84 H. D. GOOD ALE AND GRACE MACMULLEN 



(over 30 eggs),^ mediocre (under 30 eggs), and zero. The ratios 

 in which these three classes occur in the various famiUes can be 

 accounted for, if it is assumed that there are two factors (desig- 

 nated Li and L2 by Pearl) additional to the factor common to 

 all pullets which determines that they shall lay at all. The Li 

 factor follows the simple monohybrid, Mendelian scheme of in- 

 heritance, the L2 factor that of a sex-linked factor. It is further 

 assumed that absence of both factors results in zero winter 

 production, and that one factor alone , either in single or double 

 dose, gives mediocre production, while both must be present 

 to give high winter laying. 



Although in the great majority of cases the observed ratios 

 agree with the expected ratios. Pearl encounters two sorts of 

 difficulties. First, the mediocre and zero classes often contain 

 more than their expected share of the progeny. This is natural, 

 for it is obvious to anyone at all familiar with poultry that birds 

 carrying genes for a given degree of production may fail to 

 reach that production. The second difficulty that Pearl en- 

 counters is that birds theoretically lacking the proper gametic 

 constitution, nevertheless make records that cannot be dis- 

 tinguished from those that theoretically have the gametic 

 constitution for high production. The explanation usually 

 offered for these instances is that they are 'somatic variations.' 

 Pearl means, of course, that there is some overlapping between 

 the two systems of phaenotypes. This occurs through an excess 

 of birds in the high class and is most easily observed when the 

 expected number of birds is zero. 



While the agreement between the observed and expected 

 ratios is satisfactory, the question arises as to whether or not 

 this agreement alone is to be regarded as sufficient proof of the 

 validity of the theory. May there not be other conditions that 

 must be satisfied? Are there shortcomings in the observed 

 data of such a character that their value is reduced? May 

 there not be another theory (or theories) that fit the observed 

 data? We shall show that these questions are answered in the 

 affirmative. 



^ We adopt the convention for our data of calling birds laying 30 or more 

 eggs as 'over 30/ but those laying 29 or less are classified as 'under 30' or zero. 



