Sept. 15, 1915 Resemblance of Parents and Offspring of Sheep 481 



There are some cases where owners of sires of large production have 

 recorded from the same sire in two consecutive years all singles in one 

 of the years and nearly all twins in the other year. Such cases make it 

 appear that these few owners tend to select twins or singles in making 

 records. The following section, "Repetition of sires and paternal 

 grandparents," shows how we have treated such special cases. 



REPETITION OF SIRES AND PATERNAL GRANDPARENTS 



One sire may belong to a large number of recorded offspring, although 

 this happens in relatively few cases; for example, there is a case in 

 which one sire belongs to as many as 135 recorded offspring in the 

 period for which we have examined offspring, and this fact is not to be 

 neglected in making a critical examination of our data. In fact, a few 

 such cases of large production with discrimination against either twins 

 or singles might vitiate our results on the correlation of offspring with 

 sires and grandsires. On account of the possibility of error from this 

 source, we arrange a table, separating the offspring of each sire into 

 singles and twins. From this arrangement of data it is fairly clear that 

 certain cases of extreme percentages of singles or twins from a sire of 

 large production should be excluded from data used in the calculations 

 of statistical constants. We fix criteria somewhat arbitrarily as follows: 



(i) Cases are excluded where a sire has more than 10 recorded offspring 

 that are all singles or all twins. 



(2) Cases are excluded where a sire has more than 20 recorded offspring 

 if the difference in percentage of twins among this offspring and among 

 the general population of offspring is more than three times the probable 

 error of the difference. 



While we exclude from our calculations the part of the data just 

 mentioned, we give such data in Tables XV, XVI, XVII, XXXV, and 

 XXXVI, in order that anyone who may consider the above criteria for 

 exclusion too stringent or too lenient may have available for criticism 

 such excluded data. Tables I, IX to XIV, XVIII, and XXVI to XXXII 

 involve data about sires and do not include data concerning those cases 

 of high-producing sires which are to be excluded from our calculations 

 of statistical constants. 



ANALYSIS OF DATA FOR SIRES, DAMS, AND OFFSPRING 



Table 1(A) shows the frequencies with which sires and dams born in 

 states i-i, 1-2, 2-1, 2-2, 1-3, 3-1, 2-3, 3-2, or 3-3 beget recorded 

 offspring born in states i, 2, or 3. In this notation the first number of a 

 pair refers to the sire and the second to the dam. Thus, 1-2 means that 

 the sire is born as a single and the dam as a twin. To illustrate further 

 the meaning of the table, consider the number 1,276 in the column 

 marked "i" and in the row marked "2-1." This means that 1,276 off- 

 spring out of the total of 9,291 are singles with twin sires and single dams. 



