NOTES AND LITEEATUEE 



MENDELIAN FLUCTUATIONS 1 



When the observed proportions, say of dominants and reces- 

 sives, in any Mendelian experiment are worked out for small 

 groups, such as individual litters or the seeds on individual plants 

 in individual fruits, considerable fluctuations round the expected 

 proportions may be observed. In the present note the magnitude 

 of these fluctuations is compared with the. magnitude to be ex- 

 pected if the fluctuations were the result merely of chances of 

 sampling — corresponding to the fluctuations that would be ob- 

 served in drawing, say, samples of black balls from a bag con- 

 taining white and black balls in the proportion of 3 to X. In so 

 far as there is good agreement, this is additional confirmation of 

 the Mendelian process holding good in its simplest form: if 

 the fluctuation observed is markedly greater than this theory 

 would indicate, some source of disturbance is certainly present, 

 but whether this disturbance arises from irregularities in the 

 distribution of the gametes or merely from extraneous circum- 

 stances (varying death-rates or difficulties of sorting) can not, 

 of course, be determined from the data alone. For albinos in 

 individual litters of mice (Darbishire's data), and for numbers 

 of "green" or "wrinkled" in Mr. Bateson and Miss Killby's 

 crosses of peas I find exceedingly good agreement, at least if very 

 small plants are omitted. Lock's data for maize give good agree- 

 ment for the DR X DR cross, but poor agreement for the 

 DR X RR cross. Some data given me by Miss E. R. Saunders 

 for seed characters in the individual fruits of stocks show rather 

 irregular results. Further comparisons on similar lines would 

 be of interest, especially for the DR X RR cross, for which very 

 few data are available. For the case to afford a good test the 

 sorting should be clear and there should be nothing in the data 

 to suggest differential death rates obviously. 



G. U. Y. 



i "Fluctuations of Sampling in Mendelian Ratios," G. Udny Yule (Proe. 

 Cambridge Phil. Soc, XVII, 425). 



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