﻿TRAJSrSMITTING ABILITY OF HOLSTEIN-FEIESIAN SIRES 21 



bred will be prepotent. It is more difficult to judge the transmitting 

 power of the dams, because ot their limited number of offspring, and 

 also because very often m^any of the offspring will be by one sire. 

 On the other hand, the sire has a considerable number of offspring, 

 usually from different dams, so that his transmitting ability can be 

 more accurately gauged. 



A sire's transmitting ability is determined by the chance inherit- 

 ance of factors governing production, which he received at the time 

 of his conception. Should he by chance have received all his in- 

 heritance governing production from some ot his ancestry which 

 carried only factors for low production, then he will transmit only 

 low production to his offspring, regardless of how many high-produc- 

 ing ancestors he may have. 



Once a bull has proved himself to be a poor sire it would seem that 

 there is little chance of his transmitting any of the ability of his more 

 worthy ancestors. 



WHICH PARENT HAS THE GREATER INFLUENCE ON MILK YIELD, 

 BUTTERFAT PERCENTAGE, AND BUTTERFAT YIELD? 



A study was made of the correlation between the daughters and 

 their dams, with respect to total yield of butterfat, for each of 23 

 sires having 6 or more tested daughters from tested dams. The 

 results of this study are shown in Table 10. The correlation coeffi- 

 cients range from —0.39 for sire N to +0.90 for sire. P.* 



* Perhaps a brief explanation of the meahing of correlation should be made before discussing Table 10. 

 A correlation coefficient shows to what extent the variation in one character follows or is coordinated with 

 the variation in some other character. For example, many are of the opinion that in order to get high 

 production in dairy cows we must haVe large cows If this assumption is true, then there should be a 

 positive correlation with respect to production and size. If milk and butterfat were produced more eco- 

 nomically with small cows then there would be a negative correlation with respect to economical production 

 and size. Or, a correlation coefficient may indicate to what degree the same character, such as yield of 

 milk or butterfat, exists between parent and offspring; and that is the thing intended to be determined in 

 this table. 



This relation of the yield of milk and butterfat between parent and daughters is expressed as a coefficient. 

 If a high yield of milk or fat in the dam is followed by a correspondingly high yield in the daughter, the 

 correlation would be perfect and the coefficient would be 1. If, on the other hand, the highest-yielding 

 daughters all came from the lowest-yielding dams, and the lowest-yielding daughters all came from the 

 highest-yielding dams, then there would be a perfect negative correlation and the coefficient would be —1. 

 Again, if there is no relation between the yield of the daughter and the yield of her dam, indicating that 

 there is no correlation, then the coefficient would be 0. It is seldom that a perfect correlation is found; 

 usually the correlation is between and -t-1, or between and —1. 



The correlation coefficient is arrived at by a rather complicated mathematical formula. It expresses in 

 mathematical terms the extent of the relation which exists between two characters, or the extent to which 

 a character is common to two individuals. If the coefficient is low, it indicates that there is very little 

 relation; if it i^ high, there is a close relationship; and if it is so high as to indicate a perfect correlation, 

 then it may be said that one is probably the cause of the other. The correlation coefficient when expressed 

 in writing is followed by the probable error; that is, the amount to be added to or subtracted from the 

 correlation coefficient to get the two limiting figures within which there is an even chance that the true 

 value will lie. 



The following rules arc suggested in Babcock and Clausen (2) for the interpretation of coefficient of 

 correlation: 



1. If r (the coefficient of correlation) is less than the probable error, there is no evidence whatever of 

 correlation. 



2. If T is more than six times the size of the probable error, the existence of correlation is a practical 

 certainty. 



3. In cases where the probable error is relatively small: 



o. If r is less than 0.3, the correlation can not be considered at all marked. 

 b. If r Is above 0.5, there is decided correlation. 



