WEEGH‘HNG ENFORMATEQN FRCM RELATEVES TO SELECT FOR MILK EN HOLSTEINS “Thesis fie: fi’ho 909mm 5? Ph. D. MiG-{SGAN S‘EATE UM‘JERSTFY Ofli’mr Wenésgfi Emma 1964 “-4“ This is to certify that the thesis entitled WEIGHTING INFORMATION FROM RELATIVES TO SELECT FOR MILK IN HOLSTEINS presented by OLIVER WENDELL DEAT ON has been accepted towards fulfillment of the requirements for $9 mama/wt Major professor 0-169 LIBRARY Michigan Stave University WEIG WEIGHTING INFORMATION FROM RELATIVES TO SELECT FOR MILK IN HOLSTEINS By Oliver Wendell Deaton AN ABSTRACT OF A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Dairy 1964 WEI St miormatio 1113110115 of ai'Erage \I‘. use in (13 Were USE: average I c‘n‘relati “ere 0_1 Holstein I‘EQQrdS flCiths ShOUId b lOrity Of ABSTRACT WEIGHTING INFORMATION FROM RELATIVES TO SELECT FOR MILK IN HOLSTEIN S by Oliver Wendell Deaton Selection indexes for milk production in Holstein cattle using information from close relatives were developed and tested in various pop- ulations of cows recorded in Michigan DHIA. Records of lactations measured as deviations from the annual herd average were used to choose the appropriate measure of milk production to use in developing a selection index. Linear multiple regression equations were used to predict the daughter's deviation in first lactation from herd average using various records of the cow as independent variables. The simple correlations of the cow's first record with the first record of the daughter were 0. 149 for 904 Guernsey cows and their daughters, and 0.256 for 1, 526 Holstein cows and their daughters. The correlations of the cow's later records were much smaller in both breeds. The partial regression coef— ficients indicated that nearly all of the emphasis among records of the cow Should be placed on the cow's first record to predict the superiority or infer- iority of the first record of the daughter. Multiple correlation coefficients indicated that he cow were meethstr 86h breeding val usmg7,63é mmbmafion heritability Shmrsont i'ETlaDCEs') derived frc indicated that averages of either the first two or the first three records of the cow were poorer predictors of the daughter's first record than was the cow's first record alone. Selection indexes to predict with maximum accuracy the general breeding value of individual Holsteins for milk production were developed using 7, 638 deviations of first lactations from herd averages in a variety of combinations of the cow, her dam, her daughters, and her half-sisters. The heritability used was 0.246 which was derived from the regression of paternal sisters on the cow. Other estimates of heritability (with larger sampling variances) ranged from O. 123, derived from intra-sire correlation, to 0. 436, derived from intra—dam correlation. The records of a cow's dam and maternal sisters only slightly in- creased the accuracy of estimating her genotype providing the cow had an own record. Daughters and paternal sisters added considerably to the ac- curacy of estimating her genotype. The multiple correlation of the index with the cow's genotype ranged from 0.50 to 0.73 depending on the kinds and amounts of information available from relatives. Multiple correlation coefficients for individuals without an own record or offspring (heifers and young bulls) varied from O. 12 for one half—sister to 0. 55 for many relatives. In estimating the genotype of a young bull that is Sired by a well proven sire, the usefulness of information on the maternal g‘I‘andparents is limited to the dam's paternal sisters if their numbers are sui‘icient. I no apparent v Sele can record i The first rec index and 211: 0.166 with 1] accuracy HQ pmé'I‘ess f0 sires, sufficient. The maternal granddam and the dam's maternal sisters are of no apparent value. Selection by index was compared with mass selection on the cow's own record in a test population of 429 Holstein cows and their 498 daughters. The first record of an unselected daughter was correlated with the cow's index and also with the cow's own first record. The resulting correlations of 0. 166 with the index and O. 140 for the cow's record indicated an increase in accuracy near 19 per cent in favor of index selection. The index appeared to be a practical method to increase genetic progress for milk production especially to select potential dams of future sires. WEIC WEIGHTING INFORMATION FROM RELATIVES TO SELECT FOR MILK IN HOLSTEINS By Oliver Wendell Deaton A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOC TOR OF PHILOSOPHY Department of Dairy 1964 D. McCall Period of ACKNOWLEDGMENTS The author wishes to express his sincere appreciation to Dr. Lon D. McGilliard for his guidance and friendly counsel throughout the entire period of study. The advice and moral support of Dr. Clint Meadows was also greatly appreciated. Thanks are also due to A. J. Thelan and his associates for their assistance in processing the data. ii ACKOWL LIST OF I LIST OF 1 Chapter I. IN ILR HI. 3 VI. TABLE OF CONTENTS Page ACKNOWLEDGMENTS ......................... ii LIST OF TABLES ............................ iv LIST OF ILLUSTRATIONS ....................... v Chapter I. INTRODUCTION ......................... 1 II. REVIEW OF LITERATURE ................... 5 Previous Indexes Measures of Production III. SOURCE OF DATA ....................... 23 IV. METHODS AND RESULTS ................... 26 Measure of Production Theoretical Basis for Constructing an Index Estimates of Parameters The Index Evaluation of the Index on a Test Population V. APPLICATION OF RESULTS .................. 67 VI. SUMMARY ............................ 71 REFERENCES .............................. 74 iii Table 10. 11. 12. LI ST OF TABLES Per cent of total variation in production from differences between herds ................ Genetic differences between herd averages ........ Correlation of cow's records with their daughters' first records ....................... Partial regression coefficients of daughters' first records on various records of the cow ......... Estimates for heritability ................. Components of variance for milk production in first lactation ......................... Partial regression coefficients and multiple R's for all five groups of relatives .............. Partial regression coefficients and multiple R's for all information except dams records ........ Multiple correlation coefficients using various combinations of information ............... Accuracies (RIGI) of information available for young animals ...................... Accuracy of indexing a young sire ............. 6 Relationships between phenotype, index, and daughter of 498 cows in the test population . ...... iv Page 17 19 29 31 42 44 48 52 56 59 61 63 Figure l. 2. 3. RI LIST OF ILLUSTRATIONS Figure Page 1. Relationships involved in predicting G1 from the various phenotypes of the cow and her relatives ...... 35 2. Causal relationships among phenotypes of the cow and her close relatives ................... 36 3. Genetic and phenotypic relationships in the test population ........................... 64 the "de- Prhnar all imp allow ‘11 CHAPTER I IN TRODUC TION To irnprove a population genetically is to increase the frequency of the "desirable" genes or gene combinations. This change is accomplished primarily by selection although in some cases the system of mating can play an important role. Voluntary selection involves ranking individuals and allowing them to reproduce at rates proportional to their genetic worths. This selection is limited by many forces such as natural selection and econ- omic considerations, forces causing losses of individuals that would be kept for breeding purposes. A low reproductive rate and a long generation inter- val set a low limit on annual genetic changes possible in a population such as dairy cattle. An animal's breeding value for traits with small heritabilities can be estimated most accurately if aids to mass selection are utilized. Repeated observations, information on ancestors and collateral relatives, and progeny tests are such aids. The breeder must compromise between additional ac— curacy in evaluating his animal's breeding values and a shorter interval of time between generations. Yearly genetic progress actually may be in- creased by using less accurate information earlier if‘by this the generation interval construc merit. designer an objec to main breeder of an in (C) a cc gefleiic situam 3011110 93mm. PFOgra fling t '«l uSed iv. interval can be shortened sufficiently. The concept of combining information in a selection index is to construct a number to be proportional to an animal's breeding worth or net merit. Such numbers are used to rank individuals for selection and are designed to maximize genetic progress. An index helps to make selection an objective process. Merely by reducing subjective judgment and by helping to maintain consistent goals, an index can be a valuable asset to the dairy breeder. Indexes can be developed from information on (a) several traits of an individual, (b) the same trait on an individual and its relatives, or (c) a combination of the two. Even when all voluntary selection is based on the index, maximum genetic progress is limited to how close the model of the index fits the real situation. Deviations from the linear model, non-additive gene action, and non-normality of the data as well as inaccurate estimation of the population parameters usually limit genetic progress. Numerous selection indexes for Mproving the productive traits of dairy cattle have been proposed, but their application in dairy cattle breeding programs has been limited. The indexes have been constructed with simpli- fying but untested assumptions. The assumption that no relationship exists between the sire and his mates is frequently made. Seldom have the genetic and phenotypic correlations among the various sub-groups of the pepulations used to construct the index actually been calculated. The environmental correlatior or lIIiE'I'I‘EI from smai small, as tions are other que for seiem @Ughte] correlations existing among the various groups of cows are frequently assumed or inferred from other studies to avoid the large sampling errors resulting from small numbers in the population available for study. In large populations of dairy cattle where sampling errors can be small, assumptions involving the mating system and environmental correla— tions are the most obvious areas requiring further investigation. However, other questions involving the validity and applicability of a specific index for selection for production of milk in dairy cattle may concern: 1. What measure of milk production should be used in the index? Has sufficient account of the variation, reliability and inter- relationships among the different lactations been made? 2. Is the index substantially more accurate than simpler se- lection methods? 3. Are the results realized in a cow population close to the theoretical predictions? One object of this investigation was to ascertain weighting factors for various combinations of information on the milk production of a cow and her close relatives. A second objective was to compare the usefulness of in- formation from the cow and the various types of relatives by the correla- tions between indexes and genotypes. A third objective was to compare theory with results accomplished by correlating cows' indexes with their daughters' production. This cattle breeding die informatio critical analys This investigation should add to the knowledge and practice of dairy cattle breeding by suggesting improved criteria for selection, by increasing the information needed to examine breeding theory, and by stimulating more critical analyses relating to animal improvement. selectior has been lined Elli farm an merit. the m 0 1eCllOrI CES bet {army CHAPTER II REVIEW OF LITERATURE Previous Indexes The increased efficiency of net merit or total score as a basis for selection as compared to independent culling levels or the tandem method has been demonstrated by Hazel and Lush (1942). Hazel (1943) clearly out- lined the theory and genetic basis for developing a selection index to improve farm animals. This paper dealt with several traits which comprised net merit. Path coefficients and multiple regression techniques were used to maximize the linear correlation between the index and the breeding value of an animal. Lush (1947) investigated the expected consequences of selecting on individuality alone, on the family average, or on an optimum combination of the two. The conditions which favored family selection over individual se- lection were (a) a large number of individuals per family, (b) large divergen- . ces between the environmental and genetic correlations among family mem— bers, and (c) low heritabilities of the traits under selection. In the case of (b), a large genetic correlation with a small environmental correlation among family members suggested using the family average in a positive manner to determine u: large enviro: average neg: says an indi‘ credit becau than usual d based on a ( always to er ever, in dai Survival tra 19 Correlati Nu hate been )3 widesDread Drugrams E elude; [\D determine the breeding value of the individual; whereas, small genetic and large environmental correlations implied the need to consider the family average negatively as an environmental correction. The latter situation says an individual from a family with high merit should be given negative credit because its performance and the family average are likely larger than usual due to favorable environmental conditions. Gains from selection based on a combination of individual and family performance were shown always to equal or to exceed gains based solely on individual selection. How— ever, in dairy cattle low reproductive rates and inbreeding degeneration of survival traits seriously limit developing sizeable families with high gener- ic correlations among members. Numerous selection indexes for all major classes of farm animals have been pr0posed, yet their use in cattle breeding programs has not been widespread. The limited application of selection indexes in dairy breeding programs appears to be the result of several interrelated factors which in— clude: 1. Ineffective education of breeders: lack of knowledge of the existence of indexes as well as not knowing how to use indexes. 2. Labor, expense, and records required. 3. The accuracy of selection by index has not been clearly dem— onstrated to be much more than simpler methods of selection. 4. Reluctance on the part of the breeder to apply indexes. That is, bre prtl SOL get SEVEN purposes of dis use informatior which selection index for intra cow and her 6 used were: he I‘ellffatability average of a] this Was Wei real produci assured Zer hem. The selection sole 1_ 9 " depending From breeders seem in effect to overestimate heritability of the productive traits and are sometimes distrustful of "figuring" | 4n - X411 . 5 h E51 5 2 G51 : 9X51 G1 / h x511 3’x5n I \ E2 h E \Xz . Cl : V I \ x1 n £1 + (n-l) ti] where n = number of X's consti- G31 G3n tuting the average of the group, i I and t = the correlation between E 133%.], 1. / 3n i = group of relatives involved. X31 /x3n (t3 = t5 75 t4) x3 E = environment G = genotype X = phenotype °G = T", heritability X Subscripts: (first position) (second position) 1 = cow the individuals compos- 2 = dam ing the average 3 = average Of daughters 4 = average Of paternal sisters 5 = average of maternal sisters FIG. 2. —Causal relationships among phenotypes of the cow and her close relatives 37 particular group concerned and G1. The b's are derived by solving simultaneous equations from a var- iance-covariance matrix of the following form: b1 Var X1 + b2 COV X1X2 + . . . . + 135 COV X1X5 = COV XlGl b1 Cov X2X1 + b2 Var X2 + . . . . + b5 Cov X2X5 = Cov X2G1 bl Cov X5X1 + b2 Cov X5X2 + . . . . + b5 Var X5 = Cov X5G1 The b's will change as either the size of the matrix (number Of groups Of relatives included) or the magnitude Of the diagonal elements (the variances Of the groups Of relatives) change. The variances of X1 and X2 do not change (except as the records represent a selected sample) because only single records are involved. The variances Of X3, X4, and X5 decrease as the number Of individuals increases. The variance of averages from groups of size n can be measured from the formula: 2 OX+ (n—1) Cov XX' _ n 2 _ OX- 2 . . where: OX: the variance of averages Of groups of Size n. a: = the variance of individuals and Cov XX' = the covariance among individuals of the group. The multiple correlation coefficient (R) represents the correlation between I and G1 and is a measure of the accuracy of the index for predicting 38 the cow's genotype. R2 is the fraction of the variance in G1 associated with variation in I. Estimates of these expressions are Obtained in the following manner: 2 = b1(COVXG1)+... +bn(COVXnG1) IG 2 1 0 G1 2 0' 2 I _ 01 RIGl 2 . RIG " ° G G1 1 Estimates of Parameters Phenotypic variances and covariances. —The variances and covar- iances needed tO construct the index were Obtained from the first lactation records Of 8, 984 Holstein cows, 7, 638 of which had information available on some relative and 1, 346 with an own record only. Only the 7, 638 cows could be included in any Of the calculations of phenotypic covariances among related groups. The variance of the 7, 638 records was 44, 059 and differed little from 44, 971 which was the variance of the entire 8, 984 records. Since the covariances had to be drawn from the 7, 638 cows, the variance among them was used as the variance of the individual to form the index. As an index for evaluating animals in different herds as well as within herds was desired, and because differences between herds had been removed by deviations from herd averages, all variances and covariances were calculated ignoring herds. 39 The phenotypic covariances among the groups Of relatives were calculated from the sums Of products. The covariances Observed between single relatives were: X1 X2 X3 X4 X5 Cow Dam Daughter Paternal Maternal sister sister with: X1 7,987 8,145 2,698 4,651 X2 8, 704 0 7, 237 X3 437 2, 484 X 4 971 The various groups Of relatives composed a number of sub-sets Of data with different variances and different sample sizes. The variances Of individuals in the various sub—sets were in close agreement with the var- iance of 44, 059 from the larger pOpulation. Therefore, 44, 059 was used as the variance Of single records for the cow and for the individual in all groups of relatives. That is 0:1, 0&2, o§3, oil, ands;5 all equal 44,059 when they represent single relatives (n = 1). The variances of X3, X4, and X5 become smaller as more individuals are included in the average. The var— iance of the average of the group can be obtained from the appropriate variances and covariances. As previously mentioned, the variance Of an average of 11 individuals with like variance is: 40 0% + (n-I) Cov. xx' n 03: X The Cov XX' is the covariance among individuals within the group constituting the average. The daughters represented by X3 and the maternal sisters as X5 have the same genetic relationship and usually similar environments with- in sets. The Cov XX' for these groups is equivalent to the covariance between the cow and her maternal sisters. To compute 0% for X3 and X5, 4, 651 was used as Cov XX'. The variance of groups of size n for daughters or maternal sisters was: 2 2 _ 44, 059 + (n—n4g651 OX3 or OX5 — n Paternal sisters are Often distributed in numerous herds where en- vironmental similarities are usually small. Therefore, Cov XX' for the paternal sisters (X4) should represent this situation of daughters Of a sire scattered in many herds. The covariance between the cow and her paternal sisters was considered to estimate appropriately Cov XX' in determining the variances of the average of X 4. The variance of the average Of groups of paternal sisters of size n was: oz = 44,059+rn-1)2,698 X n Heritability. -—Some knowledge of heritability is needed to evaluate the covariances between the various X's and G1 that constitute the right side of the variance-covariance matrix as illustrated by the relationships in Figure 2 . 41 Estimates of heritability from various portions of the data are given in Table 5. All Of the estimates ignore sires and herds to approach more nearly the situation relating to an index to be used to compare cows from different herds. The heritabilities given were nearly the same as those indi- cated within herd-sire groups. An analysis cross-classifying herds and sires was one Of the methods used to estimate heritability from intra-sire components Of variance. The cross—classified model is more efficient than the hierarchical classification and provides an Opportunity to check for possible herd by sire interaction. The model used was: where Yijk denotes the record (as a deviation from herd average) made by the kth daughter or the jth sire in the ith herd. p. is a mean or all deviated records. hi is the amount the 1th herd causes the records made in that herd to deviate from the average of all herds. Si is the amount the jth sire causes the average Of his daughters to deviate from the average of all sires. hsij is the amount the particular combination of the ith herd and the jth sire causes the records Of this combination to deviate from the additive combination of the 1th herd and the 1th sire. eijk is the amount the ijkth record deviates from the average of all the records of the jt‘h sire in the ith herd. It was assumed that, except for u, all elements of the model are random, uncorrelated 42 TABLE 5. ~Estimates of heritability Sampling variance Method Heritability of heritability Regression of cow on dam 0. 376 . 0018 Regression of paternal sisters on cow 0. 246 . 0005 Intra-dam correlation 0. 436 . 0057 Intra —sire correlation Interaction model 0. 123 . 0008 No interaction model 0. 326 . 0026 variables with zero expectation and variances 0121, 0:, Ofisfind 0:. These parameters are estimated by statistics correspondingly designated. as H, S, HS, and E. 48 Heritability == —— S + HS + E The hierarchical model for intra-sire analysis of variance components W88: 43 Yijk = H + bi + 811 + 611k where Yijk denotes the record (as a deviation) made by the kth daughter of the jth sire in the ith herd. p. is a population mean of deviated records. hi is the amount the ith herd causes the records made in that herd to deviate from the average of all herds. sij is the amount the jth sire causes the aver-r age of his daughters in the ith herd to deviate from the average of all daugh- ters in the ith herd. eijk is the amount the ijkth record deviates from the average of all records of the daughters of the jth sire in the ith herd. It was assumed that, except forp. , all elements of the model are random, uncor- 2, 02, andoz. The h s e related variables with zero expectation and variances 0 statistics which estimate these parameters are designated H, S, and E, respectively. Heritability = Sift-SE The hierarchical model was also used for intra-dam components of variance. The model was: Yijk = i‘ + hi + dij + eijk where Yijk denotes the deviated record made by the kth daughter of the jth dam. in the ith herd. u, hi and eijk are the same as defined above. dij is the amount the Jth dam causes the average of her daughters in the 1th herd to deviate from the average of all daughters in the 1th herd. It was assumed TABLE 6.—Components of variance for milk production in first lactation* Source D. F. Mean Square Expected Mean Square Cross Classified Model for Paternal Sisters Herds 195 83,210 02+ 6.1, 613184? 6.3 6:4- 33.8 a; Sires 676 69,315 62+ 5,9 Gist 9.8 63+ 5.9 012.1 Herdx Sire 1502 39,008 642+ 0.9 0ij— 0.8 eg+ 2.6 of] Residual 4721 39,694 62 Components: H = 621, S = 1324, HS = 2199, E = 39694 Hierarchical Model for Paternal Sisters Herds 195 83,210 a: + 6.11 a: + 33.8 of] Sires/Herds 2178 48,414 (I: + 2.5 0’: Residual 4271 39, 694 6: Components: H = 617, S = 3526, E = 39694 Hierarchical Model for Maternal Sisters Herds 187 68,494 a: + 2.1, ofi + 18.3 of1 Dams/Herds 1353 46,223 0’: + 2.2 03 Residual 1899 36, 366 a: Components: H = 638, D = 4449, E = 36366 *Milk production was expressed in deviations of 10 pounds from the annual herd average. 45 that, except for if, all elements of the model are random, uncorrelated variables with zero expectation and variances 0%, 03, and 0:. The statistics which estimate these parameters are designated H, D, and B, respectively. Similarly, heritability is estimated as: 4 D / D + E. The sampling variances of the heritability estimates were calculated as described by Falconer (1960). The sampling variances for the intra—sire estimates of heritability are only rough approximations as the numbers of off- spring per sire were variable. The herd by sire interaction component in the cross-classified analysis was larger than expected on the basis of previous studies. Conse- quently, the heritability indicated from this model is much smaller than the other estimates from this population. A satisfactory explanation for this interaction is not available. Some conditions that could possibly cause a herd by sire interaction on deviated, first lactation records may include: (1) marked differences from herd to herd involving preferential treatment among the daughters of various sires, (2) wide differences in age structure among herds, and (3) a non—random distribution of year or season of calving among certain sires' daughters. The fact that many herds are involved makes the first two possibilities seem unlikely. Although (3) seems to be more likely to occur than either (1) or (2), the real nature of these effects remains unexplained. Some differences could arise from differences in fertility of sires among seasons; yet, this effect would seem to be small as 46 measured in the production of the daughters' first lactations. The estimates of heritability derived from groups of dams are notiCeably larger than those estimates obtained from groups of sires. The estimates from groups of dams appear to be somewhat inflated by common environmental effects within herds. The nature of such common environ- mental effects that may exist is not apparent. Possible causes would in- clude (1) a positive correlation between different daughters of the same dam caused by similar preferential treatment, (2) maternal effects, and (3) the use of standard age correction factors. The latter possibility would depend upon the existence of real genetic differences in the rate of maturity among cows. Due to the difficulties in finding the real nature of the herd by sire interaction and because of the lack of agreement among estimates, the heritability with the smallest sampling variance was used. The value of 0.246 derived from the regression of the paternal sisters on the cow was used as heritability. The Index The variance-covariance matrix from which the b's were derived was: b1 b2 b3 b4 b5 Equation X1 44059 7987 8145 2698 4651 = 10839 X2 7 987 44059 8704 0 7237 = 5420 X3 8145 8704 44059 437 2484 = 5420 X4 2698 0 437 44059 971 = 2710 X5 4651 7237 2484 971 44059 = 2710 47 The diagonal elements are variances of the various X's when the X's are single individuals. The diagonal elements of X3, X and X5 were changed 4, to the variances of averages and for each change a new set of equations was solved. A large number of sets of equations was solved to arrive at b's for different combinations of kinds and amounts of information. Sample portions of the weights from the index and the corresponding multiple correlation coefficients are shown in Tables 7 and 8. These tables give only a small portion of the comparisons that were made; yet, they should give a good picture of how the weights vary with changes in the number of relatives involved. A more concise picture of the relative usefulness of the various kinds and amounts of information can be judged from Table 9 which gives only the multiple correlation coefficients of the cow's index with her genotype. An R value of 0.50 may be considered as the "base" for all the com- binations which include the cow's own record. This is the value obtained where only the cow's own record is used to estimate her genic value. This value of R is the square root of heritability. The addition of the dam's record raises R only to 0.52. Eight daughters plus the cow's record gives an R of 0.62, the last few being nearly as useful as the first one or two in increasing the accuracy. The addition of maternal sisters to the cow's record makes only a small increase in R even if as many as eight are considered. 48 TABLE 7. —Partial regression coefficients and multiple R's for all five groups of relatives Part 1, N5 = 1 Paternal Daughters Sisters b1 b2 b3 b4 b5 R N3 N 4 1 1 .22 .07 .07 .05 .02 .55 1 2 .21 .07 .07 .09 .02 .56 1 3 .21 .07 .07 .13 .02 .56 1 10 .20 .07 .07 .33 .02 .60 1 20 .19 .07 -07 .45 .02 .61 1 50 .18 .07 .07 .62 .01 .64 1 100 .18 .08 .07 .71 .01 .65 1 200 .17 .08 .07 .76 .01 .66 2 1 .21 .06 .13 .05 .02 .56 2 2 .20 .06 .13 .09 .02 .57 2 3 .20 .06 .13 .13 .02 .58 2 10 .19 .06 .13 .33 .02 .61 2 20 .18 .06 .13 .45 .01 .63 2 50 .17 .06 .13 .62 .01 .65 2 100 .17 .07 .13 .71 .01 .67 2 200 .16 .07 .13 .76 .01 .67 3 1 .20 .05 .19 .05 .02 .58 3 2 .20 .05 .19 .09 .02 .58 3 3 .19 .05 .19 .13 .02 .59 3 10 .18 .05 .19 .33 .02 .62 3 20 .17 .05 .19 .45 .01 .64 3 50 .16 .05 .19 .62 .01 .66 3 100 .16 .06 .19 .71 .01 .68 3 200 .16 .06 .19 .76 .01 .68 8 1 .16 .01 .41 .05 .02 .62 8 2 .16 .01 .41 .09 .02 .63 8 3 .16 .01 .41 .13 .02 .64 8 10 .15 .01 .41 .33 .01 .67 8 20 .14 .02 .41 .45 .01 .68 8 50 .13 ,.02 .41 .62 .01 .71 8 100 .12 .02 .41 .70 .01 .72 8 200 .12 .02 .41 .76 .01 .72 TABLE 7. --Continued 49 Part 2, N5 = 2 N3 N4 b1 b2 b3 b4 b5 R 1 1 .21 .06 .07 05 .04 .55 1 2 .21 .06 .07 09 .04 .56 1 3 .21 .07 .07 .13 .04 .56 1 10 .20 .07 .07 .33 .03 .60 1 20 .19 .07 .07 .45 .03 .62 1 50 .18 .07 .07 .62 .02 .64 1 100 .17 .07 .07 70 .02 .65 1 200 .17 .08 .07 76 .02 .66 2 1 .21 .05 .13 .05 .04 .56 2 2 .20 .05 .13 .09 .04 .57 2 3 .20 .05 .13 .13 .04 .58 2 10 .19 .06 .13 .33 .03 .61 2 20 .18 .06 .13 .45 .03 .63 2 50 .17 .06 .13 .62 .02 .65 2 100 .17 .06 .13 .70 .02 .67 2 200 .16 .07 .13 .76 .02 .67 3 1 .20 .04 .19 .05 .04 .58 3 2 .19 .04 .19 .09 .04 .58 3 3 .19 .05 .19 .13 .04 .59 3 10 .18 .05 .19 .33 .03 .62 3 20 .17 .05 .19 .45 .03 .64 3 50 .16 .05 .19 .62 .02 .66 3 100 .16 .05 .19 .70 .02 .68 3 200 .15 .06 .19 .76 .02 .68 8 1 .16 .01 .41 .05 .03 .63 8 2 .16 .01 .41 .09 .03 .63 8 3 .16 .01 .41 .13 .03 .64 8 10 .15 .01 .41 .33 .03 .67 8 20 .14 .01 .41 .45 .02 .68 8 50 .13 .02 .41 .62 .02 .71 8 100 .12 .02 .41 .70 .01 .72 8 200 .12 .02 .41 .76 .01 .73 50 TABLE 7. —Continued Part 3, N5 = 3 1 1 .21 .06 .07 .05 .06 .55 1 2 .21 .06 .07 .09 .06 .56 1 3 .21 .06 .07 .13 .06 .56 1 10 .20 .07 .07 .33 .05 .60 1 20 .19 .07 .07 .45 .04 .62 1 50 .18 .07 .07 .61 .03 .64 1 100 .17 .07 .07 .70 .03 .65 1 200 .17 .07 .07 .75 .03 .66 2 1 .20 .05 .13 .05 .06 .57 2 2 .20 .05 .13 .09 .06 .57 2 3 .20 .05 .13 .13 .05 .58 2 10 .19 .06 .13 .33 .04 .61 2 20 .18 .06 .13 .45 .04 .63 2 50 .17 .06 .13 .61 .03 .65 2 100 .16 .06 .13 .70 .03 .67 2 200 .16 .06 .13 .76 .02 .67 3 1 .20 .04 .19 .05 .06 .58 3 2 .20 .04 .19 .09 .05 .59 3 3 .19 .04 .19 .13 .05 .59 3 10 .18 .05 .19 .33 .04 .62 3 20 .17 .05 .19 .45 .04 .64 3 50 .16 .05 .19 .61 .03 .66 3 100 .16 .05 .19 .70 .03 .68 3 200 .15 .05 .19 .76 .02 .68 8 1 .16 .00 .41 .05 .05 .63 8 2 .16 .01 .41 .09 .05 .63 8 3 .16 .01 .41 .13 .04 .64 8 10 .14 .01 .41 .33 .04 .67 8 20 .14 .01 .41 .45 .03 .68 8 50 .13 .02 .41 .61 .02 .71 8 100 .12 .02 .41 .70 .02 .72 8 200 .12 .02 .41 .76 .02 .73 51 TABLE 7. —Continued Part 4, N5 = 8 N3 N4 b1 b2 b3 b4 5 R 1 1 .21 .05 .07 .05 .12 .56 1 2 .21 .05 .07 .12 .11 .57 1 3 .20 .05 .07 .12 .11 .57 1 10 .19 .06 .07 .32 .09 .60 1 20 .19 .06 .07 .44 .08 .62 1 50 .18 .06 .07 .61 .07 .64 1 100 .17 .07 .07 .69 06 .65 1 200 .17 .07 .07 .75 .05 .66 2 1 .20 .04 .13 .05 .12 .57 2 2 .20 .04 .13 .09 .11 .58 2 3 .20 .04 .13 .12 .11 .58 2 10 .18 .05 .13 .32 .09 .61 2 20 .18 .05 .13 .44 .08 .63 2 50 .17 .06 .13 .61 .06 .65 2 100 .16 .06 .13 .69 .06 .67 2 200 .16 .06 .13 .75 .05 .67 3 1 .19 .03 .18 .05 .11 .58 3 2 .19 .03 .18 .09 .11 .59 3 3 .19 .04 .18 .12 .11 .59 3 10 .18 .04 .18 .32 .09 .63 3 20 .17 .04 .18 .44 .08 .64 3 50 .16 .05 .18 .61 .06 .67 3 100 .15 .05 .19 .69 .05 .68 3 200 .15 .05 .19 .75 .05 .68 8 1 .16 .00 .41 .05 .10 .63 8 2 .16 .00 .41 .09 .09 .64 8 3 .15 .00 .41 .12 .09 .64 8 10 .14 .01 .41 .33 .07 .67 8 20 .14 .01 .41 .44 .06 .68 8 50 .13 .01 .41 .61 .04 .71 8 100 .12 .01 .41 .70 .04 .72 8 200 .12 .02 .41 .75 .03 .73 52 TABLE 8. —Partial regression coefficients and multiple R's for all information except dams records Part 1, N5 = 1 Paternal Daughters Sisters b1 b3 b4 b5 R N3 N4 1 1 .23 .08 .05 .03 .53 1 2 .22 .08 .09 .03 .54 1 3 .22 .08 .12 .03 .55 1 10 .21 .08 .33 .03 .58 1 20 .20 .08 .44 .03 .60 1 50 .19 .08 .61 .02 .62 1 100 .19 .08 .69 .02 .64 1 200 .19 .08 .74 .02 .64 2 1 .21 .15 .05 .03 .55 2 2 .21 .15 .09 .03 .56 2 3 .21 .15 .12 .03 .57 2 10 .20 .15 .33 .03 .60 2 20 .19 .15 .44 .02 .62 2 50 .18 .15 .61 .02 .64 2 100 .17 .15 .69 .02 .65 2 200 .17 .15 .75 .02 .66 3 1 .20 .21 .05 .03 .57 3 2 .20 .21 .09 .03 .58 3 3 .20 .21 .13 .03 .58 3 10 .18 .21 .33 .02 .61 3 20 .18 .21 .44 .02 .63 3 50 .17 .21 .61 .02 .66 3 100 .16 .21 .69 .02 .67 3 200 .16 .21 .75 .02 .68 8 1 .16 .42 .05 .02 .62 8 2 .16 .42 .09 .02 .63 8 3 .16 .42 .13 .02 .64 8 10 .15 .42 .33 .01 .67 8 20 .14 .42 .45 .01 .68 8 50 .13 .43 .61 .01 .71 8 100 .12 .43 .70 .01 .72 8 200 .12 .43 .75 .01 .72 53 TABLE 8. —Continued Part 2, N5 = 2 N3 N4 b1 b3 b4 b5 R 1 1 .22 .08 .05 .06 54 1 2 .22 .08 .09 .06 .54 1 3 .22 .08 .12 .06 .55 1 10 .21 .08 .32 .05 .58 1 20 .20 .08 .44 .05 .60 1 so .19 .08 .60 .04 .63 1 100 .18 .08 .69 .04 .64 1 200 .18 .08 .74 .04 .65 2 1 .21 .15 .05 .05 .56 2 2 .21 .15 .09 .05 .56 2 3 .21 .15 .12 .05 .57 2 1o .19 .15 .33 .05 .60 2 20 .19 .15 .44 .04 .62 2 50 .18 .15 .60 .04 .64 2 100 .17 .15 .69 .04 .65 2 200 .17 .15 .74 .03 .66 3 1 .20 .20 .05 .05 .57 3 2 .20 .21 .09 .05 .58 3 3 .20 .21 .12 .05 .58 3 1o .18 .21 .83 .04 .62 3 20 .18 .21 .44 .04 .63 3 50 .17 .21 .61 .03 .66 3 100 .16 .21 .69 .03 .67 3 200 .16 .21 .74 .03 .68 8 1 .16 .42 .05 .04 .63 8 2 .16 .42 .09 .03 .63 8 3 .16 .42 .13 .03 .64 8 1o .15 .42 .33 .03 .67 8 20 .14 .42 .45 .02 .68 8 50 .13 .42 .61 .02 .71 8 100 .12 .43 .70 .02 .72 8 200 .12 .43 .75 .01 .72 54 TABLE 8. ~m Part 3, N5 = 3 1 1 .22 .08 .05 .08 .54 1 2 .22 .08 .09 .08 .55 1 3 .22 .08 .12 .08 .55 1 10 .20 .08 .32 .07 .58 1 20 .20 .08 .44 .07 .60 1 50 .19 .08 .60 .06 .63 1 100 .18 .08 .06 .06 .64 1 200 .18 .08 .74 .05 .65 2 1 .21 .14 .05 .08 .56 2 2 .21 .14 .09 .07 .56 2 3 .20 .14 .12 .07 .57 2 10 .19 .15 .32 .06 .60 2 20 .19 .15 .44 .06 .62 2 50 .18 .15 .60 .05 .64 2 100 .17 .15 .69 .05 .66 2 200 .17 .15 .74 .05 .66 3 1 .20 .20 .05 .07 .57 3 2 .20 .20 .09 .07 .58 3 3 .19 .20 .12 .07 .59 3 10 .18 .21 .32 .06 .62 3 20 .18 .21 .44 .05 .63 3 50 .17 .21 .60 .05 .66 3 100 .16 .21 .69 .04 .67 3 200 .16 .21 .74 .04 .68 8 l .16 .41 .05 .05 .63 8 2 .16 .41 .09 .05 .63 8 3 .16 .41 .12 .05 .64 8 10 .14 .42 .33 .04 .67 8 20 .14 .42 .45 .03 .68 8 50 .13 .42 .61 .03 .71 8 100 .12 .42 .70 .02 .72 8 200 .12 .42 .75 .02 .72 .I-b 55 TABLE 8. —C0ntinued Part 4, N5 = 8 N3 N4 b1 b3 b4 b5 11 1 1 .21 .07 .04 .16 .55 1 2 .21 .07 .08 .15 .55 1 3 .21 .07 .12 .15 .56 1 10 .20 .08 .31 .14 .59 1 20 .19 .08 .43 .13 .61 1 50 .18 .08 .59 .11 .63 1 100 .18 .08 .67 .11 .64 1 200 .18 .08 .72 .10 65 2 1 .20 .14 .04 .14 .56 2 2 .20 .14 .08 .14 .57 2 3 .20 .14 .12 .14 .58 2 10 .19 .14 .32 .12 .61 2 20 .18 .14 .43 .11 .62 2 50 .17 .14 .59 .10 .65 2 100 .17 .14 .68 .10 .66 2 200 .17 .14 .73 .09 .66 3 1 .19 .20 .04 .13 .58 3 2 .19 .20 .08 .13 .59 3 3 .19 .20 .12 .13 .59 3 10 .18 .20 .32 .11 .62 3 20 .17 .20 .43 .10 .64 3 50 .16 .20 .59 .09 .66 3 100 .16 .20 .68 .08 .67 3 200 .15 .20 .73 .08 .68 8 1 .16 .40 .05 .10 .63 8 2 .16 .41 .09 .09 .64 8 3 .15 .41 .12 .09 .64 8 10 .14 .41 .32 .07 .67 8 20 .14 .41 .44 .07 .68 8 50 .13 .42 .61 .05 .71 8 100 .12 .42 .69 .05 .72 8 200 .12 .42 .75 .04 .72 56 TABLE 9. —Multiple correlation coefficients using various combinat ions of information Information Available Paternal Sisters X4 Maternal Cow Dam Dau's. Sisters 0 1 2 3 10 20 50 100 200 x1 x2 x3 x5 1 .50 .50 .51 .52 .56 .57 .60 .61 62 1 1 .52 .53 .54 .54 .58 .60 63 .64 .65 1 1 .52 .53 .54 .54 .58 .60 .62 .63 .64 1 2 .54 .55 .56 .56 .60 .61 .64 .65 .66 1 3 .56 .57 .57 .58 .61 .63 .65 .67 .67 1 8 .62 .62 .63 .64 .67 .68 .71 .72 .72 1 1 .50 .51 .52 .52 .56 .58 .58 .59 .60 1 2 .51 .51 .52 .53 .56 .58 .61 .62 .63 1 3 .51 .52 .52 .53 .56 .58 .61 .62 .63 1 8 .52 .53 .53 .54 .57 .59 .61 .62 .63 1 1 1 .55 .55 .55 .56 .60 .61 .64 .65 .66 1 1 2 .55 .56 .57 .57 .61 .63 .65 .66 .67 1 1 3 .57 .57 .58 .59 .62 .64 .66 .68 .68 1 1 8 .62 .62 .63 .64 .67 .68 .71 .72 .72 1 1 1 .52 .53 .64 .55 .58 .60 .63 .64 .65 1 1 2 .53 .53 .54 .55 .58 .60 .63 .64 .65 1 1 3 .53 .54 .54 .55 .58 .60 .63 .64 .65 1 1 8 .53 .54 .55 .55 .59 .60 .63 .64 -.65 1 1 1 1 .54 .55 .56 .56 .60 .61 .64 .65 .66 1 1 2 1 .56 .56 .57 .58 .61 .63 .65 .67 .67 1 1 3 1 .57 .58 .58 .59 .62 .64 .66 .68 .68 1 1 8 1 .62 .62 .63 .64 .67 .68 .71 .72 .72 1 1 1 2 .54 .55 .56 .56 .60 .62 .64 .65 .66 1 1 2 2 .56 .56 .57 .58 .61 .63 .65 .67 .67 1 1 3 2 .57 .58 .58 .59 .62 .64 .66 .68 .68 1 1 8 2 .62 .63 .63 .64 .67 .68 .71 .72 .73 1' 1 1 3 .54 .55 .56 .56 .60 .62 .64 .65 .66 1 1 2 3 .56 .57 .57 .58 .61 .63 .65 .67 .67 1 1 3 3 .57 .58 .59 .59 .62 .64 .66 .68 .68 1 1 8 3 .62 .63 .63 .64 .67 .68 .71 .72 .73 1 1 1 8 .55 .56 .56 .57 .60 .62 .64 .65 .66 1 1 2 8 .56 .57 .58 .58 .61 .63 .65 .67 .67 1 1 3 8 .57 .58 .59 .59 .63 .64 .67 .68 .68 1 1 8 8 .62 .63 .64 .64 .67 .68 .71 .72 .73 57 The situation is quite different in the case of adding paternal sisters to the cow's record. The first three paternal sisters increase R the same amount as do eight maternal sisters; whereas, additional paternal sisters continue to raise R. The number of paternal sisters required to equal the information furnished by eight daughters is somewhere between 100 and 200; yet, this accuracy is closely approached when 50 paternal sisters are used. In the cases where a third source of information is added to that from records of the cow and dam, much the same situation exists as if no record of the dam was used. When the numbers involved in the third source of information are at all large, little change in R would occur if the dam's record were omitted. The limited value of the maternal sisters in increasing R is an obvious feature of Table 9. The highest increase in R that can be made by maximum use of the maternal sisters is 0. 02 units; yet, for most situations additional maternal sisters do not change R at all. Substantial increases in R can be obtained by the addition of paternal sisters. This appears to be true for all combinations except those cases where very large numbers of the other groups of relatives are used. Some justification could be made for deleting completely the dam and maternal sisters. However, the addition of a record from a dam or a maternal sister is most useful in situations where other information is limited. Such situations are common most of the time. 58 Table 10 lists a number of correlation coefficients applicable to heifers and young bulls. This table gives R values for several combinations of information which do not include the individual's own record or records on daughters. In such situations the dam's record alone provides only a fair indication of the individual's genotype as indicated by an R of 0.25 Neither maternal nor paternal sisters give a high R unless large numbers are used. However, when both maternal and paternal sisters are used in sufficient numbers, quite large R's can be obtained. Obtaining some information from both sides of the pedigree adds considerably to the accuracy of estimating an individual's genotype. However, the use of both dam and maternal sister information furnish little more accuracy than either source used alone. Records of paternal sisters can be more valuable than information from the female side of the pedigree because of the larger numbers of relatives possible and also because of the independence of the information due to less covariance among paternal sisters as compared to female relatives. The R values from Table 10 indicate that indexing a young sire, with only the information considered here, cannot become highly accurate in esti- mating his genotype. Such mediocre accuracy is a result of utilizing only three sources of information, two of which furnish little evidence. If 20 or more paternal sisters are available, most of the information from the sire's side of the pedigree is utilized. However, the dam's record and records of a few maternal sisters do not render nearly so much information 59 TABLE 10. —Accuracies (RIG 1) of information available for young animals Information Paternal sisters X4 Available D Maternal Sisters 0 1 2 3 10 20 50 100 200 X2 X5 1 - 25 28 30 32 .41 45 50 53 54 - 1 .12 .17 .21 .23 .34 .39 .45 .47 .49 - 2 .14 .20 .23 .26 .34 .40 .45 .48 .50 - 3 .18 .23 .25 .27 .37 .41 .46 .49 .50 - 8 .26 .29 .31 .32 .40 .43 .48 .50 .52 .26 .29 .31 .33 .41 .46 .51 .53 .54 .27 .30 .32 .34 .42 .46 .51 .53 .55 .28 .31 .33 .34 .42 .46 .51 .53 .55 .31 .33 .35 .36 .44 .47 .52 .54 .55 HHI—‘H (ECONH about the female side of the pedigree. The question then arises as to the possi- bility of including the other close relatives of the dam of the young sire. The value of information from the relatives of the son's dam (other than those which are already included in the son's index) will vary as the kind and amount of relatives change. Several sets of simultaneous equations were solved to evaluate the usefulness of information from the dam's other relatives. The R's, correlations between the young sire's index and his genotype, for various combinations of information on the cow (dam of the young sire) are listed in Table 11. The young son is considered to be sired by a sire unrelated to the dam and proven in A. I. by 50 daughters (paternal sisters to the young son). 60 Method A comes from Table 10 and represents the index on the son using nothing beyond the parents. Method B uses all the information included in Method A in addition to information on the maternal grandparents. The 50 paternal sisters of the young sire alone give an R of 0.44, and the addition of the record of his dam raises the accuracy to 0.50. Method B raises the accuracy to 0. 51, 0. 51, and 0. 52 if the dam has 10, 20, or 100 paternal sisters, respectively. If the son's dam and his 3 maternal sisters are used, both the methods use the same information and give an R of 0. 51. The addition of 100 paternal sisters of the son's dam increases the accuracy of Method B to only 0.52 However, the dam's dam and the dam's maternal sisters add no accuracy to estimating the son's geno— type if several of the dam's paternal sisters are available. The R's listed in Table 11 would be somewhat altered if the in- formation from the A. I. sire was not independent of the information on the female side of the pedigree. Inbreeding would tend to increase the R's due to the reduction of sampling variation caused by Mendelian segregation. On the other hand, the R's would be lowered by environmental similarities which increase the covariance among relatives in the individual's pedigree. From Table 11 the accuracy of estimating a young sire's genotype can be increased slightly by considering his dam's relatives which are not already included in his index. All of the increase in accuracy comes from his dam's paternal sisters. The maternal granddam and the dam's maternal 61 TABLE 11. —Accuracy of indexing a young sire Information on cow Daughters of Accuracy* (dam of young sire) A. I. sire (Rm) (paternal sisters X X2 X3 X4 X5 MethodA MethodB 1 of young sire) - - - - - 50 .44 .44 1 - - — - 50 .50 .50 1 - — 10 - 50 . 50 . 51 1 - - 20 - 50 .50 .51 1 — - 100 - 50 .50 . 52 1 - 3 - — 50 . 51 . 51 1 - 3 100 - 50 .51 .52 1 1 3 100 - 50 . 51 . 52 1 l 3 100 3 50 .51 .52 *Correlation of young sire's genotype with his index. Method A uses information on the young sire's dam and sibs. Method B uses information as in Method A plus maternal grandam and dam's sibs. sisters appear to be of no value in estimating the genotype of a young sire. In estimating the genotype of a young bull whose sire's and dam's genotypes are relatively well known, the dam's paternal sisters can be of some use, especially if several are available. 62 Evaluation of the Index on a Test Population The multiple correlation coefficient between the genotype of a cow and her index was considered not to be a completely adequate method of evaluating the index. A test of the practical usefulness in a population of cows was desired. A comparison of selection by index with mass selection on the cow's record was made. The test population was chosen on the same basis as the population used to derive the index (Phase II). The records from 145 herds were used in this analysis. The records were made during the same years as were those in Phase II, but none of the same herds were involved. The first lactation record (as a deviation from herd average) of an unselected daughter was used as the criterion for comparing selection of the cow by index with selection based on own phenotype. The test population was limited to cows that had an own record as well as at least one daughter with a record. This limitation reduced the test population to 429 cows and 498 daughters. In calculating the indexes of the cows, the particular daughter considered as the dependent variable was excluded to avoid in— jecting a part-whole relationship into the correlations. The relationships from the test population appear in Table 12. The test population was noticeably more variable than the population used to derive the index, but the heritability was nearly the same. However, the small numbers involved leave a wide margin for sampling variation. 63 TABLE 12. —Relationships between phenotype, index, and daughter of 498 cows in the test p0pulation Daughter Cow Index Y X I XY IY Average production (pounds deviation from herd average) 44 370 137 Variances and Covariances* 53, 297 58, 916 4, 568 7, 825 2, 582 Standard deviation (pounds deviation from herd average) 2, 309 2, 427 676 rXY = 0. 140 r IY _ rIY = 0. 166 r - 1. 19 XY bYX = 0. 133 Heritability = 0. 266 *Coded units of 100 pounds. The correlation of the cow's index with an unselected daughter's record was 0. 166 as compared to O. 140 for the correlation of the cow's own phenotype with her daughter's record. These correlations indicate that selection by index in this p0pulation would have been 19 per cent more effective than selection based on the cow's ownphenotype. An average or aggregate R for the test population was determined by using Fisher's Z transformation. This procedure consisted of (a) obtaining 64 an R value based on the number of each type of relatives available for each cow, (b) converting to Z by use of standard statistical tables, (0) averaging the Z values for the test p0pulation, and (d) converting back to R from the Z table. The resulting R value of 0.542 was an indication of the average amount of information used in deriving the indexes. Figure 3 shows the relationships involved in the test population. These relationships were the basis for comparing the calculated correlations with those that would be expected by theoretical inferences. / \ Gf- . 5 ~—-—) GY h /*,Y o 542 . 16% I = index of cow E = environment G1=genotype of cow Gy=genotype of daughter Y = daughter's phenotype h = Vheritability = . 516 X = cow's phenotype FIG. 3. —Genetic and phenotypic relationships in the test population The correlation of O. 166 between the cow's index and her daugh- ter's phenotype is higher than would be expected on the basis of the other relationships shown in Figure 3. Sampling variation in this small population seems to be the most likely cause of divergence between calculated and theoretical values. Other possibilities would include (a) underestimation 65 of heritability in the test p0pu1ation, the index p0pu1ation, or both; or (b) underestimating aggregate R by a different weighting of the individual R's. In the case of (a) a heritability of either 0. 378 in the test population or approximately 0.40 in the index population would be required singly to make the theoretical correlation between I and Y agree with the calculated value of 0. 166. A more plausible explanation would seem to be that heritability was underestimated to a lesser degree in both populations. In reference to (b) it seems probable that aggregate R would be underestimated by the use of large numbers of cows with low R's. That is, the most abundant groups of cows were those with the least amount of information, the most variable in genic values, and yet influence aggregate R the most. Regardless of the nature of the difference between actual and theoret- ical estimates, the 19 per cent advantage of index selection over mass se— lection appears to be sufficient evidence to justify a moderate amount of effort and expense to index cows, especially dams of sires, for selection. The increased accuracy of selection in the test p0pu1ation cannot, in itself, be taken as pr0portional to genetic gain in a practical situation. The amount of information available from relatives in a typical herd should be in close proximity to that of the test p0pu1ation. Although the test popu- lation should have more than average information available from relatives as a result of being a selected sample of older cows, this accuracy should be offset by the loss of one daughter per cow omitted from consideration as 66 the dependent variable. The amount of information which would normally be available on potential dams of sires may be considered considerably more than that of the test population. The influence of selection for other traits and any factor reducing the selection differential or increasing the generation interval would result in less genetic progress for milk production than that indicated in the test population. CHAPTER V APPLICATION OF RESULTS The index was developed to measure breeding values of cows and young animals and was not intended to substitute for or to replace current methods of evaluating sires with progeny information. The existing methods of evaluating sires have been developed to a high degree of refinement and accuracy. The index was developed for the purpose of increasing the accuracy of female selection within as well as between herds. The increase in accuracy of female selection by index over selection on own performance should be from 10 to 20 per cent depending on the amount of information available from relatives. The genetic gain which can be obtained directly by female selection with the use of the index appears to be real but not large. The greatest usefulness of the index appears to be in selecting the cows that will become the dams of future sires. The economic and bio- logical limitations which reduce both the number of bulls that a stud can test and the intensity with which tested bulls can be selected will result in genetic progress below the maximum possible. A. 1. units, however, have wide latitude in deciding which bulls will be tested, and this index offers an effective method of selecting cows to produce these sires. The most 67 68 promising and practical approach to genetic progress and breed improvement appears to be in producing numerous young bulls from well proven sires and out of intensely selected dams, testing as many of these as possible, and culling among these bulls as severely as feasible on the basis of information from progeny. Prediction equations applicable to heifers and young sires were among those deve10ped. The accuracy of these equations is generally low in com- parison to those which utilize the individuals's own record or records of daughters. In estimating the genotype of a young bull sired by a well proven sire, the dam's paternal sisters can be of limited use if several are avail- able; yet the dam's maternal sisters and the dam's dam are of no apparent value. The situation is to be expected since these relatives are of limited use in estimating the breeding value of the dam herself. Prediction equations could easily be deve10ped from the parameters available wherein young sires could be indexed using all the information included in the dam's index. Actually there seems to be little occasion to use such information. The weights for the various relatives would be nearly the same as would result from an average of the sire's index and the dam's index if there were a moderate amount of information available from both sire and dam. Although the index could be used to advantage by the breeder doing his own computations, the calculations required could become quite involved. Widespread use of the index would be expected to be in herds which obtain 69 periodical listings of individual cow records. A computer program to index routinely the cows in cooperator herds would seem to be a worthwhile enter— prise for universities or A. I. organizations concerned with young sire programs. Such a program could serve as a pilot project which could eventually be applied to all tested herds. This investigation was intended primarily to develop index weights which could be applied in dairy breeding programs to improve milk produc- tion. The index has furnished little evidence to answer fundamental questions on breeding theory. Many perennial questions have been raised anew during the course of this investigation. These questions include: 1. What are the major sources of environmental correlations between various related groups of cows? 2. What is the nature of the apparent difference in reliability of the different lactations of a cow? 3. Do different genes affect production in different lactations ? 4. How is milk yield related to longevity, fertility, and rate of maturity? 5. What genetic and management factors are responsible for herd by sire interactions? 6. Do deviated records have inherent biases or require special analytic procedures? Other questions whose answers will lead to more useful indexes and 70 sounder breeding practices would relate to: 1. 2. Curvilinear analysis of production data. Non-additive gene action affecting productive traits. Effects of various mating systems on productive traits. Genetic correlations among various traits. Applicability of age correction factors for genetic studies. CHAPTER VI SUMMARY Selection indexes for milk production in Holstein cattle using infor- mation from close relatives were developed and tested in various populations of cows recorded in Michigan DHIA. Records of lactations measured as deviations from the annual herd average were used to choose the appropriate measure of milk production to use in developing a selection index. Linear multiple regression equations were used to predict the. daughter's deviation in first lactation from herd average in using various records of the cow as independent variables. The simple correlations of the cow's first record with the first record of the daughter were 0. 149 for 904 Guernsey cows and their daughters, and 0. 256 for 1, 526 Holstein cows and their daughters. The correlations of the cow's later records were much smaller in both breeds. The partial regression coefficients indicated that nearly all of the emphasis among records of the cow should be placed on the cow's first record to predict the superiority or inferiority of the first record of the daughter. Multiple correlation co- efficients indicated that averages of either the first two or the first three records of the cow were poorer predictors of the daughter's first record than 71 72 was the cow's first record alone. Selection indexes to predict with maximum accuracy the general breeding value of individual Holsteins for milk production were developed using 7, 638 deviations of first lactations from herd averages in a variety of combinations of the cow, her dam, her daughters, and her half-sisters. The heritability used was 0. 246 which was derived from the regression of paternal sisters on the cow. Other estimates of heritability (with larger sampling variances) ranged from 0. 123, derived from intra —sire corre- lation, to 0. 436, derived from intra—dam correlation. The records of a cow's dam and maternal sisters only slightly increased the accuracy of estimating her genotype providing the cow had an own record. Daughters and paternal sisters added considerably to the ac- curacy of estimating her genotype. The multiple correlation of the index with the cow's genotype ranged from 0. 50 to 0. 73 depending on the kinds and amounts of information available from relatives. Multiple correlation coefficients for individuals without an own record or offspring (heifers and young bulls) varied from 0. 12 for one half- sister to 0.55 for my relatives. In estimating the genotype of a young bull that is sired by a well proven sire, the usefulness of information on the maternal grandparents is limited to the dam's paternal sisters if their numbers are sufficient. The maternal granddam and the dam's maternal sisters are of no apparent value. 73 Selection by index was compared with mass selection on the cow's own record in a test population of 429 Holstein cows and their 498 daughters. The first record of an unselected daughter was correlated with the cow's index and also with the cow's own first record. The resulting correlations of 0. 166 with the index and 0. 140 for the cow's record indicated an increase in accuracy near 19 per cent in favor of index selection. The index appeared to be a practical method to increase genetic progress for milk production especially to select potential dams of future sires. REFERENCES REFERENCES BARR, G. R. Selecting Young Dairy Bulls on Differences Between Relatives and Their Contemporaries. Ph. D. Thesis, Iowa State- University Library, Ames, Iowa. 1962. BERESKIN, B. and HAZEL, L. N. The Role of Herd Averages in Dairy Sire Evaluation. Unpublished Mimeograph. Iowa State University, Ames Iowa. 1962. BERRY, J. C. Reliability of Averages of Different Numbers of Lactation Records for Comparing Dairy Cows. J. Dairy Sci. , 28; 355. 1945. BERRY, J. C. and LUSH, J. L. High Records Contrasted with Unselected Records and with Average Records as a Basis for Selecting Cows. J. Dairy Sci. 22:607. .1939. BRUMBY, P. J. The Relationship of Inheritance and Environment to Herd Production. Ruakura Farmers' Conference Week, Hamilton, New Zealand. Proceedings: 188. 1959. FALCONER, D. S. Introduction to Quantative Genetics. The Ronald Press Co. , New York. 1960. FREEMAN, A. E. Genetic Relationships among the First Three Lactations of Holstein Cows. (Abstr'.)J. Dairy Sci. 43:876. 1960. GAALAAS, R. F. and PLOWMAN, R. W. Relationship between Longevity and Production in Holstein-Friesian Cattle. J. Dairy Sci. 46:27. 1963. HARVEY, W. R. and LUSH, J. L. Genetic Correlation between Type and Productionin Jersey Cattle. J. Dairy Sci. 35:199. 1952. HAZEL, L. N. The Genetic Basis for Constructing Selection Indexes. Genetics 28:476. 1943. HAZEL, L. N. and LUSH, J. L. The Efficiency of Three Methods of Se- lection. J. Heredity 33:393. 1942. 75 76 HENDERSON, C. R. and CARTER, H. W. Improvement of Progeny Tests by Adjusting for Herd, Year, and Season of Freshening. (Abstr. ) J. Dairy Sci. 40:638. 1957. HENDERSON, C. R. , CARTER, H. W. and GODFREY, J. T. Use of the Contemporary Herd Average in Appraising the Progeny Tests of Dairy Bulls. (Abstr.) J. Animal Sci. 13:959. 1954. HICKMAN, C. G. and HENDERSON, C. R. Components of the Relationship between Level of Production and Rate of Maturity in Dairy Cattle. J. Dairy Sci. 38:883. 1955. JOHANSSON, I. The First Lactation Yield as a Basis for Selection as Com— pared with the Second and Third Lactations. Proc. Brit. Soc. Animal Prod. :102. 1955. JOHANSSON, I. Genetic Aspects of Dairy Cattle Breeding. Univ. Illinois Press. Urbana, Ill. 1961. JOHANSSON, I. and HANSSON, A. Causes of Variation in Milk and Butter- fat Yield of Dairy Cows. Kungl. Lantb. Tidersk. 79, No. 6-1/2:1. 1940. JOHNSON, L. A. and CORLEY, E. L. Heritability and Repeatability of First, Second, Third and Fourth Records of Varying Duration in Brown Swiss Cattle. J. Dairy Sci. 44:535. 1961. LEGATES, J. E. and LUSH, J. L. A selection Index for Fat Production in Dairy Cattle Utilizing the Yields of the Cow and her Close Relatives. J. Dairy Sci. 37:744. 1954. LUSH, J. L. Family Merit and Individual Merit as a Basis for Selection. Part 1. Amer. Naturalist 81:362. 1947. LUSH, J. L. and STRAUS, F. S. The Heritability of Butterfat Production in Dairy Cattle. J. Dairy Sci. 25:975. 1942. McGILLIARD, L. D. Usefulness of the Herd Average in Estimating Breeding Values of Dairy Cattle. Ph. D. Thesis. Iowa State University Library, Ames, Iowa. 1952. McGILLIARD, L. D. Unpublished Data. Michigan State University. East Lansing, Michigan. 1962. 77 MILLER, R. H. and McGILLIARD, L. D. Relations between Weight at First Calving and Milk Production During the First Lactation. J . Dairy Sci. 42:1932. 1959. PARKER, R. J. The Relationship between First Lactation Production, Size, and Type and Subsequent Performance in Holstein-Friesian Cattle. M. S.A. Thesis. University of Toronto Library, T01 onto, Ontario. PIRCHNER, F. and LUSH, J. L. Genetic and Environmental Portions of the Variation among Herds in Butterfat Production. J. Dairy Sci. 42:115. 1959. PLUM, M. Causes of Differences in Butterfat Production of Cows in Iowa Cow Testing Associations. J. Dairy Sci. 18:811. 1935. PUTNAM. D. N. , BOWLING, G. A. and CONKLIN, C. T. The use of First. Records Versus Average of All Records in Dam—Daughter Com- parisons when Proving Sires. J. Dairy Sci. 26:967. 1943. RENDEL, J. M. , ROBERTSON, A. , ASKER, A. A., KHISHIN, S. S. and RAGAB, M. T. The Inheritance of Milk Production Characteristics. J. Agric. Sci. 48:426. 1956. RENNIE, J. C. and BREMNER, J. Relationship of Levels of Production between First Lactation Records and Subsequent Records Made by Jersey Cattle in Canada. Paper presented at the Fourth International Conference of the World Jersey Cattle Bureau, Cambridge, England. 1961.. ROBERTSON, A. and KHISHIN, S. S. The Effect of Selection for Heifer Yield on the Production Level of Mature Cows. J. Agric. Sci. 50:12. 1958. ROBERTSON, A. and McARTHUR, A. T. G. Genetic Differences between Bull Breeding Herds. Proc. Brit. Soc. Animal Prod. 94. 1955. ROBERTSON, A. and RENDEL, J. M. The Performance of Heifers Got by Artificial Insemination. J. Agric. Sci. 44:184. 1954. SPECHT, L. W. Rates of Improvement by Progeny Testing in Herds of Various Sizes. Ph. D. Thesis. Michigan State University Library, East Lansing, Michigan. 78 SKJERVOLD, H. and ODEGARD, A. K. Estimation of Breeding Value on the Basis of the Individual's Own Phenotype and Ancestor’s Merits. Acta Agric. Scand. 9:341. 1959. TABLER, K. A. and TOUCHBERRY, R. W. Selection Indices Based on Milk and Fat Yield, Fat Per Cent, and Type Classification. J. Dairy Sci. 38: 1155. 1955. TABLER, K. A. and TOUCHBERRY, R. W. Selection Indices for Milk and Fat Yield of Holstein-Friesian Dairy Cattle. J. Dairy Sci. 42:123. 1959. TUCKER, W. L. and LEGATES, J. E. Effective Use of Herdmates in Dairy Sire Evaluation. Paper presented at the Fifty-Fourth Annual Meet- ing of the Amer. Soc. Animal Prod. Chicago, Illinois. 1962. VANVLECK, L. D., O'BLENESS, G. W. and HENDERSON, C. R. Compari- son of Procedures Used for Evaluating Sires Used in Artificial Insemination. J. Dairy Sci. 44:708. 1961. VANVLECK, L. D. , HEIDHUES, T. and HENDERSON, C. R. Analysis of Deviations of Dairy Records from Different Contemporary Averages. J. Dairy Sci. 44:269. 1961. .5"