522 



The Journal of Heredity 



arise could be explained. Unfortunately 

 the ^'eneral facts become inexi^licable 

 on this view. Wentworth ad\anced a 

 more easily tested hypothesis; viz., 

 that there are separate factors for roan 

 and white. Factor P for roan is con- 

 sidered dominant over p for red and 

 factor R for color is dominant over r 

 for white. 



hence the proportion of each color of 

 }'oung in any cross. The per cent of 

 whites (rr) is 8.7. The relative pro- 

 portions of heterozyj^ous and homozy- 

 gous colored (Rr and RR) must be such 

 that the number of heterozygotes is 

 twice the product of the square roots of 

 the number of the two homozygous 

 classes by the well-known formula for a 

 iMendelian population in equilibrium. 

 This gives 41.6' ^ heterozygous colored 

 and 49.7% homozygous colored. By 

 excluding from consideration the whites, 

 in which the distinction between roan 

 and red is considered to be hidden, the 

 This view also, however, may be per cents of homozygous roans, hetero- 

 shown to account for the discrepancies zygous roans and reds can be calculated 

 from the simple one-factor hypothesis at in a similar manner. By multiplying 

 the expense of the general facts. An together these two sets of calculations. 

 anal>-sis of Wentworth's data on the as- the per cents of each of the nine com- 

 sun"iption that cattle breeders pay little binations of factors can be found. Thus 

 attention to color gives some interesting with 49.7% homozygous colored (RR) 

 results. From comparison of the total and 40.0% heterozygous roan (Pp), the 

 number of young from each kind of mat- product, 19.9%, is the proportion of 

 ing in the data above with the number roans of formula RRPp. The tables 

 expected on random mating (cohmin below summarize the results : 

 "expected") the degree to which mating 

 is preferential in regard to color may be Pormnla % 



estimated. The expected number of ^^ ^^-^ '°'^^''~^^'",rula°tio^'^'''^^^ 

 young from each kind of m.ating has been r,. 416 29.5 %— per cent''of°?s in the 

 calculated on the assiunption that the popalation. 



Shorthorn population is in equilibrium ^r 8.7 



as regards color and that matings actual- 

 ly are by chance in this respect. Thus 

 with 47.9% of the animals red, .479 X PP 

 .479 of the matings should be red by red 

 giving an expected nimiber of calves of ^P 

 1998, where the actual number was 1851. pp 

 The table indicates a distinct excess of 

 matings of roan by roan and white by 

 white. Roan by white and roan by red 



, , "l 1- • ■ . 1 • , PER CENT OF K.\CTOK COMBINATIONS 



seem to be most discriminated against. 

 On the whole the assimiption of random 

 mating should give .sufliciently accurate 

 results for the present jjurpose. 



Red is rather more common than roan 

 which means that factor p is more com- 

 mon than P. Thus most whites should 

 be of formula pi)rr or Pprr and very few 

 PPrr in a population breeding at random. From these data we can make up all 

 Thus whites crossed with reds (pp) kinds of matings and calculate the per 

 should produce more reds than roans cent of each color, which should be pro- 

 which is very far from the case. On the duced. The matings red by white and 

 basis of eciuilibrium, it is easy to calcu- roan by roan are most significant, 

 late the expected proportions of each Allowing for the j^roportion of the four 

 genetic formula in the pf)i)ulation and kinds of roans, two kinds of reds and 



100.0 



7.6 27.6% — per cent of P's in the 

 population. 



40.0 72.4% — per cent of p's in the 

 population. 



52.4 



100.0 



