114 H. D. GOODALE AND GRACE MACMULLEN 



Third, the sample must be sufficiently large to include a proper 

 proportion of all kinds of females. Fourth, the various females 

 must produce approximately equal numbers of progeny. Not 

 one of these points is fulfilled. The first, because it is evident 

 that a bias exists which is the endeavor on the part of the in- 

 terpreter of the data to secure a good fit between observed and 

 theoretical ratios. No method exists by which this bias can be 

 overcome. The second point is not met because the females 

 are selected samples. The third, because the samples are com- 

 paratively small. The fourth, because some females produce 

 many more progeny than others. It must also be remembered 

 that the application of ratios is made to the progeny of each 

 mother separately. 



The importance of size of family is not merely an academic 

 consideration, but very real as anyone who has worked with 

 Mendelian ratios will readily appreciate. Even when dealing 

 with the simple monohybrid ratio of a morphological character 

 the progeny of a single pair often deviates widely from the 

 expected ratio even when fairly large numbers are secured. 

 The average number of adult offspring per mother in Pearl's 

 experiments with pure Barred Plymouth Rocks is only 2.85, 

 while in my experiments it ranges from 2.5 in 1913 to 6.97 in 

 1916. The largest family (i.e., offspring of one mother) of pullets 

 I secured, hatched in April and May, is 19. One can only guess 

 at the size of Pear.'s largest family, but it cannot be much 

 greater, for with the sexes evenly divided and with maximum 

 production and perfect hatchability, the maximum number of 

 April- and May-hatched pullets that can be expected in any one 

 year from a single mother can hardly exceed 25. If 10 pullets 

 per mother are available and if their records appear in the 

 ratios of 4:6, 5:5, 3:7, or even 2:8, they would not be im- 

 probable deviations from 1:3, 3:5, or 1:1 ratios, for three birds 

 moved from one side to the other in the extreme case of the 2 : 8 

 ratio changes it to equality. Thus, if one encounters a series 

 of ratios which corresponds in general to that of a particular male 

 mated with females of several types, but among which one female 

 occurs that gives a ratio of 2:8, when equality is required, the 



