308 



THE AMERICAN NATURALIST 



[Vol. LII 



upper limit of the range at 90. If the observed distribu- 

 tion of winter egg production is mono-modal, and if its 

 curve, base, mode and range correspond approximately 

 to those of the curve assumed in the preceding para- 

 graph, the mean of the numbers 1-30 will be larger than 

 tin' mean ( 15.5) obtained from the abstract numbers in the 

 manner chosen at the beginning of the paragraph. That 

 is, there is a tendency for the means of the two parts of 

 the mono-modal curve, i. e., the ones derived from 1-30 

 and 30-90, respectively, to approach each other in value. 

 If, however, the curve of winter egg production is a com- 

 posite of two curves, i. e., mediocre and high producers, 

 then the means tend to approach those of the abstract 

 numbers involved when distributed symmetrically. 



Some doubt exists as to how our data are to be inter- 

 preted in the light of the statements in the preceding para- 

 graph. The mean of the under-thirty group— viz., 16— 

 while slightly higher than that of the mean for the ab- 

 stract numbers— viz., 15.5— probably is not significant, 

 though it may perhaps be taken as an indication of the 

 existence of two genotypes. Since, however, the mean 

 of the over-thirty group increases with increasing age 

 and since the percentage of birds falling in the over- 

 tin rty classes increases with increasing age, it seems 

 probable that the shape of the observed egg production 

 curves is due to the artificial division point at March 1. 

 while the irregularities in the curves are due to too few 

 numbers. Since these irregularities largely disappear 

 if the class intervals are doubled and since, if the time 

 limits were to be extended so as to permit all birds to 

 begin laying, it appears probable that the curve would 

 become a symmetrical unimodal curve. Moreover, this 

 conclusion is strengthened by the fact that the observed 

 mean, 46.3, of the over-thirty class of the April-hatched 

 pullets with its upper range at 77 is lower than the value 

 (56.2) noted for the abstract numbers 31-80. For Barred 

 Plymouth Rocks, however, the means do not rest upon 

 the relation between the abstract numbers, but are an 

 expression of the average production of the two types. 



