164 



or „selective elimination" of the Heegeri 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 Antirrhinnm x ) 

 and in yellow mice. 2 ) 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 differ 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 3 ) 

 in Computing the Standard deviation in the case of alternative 

 characters by the formula a = Y~ %Po • %Pi> m which %p 

 represents the percentage of individuals in the one class and 

 %p x 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 sufhcient degree of probability. These limits for 



x ) Baur, E., Untersuchungen über die Erblichkeitsverhältnisse 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. 



