116 H. D. goodaxjE and grace macmullen 



RATIOS AMONG THE PARENTS NEEDED TO GIVE THE OBSERVED 



MEAN WINTER EGG PRODUCTION OF AMERICAN 



BREEDS WITH RANDOM MATINGS 



The mean winter egg production of several American breeds 

 of poultry is about 36 eggs as has been pointed out by Pearl 

 ('15b). This average results from random matings. To secure 

 this average requires that the ratios in which the various classes 

 of females appear shall be 12 high, 8 mediocre, and 1 zero, if 

 the average winter production for the high group is about 55 

 eggs. The high-producing Barred Plymouth Rocks studied by 

 Pearl ('12) averaged 53.08 eggs, the mediocre 15.58, and occur 

 in the observed ratio of 360.5 high to 252.5 mediocre to 30 zero, 

 which is close to that expected. If 36 eggs or thereabouts is the 

 general winter average of American breeds that are properly 

 managed, it follows that the three classes of females should 

 occur in the proportions given above. To produce females in 

 this ratio with random matings requires that the various classes 

 of males also appear in certain definite ratios. We have de- 

 termined one set of ratios (percentage), viz., 14.7 : 15.5 : 25.0 : 

 3.9 : 3.3 : 5.3 : 11.0 : 19.2 : 0.2, that with females in the ratio of 12 

 high: 8 mediocre: 1 zero (percentage ratios, 57.1 high, 38.1 

 mediocre, 4.8 zero) reproduces very nearly the initial ratio among 

 the female offspring. It does not, however, exactly reproduce 

 itself among the males. Whether or not it is theoretically possi- 

 ble to secure a ratio among the males that with random matings 

 will yield females in the proper proportions and reproduce both 

 itself and the proper female ratio in each generation we will 

 leave to those who have the necessary taste and attainments in 

 mathematics. It is evident, however, that such theoretical 

 ratios must exist if either theory has. any basis in fact. 



CRITICAL VALUE OF MALES OF CLASSES I, II, AND V FOR 

 PEARL'S THEORY 



There are three classes of males, viz., 7, II and V, that have a 

 critical value in determining the validity of Pearl's theory, 

 because the ratios in which their daughters appear is the same 

 whatever the mother may be. Thus, class / males throw all 



