﻿16 BULLETIN 1372, IJ. S. DEPARTMENT OF AGRICULTURE 



Thus sires Q and T, who decreased the average butterfat yield of 

 their daughters, have a higher ranking than do sires M, O, and P, 

 who increased the average butterfat yield of their daughters. This 

 is brought about largely through the much higher average yield of 

 milk and butterfat of the daughters of the sires Q and T, though the 

 relative ranking among these five sires in the percentage of daughters 

 better than their dams is high for sire Q in both milk and butterfat 

 and for sire T in milk. 



Such inconsistencies do not appear in the rankings of the other 

 sires, though the final ranking is not always in the same order as the 

 amount of the average increase or decrease of the daughters for any 

 one class. 



THE STANDARD DEVIATION AND COEFFICIENT OF VARIABIUTY FOR BUTTERFAT YIELD 

 OF THE DAUGHTERS OF THE 23 SIRES AND OF THEIR DAMS 



Judging by the records of the daughters of the 23 sires in this study, 

 it is not to be expected that any sire, at this stage of breed improve- 

 ment, will get daughters all of which will have the capacity to make 

 uniform records of any certain standard. This is true regardless 

 of how uniform the production records may be of the dams to which 

 a sire is mated. A study of the detailed records given in Table 2 

 readily shows the great variation in the producing capacity of 

 each sire's daughters. It is not strange that there should be such 

 a great variation when the double nature of the hereditary make-up 

 of each individual is considered and when we realize how few matings 

 are made where the animals are laiown to be homozygous or pure 

 in their inheritance for the desired characters. If a sire's inheritance 

 for a character, such as milk and butterfat producing capacity, is 

 not homozygous, so that he can not transmit to each of his offspring 

 the same capacity for production, and then if this sire is mated!^ to a 

 group of dams, each of whose 30 ancestors in 4 ancestral generations 

 show varying degrees of producing capacity, it is not surprising that 

 the offspring should show a wide variation in producing ability. 



It would seem that a prepotent sire, mated to a group of cows 

 having a considerable range in producing capacity, would get 

 daughters showing greater uniformity of production. The standard 

 deviation ^ and the coefficient of variability of the butterfat yields . 

 of daughters, and of their dams, as given in Table 7, does not show 

 that the sires who decrease the coefficient of variability were any 

 more prepotent in increasing production as measured in Table 5, 

 than were the sires who increased the variability of the butterfat 

 producing capacity of their daughters. The dams to which sire N 

 was mated had a standard deviation of 148 pounds butterfat, whereas 

 his daughters had a standard deviation of only 76 pounds butterfat — 

 a decrease in the coefficient of variability from 25.22 per cent for 

 the dams, to 12.57 per cent for the daughters. Yet sire N ranks 

 thirteenth in prepotency for producing capacity as measured in 

 Table 5. 



On the other hand sire I's daughters show a standard deviation of 

 170 pounds butterfat as compared with a standard deviation of only 

 62 pounds butterfat in their dams. The coefficient of variability is 

 increased from 11.56 per cent for the dams to 26.91 per cent for the 



' "Standard deviation" is a term used in statistical calculations to denote a mathematical measure of 

 the variability of the items in a group from the mean, or average, of the whole group. "GoeflQcient of 

 variation" is an index of variabOity appearing in the form of rate per cent. 



