaps 
to the probable errors of their results. If we follow Johannsen ^) 
in Computing the Standard deviation in the case of alternative 
characters by the formula a = J^%Po . %Pi, in which %Po 
represents the percentage of individuals in the one class and 
% p^ the percentage in the alternative class, it is easy to deter- 
mine within what limits a single observed ratio might be referred 
to 3 : 1 with a sufficient degree of probability. These limits for 
1) Baur, E., Untersuchungen über die Erbliehkeitsverhältnisse in 
einer nur in Bastardform lebensfähigen Sippe von Antirrhinum majus. 
Ber. d. Deutsch. Bot. Gesell. 25 : 442, 1907. 
2) Castle, W. E., and Little, C. C, On a modified Mendelian ratio 
among yellow mice. Science N. S. 32 : 868—870, 16 D 1910. 
3) Johannsen, W., Elemente der exakten Erblichkeitslehre, pp. VI |- 
516, 1909. Jena: Gustav Fischer. See p. 57. 
