DIVERSITY OF N.QN CIRCULATING CHECK FOR UNBOUND CIRCULATING COPY UNIVERSITY OF ILLINOIS Agricultural Experiment Station BULLETIN No. 270 MEASURING THE BREEDING VALUE OF DAIRY SIRES BY THE RECORDS OF THEIR FIRST FEW ADVANCED REGISTRY DAUGHTERS BY F. A. DAVIDSON URBANA, ILLINOIS, JUNE, 1925 CONTENTS PAGE INTRODUCTION 545 SOURCE OF DATA 546 OUTLINE OF INVESTIGATION 546 Number of Tested Daughters Necessary to Measure Relative Breeding Value of Sire 548 Smallest Number of Tested Daughters Whose Average Production Will Approximate Average of Large Number 548 DISCUSSION OF RESULTS 556 DERIVATION OF METHOD 560 APPLICATION OF METHOD 564 Cautions in Use of Method 564 CONCLUSIONS 564 LITERATURE CITED.. . 565 MEASURING THE BREEDING VALUE OF DAIRY SIRES BY THE RECORDS OF THEIR FIRST FEW ADVANCED REGISTRY DAUGHTERS By F. A. DAVIDSON, First Assistant in Dairy Husbandry INTRODUCTION The breeding value of dairy sires lies mainly in their ability to transmit to their offspring factors for high milk and butterfat produc- tion. The fact that all sires are not equal in this respect makes it necessary to select for breeding purposes only those sires transmitting the largest number of such factors. An expression of this transmitting ability may be found in part in the milk and butterfat productions of the daughters, and it is by means of these productions that breeders in general have measured the breeding value of dairy sires. This method of measuring breeding values, altho used extensively at the present time, is open to several objections. The productions of the daughters used in measuring the breeding value of dairy sires are those that are recorded in the advanced registers of the various purebred dairy cattle associations; daughters with records in these registers have fulfilled certain production requirements and are spoken of as tested daughters. The tested daughters of a sire, in most cases, represent only his best daughters, which are a small percentage of all his daughters. This selection is due in part to the requirements of the advanced registers, but in the main to the fact that under the present system of advanced registry testing it is exceedingly unprofitable to test daughters other than those showing signs of high producing ability. The productions of only the tested daughters, there- fore, do not provide an absolute basis upon which to measure the breeding value of the sires. However, since the tested daughters of all sires have been subjected to the same type of selection, their produc- tions provide a uniform basis and may be used as a means of measure- ment with the limitation that they will give only relative results. The primary object in measuring the breeding value of 'dairy sires is to determine whether or not they are increasing the productions of their daughters over that of their daughters' dams. Inasmuch as there is convincing evidence that the inherited producing ability of the daughters is influenced as much by their dams as by their sires, the productions of the daughters' dams as well as of the daughters should be taken into account. Since, however, in many dairy herds the produc- tions of very few of the dams have been recorded, the recorded 545 546 BULLETIN No. 270 [June, productions of the daughters provide the only available means of measuring the sire's breeding value. Altho the productions of the daughters cannot be used alone to measure the actual breeding value of the sire, they can be used to determine the approximate breeding value. Breeders in general have found that the average of the milk and butterfat productions of a large number of tested daughters may be used as a relative measure of the transmitting ability of the sire. The testing of a large number of daughters, however, necessitates the ex- penditure of a great deal of time and money, and would be impractical in the majority of dairy herds at the present time. Furthermore, very few sires are kept in herds long enough for many of their daughters to be tested, being sold or killed long before their breeding value is determined. Many good sires have been lost in this way and many more will be lost, unless some means is provided whereby their breed- ing value can be determined when their first few daughters are tested. W hat is needed is a method which will enable breeders to predict, with- in given limits, the average production of a large number of tested daughters of a sire from the average production of his first few tested daughters. Such a method will save breeders a great deal of time and money and will also be an important factor in improving the trans- mitting ability of the dairy sire population in general. In view of these facts, an investigation was planned in which the milk and butterfat productions of the tested daughters of a large number of dairy sires were studied. The purpose of the investigation was to derive a method by which the productions of the first few tested daughters of a sire might be used as a criterion to measure his relative breeding value. SOURCE OF DATA The Register of Merit of the American Jersey Cattle Club lists the names of Jersey sires having three or more tested daughters. Under each sire's name is listed the names of his tested daughters. Volumes 1911 to 1921 inclusive of the Register of Merit contain 133 sires having fifteen or more tested daughters with yearly or long-time records. The Jersey Register of Merit was chosen as the source of data because it contained the largest number of sires having fifteen or more tested daughters with yearly records. OUTLINE OF INVESTIGATION The investigation as planned involved three steps: 1. The determination of a definite large number of tested daughters of a sire, the average of whose productions could be used as a relative measure of the sire's breeding value. 1925] MEASURING THE BREEDING VALUE OF DAIRY SIRES 547 2. The determination of the smallest number of first tested daugh- ters of a sire, the average of whose productions will closely approximate the average production of this determined large number of tested daughters. 3. The derivation of a method by which the average production of the determined small number of tested daughters of a sire may be used to predict within given limits the average production of the determined large number of tested daughters. Before proceeding with the three steps outlined above, it was neces- sary to correct the recorded production of each daughter for the in- fluence of age of cow and percentage of fat in the milk. The correction for the influence of age was necessary because, on the average, the production of a cow increases up to the age of eight or nine years and then gradually decreases. This influence of age on production has been demonstrated very clearly by Gowen (1919), Pearl (1919), and Brody, Ragsdale, and Turner (1923). The correction for age was accomplished by reducing the production record (milk and fat) of each daughter to the production at the age of maximum production, which for Jerseys is eight years and one month. The factors used for these corrections are given in Table 6. Owing to the fact that the percentage of fat in the milk produced changes only very slightly with the age of the cow (Gowen 1919), the age-correction factors derived for the milk yield can also be used to correct the fat yield. The productions of the daughters as recorded in the Register of Merit include the pounds of milk and the pounds of butterfat pro- duced, both of which are needed to secure a complete expression of each daughter's production. 1 Therefore, it was necessary to find a single expression for both products. Such an expression may be secured by reducing the milk and butterfat productions of all the daughters to milk with a common percentage of fat. If all the milk productions of the daughters contain the same percentage of fat, the amount of fat in the milk will vary directly with the milk yield and need not be con- sidered separately. By using the formula .4M-J-15F, where M = recorded milk yield in pounds and F recorded fat yield in pounds, all milk with varying fat percentages may be reduced to milk contain- ing 4 percent of fat (indicated as F. C. M., fat-corrected milk). 2 In the statistical study which follows, the recorded productions of all the daughters have been corrected, as explained above, both for influence of age of cow and for percentage of fat in the milk; that is, all productions are reported in terms of A.-F. C. M. (age- and fat- corrected milk). contains solid material other than fat, collectively known as solids-not-fat. It requires work on the part of the cow to produce these solids; hence they should be taken into consideration as well as the fat when measuring her producing ability. 2 This formula was determined by Gaines and Davidson (1923) and is based on the energy value of milk at varying fat percentages. Bulletin 245 of this Experiment Station gives a complete discussion of the derivation of this formula. 548 BULLETIN No. 270 [June, NUMBER OF TESTED DAUGHTERS NECESSARY TO MEASURE RELATIVE BREEDING VALUE OF SIRE From a preliminary statistical study of the production records of the tested daughters of dairy sires it was found that the mathematical constants measuring the variability in the productions of the first fifteen tested daughters were in every case many times their probable errors and were changed only very slightly by the productions of addi- tional daughters. The mathematical constants measuring the variability in the productions of the first fifteen tested daughters of ten of the 133 Jersey sires chosen at random are reported in Table A. TABLE A. MEASURES OF VARIABILITY IN THE A.-F.C.M. PRODUCTIONS OF THE FIRST FIFTEEN TESTED DAUGHTERS OF TEN JERSEY SIRES CHOSEN AT RANDOM FROM THE 133 JERSEY SIRES Name of sire Mean (pounds of A.-F.C.M.) Standard deviation (pounds of A.-F.C.M.) Coefficient of variability (percentage) Sayda's Heir 3d 11483 347 1990 245 17.3 =t 2.2 Gamboge's Knight 11417 271 1556 192 13 6 == 1.7 Hood Farm Torono 12183 375 2152 265 17.7 2.2 Loretta's King 10250 252 1449 178 14.1 == 1.8 Pogis 99th of Hood Farm 14383 583 3349 412 23 3 == 3.0 Raleigh's Fairy Boy . 10783 245 1408 173 13 1 1.6 Royal Majesty of St. Cloud 10917 374 2150 265 19.7 * 2.5 Hood Farm Pogis 9th 10450 269 1547 191 14.8 1.9 Imp. Oxford You'll Do 10417 358 2055 253 19.7 =*= 2.5 Irene's King Pogis 9983 252 1448 178 14.5 1.8 These constants in Table A are also many times their probable errors. Hence it may be assumed that the variability in the productions of the first fifteen tested daughters of a Jersey sire is representative of the variability in the productions of any larger number of his tested daughters. Accordingly, the average production of the first fifteen tested daughters of a Jersey sire may be used as a relative measure of his breeding value and also as a basis with which may be compared the average production of any smaller number of his tested daughters. SMALLEST NUMBER OF TESTED DAUGHTERS WHOSE AVERAGE PRODUCTION WILL APPROXIMATE AVERAGE OF LARGE NUMBER In order to determine the smallest number of a sire's first tested daughters the average of whose productions would closely approximate the average production of his first fifteen tested daughters, it was necessary to classify the tested daughters of each of the 133 sires in the following manner: 1. Each daughter of each sire was first classified chronologically, i.e., as the first, second, third, etc., daughter of the sire to appear in the Register of Merit. 1925~\ MEASURING THE BREEDING VALUE OF DAIRY SIRES 549 2. According to the first classification, the daughters of each sire were then separated into fifteen daughter-groups. These daughter- groups were produced by cumulation of the daughters from each preceding group; i.e., the first daughter appearing in the Register of Merit formed the first group, the first and second daughters appearing in the Register formed the second group, the first, second, and third daughters, the third group, etc., until all fifteen daughters were formed into the fifteenth group. A tabular illustration of this classifica- tion may be found in Table B. 3. A further classification was then made by combining all the daughter-groups of the 133 sires into fifteen aggregates. The first aggregate composed all the first daughter-groups, the second aggregate composed all the second daughter-groups, etc., the fifteenth aggre- gate composing all of the fifteenth daughter-groups. This classification is also illustrated in Table B. The further analysis of the tested daughters of the 133 sires con- sisted of comparisons between the A.-F. C. M. productions of the first few daughters of each sire and the A.-F. C. M. productions of the first fifteen daughters of the sire. These comparisons were made as follows: 1. The average A.-F. C. M. production or mean A.-F. C. M. milk yield of each daughter-group was determined, i.e., the productions or milk yields of the daughters in each group were added and the sum divided by the number of daughters in the group. 1 The mean milk yields of the daughter-groups in each aggregate were correlated with the mean milk yields of their respective fifteenth daughter-groups in the fifteenth aggregate. In other words, the mean milk yields of all the first daughter-groups were correlated with the mean milk yields of their respective fifteenth daughter-groups, the mean milk yields of all the second daughter-groups were correlated with the mean milk yields of their respective fifteenth daughter-groups, etc., until every daughter- group was correlated with its respective fifteenth daughter-group. The means of the fifteenth daughter-groups were in every case used as the basis with which were correlated the means of the other daughter- groups. By making this comparison, a series of fifteen correlation coefficients was set up which indicated the relation existing between the mean milk yields of the daughter-groups in each aggregate and the mean milk yields of their respective daughter-groups in the fifteenth aggregate. 2. The standard deviation of the milk yields of the individual daughters in each aggregate (Table B) was compared with the standard deviation of the milk yields of the individual daughters in the fifteenth aggregate. A similar comparison was made between the co- 1 Hereinafter for the sake of convenience the term "milk yield" will be used interchangeably with the term "production." It must always be remembered, how- ever, that "milk yield" refers here to age- and fat-corrected milk and not to the recorded milk yield. 550 BULLETIN No. 270 \_June, 4- 10 n C*5 w-> <7\ JS J^ O\ vn JS * CO O CN VO S Tf 1 oo * O, g _c 4> CO t*J CO ON r4 JS bo M 1 -- t^- CO c ''S s r4 CO CO VO <7\ J= u 8 I-------- u-> CN OH 45 JS 5 CO CO CO sC 4J rt U - |S;s;s5S! * - g JS c CO CO % _c < CO o 1 - CO o 1) 4? js OS CO CO r^- o\ _c 3 m . _c VO CO CO oo o _c T3 VO r^- vo JS W) CO CO U-) MD _c v2 f> VO vo a o JS * CO CO cN CO JS Ml tl 4h LO T U TJ CO CO CO O\ O\ "O rt co CO CO Q T3 7 CO CO VO VO d cs ~ CN fN 4., CO CO CO CO n 11 *" o . U 4-1 -c rt 3 a c o : 5 60 ' 3 ' CS > T3 rt 6 CO a F TJ P 3 < i P O m' Mi 11 o 1> fc u 6 S. E- ti OJ-g, 3 3 a o S 3 C ri TO 3 o 3 4-J s' 3 4- aj-O bo (*) -iCSO'f^OVOt^OO-H H H < = u o u feb-S a c c - o -. .a 8 f 3 o rt u -O bo 1925] MEASURING THE BREEDING VALUE OF DAIRY SIRES 551 efficients of variability of the milk yields of the individual daughters in the aggregates. This comparison was necessary in order to determine whether or not the productions of the first few tested daughters of the 133 sires were more variable than the productions of the first fifteen tested daughters. 3. The mean milk yield of the fifteenth daughter-group of each sire was subtracted from the mean milk yield of each smaller group of tested daughters. The daughter-groups of the 133 sires were combined into aggregates; and the mean milk yields of the daughter-groups in the fifteenth aggregate were subtracted from the mean milk yields of their respective daughter-groups in each of the other aggregates. In this way a class of 133 differences was set up for each aggregate, there being 133 daughter-groups in each aggregate. The series of differences for each aggregate was given the same number as the aggregate from which it was determined, i.e., the differences between the mean milk yields of the daughter-groups in the fifteenth aggregate and the mean milk yields of their respective daughter-groups in the first aggregate formed the first class, etc. These classes of differences are shown graphically in Figs. 1 to 14. The mean and the standard deviation of each class of differences were determined. A comparison was then made between the means of the classes of differences and likewise between the standard deviations. The mean of the first class of differences is equivalent to the difference between the mean milk yield of all the individual daughters in the fifteenth aggregate and the mean milk yield of all the individual daughters in the first aggregate. The same relation holds true for the mean of each class of differences. Hence the comparison between the means of the classes of differences indicates the relation existing be- tween the mean milk yield of all the daughters in the fifteenth aggre- gate and the mean milk yield of all the daughters in each of the other aggregates. The standard deviations of each class of differences measures the variability among the differences in each class. Hence a comparison between these standard deviations indicates the relation existing between classes in regard to the variability among the differences with- in them. In other words, this comparison indicates the extent to which the mean milk yields of the daughter-groups in each aggregate deviated from the mean milk yields of their respective daughter-groups in the fifteenth aggregate. It also provides another means of expressing the same relation as indicated by the correlations in the first comparison, i.e., it determines on the average how closely the mean milk yield of each daughter-group approximates the mean milk yield of the fifteenth daughter-group. 552 BULLETIN No. 270 [June, 19251 MEASURING THE BREEDING VALUE OF DAIRY SIRES 553 -33 -29 -25 -21 -17 -13 -9 -5 -l+l + 5 +9 -H3 + 17 +n -1-25 +zg +33 6 3 T 51 A HOa 11 97563211 -33 -29 -25 - ~ 1 T -13 -9 -5 - l-t-l -1-5 +9 +13 +17 +21 +5 +29 +33 * Curss Plio-PoiNTS -33 -9 -25 -21 -IT -13 -9 -5 -l+l +5 +9 +13 +17 + +5 +29 +33 - CLASS f1iD-ft>MT AGGREGATES The mathematical constants in Tables 1, 2, and 3, which describe the relation existing between the milk yields of the first fifteen tested daughters of the 133 Jersey sires taken as a whole, are all many times their probable errors. Hence it may be assumed that these tested daughters of the 133 Jersey sires, as classified into the daughter-groups, aggregates, etc., are representative of the corresponding tested daughters of all Jersey sires. Following this supposition it may also be assumed that on the average the above mathematical constants repre- 560 BULLETIN No. 270 [June, sent the relations existing between the milk yields of the first fifteen tested daughters of any Jersey sire. Accordingly then, a method can be derived by which the mean milk yield of the first fifteen tested daughters of any Jersey sire can be predicted to fall within given limits from the mean milk yield of any smaller number of his first tested daughters. DERIVATION OF METHOD Each class of differences, as shown graphically in Figs. 1 to 14, tends to approximate a normal frequency curve, some of the curves, however, being distinctly of the "cocked hat" type. The mean of any class of differences 2.14 1 times the standard deviation of that class gives limits such that the odds are 30 to 1 that any single difference, TABLE 4. LIMITS X AT ODDS OF 30 TO 1 AND 100 TO 1 FOR EACH GROUP OF FIRST TESTED DAUGHTERS OF ANY JERSEY SIRE Daughter groups Limits at odds of 30 to 1 (pounds of A.-F.C.M.) Limits at odds of 100 to 1 (pounds of A.-F.C.M.) 1. . +4235 to -3593 +5040 to -4398 2 +2872 to -2486 +3423 to -3037 3 +2203 to -1945 +2629 to -2371 4 + 1805 to -1623 +2158 to 1976 5 + 1536 to -1404 + 1838 to -1706 6 + 1337 to -1239 + 1602 to 1504 7 + 1179 to -1107 + 1414 to -1342 8 + 1046 to 992 + 1255 to 1201 9 + 926 to - 884 + 1112 to -1070 10 + 812 to - 780 + 976 to - 944 11 + 703 to - 675 + 845 to 817 12 ... + 589 to 563 + 707 to 681 13 + 471 to - 445 + 565 to - 539 14 + 347 to - 317 + 415 to - 385 limits were determined from the calculated means and standard deviations of the classes of differences. determined by the above methods for that class, will lie within them. Any single difference in a class of differences represents the difference between the mean milk yield of a corresponding daughter-group and the mean milk yield of the fifteenth daughter-group of an individual sire. Hence the mean of a class of differences 2.14 times the standard deviation of that class gives limits such that the chances are 30 to 1 that the difference between the mean milk yields of the corresponding group of tested daughters and the fifteenth group of tested daughters of any Jersey sire, will lie within them. 2 For example, the mean of the sixth The constant 2.14 was determined by means of the equation given on page XVIII of Karl Pearson's Tables for Statisticians. "Odds of 30 to 1 are considered by most investigators as being great enough to be dependable; however, if greater odds are desired 2.58 X a will give odds of 100 to 1. The limits for these odds are also included in Table 5. 1925} MEASURING THE BREEDING VALUE OF DAIRY SIRES 561 class of differences 2.14 times the standard deviation of that class, gives limits of -(- 1,337 pounds to 1,239 pounds. 1 The chances are 30 to 1 then that the difference between the mean milk yield of the first fifteen tested daughters and the mean milk yield of the first six tested daughters of any Jersey sire will fall within them. 2 In other words, the chances are 30 to 1 that the mean milk yield of the first six tested daughters of any Jersey sire will not be more than 1,337 pounds above nor less than 1,239 pounds below the mean milk yield of his first fifteen tested daughters. In like manner similar limits were determined for each group of tested daughters. These limits are re- ported in Table 4 and shown graphically in Fig. D. +5000 + 1(000 -3000 5 6 T e 9 DaUGHTER G-&OUP3 Hence limits may be found (Table 4) within which the chances are 30 to 1 that the mean milk yield of any small group of a sire's first tested daughters will deviate from the mean milk yield of his first fifteen tested daughters. lr The means and the standard deviations used to determine these limits were the calculated means and standard deviations given in Table 3. "Any difference between the mean milk yield of the fifteenth group of tested daughters and the mean milk yield of any smaller group of tested daughters is always determined by subtracting the mean milk yield of the fifteenth group from the mean milk yield of the smaller group. 562 BULLETIN No. 270 TABLE 5. AGE-CORRECTION FACTORS FOR GUERNSEY MILK YIELDS Age refers to the age of the cow at date of last calving preceding the commencement of the record. (Additional months) 1 year 2 years 3 years 4 years 1 2 3 4 5 6 7 1.61443 8 1.56493 9 1.54841 10 .49109 11 46191 5 years 0... .08633 1 .08214 2 07810 3 07419 4 07041 5 .06676 6 06324 7 .05983 8 05655 9 05338 10 05032 11 1.04737 9 years 0... 1.00010 1 .00025 2 .00047 3 00076 4 00113 5 .00155 6 .00205 7 00263 8 .00326 9 .00397 10 00475 11 00559 3 years .09107 1 .09508 2 .09920 3 10342 4 . 10776 5 .11221 6 .11678 7 .12147 8 .12628 9 13121 10 13628 11 .14146 1.43613 1.41304 1.39210 1 . 37294 1.35527 1.33888 1.32359 .30926 .29578 .28306 .27103 . 25962 .24875 .23840 . 22854 .21910 .21007 .20142 .19312 .18514 . 17748 .17011 . 16302 .15619 . 14961 . 14326 .13714 .13123 .12552 .12001 .11469 .10955 .10459 .09979 .09515 1.09067 6 years 7 years 8 years 1.04453 .04179 .03916 .03663 .03420 .03186 .02961 .02746 .02538 .02342 .02154 1.01974 .01803 .01641 .01486 .01339 .01201 .01071 .00948 .00834 .00726 .00627 .00535 .00451 1.00374 .00304 .00242 .00186 .00139 .00098 .00064 .00038 .00018 .00005 .00000 .00001 10 years 1 years 2 years .00651 .00750 .00856 .00969 .01089 .01216 .01351 .01493 .01641 .01798 .01962 .02133 .02312 .02499 .02693 .02894 .03105 .03322 .03548 .03782 .04024 .04274 .04533 .04800 .05076 .05361 .05654 .05956 .06268 .06589 .06919 .07259 .07608 .07968 .08338 .08717 14 years 15 years 16 years 1.14678 1.15224 .15784 .16358 .16946 .17549 .18167 .18802 . 19452 .20118 .20802 .21502 1.22220 .22957 .23712 .24487 .25282 .26096 .26932 .27789 .28669 .29571 .30497 .31447 EXPLANATION OF TABLE. The factors given in this table were derived from the equation: Y = 7017.4 + 328.0 X - 12.4 X 2 + 1729.2 Log,o X. (Y = yield of milk in pounds; X = age in units of six months commencing at 1 year and 3 months for the zero point.) This equation was determined by the author, and is the equation of the curve ex- pressing the influence of age on the milk yield of Guernsey cows. It is based upon 3,000 yearly milk records of cows as published in Vols. 12 to 34 of the Guernsey Advanced Register. According to the above equation, the milk yield at a given age multiplied by the factor given in the table for that age, reduces the yield to that of the age of maximum production, that is, to the yield at 8 years and 10 months. 1925] MEASURING THE BREEDING VALUE OF DAIRY SIRES 563 TABLE 6. AGE-CORRECTION FACTORS FOR JERSEY MILK. YIELDS Age refers to the age of the cow at date of last calving preceding the commencement of the records. (Additional months) 1 year 2 years 3 years 4 years 2.19925 1... 2.03645 2... .92160 3... 83385 4... 76336 5 .. .70474 6... .65481 7... 61134 .57282 .53846 .50761 .47951 5 years 0... 1.07285 1... 1.06849 2 1.06440 3... 1.06045 4... 1.05664 5... 1.05296 6 1.04943 7 1.04603 1.04286 1.03972 1.03681 1.03402 9 years 0... .00543 1 .00644 2 00766 3 00888 4 .01020 5 .01163 6 01317 7 .01471 .01647 9 01823 10 1.02010 11 1 02218 13 years 0... .18120 1 .18835 2 19574 3 20351 4 .21153 5 21966 6 .22790 7 23655 8 24533 9 25455 10 26390 11... ... .27355 .45349 .42959 .40766 .38735 .36836 .35044 .33351 .31752 .30259 .28833 .27486 .26215 .25000 .23839 .22730 .21669 .20656 . 19689 .18779 .17911 .17069 .16252 1.15473 1.14732 6 years 7 years 1.14012 1.13327 1.12663 1.12020 1.11408 1.10816 1.10241 1.09709 1.09182 1.08684 1.08202 1.07735 8 years .03135 .02870 .02627 .02396 .02176 1.01968 1.01771 1.01585 1.01410 1.01245 1.01092 1.00949 1.00817 1.00695 1.00583 1.00482 1.00392 1.00311 1.00241 1.00170 1.00120 1.00080 1.00050 1.00020 .00010 .00000 .00010 .00020 .00040 .00070 .00110 .00160 .00220 .00280 .00361 .00452 10 years 11 years 12 years 1.02428 1.02648 .02881 .03125 .03370 .03627 .03907 .04188 .04482 .04789 .05108 .05441 1.05775 .06123 .06485 .06872 .07262 .07666 .08073 .08495 .08944 .09397 .09866 .10351 1.10853 .11359 .11894 . 12435 . 12994 .13572 .14168 . 14784 .15407 . 16050 . 16727 .17412 14 years 5 years 16 years 1.28351 1.29375 1.30430 1.31517 1.32637 1.33791 1 . 34982 1.36208 1.37471 1.38773 1.40118 1.41507 . 42939 .44418 .45946 .47521 .49151 . 50840 .52583 . 54386 . 56254 .58187 .60191 .62267 EXPLANATION OF TABLE. The factors given in this table were derived from the equation: Y = 4586.5 + 307.6 X - 12.7 X 2 + 2216.6 LogioX. (Y = yield of milk in pounds; X = age in units of six months commencing at nine months for the zero point.) This equation was determined by John W. Gowen (Bui. 281, Maine Agr. Exp. Sta.) and is the equation of the curve expressing the influence of age on the milk yields of Jersey cows. It is based on 2,153 yearly milk records of cows as published in Vols. 1911 and 1913 of the Jersey Registry of Merit. 564 BULLETIN No. 270 [June, APPLICATION OF METHOD In order to illustrate the accuracy of these limits and also their possible application to the tested daughters of Guernsey sires, five Jersey sires not included in the original 133 sires, and five Guernsey sires with fifteen or more tested daughters, were chosen at random, and the differences between the mean milk yields of their first fifteen tested daughters and the mean milk yields of each smaller group of first tested daughters determined by the above procedure. These differ- ences are given in Table 8. The limits for each group of tested daughters, such that the chances are 30 to 1 that any of the above corres- ponding differences should fall within them, are also given in Table 8. In comparing the difference for each group of daughters of the Jersey sires with its corresponding limits, it will be found that in every case the difference falls within them. These limits, therefore, appear to provide a dependable method by which the average productions (mean milk yields) of the first fifteen tested daughters of Jersey sires can be predicted from the average productions (mean milk yields) of any smaller number of their first tested daughters. From Table 8 it would seem that these limits may also be used in predicting the average pro- ductions of the first fifteen tested daughters of Guernsey sires from the average productions of any smaller number of their first tested daughters. CAUTIONS IN USE OF METHOD In using the limits set forth in Table 4, it must always be remembered that they refer to the corrected milk and butterfat produc- tions of the tested daughters and not to their recorded productions. The method for correcting the recorded productions of the tested daughters of Guernsey and Jersey sires is described on page 547 and in Tables 5 and 6 of this bulletin. It must also be remembered that on the aver- age the first six tested daughters of a sire is the smallest number of tested daughters the average of whose productions closely approximates the average production of his first fifteen tested daughters. The limits for smaller groups of tested daughters are much wider and only in ex- ceptional cases would they be of much practical value. CONCLUSIONS The results from a statistical study of the variability within the corrected milk and butterfat productions of the tested daughters of 133 Jersey sires are as follows: 1 1. In general the average production and variability among the productions of the first fifteen tested daughters of a Jersey sire are representative of the average production and variability among the productions of any larger number of the sire's tested daughters. 2. On the average, the first six tested daughters of a Jersey sire is the smallest number of tested daughters the average of whose produc- The recorded milk and butterfat productions of the tested daughters were corrected for age of cow and percentage of fat in the milk. See page 547 of text. 1925~\ MEASURING THE BREEDING VALUE OF DAIRY SIRES 565 TABLE 7. EQUATIONS TO FITTED CURVES IN FIGS. A, B, AND C Fig. A AQ7 Coefficients of correlations: Y = x+ 3?9 + 1.0256 + .000006X 3 Fig. B Standard deviations: Y = 2311.4 + 2.765X Coefficients of variability: Y = 20.219 + .0051 IX Fig.C Standard deviations: y = 3129 + ^ ? _ ^ A. "r .oo2 Means: Y=-_- 63.6 + .01X' -X. + 1 NOTE. X in every curve is a variable in units from 1 to 15, and Y is the variable whose quantity is determined by the equation. tions closely approximates the average production of the first fifteen tested daughters of the sire. 3. A numerical measure of this closeness of agreement between the average productions of the first six tested daughters and the first fifteen tested daughters of a Jersey sire is as follows: The chances are 30 to 1 that the average production of the first six tested daughters of a Jersey sire will not be more than 1,337 pounds above nor less than 1,239 pounds below the average production of the first fifteen tested daughters. In other words, this relation between the average productions of the first six tested daughters and the first fifteen tested daughters of a Jersey sire can be expected to hold true for 30 out of every 31 Jersey sires. 4. Breeders in general have found that the average production of a large number of tested daughters of a sire can be used as a relative measure of the sire's breeding value. 1 The first six tested daughters of a Jersey sire is the smallest number of first tested daughters whose average production can be used as a means to measure the approximate breeding value of the sire. LITERATURE CITED BRODY S., RACSDALE, A. C. and TURNER, C. W. Rate of growth of the dairy cow. Jour, of Gen. Physiol. 6, 21-40. 1923. GAINES, W. L. and DAVIDSON, F. A. Relation between percentage fat content and yield of milk. 111. Agr. Exp. Sta. Bui. 245. 1923. GOWEN, J. W. Animal husbandry investigations in 1919. Maine Agr. Exp. Sta. Ann. Rot. 1919, 249-284. 1919. PEARL, R. and MINER, J. C. Variation of the milk of Ayrshire cows in quantity and fat content of their milk. Maine Agr. Exp. Sta. Bui. 279. 1919. PEARSON, KARL. Tables for statisticians and biometricians. Cambridge University Press. 1914. 1 Owing to the equal influence of both the sire and dam upon the inherited producing ability of the daughters, and also to the fact that the tested daughters of a sire in most cases represent only the best daughters, this average can be used only as a relative measure of the breeding value of the sire. See page 545 of text. 566 BULLETIN No. 270 p Q j H ^ s *t o * Q ?! 2< i 2 c/ w . < 5 Q a - X , jQ 5 D ^, w w 2 s3 ss Sc^ JO JOUJ3AOQ pnbag pn + i i i i i i i ++ Tf T-I if CN Tt> o > CS i CS i 7 i ++ i i i i i i i i i + 77 i 7 i i + i i i i i i + i i +++ i ++++ i + co ts ^ ~ --i -> ^ I I I I I I I I I I I I I I oooooooooooooo UNIVERSITY OF ILLINOIS-URBAN*