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Most photographs reproduce acceptably on positive microfilm or microfiche but lack the clarity on xerographic copies made from the microfilm. For an additional charge, 35mm slides of 6"x 9” black and white photographic prints are available for any photographs or illustrations that cannot be reproduced satisfactorily by xerography. 8700439 B a n k s , B o b b y D e n n is ESTIMATION OF GENETIC PARAMETERS AND SIRE RANKINGS FOR HOLSTEIN LINEAR TYPE SCO RES AND MILK PRODUCTION BY MULTIPLE TRAIT ANALYSIS Michigan S tate University University Microfilms International 300 N. Zeeb Road, Ann Arbor, Ml 48106 Ph.D. 1986 PLEASE NOTE: In all c a s e s th is m aterial h a s b een filmed in th e b est possible w ay from th e available copy. Problem s e n c o u n te re d with this d o c u m e n t have been identified here with a c h e c k mark -J . 1. Glossy p h o to g ra p h s or p a g e s ______ 2. Colored illustrations, p a p e r o r p rin t_______ 3. P h o tographs with d a rk b a c k g ro u n d _____ 4. Illustrations a re p o o r c o p y _______ 5. P a g e s with black m arks, not original c o p y _______ 6. Print show s th ro u g h a s th ere is tex t on both sides of p a g e _______ 7. Indistinct, broken o r small print on several pages 8. Print e x c e e d s m argin re q u ire m e n ts______ 9. Tightly bound c o p y with print lost in s p in e ________ 10. f C om puter printout p a g e s with indistinct prin t_______ 11. P a g e (s )_____________ lacking w hen m aterial received, a n d not available from school o r author. 12. P a g e (s )_____________ seem to b e m issing in num bering only a s text follows. 13. Two p a g e s n u m be r e d ________. Text foil ows. 14. Curling and w rinkled p a g e s ______ 15. D issertation c o n ta in s p a g e s w ith print at a slant, filmed a s received 16. i f O ther______________________________________________________________________________ University Microfilms International ESTIMATION OF GENETIC PARAMETERS AND SIRE RANKINGS FOR HOLSTEIN LINEAR TYPE SCORES AND MILK PRODUCTION BY MULTIPLE TRAIT ANALYSIS By Bobby Dennis Banks A DISSERTATION Submitted to Michigan State University In partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Animal Science 1986 ABSTRACT ESTIMATION OF GENETIC PARAMETERS AND SIRE RANKINGS FOR HOLSTEIN LINEAR TYPE SCORES AND MILK PRODUCTION BY MULTIPLE TRAIT ANALYSIS By Bobby Dennis Banks Linear scores of 15 primary type traits on Holstein cattle in Michigan and Wisconsin were analyzed by a mixed model containing fixed effects of herd, group of sires and a random sire effect. The intra-herd heritability estimates using sire and residual variance components for the t^rpe traits ranged from .10 to .39. The phenotypic correlations between the type traits were all positive and generally large, while genetic correlations were gener­ ally smaller than the corresponding phenotypic correlations. These correlation estimates suggest a strong positive environmental corre­ lation exists among type traits. The same single trait mixed model and a multiple trait mixed model containing the same factors were then used to examine the relationships between milk and type. The differences between the estimates obtained by the single trait method and those by the multiple trait method were examined In order to ascertain if selec­ tion would introduce significant bias in the estimates of genetic parameters involving linear type data. Five data sets of 150 sires each were independently sampled at random from a data set containing 475,855 daughter records from i 1,495 sires. Each sire had at least one daughter measured for both milk and type traits, and 20 daughters in 10 herds. transformation algorithm was implemented in the A triangular expectation maximi- Bobby Dennis Banks zatlon of restricted maximum likelihood estimation procedure to estimate genetic parameters and sire rankings from each data set. Over the data sets, mean and sampling variances for each parameter were computed. Heritability estimates of type traits from the multiple trait analysis ranged between .05 and .38. Genetic correlations were negative between milk and linear type traits except those involving angularity, rump angle, rear leg side view and foot angle. Phenoty­ pic correlations were positive except between milk and strength, foot angle, fore udder attachment or udder depth. Standard devia­ tions for genetic correlations exceeded mean estimates in most cases, while those for heritabilities and phenotypic correlations were consistently smaller than mean estimates. Sire rankings and estimates of heritability between single and multiple trait methods did not differ greatly. Acknowledgments The author wishes to thank Dr. Ivan Mao for his advice and for allowing me to pursue a graduate degree at Michigan State Univer­ sity. I wish to express my appreciation to the members of my Ph.D. guidance committee, Dr. W. T. Magee, Dr. T. A. Ferris and Dr. J. R. Black for their support and suggestions. Special thanks are extended to the other faculty members of the Department of Animal Science who gave me encouragement and support during my studies at Michigan State University. In addition, I would like to thank Dr. J. P. Walter for his friendship and techni­ cal support provided me during the course of my studies. Finally, I wish to express my deepest thanks to ray wife, Donna, and daughters, Cynthia and Elizabeth, for their encouragement and for giving me the impetus to complete the graduate degree. ii Table of Contents Page List of Tables . ....................... vi I .Introduction ............................................. 1 II. 3 Literature Review, .................................. 11.1 Body conformation systems . . . . . . . . ......... 3 11.2 Environmental effects on body conformation .. ... 4 II. 2.1 H e r d ......................................... 4 11.2.2 Y e a r ......................................... 5 11.2.3 Herd by year interaction..................... 5 11.2.4 Age at classification......... 6 11.2.5 Parity ....................................... 7 11.2.6 Stage of lactation ........................... 8 11.2.7 Age by stage of l a c t a t i o n ............. 9 11.2.8 Season of classification ..................... 9 11.2.9 Classifier 11.2.10 11.3 ....................... Interactions involving classifiers 10 .......... 11 Phenotypic and genetic parameters ................. 12 11.3.1 Heritability estimators ..................... 12 11.3.2 Genetic correlation estimators ............... 14 11.3.3 Phenotypic correlation estimators 14 11.4 ........... Genetic parameters of body conformation type .... IS 11.4.1 Descriptively scored type traits ............. 15 11.4.2 Linearly scored type traits 21 11.5 11.6 ................. Phenotypic and genetic correlations between type t r a i t s .................................. Sire evaluation........................ iii 27 36 Page 11.7 Maximum likelihood and restricted maximum likelihood estimators of variance and covariancecomponents . . 39 11.8 Multiple 40 III. trait analysis . . . . . . 11.8.1 Selection b i a s ............................... 41 11.8.2 Sire evaluation and variance and covariance estimation................................... 45 Materials and M e t h o d s ............................... 49 111.1 Genetic parameters of linear type traits .......... III. 1.1 D a t a ...................................... 49 111.1.2 A priori adjustments 111.1.3 Modal ....................................... 54 111.1.4 Absorption of herds ......................... 56 111.1.5 Variance component estimation ................ 59 111.1.6 Heritability'and genetic and phenotypic correlations ............................... 61 111.2 ........................ 49 51 Genetic parameters of milk production and linear scored type t r a i t s ....................... 62 111.2.1 D a t a ....................................... 111.2.1.1 Linear type data 111.2.1.2 Milk production data .......... 111.2.1.3 Mergdr of milk production and linear type d a t a ............... 111.2.1.4 111.2.2 Sampling procedures ...................... .. ... ................ A priori adjustments and assumptions 63 63 63 64 . . 64 ........ 68 111.2.2.1 Single trait model . . . ................ 68 111.2.2.2 Multiple trait model .................... 70 111.2.2.2.1 Triangular transformation of MTMME. . 77 111.2.2.2.2 Absorption of herds . . . . ........ 80 111.2.2.2.3 Variance component estimation . . . . 81 iv Page 111.2.3 111.2.4 IV. Heritabilities and genetic and phenotypic correlations ............................... Comparison of sire BLUPS from single and multiple trait a n a l y s i s ............................. 89 Results and Discussion IV.1 ................... Heritability and genetic and phenotypic correlations of linear scoredtype traits ................... 90 Heritability estimates ....................... 90 IV.1.2 Phenotypic correlations ..................... 92 IV.1.3 Genetic correlations . . . .. .................. 94 IV.1.4 Environmental correlations .............. . . . 97 Heritability and genetic and phenotypic correlations of milk production and linearly scoredtype traits . . . 98 IV.2.1 Single trait MME methods ..................... IV. 2.1.1 H e r i t a b i l i t y ............. IV.2.2 Multiple t r a i t ............ .. ............... 99 99 99 IV.2.2.1 Heritability ........................... 99 IV.2.2.2 Phenotypic correlations ................. 119 IV.2,2.3 Genetic correlations ................... 121 Correlations of sire solutionsfrom single and multiple trait methodology. . . ............... 123 IV.2.3 VI. 90 IV.1.1 IV,2 V. 87 Summary and C o n c l u s i o n s ..................................129 A p p e n d i c e s ............... VI.A The Holstein Association linear classification program ......................................... VII. Literature C i t e d ........... v 134 134 144 List: of Tables PaKe Phenotypic and genetic correlations of descriptively scored type t r a i t s ............................. . 2 17 Heritability, phenotypic and genetic correlations among descriptively scored type traits ............ t Heritabilities of linearly scored type traits . . . . 20 Heritability estimates of linear type traits from Midwest Breeders' mating appraisal program ........ 22 Phenotypic and genetic correlations for Midwest Breeders linear conformation appraisalprogram . . . 23 6 Heritabilities of type traits scoredlinearly . . . . 25 7 Phenotypic and genetic correlations among type traits scored linearly ........................... 26 3 4 5 8 9 Heritability, genetic and phenotypic correlations for body measurements and milkproduction........ 18 27 Heritability estimates of type and production t r a i t s ..................... 29 10 Phenotypic and genetic correlations between type rating and milk yield stratified into (L)low; <11,960, (M)edium:11,960-13,230 and (H)igh:>13,230 lbs. milk production groups ........................... 31 11 Phenotypic correlations between type traits and predicted difference (PD) m i l k ............. 33 Phenotypic correlations between milk production and type t r a i t s ........................ .............. 34 12 13 Genetic correlations between milk production and type t r a i t s ........................................ 35 14 Genetic correlations between type and m i l k ........ 37 15 Comparison of genetic correlations for traits 1 and 2 computed from single trait (ST), multiple traits with with residual covariance assumed zero (MT-0), and multiple trait (MT) restricted maximum likelihood a p p r o a c h e s ............................... 43 vi Table 16 17 Page Comparison of residual correlations for trait 2 computed from single trait (ST) and multiple trait (MT) restricted maximum likelihood approaches ........... 44 Percentage reduction of variances of prediction error variance for a multiple trait analysis versus single trait analysis . . . . . . . . . . . . . .......... 46 Average percentage increase of variances of prediction error for various absolute differences of estimated correlations from true correlations ................ 48 19 Primary and secondary linear type t r a i t s ........... 50 20 Crude averages, ranges and standard deviations from the original linear type d a t a ..................... 52 Data editing criteria and number of records deleted from linearly scored type d a t a ................... 53 Data editing criteria and number of records deleted from milk production d a t a ......................... 65 Distribution of sires by number of daughters and h e r d s ............................................. 66 24 Descriptions of sampled data s e t s .................. 67 25 Heritability values and variance ratios used as initial values in the single trait analyses of milk production and linear scored type t r aits........... 71 Estimates sire and error variance components and heritability values for primary linear type scores ........... 91 Phenotypic correlations among the fifteen linear type t r aits....................................... 93 Genetic correlations among the fifteen linear type t r a i t s ........................................... 95 18 21 22 23 26 27 28 29 Estimated sire variance components of milk and linear type traits obtained through single trait methodology......................................... 100 30 Estimated error variance components of milk and linear type traits obtained through single trait methodology......................................... 101 31 Estimated heritabilities for milk and linear type traits obtained through single trait methodology .......... 102 vii . p, aae 32 33 34 Estimated genetic parameters between milk and stature....................................... 104 Estimated genetic parameters between milk and s t r e n g t h ......................... 105 Estimated genetic parameters between milk and body depth ........... 106 35 Estimated genetic parameters between milk and a n g u l a r i t y ......................................... 107 36 Estimated genetic parameters between milk and rump angle ............. 108 37 Estimated genetic parameters between milk and rump l e n g t h ............................................. 109 38 Estimated genetic parameters between milk and rump width ............................................. 110 39 Estimated genetic parameters between milk and rear leg side view . . . 1.................................. . Ill 40 Estimated genetic parameters between milk and foot a n g l e ..................................... 112 41 Estimated genetic parameters between milk and fore udder attachment . ........... 113 42 Estimated genetic parameters between milk and rear udder h e i g h t ....................... 114 43 Estimated genetic parameters between milk and rear udder w i d t h ............................................... 115 44 Estimated genetic parameters between milk and udder support............. .. ........................... 116 45 Estimated genetic parameters between milk and udder d e p t h ............................................... 117 46 Estimated genetic parameters between milk and teat placement rear v i e w ..................................118 47 Rank correlations between sire solutions for single and multiple trait analysis ........................... 125 48 Product moment correlations between sire solutions for single and multipletrait analysis . . . . ......... 126 49 Standard deviation of sire estimates for type traits analyzed by single and multiple trait methodology , . viii 128 Table Page A.B1 Description of the linear typed a t a .................... 135 A.B2 Distribution of cows by p a r i t y .......................136 A.Cl Lactation number distribution ...................... A.C2 Distribution of month of last c a l f .................. 138 A.D1 Distribution of sires by number of daughters and herds: data set 1.. ........................................ 139 A.D2 Distribution of sires by number of daughters and herds: data set 2 ................................... 140 A.D3 Distribution of sires by number of daughters and herds: data set 3 ..........................................141 A.D4 Distribution of sires by number of daughters and herds: data set 4 ..........................................142 A.D5 Distribution of sires by number data set 5 ............... ix 137 of daughters and herds: 143 I. Introduction The primary goal of dairy cattle breeding is to develop more profitable cows. The selection for increased milk yield has been the major means of attaining this goal. However, other traits, such as type have been recognized as a factor affecting profitability. Sound functional type traits may extend a cow's productive life. Type traits are jointly selected with other traits. These selection pressures have been accomplished by either voluntary or involuntary culling. The voluntary selection is the result of mating systems such as independent culling levels or tandem selec­ tion. Other criteria used for selection of type characteristics have been based on a mixture of common sense, physical attributes, beliefs and rumors. Theoretically, the best approach is the use of a selection index which pools different traits by genetic parameters and desired relative weights. However, many such applications were done in a manner which pools the breeding values of different traits estimated by different procedures (e.g. Total Performance Index, HolsteinFriesian Association of America, 1985). The accuracy and precision of such indices are questionable due to the lack of knowledge of the statistical properties of some of the procedures. The ultimate solution is to use the best linear unbiased prediction (BLUP) proce­ dure and mixed model methodology. The genetic parameters of type traits have been estimated for various populations numerous times. However, only a fraction of the total milk recorded population is measured for type. 1 This popula- 2 cion may noc represent a random sample of the total population. The implementation of the new linear scoring system may additionally restrict the subpopulation of cows with recorded type scores while it is becoming established as a scoring procedure. If the subpopulation of individuals scored for type is a nonrandom sample, the estimated genetic parameters and ranking of sires may be inaccurate for the total population. A recently developed statistical procedure, multiple trait analysis, can remove such possible inaccuracies by jointly analyzing type traits and milk production. The type data is from a selected subpopulation and the more abundant production data is more repre­ sentative of the entire population. The objectives of this study are: 1) Estimate the heritabilities for the new type traits, and the phenotypic and genetic correlations between type and production, for the entire population in which selection for both type and milk production are of interest; 2) For the same population, rank the breeding values of Holstein bulls for type traits; 3} Establish the differences, if any, in the genetic parameters and bull ranking between the subpopulation which provides the linear type scores and the total population. II. Literature Review II.1 Body conformation systems Systems to evaluate the body conformation of dairy cattle have evolved from the assignment of a single score of the cow to a complex system that consists of a final score of the cow, and the scorecard divisions for general appearance, dairy character, body capacity and mammary systems. The Holstein-Friesian Association of America (HFAA) introduced the classification of body conformation traits to the United States in 1929 (White, 1974). The early systems compared the cow's body conformation to that of the prototype of the breed. This system did not allow for specific identification of strengths or weaknesses of the individual. Another undesirable property of the descriptive system was that the traits were scored from one to six and did not lend themselves to statistical methods assuming a continuous scale of measurement. The scoring from one to six also reduced the potential measurable variation within a body conformation trait. The HFAA implemented a linear system of scoring type traits on January of 1983. This new system allowed classifiers to separate many biological traits that were included in the scorecard divi­ sions. The scoring system consists of 29 linear type traits each scored on a scale of one to 50, The wide range of scores produced more biologically meaningful scores and are more desirable for statistical methods. Fifteen of the linear type traits have been designated as primary traits. They are considered by the HFAA to be important 3 4 economically. The other 14 traits are secondary traits. The secon­ dary traits have been included to gather additional information for research and development. The new system also includes the traditional scorecard traits of general appearance, dairy character, body and mammary and the final score of the cow. The linear scoring system adopted by HFAA should provide the information necessary to estimate the genetic parameters and breeding values of animals in many different biological areas. The retention of the traditional scorecard traits and final score pro­ vide comparison to the prototype of the breed and provide an excel­ lent merchandising tool for the purebred breeder. The Holstein Association Linear Classification Program is in­ cluded in Appendix A. II.2 Environmental effects on body conformation traits II. 2.1 Herd Legates (1971) estimated the variance component of herd effect on 130,000 Holstein cows for final score and the four scorecard traits (general appearance, dairy character, body capacity and mam­ mary system). As percentages of the total variation, they varied from 13% to 25%. data. These results are based on discretely measured The results will be assumed to come from discrete data if not indicated as linear. Carter at al. (1965) used Canadian Holsteins and reported herd effect to account for 8% of the total variation in final score. Norman and Van Vleck (1972b) estimated the variance components of the herd effect for body, udder and management traits. The 5 estimates were all less than 25% of the total variation. The portion of total variation accounted for by the herd effect ranged from 14% for final score to 1% for udder support in a study by Vinson et al. (1976). These were data collected on 78,151 Hol­ stein cows distributed across 2,117 herds. Thompson et al. (1983) reported a significant herd-classifier subclass effect when investigating sources of variation of 11,240 appraisals of Holsteins scored linearly (50 point scale). Norman et al. (1983a) analyzed data collected on Ayrshires, Guernseys, Jerseys and Milking Shorthorns. linearly from 50 to 99. from 2% to 23%. These cattle were scored Herd variances by trait and breed ranged Herd effects were largest for stature and rear udder width of Ayrshires and udder depth in Milking Shorthorn. 11.2.2 Year Norman et al. (1978) reported that the effects of year ac­ counted for only 1% to 4% of the total variation. collected on Jerseys from 1968 through 1976. These data were The model contained the additional effects of herd and herd by year interaction. Norman and Van Vleck (1972b) analyzed 16,000 appraisals that were performed every two years from 1961 to 1968 through the New York type apprai­ sal program. They found the variance components for year almost nonexistent as they ranged from 2% to 3% for udder halving and mastitis, respectively. 11.2.3 Herd by year interaction Norman et al. (1983b) reported that the herd by year interac­ tion effect explained a high of 23% of the total variation in final 6 score to a low of only 9% in suspensory ligament. Horeno et al. <1979) observed the fraction of variance due to herd-year subclass to range from 8% for mammary system to 17% for body capacity. These proportions were generally below 10% for the descriptive traits. However, these data were not adjusted for stage nor age at classifi­ cation effects. Hay et al. (1983) found that the effect of the herd-year sub­ class needed to be removed when estimating the components of genetic variation for descriptive type traits in Holsteins, Norman et al. (1979) followed the same strategy in a sire evaluation model de­ veloped for Jersey type data. Norman et al. (1978) observed that herd-year subclass effects accounted for 21% of the variation in final score and 14% to 18% in the component traits. Herd-year explained a substantial amount of variation abovethat explained by years or herds. They postulated that this could have indicated a change in type confo mation within herds over time or could have been caused by classifiers. II.2.4 Age at classification Hyatt and Tyler (1948) remarked that as cows advanced in age there was a tendency for the inspectors to raise their ratings. On a scale of one to five, with five preferred, the average score increased from 2.27 for a 2-year-old to 4.06 for an eleven-year-old. They commented that this factor was not all age effect as selection had to be considered in the interpretation of the results. later analyzed multiple classifications within the same cow. They Re­ sults indicated the change in type rating due to age was not large but was significant in the case of 30 animals classified as four and 7 five-year-olds. Hansen et al. (1969) found age at classification to be a signi­ ficant source of variation among classification scores of Holstein cows, in final score as well as for the four major descriptive categories. Norman and Van Vleck (1972a) showed age differences were large for about one-third of 35 traits studied, especially for mastitis, body weight and depth of udder. Older cows tended to be coded as longer in the rear udder, weaker in the fore and rear attachments and deeper in the udder than younger cows. The linear effect of age accounted for 93% to 100% of age sum of squares. Cassell et al. (1973b) concluded age to be a significant effect for all traits in the analysis of 336,253 Holstein records scored for final score, five descriptive traits as well as twelve scorecard traits. Multiplicative age adjustment factors for final score and five descriptively scored traits were developed. A significant age effect was reported for all traits by Norman et al. (1978). They concluded the greatest effect was on body capacity and dairy charac­ ter, changing the multiple correlation coefficient squared by 10.1% } and 7.6%, respectively. Mammary score and feet and legs were least affected by age. Thompson et al. (1983), in evaluating scores on 19,152 Holstein cows under the Mating Appraisal for Profit (M A P) program, found age to be significant (PC.01) for all traits except rear legs and heel depth. II.2.5 Parity Thompson et al. (1980) showed parity to affect all traits with the exception of basic form and legs (P<.05). Constants for the 8 four udder traits, legs and feet were negative for first and second parities and positive for fourth and fifth plus parities. Since a score of one was superior, they suggested a deterioration of these traits as a cow aged. All other traits had a positive constant for first and negative for fifth parities. Barton et al. (1982) found similar results as they stated that in general, younger cows had lower scores for most traits. However, udder depth and foot shape had higher scores for younger cows. Hayes et al. (1985), using the same data base as this study, reported a parity by age(interaction. First and second parity interactions were evident in form and rump traits and in teat place­ ment. 11.2.6 Stage of lactation Differences in type scores due to stage of lactation effects were highly significant (F<.01) for final score and the four type components in a study by Hansen et al. (1969). The first and seventh months of lactation were significantly different from the average of other months. Cows averaged .82 points above the mean in the first month and .42 points below in the seventh month. Dairy character scores improved until the third month of lactation while body capacity showed the reverse trend. Mammary system scored lowest at the seventh month and lower than any other type trait. Norman and Van Vleck (1972a) observed small differences were accounted for by stage of lactation among 44 type traits. Norman et al. (1978) concluded that stage of lactation had little effect on type traits except on body capacity and dairy character. The effect of stage of lactation was nonsignificant for feet, and accounted for 9 only 1.7% and 1.6% of the variability in dairy character and chest and barrel, respectively. Thompson et al. (1980) found all traits except frame were affected by a quadratic term of days milked and all traits by the linear term of days milked. A significant stage of lactation effect was reported by Thompson et al. (1983). They reported that the traits that might be most affected by body weight (strength, dairy character) or edema and udder condition (fore udder attachment, udder depth) were most affected by stage of lactation. Rear leg side view was least affected by stage of lactation. 11.2.7 Age by stage of lactation Hansen et al. (1969) reported the interaction of age by stage of lactation was significant (PC.01) only for dairy character. At older ages the effect of stage was to lower the score for dairy character more drastically than younger cows. Norman and Van Vleck (1972a) found the interaction between age and stage of lactation to be relatively small. They concluded that such interaction could be ignored if corrections were made for age and stage separately, Norman et al. (1978) showed a nonsignificant interaction for all but four traits studied. The inclusion of the interaction term in the model explained only .2% to .5% additional variation. 11.2.8 Season of classification Mao et al. (1977) noticed an increase in Guernsey type scores for cows classified during the month of August and February. They hypothesized the August increase was due to a preparation of cattle 10 for showing. Carter et al. (1965) used Canadian Holsteins and reported month of classification to have a small effect on final type score. Walter and Mao (1983) reported many type traits of Guernseys appeared to exhibit seasonal trends, but no consistent pattern was apparent across traits. Norman et al. (1983b) suggested the month of classification was a trivial source of environmental variation. Their month constants also showed August to have the greatest effect while November had the smallest constant. The dif­ ference between the August and November constants was only 1.5. They noted the sire evaluation within herd-year was invariant to the effect of season regardless of the size of constants. Bensen et al. (1951) concluded season to be insignificant in its effect upon classification scores of Ayrshire cows. Wilcox et al. (1958) observed type scores were lower for cows scored in the fall in comparison to those scored in the spring. Traits most affected were feet and legs, body capacity and rear udder. However, they offered no reason for the origins of these differences. II.2.9 Classifier Tyler and Hyatt (1948) found a significant (PC.01) component of variance for classifiers when they studied the scoring of 3,738 Ayr­ shire cows by 10 classifiers. McGilliard and Lush (1956) found the differences between judges were negligible. They further commented that In all kinds of subjective measurements the knowledge of the range may unconsciously cause the observer to offset high ratings with low ones. The difference in judges' scores was moderately affected by years. They suggested a change in the appearance of the animal may be an environmental effect of the animal or a different 11 intangible optimistic or pessimistic frame of mind possessed by the judge that day. However, a more precise measure was obtained for old cows than for younger and judges agreed more closely with each other on the same date than with themselves on different dates. Vinson et al. (1976) reported differences in the emphasis placed on specific descriptive traits in arriving at final score. Classifiers tended to disagree more on less specifically and clearly defined traits (e.g. udder quality, feet and front end) than on more clearly defined attributes (e.g. stature, back, rump and udder support). However, the percent of variance due to classifier was small for all traits (0.7% to 5.0%). Thompson et al. (1980) observed that differences between eval­ uators among all traits were small. Norman et al. (1983b) observed, however, a significant classifier effect across all traits. Final score, general appearance and mammary system were most affected by classifier differences which explained 18.6%, 17.8% and 16.9% of the total variation, respectively. II.2.10 Interactions involving classifier McGilliard and Lush (1956) observed a cow by judge interaction, which could be a measure of disagreement among judges concerning the ideal they have established. prioritize traits differently. This is to say that classifiers may However, this interaction effect ex­ plained only 3% to 11% of the total variation. The effect of a cow by year interaction on the scores accounted for 12% to 31% of the total variation. They stated that this factor may have been partly due to a stage of lactation effect unaccounted for in the model. This study indicated nonsignificant judge by year interaction. 12 Thompson at al. (1983) reported a significant classifier by age effect for all traits except for final score and stature. A model including classifier, herd within classifier, age at classification, the interaction of classifier by age and stage of lactation was used to partition the total sum of squares. Two classifiers were found to be the greatest contributors to this interaction. They were also the two who had the least experience. Vinson et al. (1976) found herd by classifier interaction effect to be of more importance than classifier effect for all traits, and more important than herd effect for all descriptive traits. However, only 16% of the subclasses were filled and the effects of stage of lactation, herd by year and classifier by year were not included in the model. The effect of evaluator was re­ ported by Thompson et al. (1980) to interact with the parity effect in the study of 42,539 cows involved in the Mating Appraisal Pro­ gram. XI.3 Phenotypic and genetic parameters The literature review of milk and type traits has covered not only a large number of traits but also many different models and estimators of parameters. No estimator clearly surfaces as the most desirable for all data collection schemes. Therefore, some time should be spent reviewing these estimators. * IX.3.1 Heritability estimators Lush (1940) defined heritability in the narrow sense as the proportion of the total variance in a trait that is attributable to the average or additive effects of genes. Shelby et al. (1963) 13 noted the phenotypic and genetic relationships existing between and within various traits used as criteria for selection must be known to maximize the rate of progress in selection programs. Dickerson (1958) discussed the advantages and disadvantages of various estimates of heritability. He suggested the regression of offspring on midparent is the most nearly unbiased estimate of heritability. This estimate is, however, subject to bias from environmental correlations between parent and offspring by selection of parents. Other estimates included double regression of offspring on dam and twice the regression of offspring on sire. The prior tends to overestimate heritability while the latter produces an underestimation. Three additional methods were presented by Dicker­ son: 1) from the sire component, 2) from the dam component and 3) from the full-sib correlation. The estimate from the sire component or the paternal half-sib correlation lends itself more readily to sire evaluation models and the data collection scheme currently intact in today's dairy cattle populations. Heritability estimates from the sire component may be obtained as follows: AO h - estimated heritability; where A 2 os “ estimated sire variance component; and A ae o - estimated error variance component. The denominator is the phenotypic variance adjusted per se for fixed effects which were included in the model. Two sources of bias 14 are Inherent: Co this estimator: 1) epistatic bias (Dickerson, 1969) and 2) ratio bias (Kendal and Stuart, 1969). The expectation of the estimator is then: E(h^] - (h^ + epistatic bias)(l + ratio bias). 11.3.2 Genetic correlation estimators Warwick and Legates (1979) defined genetic correlation as the correlation between the additive breeding values for two traits or between the sum of additive effects of the genes influencing these two traits. Falconer (1960) identified the need to distinguish the two causes of correlation between characters, genetic and environ­ mental. The genetic cause of correlation is chiefly pleiotropy. Fleiotropy is the property of a gene affecting two or more charac­ ters. The genetic correlation between traits can be affected if selection is placed on the parents. Van Vleck (1968) reported large biases in estimates of the genetic correlation when selection was intense. 11.3.3 Phenotypic correlation estimators The phenotypic correlations ore the gross correlations that In­ clude both the environmental and genetic portions of the covarian­ ces. The phenotypic correlations calculated by means of estimated components of sire and residual variance are dependent upon the specified model with many relevant fixed effects not considered. 15 II.4 Genetic parameters of body conformation traits II.4.1 Descriptively scored type traits Wilcox et al. (1955) analyzed semi-annual official type classi­ fication scores from the Holstein-Friesian herd of the New Jersey Agricultural Experiment Station. They reported repeatabilities of .41, .43, .32, .56, .26, .19, .33, .36, and .29 for overall type, general appearance, feet and legs, rump, dairy character, body capacity, mammary system, fore udder and rear udder, respectively. These data were coded as 1 through 6 with the latter being the superior score. The Mating Appraisal for Profit (M A P) database was used by Thompson et al. (1980) in studying the sources of variation in type data. Cows were scored on 12 components of type on a scale of 1 to 5 with 1 being the most desirable. The model included effects of evaluator, evaluator by herd, parity, evaluator by parity and days in milk which was classified as both a linear and quadratic effect. Heritabilities ranged from .55 (scale) to .13 (back, rump, rear udder and center support) for cows in milk. basic form was .95. The heritability of The authors suggested that this large herita­ bility was partially caused by the knowledge of parentage while scoring, thus producing a correlation between paternal half sisters. Heritability of basic form was recalculated by the method of regres­ sion of daughter on dam and produced an estimate of .14. Analysis of subtrait heritability adjusted for discontinuity, ranged from .52 (wide front teats) to .00 (teats too far back on the udder). Other traits with heritability above ,20 were low front end, wing shoul­ ders, weak crops, too much set to the legs, stance, toes out in front, teats too large, fore udder too shallow-tilted, rear udder 16 too deep-tilted, high tailhead, narrow rump and toes spread. Genetic and phenotypic correlations between type traits from Thompson et al. (1980) are presented in Table 1. Genetic correla­ tions are higher in absolute value in general than phenotypic corre­ lations. Feet and legs exhibited the largest genetic correlation (.89) and the third largest phenotypic correlation (.41). Norman and Van Vleck (1972c) analyzed 49 body, udder and man­ agement traits of over 16,000 daughters sired by Holstein artificial insemination sires. Henderson's Method 1 estimates of variance components from a model consisting of year, herd, sire, herd by sire and error were used to estimate heritabilities over all lactations. The highest heritabilities were for measures related to body size. Heritability of upstandingness was estimated to be .43 for first lactation records and .38 for later lactation data. Rump characteristics ranged in heritability from .16 to .19. The remaining body traits were more lowly heritable. Fifteen of the 21 heritabilities for the udder traits were equal to or less than .10. Strength of rear udder attachment, rear teat spacing, depth of udder, height of rear udder, slope of udder and udder quartering had estimates between .11 to .16. Most of these type traits were threshold characters and eighteen of the 49 were scored binomially; thus some underestimation may have occurred. Cassell et al. (1973) analyzed 336,253 first scores at classi­ fication of records supplied by the Holsteln-Friesian Association of America. The data set consisted of 12 descriptive traits, scored 1 through 6 with 1 being superior, in addition to final score (60 to 100) and four descriptive measures. Heritability and genetic and phenotypic correlations are shown in Table 2. Heritabilities were Table 1. Phenotypic and genetic correlations of descriptively scored typea *^ Trait Basic Form Basic Form Scale Front Body Back Legs Feet Rump Rear Udder Fore Udder Center Support Teats -.05 -.70 -.56 -.20 -.35 .32 -.33 -.12 -.26 .04 .18 Scale Front Body -.08 -.29 .26 -.18 .07 .26 - .32 -.09 .38 .03 .12 -.36 -.09 -.10 .10 .18 - .56 .50 .41 .45 .10 ..06 -.01 .16 -.15 - .51 .58 .52 .42 .02 .01 .02 -.32 Back Legs Feet Rump -.01 .16 .16 .26 -.08 .06 .13 .14 .08 -.01 .08 .09 .10 .05 .41 -.06 .01 .13 .14 .19 .14 .12 - .35 .32 -.03 -.28 -.29 .19 -.07 - .89 .14 .08 .04 .24 -.09 - .10 -.01 -.05 .23 -.17 - .24 .31 .02 .02 Rear Udder Fore Udder Center Support -.09 .03 .09 .06 .03 .15 .12 .15 -.08 .03 .07 .08 .03 .11 .08 .13 .42 .04 .02 .04 .06 .04 .10 .08 .09 .33 .31 .67 - .72 .28 .23 - .38 .50 Teats .05 .02 .02 .02 .04 .06 .05 .08 .30 .38 .46 ^Thompson et al. (1980) Phenotypic correlations are above the diagonal while the genetic correlations are below the diagonal - Tibia 2. llerltablllty, phenotypic and genetic correlations anong descriptively scored type tritt**,b,c,d Trait Canaral Final* Final Scora Claaalflcatlon Appaaranca Filial Scora Final Claaalflcatlon Canaral Appaaranca Dairy Character Body Capacity Haanary Syatan Stature Head Front End Back Kuap lllnd Legs Feat Fore Udder Bear Udder Udder Support Udder Quality Teat Placement (.31) .91 .79 .47 .St .74 .46 .19 .41 .30 .41 .11 .23 .43 .30 .IS .31 .35 ■Caaiall at a K 1.01 (23) .77 .43 .33 .71 .44 .28 .39 .19 .40 .27 .24 .44 .41 .36 .29 .34 .91 .94 (.26) .34 .33 .43 .50 .30 .44 .31 .47 .33 .2B .27 .33 .19 .If .19 Dairy Character ,44 .61 .37 (.13) .23 .27 .2) .17 .11 .11 .14 .11 .oa .0B .22 .10 .17 .11 Body HiMary Capacity Syatan Stature .ai .82 .84 .49 (.23) .13 .31 .23 .34 .26 .26 .20 .16 .14 .IB .08 .04 .07 (1973) Genetic corralatlona above and, phenotypic correlations balov the diagonal cllerltablllty on tha diagonal, atandatd arror approximately .10 All phenotypic corralatlona significant (f<.01) 'Scored £0-100 .82 .B2 .to .36 .42 (.20) .IB .IB .19 .14 .23 .16 .13 .60 .57 .46 .IB .41 .70 .70 .74 .55 .77 .31 (.39) .16 .34 .20 .19 .12 .13 .11 .14 .04 .09 .05 llaad Front End lllnd Fere Bear Back ■unp legi Feat Udder Udder .43 .79 .44 .58 .48 .40 .56 .50 .46 .79 • .47 .69 .42 .60 .43 .82 .49 .51 .66 .47 .35 .23 .45 .27 .34 .23 .03 .10 .41 .95 .44 .42 .46 .44 .26 .36 .43 .22 .37 .39 .32 .84 .20 .29 .25 .24 .61 .32 .13 .24 .30 .10 .23 .24 (.11) .49 .29 (.11) .47 .51 .39 .32 .20 .16 .25 .16 .11 .10 (.14) .34 .19 .25 .26 (.21) .48 .19 .16 .16 .19 .10 .20 (.07) .11 .22 .12 .0B .16 .13 .24 (IB) .30 .13 .14 .11 .IB .09 .10 (.16) .14 .18 .11 .22 .13 .12 .25 .03 .06 .04 .09 .05 .05 .25 .09 .05 .06 .10 .05 .01 .19 .10 .07 .08 .12 .08 .06 .34 .62 .61 .43 .34 .20 .BO .13 .31 .32 .10 .31 .07 .IB .50 (17) .25 .20 .19 Udder Udder Support Quality .44 .44 .27 .11 .16 .39 .CS .12 .11 .09 .13 .13 .18 .42 .38 (.13) .24 .23 4 .52 .64 .42 .46 .14 .74 .27 .02 .02 .09 .08 .19 .16 .56 .58 .62 (.04) .23 Teat Flacaaent .48 .49 .30 .14 .14 .27 .12 .07 .08 .12 .20 .21 .22 .53 .36 .42 .54 (.17) 19 determined by an intraherd analysis of daughter-dam type scores. Age effects were removed by adjustment factors. Stature was the most highly heritable trait (.38), while udder quality, hind leg, feet, head and front end were low. The correlations between final score with all type traits indi­ cated selection on final score alone would produce significant im­ provement in the other traits. larger than the phenotypic. Genetic correlations were generally Among the scorecard traits, general appearance was most genetically related to final score (.93) and descriptive traits including stature (.46), front end (.42), rump (.41), fore udder (.45) and rear udder (.50). The components of genetic variation in various type traits were investigated by Hay et al. (1983). mates are presented in Table 3. Within herd heritability esti­ Heritability estimates from daugh­ ter-dam regressions were slightly higher than those from paternal half-sib correlations for all traits, indicating the possibility of common environmental effects and maternal effects. Covariances among maternal half sisters ranged from 3' to 8 times as large as those for paternal half sisters. These differences could have been caused by either maternal genetic or common environment effects. Dominance components ranged from 1.3 to 7 times as great as the additive components. Hind legs and udder support were greatly influenced by dominant genic effects. Additive maternal components were similar to additive direct effects in most traits. All traits showed negative components of covariance between additive direct and additive maternal effects. This would seem to indicate a generally small but consistently negative relationship between additive ef­ fects of genes directly affecting the trait in the offspring and 20 Table 3. Heritabilities of linearly scored type traits3 Trait Heritabilities from daughter-dam regression S.E. Final Score Stature Head Front end Back Rump Hind legs Feet Fore udder Rear udder Udder support Teats .482 .380 .148 .189 .184 .246 .099 .127 .189 .225 .135 .189 .003 .004 .004 .004 .003 .004 .004 .004 .003 .004 .003 .003 aHay et al^ (1983) Heritabilities from paternal half sib correlation .393 .390 .128 .185 .158 .237 .056 .110 .180 .196 .113 .186 S.E. .08 .08 .03 .04 .04 .05 .02 .03 .04 .04 .03 .04 21 additive effects of genes for maternal performance. The authors suggested that the large effects of nonadditive genetic effects may be used to maximize the frequency of desirable genes in the progeny through the use of corrective mating. II.4.2 Linearly scored type traits Thompson e£ al. (1981) analyzed 18 traits in the linearized type appraisal program at Midwest Breeders Cooperative. Traits were scored on a scale of one to 50. Heritability estimates from their study of linear type traits are shown in Table 4. Heritability estimates ranged from .11 (legs, rear view) to .68 (basic form) and were all greater than the herita­ bility estimates for the descriptive traits. Heritability of legs viewed from the rear (.11) was slightly less than heritability for a single appraisal of legs (.14) in the descriptive program. Heritability for legs viewed from the side (.24) was larger than the single appraisal. Heritability estimates for linearly scored fore udder, rear udder height and rear udder width were larger than the heritability estimates of the fore udder and rear udder (both .21) from the Holstein-Friesian classification program (White and Vinson, 1976). Their estimates of phenotypic and genetic correlations among linear type traits are in Table 5. were less than .30. Most phenotypic correlations Phenotypic correlations were negative between linearly scored traits in contrast to few, If any, negative phenoty­ pic correlations in the descriptive program (Aitchison et al.. 1972 and Thompson et al., 1980). Large phenotypic correlations in the data indicated that cows 22 Table 4. Heritability estimates of linear type traits from Midwest Breeders' mating appraisal program3. Trait Basic form Strength Dairy character Stature Body depth Rump (side) Legs (side view) Foot angle Fore udder Udder depth Rump width Legs (rear view) Rear udder height Rear udder width Center support Teat placement Disposition Milkout heritability .68 .39 .28 .59 .48 .27 .24 .19 .28 .27 .25 .11 .27 .28 .20 .19 .07 .10 S.E.S .08 .05 .04 .07 .06 .04 .03 .03 .04 .04 .04 .02 .04 .04 .03 .03 .02 .02 Deviation'5 -.28 . . -c -- .04 .06 .14 .10e .03 .14 -.12d -.03* *14f .15 .07 .00 -•■" ^Thompson et al. (1981) Heritability of linear trait minus heritability from descrip tive program of Midwest Breeders' Cooperative ‘'No simnilar trait in descriptive trait program Single appraisal for rump in descriptive program ®Single appraisal for legs in descriptive program ^Single appraisal for rear udder in descriptive program ^Approximate standard error Table 5. Trait 1 4 5 .18 .22 .0B .22 .26 -.62 .11 .02 .20 .07 .18 .12 -.22 -.26 .40 -.31 .33 .21 -.55 .27 .05 .09 -.25 .49 -.16 .05 .19 .25 -.08 .41 -.37 -.06 .34 .40 -.32 -.20 .95 .63 -.30 -.10 -.05 2 in .94 -.79 .06 .10 -.30 -.45 .37 .05 -.15 .38 .49 3 -.48 -.22 6 10 11 12 13 14 15 16 17 IB .07 -.02 .10 -.05 .22 .24 .12 .14 -.05 .02 .05 .10 -.11 -.08 -.11 -.08 -.06 -.06 -.09 -.07 -.08 -.01 -.13 -.04 .06 .01 .16 .11 .14 -.02 -.02 -.28 -.12 -.13 -.10 -.18 -.23 -.11 -.12 -.09 .06 .04 .11 .30 .43 .03 .61 .16 -.07 .09 -.12 ., .18 .55 .12 .07 .63 -.06 -.02 -.01 -.15 -.30 .27 .10 .05 .07 7 8 -.16 -.16 -.22 -.21 .15 .17 -.01 .07 -.10 .05 -.06 -.02 .03 .26 .12 -.10 .30 -.42 -.05 -.57 -.52 -.22 -.25 -.48 9 .05 .23 -.20 .06 -.17 -.44 .30 .57 .39 .34 .35 .10 .23 .02 -.27 .07 -.32 .08 are algnlfloant (P<.01) “These correlations computed by model Including herd, sire, parity and error .08 -.14 -.43 -.29 .08 .08 .11 .07 -.03 -.02 -.04 -.02 ,06 .06 -.01 .00 -.18 -.18 -.10 -.09 ,00 -.11 -.11 -.01 .06 -.01 -.01 .06 .26 .30 .26 .28 ,04 .26 .25 .12 .14 -.02 -.05 .07 .04 -.02 .16 .15 .72 .93 .26 .13 -.35 .05 .11 .00 -.38 -.11 .01 .03 .00 -.02 -.02 -.04 -.03 -.06 -.04 -.03 -.03 -.02 .06 -.01 -.04 .07 .01 -.03 -.02 -.01 .24 .20 .00 .01 .14 .14 -.01 -.01 .67 -.01 .00 .92 -.09 .42 .06 .54 Jk .51 .04 •°5, .I1d 24 with wide rear udders also have higher rear udders and cows scored as thick in basic forms were stronger but less dairy. Stronger fore udder attachment was related to shallow udder depth and strong suspensory ligaments were associated with close teat placement. Correlations among udder characteristics were greater than .20 and were more highly correlated among themselves. Genetic correlations were generally greater than corresponding phenotypic correlations. Dairy character had large negative genetic correlations with basic form (-.79) and strength (-.62). Thus, selecting for animals with favorable dairy character also would result in a more angular female. Selection for dairy character would also result in taller animals, stronger in all udder traits, narrower and slightly sloping in rump and more sickled in rear legs. Thompson et al. (1983) analyzed 19,152 cows scored from 50 to 99 with a model including classifier, herd, herd by classifier, age, classifier by age, stage of lactations, sire and error. Heritabili­ ty estimates of the traits in the Linear Scoring System (Table 6) were very similar to those in the Uniform Functional Type Trait Appraisal Program, Stature was the most highly heritable trait (.50) followed by rump width, udder depth, final score and body. Phenotypic and genetic correlations are in Table 7. lations were again generally greater than phenotypic. Genetic corre­ Phenotypic correlations ranged from -.29 (rear legs, rear view with rear legs, side view) to .76 (rear udder height with rear udder width). traits yielded the highest correlations. Udder 25 Table 6. Heritabilities of type traits scored linearly2 ’^ Trait Heritability Standard Error Stature Strength of body Dairy character Rump Rump width Rear leg, side view Rear leg, rear view Heel depth Fore udder attachment Rear udder height Rear udder depth Udder depth Suspensory ligament Teat placement Final scorec Stature® General appearance® Body® Dairy character® Mammary system® .32 .22 .16 .17 .26 .15 .12 .15 .15 .22 .15 .26 .12 .23 ,28 .25 .24 .26 .24 .23 .04 .03 .02 .03 .03 .02 .02 .02 .02 .03 .02 .03 .02 .03 .03 .03 .03 .03 .03 .03 ^Thompson et al. (1983) Variance components estimated by Henderson's Method III Classification traits scored 1 through 5 Table 7. Phenotypic and fenetlc corralatlona aaoit| type tralta aoored llnaarly,'b,° Trait Strength Stature or Body _ Stature Strength of Body .65 Dairy Charaoter -,0V Rump -.02 Rump Width .28 Rear Let, Side lltw -.17 Rear Leg, Rear View Heel Depth .38 Fore Udder Attachment .3' Rear Udder Height .22 Rear lfddar Width .22 Udder Depth .36 Suspensory Ligament .18 Teat Placeaent .17 .11 Dairy Character Ruap - .12 -.06 -.28 -.18 .35 -.81 .11 .62 .80 .81 .8V .21 .19 .12 .11 - .1 6 .36 -;o2 -.11 -.06 .08 .11 -.18 -.08 .15 - “Thompson at 8 K 11983) Phenotypic above the diagonal and genetla below cJlenderatxi'a Method III aatlaatea .08 .01 .00 lump Rear Let ■ear Let Heel Width Side View Rear View Depth - .30 .31 ,12 -.01 .00 .27 -.29 -.19 -.33 -.35 -.31 -.18 -.22 -.18 - -.06 -.12 .tl -.01 -.01 .12 .09 .21 .23 -.03 .05 .10 .03 .19 -.57 -.59 -.32 -.38 -.32 -.29 -.28 -.16 - .12 .17 .06 -.05 .15 -.29 - .60 .81 .89 .50 .81 .51 .89 .17 .23 .02 -.05 .16 -.18 .15 - .88 .86 .89 .30 .30 .30 Fere Udder Attachment .18 .17 .07 -.09 .18 -.06 .15 .19 - .73 .72 .79 .68 .65 tear Udder Height .15 .20 .15 -.10 .19 -.10 .20' .23 .85 - .95 .53 .51 .82 Rear Udder Udder Depth Width .19 .28 .16 -.0B .28 -.09 .22 .23 .81 .76 - .87 .50 .88 .16 .09 .03 -.07 .11 -.08 .18 .17 .53 .38 .35 - .75 .63 Teat Suapenaory Li|aaent Placeaent .08 .06 .13 -.08 .08 -.03 .12 .12 .39 .38 .32 .58 .82 .08 .07 .11 -.06 .10 -.03 .11 .12 .81 .32 .31 .83 .57 27 II.5 Phenotypic and genetic correlations between type traits Touchberry (1951) used data from Iowa State College Holstein herd to investigate the genetic and phenotypic correlations between five body measurements and a single type rating, scored 0 to 17, with milk yield. Table 8. Results are shown in Table 8. The three phenoty- Heritability, genetic and phenotypic correlations for body measurements and milk production*’ ,0 Trait Wither height (WH) Chest depth (CD) Body length (BL) Heart girth (HG) Paunch girth (PG) Weight (W) Type (T) Milk Production (MP) WH CD .73 .74 .67 .63 .27 .53 .14 .02 .81 .80 .71 .81 .43 .67 .18 .02 HG PG W .80 .05 .75 .84 .58 .56 .58 .61 .40 .61 .70 .81 .15 .21 .02 -.08 .31 .51 .18 .79 .27 .84 .20 - .00 .70 .72 .83 .88 .69 .37 .23 -.04 BL T 0 0 0 0 0 0 .25 .18 MP -.08 -.14 -.32 - .35 -.58 -.53 0 .35 touchberry, 1951 aGenetic correlations above diagonal, phenotypic below and heritability on the diagonal ^Phenotypic correlations are intra-sire 2X,243-day mature equivalent pic correlation estimates between body length and heart girth, body length and paunch girth, paunch girth and weight show evidence of a high environmental correlation, or physiological correlation or both. Genetic correlation estimates are high among body measurements. However, milk seems to be genetically independent of the body mea­ surements and weight. Blackraore et al. (1958) also used the data from the Iowa State College herd to observe negative genetic associations between milk 28 production and all measures of size except wither height. reported genetic correlations of 0.23, -0.23, -0.12, They -0.34, -0.13 and -0.02 between milk yield and wither height, chest depth, chest girth, paunch girth and weight, respectively. They concluded that selection for milk production alone would eventually lead to animals with some decrease in chest depth, body length and paunch girth and with even more drastic reduction in chest girth. They further stated that selection on milk would result in an increase in height at the withers with no weight change. O'Bleness et al. (1960) investigated the phenotypic and genetic relationships between type traits and milk yield using data from the New York Type Appraisal Program (Table 9). The majority of genetic correlation estimates were positive but small with the exception of that between milk yield and dairy character. Three traits were found to have an antagonistic relationship with milk production, namely hind leg, rear leg movement and udder quartering. Phenotypic correlation estimates were small with many of them approaching zero. They observed that head, depth of barrel and depth of udder were positively correlated with dairy character and attributed this to the influence of these traits on the rating of dairy character. Intra-sire and intra-herd variances and covariances of daugh­ ters and dams were used by Hitchel et al. (1961) to estimate the phenotypic and genetic correlations between type ratings and milk production in Holstein-Friesian cattle. Type ratings were scored as i 1 through 5 with 5 being superior. Hilk yield was adjusted to a twice a day, 305-day lactation and a mature equivalent base. Three milk production levels were used to stratify the cows into produc- 29 Table 9. Heritability estimates of type and production traitsa,^ ,c Correlation with Milk Production l Trait Production and body traits Dairy character Head Shoulder Withers Hind leg (side) Hind leg (rear) Pasterns Rear leg movement Depth of barrel Pin bone width Milk yield Udder characteristics Udder shape (rear) Udder shape (fore) Udder texture Depth Levelness Strength of: rear attachment fore attachment Udder quartering Teat length (rear) Teat length (fore) h2 S.E. Phenotypic Genetic .10 .15 .10 .16 .08 .06 .12 .07 .33 .05 .40 .080 .092 .062 .118 .078 .077 .075 .057 .115 .096 .077 .209 .080 -.077 .150 .021 .004 -.033 -.033 .158 .054 — .98 .24 .20 .22 -.05 .14 .32 -.10 .24 .30 .04 -.05 .28 .22 .09 .109 .094 .069 .096 .072 .177 .093 -.026 .191 -.017 .29 .30 .16 .18 -.09 .05 .065 .060 .078 .090 .088 -.044 -.088 .003 .02 .12 -.02 -.022 .66 aO'Bleness et al. (1960) Within herd-year analysis aTwice the daughter-dam regression Correlations > .08 are different from zero (Pc.05) .14 .14 .14 30 tion groups. This was done to examine the possibility of a produc­ tion level by rating interaction. Phenotypic and genetic correlation estimates for the three pro­ duction levels are presented in Table 10. The most highly corre­ lated, both phenotypically and genetically, trait with milk produc­ tion was dairy character in all three groups. Phenotypic correla­ tions were approximately the same in all production levels. How­ ever, the genetic correlations varied greatly both in signs and magnitudes. The inconsistency in genetic correlations in different produc­ tion groups, as compared to the consistency in phenotypic correla­ tions, could be attributed to the environmental correlation. McDaniel and Legates (1965) stated that the role of body size is very influential in the showring and in the official breed type classification programs. smaller. Generally larger animals are chosen over Environmental conditions that favor higher milk yields are also conducive to heavier body weights. In their study, larger cows in all four age classes showed slight but significant linear in­ creases in both 90-day and 305-day milk yield. A change of 181 pounds of milk per 100 pounds of weight in first lactation cows was observed. Heritability estimates of body weight ranged from .44 to and length of productive life and stated than an opportunity exists to increase milk yield without materially increasing body size. Atkeson et al. (1969) investigated the phenotypic relationships between type traits, scored on a five point scale, with milk yield. The correlations between milk yield and dairy character (.36) was the strongest. The next largest correlation was between body capa- 31 Table 10. Phenotypic and genetic correlations between type rating and milk yield stratified into (L)ow:13,230 lbs. milk production groups3 ’ ,c Correlation with milk yield Type Trait Genetic L General Appearance Dairy Character Breed Character Mammary System Rump .08 L M H .01 L M H .61 L M H -.06 L M H .11 L H H -.17 L M H -.05 L H M .13 .28 .16 .14 -.04 .09 .02 .12 .09 .23 .82 .25 .61 .24 .08 .33 .10 .12 .06 .11 .23 .13 .15 .140 .076 .055 .040 .158 .084 .052 .041 .140 .132 .121 .129 .436 .378 .359 .330 .453 .387 .359 .346 .436 .427 .419 .424 .736 .699 .692 .651 .753 .709 .691 .672 .736 .728 .724 .723 0 20 40 60 .35 .144 -.001 -.052 - .078 .185 .020 -.047 -.081 .144 .136 .125 .133 .439 .306 .255 .211 .481 .331 .266 .230 .439 .431 .423 .428 .738 .653 .619 .563 .779 .682 .637 .605 .738 .731 .727 .727 0 20 60 60 .55 .147 .078 -.156 -.189 .213 -.045 -.143 -.197 .147 .140 .130 .138 .442 .230 .144 .008 .508 .270 .165 .102 .442 .435 .428 .423 .741 .600 .531 .457 .806 .647 .563 .505 .741 .735 .732 .732 0 20 40 60 aWalter and Mao (1985) 44 Table 16. Comparison of residual correlations for trait 2 computed from single trait (ST) and multiple trait (MT) restricted maximum likelihood approaches3. Genetic correlation simulated Residual correlation simulated .15 ST .45 MT ST .75 MT ST MT Culling <%> .15 .148 .112 .091 .084 .148 .143 .136 .143 .148 .112 .091 .084 .149 .144 ,138 .144 .148 .112 .091 .084 .149 .144 .139 .145 0 ■ 20 40 60 .35 .348 .274 .233 .207 .348 .343 .338 .343 .348 .274. ,233 .208 .348 .344 .339 .344 .348 .274 .233 .208 .349 .345 .340 .346 0 20 40 60 .55 .549 .452 .395 .352 .548 .545 .541 .541 .549 .452 .395 .353 .548 .545 .542 .545 .549 .452 .395 .353 .549 .546 .543 .547 0 20 40 60 aWalter and Mao (1985) 45 occur ing in model 2. Model 3, the multi-trait model, was not af­ fected by the differential selection; however, the variability was dependent on the genetic correlation. II.8.2 Sire evaluation and variance and covariance estimation Schaeffer (1984) suggested that multiple trait analysis im­ proved the accuracy of evaluations as compared to single trait analysis. A multiple trait analysis should, theoretically, Improve the accuracy of ranking animals for genetic merit of each trait. Table 17 shows the percentage reduction in prediction error variance over single trait analysis (Schaeffer, 1984). The greater the absolute difference in the correlations, the greater the reduction in prediction error variance for both traits. When the error corre­ lation was less (greater) than the genetic correlation, in absolute terms, then the trait with the lower (higher) heritabillty achieved the greatest percentage reduction of prediction error variance. The effect of additional numbers of animals in the evaluation was mini­ mal compared to the influence of the correlations. Schaeffer (1984) also noted that the type of multiple trait model had an effect on the influence of the correlations on the solutions. An individual animal model may be affected more by error and genetic correlations than a sire model. Accuracy also may be improved more in the animal model as compared to a sire evaluation model. The sensitivity of multiple trait analysis to erroneous assump­ tions was Investigated by Schaeffer (1984), Although dependent on the model, the increase in prediction error variance was directly related to the differences between true and estimated correlations. Table 17. Percentage reduction of variances of prediction error variance for a multiple trait analysis versus single trait analysisa,b,c Correlation Between Traits Error Genetic Number of Animals Evaluated— 20 30 10 Trait 1 Trait 2 Trait 1 Trait 2 Trait 1 Trait 2 40 Trait 1 Trait 2 .1 .1 .1 .1 .3 -.3 .7 -.7 .92 2.15 6.77 9.*16 .13 1.35 1.92 4.72 .97 2.28 7.19 10.03 .14 1.45 2.06 5.05 .99 2.33 7.32 10.23 .14 1.48 2.10 5.16 1.00 2.35 7.39 10.32 .14 1.49 2.12 5.21 .5 .5 .5 .5 .3 -.3 .7 -.7 .01 7.22 3.28 18.79 1.96 8.91 .07 15.93 .01 7.66 3.48 19.93 2.09 9.52 .08 17.02 .01 7.81 3.54 20.32 2.14 9.73 .08 17.39 .01 7.88 3.58 20.51 2.16 9.84 .08 17.58 aSchaeffer, 198*1 bHeritability of Trait 1 = .1 “Heritability of Trait 2 = .25 “Animals measured on all traits 47 The trait with the smaller heritability usually showed the greater increase in prediction error variance from incorrect estimates, unless the estimated error correlation was greater than the esti­ mated genetic correlation. The absolute difference was defined as: AD - |(re - re ') - (rg - rg ')| where re re ’ r„ rg ' -estimated correlation residual; -parameter residual; - estimated genetic correlation; and -parameter genetic. The average percentage increase in the prediction error vari­ ance for various deviations of estimated correlations from the true correlations are shown in Table 18. The largest percentage increase in prediction error variance was 35,45%. |(.5 - .1) - (-.7 - .7)|. However, This resulted from AD - small errors in estimated corre­ lations compared to true correlations should result in less than a 5% increase of the prediction error variance. Two types of error may exist in assumed a priori values. One error is nonpositive definiteness of the variance-covariance matrix. If this is the case, the eigenvalue, which by definition must be positive, must be modified such that all eigenvalues are greater than zero. The second and most frequent error is that the a priori estimates of variances and covariances may be greatly different than i the underlying true values. Henderson (1975) showed that solutions to mixed model equations were not biased by an incorrect variance-covariance structure. How­ ever, he noted this did result in increased prediction error vari­ ances . 48 Table 18. Average percentage Increase of variances of prediction for various absolute differences of estimated correlations from true correlations3 Absolute Deviation 0 .1 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.8 aSchaeffer, 1984 Percentage errors in Prediction Error Variance Trait 1 Trait 2 1.36 .87 1.61 4.62 4.45 6.20 6.96 11.55 12.85 14.39 15.59 21.05 24.20 24.66 35.45 1.09 .76 3.35 1.39 2.51 5.11 6.44 4.95 5.05 10.87 13.03 12.04 9.35 17.08 24.18 III. 111.1 MATERIALS AND METHODS Genetic parameters of linear type traits 111.1.1 Data Linear type scores of 64,875 cows distributed across 2,168 herds were supplied by the Holstein-Friesian Association of America (HFAA). These data were recorded from cows in Michigan and Wiscon­ sin that were classified between January one and November 31, 1983. Grade and registered daughters represented a total of 64,875 records. Each cow had 29 linear type scores each on a scale ranging from one to 50, four classification scores each on a scale from one through five and final score with a range of 50 to 100. The Dairy Herd Improvement Association (DHIA) herd number and the identifica­ tion of the cow, sire, dam and maternal grandsire were provided for each cow as well as dates of birth, classification and calving, classifier, lactation number and stage of lactation at classifi­ cation. The linear type scores were given by twenty-five HFAA classifiers. The average number of cows scored by a given classi­ fier was 2,595 and ranged from one to 9,871 cows scored. The linear type traits were subdivided by the HFAA into 15 pri­ mary and 14 secondary traits (Table 19). considered The primary traits are economically Important and sufficiently variable to merit recognition in a selection program. A complete description of the linear type scoring system is presented in Appendix A. This data base of type scores represents a highly selected population, since it is a subpopulation of cows from Michigan and Wisconsin that were scored for type. A further restriction, which is necessary for any genetic study involving a paternal half-sib 49 50 Table 19. Primary and secondary linear type traits3. Primary Stature Strength Body Depth Angularity Rump Angle Rump Length Rump Width Rear Leg Side View Foot Angle Fore Udder Attachment Rear Udder Height 1 Rear Udder Width Udder Support Udder Depth Teat Placement Rear View Secondary Relative Height Front End Shoulders Back Tallhead Vulva Angle Rear Leg Position Rear Leg Rear View Mobility Pasterns Toes Fore Udder Length Udder Balance Teat Placement Side View Teat Size aHolstein-Friesian Association of America, 1985 51 analysis, is that daughters must be identified by sire. Crude averages, ranges and standard deviations of the data are shown in Table 20. And, additional data characteristics are shown in Appendix B. The criteria used to edit the HFAA type data are shown in Table i 21. To enhance connectedness of the data structure, sires were re­ quired to have at least 20 daughters distributed in at least 10 herds. A total of 15,070 records were deleted leaving a data set of 299 sires with 41,834 daughters distributed in 1,945 herds. III.1.2 A priori adjustments Individual scores of 15 primary type traits were adjusted separately for differences due to stage of lactation and age within lactation number. The multiplicative adjustment factors were sup­ plied by the HFAA. The origin of the derivation of these factors was not known, but it is evident that these factors were not derived from solutions of a simultaneous model. It was assumed that the adjustments were perfect such that stage of lactation and within lactation age effects were considered simultaneously and only these effects were adjusted. Hayes et al. (1985) reported no interaction between stage of lactation and age within lactation number. These results would justify the use of a two stage adjustment for stage and age within lactation. The structure of the data set for type was such that all the data were collected within one year, 1-1-83 to 11-31-83. The admin­ istration of the linear scoring system at the time of the procure- 52 Table 20, Crude averages, ranges and standard deviations from the original linear type data basea Variable Date of Birth Date of Classification Last Date of Calving Lactation Number Stature Strength Body Depth Angularity Rump Angle Rump Length Rump Width Rear Leg Side View Foot Angle Fore Udder Attachment Rear Udder Height Rear Udder Width Udder Support Udder Depth Teat Placement Rear View Range Mean 6-15-78 6-15-83 6-15-80 2.07 28.43 26.08 28.03 28.47 25.24 28.29 24.78 26.59 23.44 24.83 25.36 24.82 26.71 25.53 24.59 1-1 -66 1-1 -83 0-0 -00 0 1 1 1 1 1 5 1 1 1 1 1 1 1 1 1 aPrimary traits with 64,875 observations to to to to to to to to to to to to to to to to to to to 12- 31-84 11- 31-83 12- 31-83 22 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 Standard Deviation N/A N/A N/A 1.41 7.52 7.30 7.26 7.79 5.70 5.63 6.73 6.68 6.76 7.76 7.68 7.56 6.91 6.72 6.46 53 Table 21. Data editing criteria and number of records deleted from linearly scored type data Number of Records Deleted Editing Criteria No DHIA Herd Code No Lactation Code No Calving Date Lactation > 10 1 Lactation — Lactation 2 Lactation 3 Lactation 4 Lactation — 5 Lactation 6 Lactation 7 Lactation > 8 and < 10 and 21 and 27 and 40 and 49 and 65 and 75 and 98 and 111 < < < < < < < < aAge at classification in months t Agea Agea Age Age Agea Age Agea Agea < < < < < < < < 67 77 89 98 120 124 136 167 4031 3450 359 34 11 5 6 17 10 19 15 17 54 ment of the data allowed only one classification within a years time. Thus, the effect of year is nonexistent in our model. III.1.3 Model The model used to estimate the genetic parameters of each linear type trait and relationships between those traits was: y - pi + Hh + Gg + Ss + e III.l where: y Is the observation vector of 41,334 observations on one of 15 primary type traits. Observations were individually adjusted for stage of lactation and within lactation number age ef­ fects ; p Is the overall constant; l i s a column vector of ones; h is a vector of length 1,945 containing unknown constants of the fixed effect of herds; H Is an incidence matrix for the number of cows and herds, re­ spectively, corresponding to h with size 41,834 by 1,945; g Is a vector of length seven containing unknown constants of the fixed effects of sire groups; G Is an incidence matrix corresponding to g with size 41,834 by seven; s is a vector of length 299 containing unknown random effects of sire; S is an incidence matrix corresponding to a of size 41,834 by 299; and e is a vector of nonobservable random residuals corresponding to y. The expectations are: E[y] - pi + Hh + Gg E[e] - 0 E[s] - 0 55 The variance-covariance matrix of the random factors is: Var y s "Vn - e where °is * Jn °l Sas2 t V s 0 n a2 e 0 I a2 n e. Vn - SS*of + In af. Further assumptions implicit to the given model are: Since each herd was scored only once and by only one classifier in our sample of data, the herd and classifier effects were com­ pletely confounded. For the same reason, the season at classifica­ tion and season by classifier effect were also confounded with herd. Henderson (1975) pointed out that ignoring groups, if bulls come from differing genetic populations, could lead to biased esti­ mators. Additionally, if groups are included and not significant, the result would be an increase in the prediction error. Jensen (1979) suggested using the registration number of the bull as a convenient method of grouping by sire's age. The 299 bulls in this study were assigned to seven groups by their registration numbers. The mixed model equations (MHE) are: 1*1 l'H l'G l ’S U H*1 H'H H'G H'S h G* 1 G'H G'G G'S g G'y S*1 S'H S'G S'S + Ik s S'y where k - a e/°s- i'y - H'y 56 III.1.4 Absorption of herds The total number of mixed model equations (MME), if con­ structed as above, would be 2,254. Therefore, the 1,495 herd equa­ tions were absorbed by loop absorption, one herd at a time, while constructing equations for y, group and sire. After absorption the total number of equations was 307. The variance ratio, k, is assumed to be constant. k to be added after absorption. This allows The process of absorption reduces the number of equations but does not change the total sum of squares or the rank of the matrix. Therefore, the sum of squares of ab­ sorbed factors must be accounted for in the process of variance component estimation. Consider the original equations without the variance ratio: ' i 1*1 l'G I'S l'H U S iH G'l G'G G'S G'H e G'y S'l S'G S ’S S'H s S'y H'l H'G S ’H H'H h H ’y The equation for herd can be written as (H’l)y + (H'G)g + (S'H)s + (H'H)h - H'y and subsequently the herd solutions are: h - (H'H)_1(H'y - The total sum of squares for the model is defined as the transposed 57 solutions postmultiplied by their right hand sides. Total Sum of Squares - p'(l'y) + g' (G*y) - M'(l'y) + g'(G'y) + s*(S'y) + h*(H'y) + s’(S'y) + (H'y - (H'l)u - (H'G)g - (H'S)s)’(H'H)'1(H'y) - U ’(l'y) + g'(G'y) + s'(S'y) + (y'H(H'H) ’1(H*y) - U' (l'H) (H'H) " ^(H'y) - g'(G'H)(H'H) "1(H'y) s*(S'H)(H'H)~1(H'y) -y'(l'y) - U'(l'H)(H'H)"1(H'y) + g'(G'y) - g* (G'H) (H’H) _1 (H'y) + s'(S'y) - s* (S'H) (H’H)-1(H'y) + (y'H)(H'H)”1(H'y) - p'(l'y - l'H(H'H) ‘1H*y) + g'(G*H(H'H) ^H'y) + s'(S'y - S'H(H'H)“1H ’y) + (y'H)(H'H)’^(H'y) where U '(l'y - l'H(H'H)"^H'y) is the overall constant multiplied by the total sum, adjusted for herds; g'(G'y - G'H(H'H)"^H'y) is the solution for groups multiplied by the group right hand sides, adjusted for herds; s'(S'y - S'H(H'H)-^H*y) is the solution for sires multiplied by the sire right hand sides, adjusted for herds; y'H(H'H)“^H'y is the uncorrected total sum of squares for herds; The process of loop absorption was performed to reduce the number of MME. This method allows the effect of herd to be absorbed into other factors in the model while reading the data. This pro­ cess also allows for the accumulation of the herd sums of squares, y'HOl'HJ'^H'y, for the variance component estimation. Absorption 58 was performed as follows: 1. Data were first sorted by herd and sire within herd. 2. Absorbing herd right hand sides into the right hand sides of factor j - the sum of the observations for factor j in a herd - (number of daughters in factor j for that herd * the herd sum/ the number of daughters in that herd). where j - M, group, sire 3. Absorbing the incidence matrix for herds into the diagonal matrices of factor j « number of daughters in factor j (number of daughters in factor j ) /number of daughters in the herd. where j — p, group, sire A. Absorbing the incidence matrix for herds into the offdiagonal matrices of factor j - number of daughters in factor j - (number of daughters in factor j * the number of daughters in factor j')/number of daughters in the herd. where j - p, group, sire and j / j' After the absorption of one herd the storage vectors for herd were zeroed and absorption of the next herd began. This procedure requires only one pass of the data to complete the absorption pro­ cess and set up the normal equations. The MME are then constructed by the addition of the variance ratio, k, to the diagonal of the random portion, S*S, of the normal equation and are shown below: l'Al l'AG 1'AS y G'Al G'AG G* AS S S ’Al S'AG s l'Ay w* G'Ay III. 2 S'Ay H(H'H) The reduced equations were then solved by direct inverse of the coefficient matrix. 59 III,1.5 Variance component estimation An iterative restricted maximum likelihood estimator (REML) (Patterson and Thompson, 1971) using an expectation maximization (EM) algorithm (Dempster et al, 1977) was utilized for variance and covariance component estimation. involved two steps. Each iteration of the EM algorithm The first step is that the expectation is taken under the pretense that G - G and R ~ R. The second is the maximi­ zation of the log-likelihood function of the data vector. Henderson (1983) pointed out that solutions and estimates ob­ tained by the use of the EM algorithm are guaranteed to converge within the parameter space. The EM algorithm for variance component estimation is obtained as a by-product of the solution to the ordi­ nary mixed model equations. Let C be the generalized inverse of the MME. G'AG G'AS S'AG S 'AS + Ik “ Cgtg Cglg Cs ,g Cs ,g The EM REML estimator for the residual variance component is “ Cy'y - g'G’Ay - s’Z'Ay - y ,H(H'H)'1H'y)/(n-r(G) - r(H)) II1.3 where y'y Is the total unadjusted sum of squares of one of 15 type traits. g'G'Ay are the solutions to the fixed effects of 7 groups in the MME multiplied by their respective right hand sides adjusted for herds. s'S*Ay are the solutions to the random effects of the 299 sires In the MME multiplied by their respective 60 right hand sides adjusted for herds. y'H(H*H)~^H'y is the sum of squares due to herd which was accumu­ lated during the process of loop absorption. n is the number of observations. r(G) is the rank of the coefficient matrix pertaining to group fixed effects. r(H) is the rank of the coefficient matrix pertaining to herd fixed effects. The estimator for the sire component of variance is a2 - (s's + ti|(tr(Cs ,s)))/qs * III.4 where s's is the sum of squares of sire solutions. tr Ccs's> t*ie trace the random portion of the inverse of the coefficient matrix. qs is the number of sires. Iterations were continued until the absolute change in the ratio of e/ s wa3 less than .1 or after 20 rounds of iteration. The a priori variance ratio may be computed for a given heritability since h 2 - 4 / [0g/ag + 1], Thus, o2e/a2s - 4/h2 - 1. For all analyses involving the relationships among type traits the a priori variance used was 25.0 which corresponds to a heritability of 0.15. If A and B represent two linear type traits, the covariance between the two type traits was estimated by the fol­ lowing method: First, a new trait, A+B, was generated by summing A and B. Then, variance components were estimated for A, B and A+B. The 61 relationship below was then used to estimate the covariance between the two type traits, Var(A+B) - Var(A) + Var(B) + 2Cov(AB) and Cov(AB) - (Var(A+B) - Var(A) - Var(B))/2 III.1.6 Heritability and genotypic and phenotypic correlations The heritability estimates were calculated using the paternal half-sib correlation method with the EM REML estimates of _ and S 6 h2 The approximate standard errors of the estimated heritabilities were calculated according to Gill (1978). Var[Yx/Y2] “ [ 10 Lactation - 1 and 21 < Lactation — 2 and 27 < Lactation — 3 and 40 < Lactation - 4 and 49 < Lactation — 5 and 65 < Lactation - 6 and 75 < Lactation — 7 and 98 < Lactation > 8 and < 10 Michigan 323,795 8 2,882 599 0 0 1 or > 60,500 - Agea < 67 Agea < 77 Agea < 89 Agea < 98 Agea < 120 Agea < 124 Agea < 136 and 111 < Age aAge at last calving in months - < 167 Wisconsin 0 0 119 - 0 0 1,677 1,501 14 366 239 694 443 3,584 2,544 Table 33. Distribution of liras by nuebar of daughters and herds Mtieber o f H ards Codo H U H B ■ t) O 1 3 3 4 S £ . 3 0 9 10 r 11 D 0 U C U T It R 3 13 13 14 15 16 13 10 19 30 31 33 23 34 T o ta l S ir e s 1 3 1 3 3 3 001 T o ta l BOO 9999 S ir e s 4 6 0 11 16 31 36 31 41 51 61 71 01 91 101 301 301 401 501 ■ 651 3 7 10 15 30 35 30 40 50 60 70 00 90 100 200 300 400 500 650 4 5 6 7 0 9 10 11 13 13 14 15 16 17 10 19 20 21 22 ' 23 11,139 3 .066 975 1,001 065 303 416 195 09 60 53 17 6 6 1 0 0 0 a 0 0 0 0 0 3 ,2 5 5 463 979 332 494 1 .059 4B6 755 151 177 79 44 106 255 96 30 127 172 45 61 12 45 31 20 5 IS 10 7 0 3 £ 0 7 3 2 1 1 4 a 3 1 2 0 1 0 1 0 0 0 0 O' 0 0 0 0 0 a 0 a 0 0 0 0 0 0 0 a a 0 0 0 0 0 Q 0 0 0 0 0 0 . 0 0 0 0 0 0 359 174 37 IB 9 4 0 2 1 a 0 0 0 0 0 0 a 0 0 507 152 204 03 41 9 17 17 14 6 4 0 1 0 0 a 0 0 0 0 0 o 0 0 ■ 0 0 0 0 a 0 0 0 0 0 0 167 47 140 10 57 7 5 1 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 346 49 4 1 0 0 1 0 0 0 0 0 0 0 175 27 1 2 0 0 0 0 0 0 0 0 0 00 21 0 0 0 0 0 0 0 0 0 0 70 30 1 0 0 0 0 0 0 0 0 59 10 1 0 0 0 0 0 0 0 33 10 0 0 0 0 0 0 0 17.365 3 ,303 1,909 1,067 1,277 504 731 401 210 215 301 305 109 91 70 43 34 42 0 0 0 0 0 0 311 5 0 0 0 0 0 115 3 0 0 0 0 67 3 0 0 0 46 0 0 0 42 1 0 39 0 151 51 316 117 £9 46 41 39 153 29,346 9 67 300. Therefore, a random sample of 150 sires without replacement was selected from the 1,495 sires in the merged data set. sires represented 10% of the total number of sires. These 150 Daughter records of these sires then were pulled from the 475,855 in the edited research file for all analyses outlined in the next section. The sampling was repeated five times independent of each other using different randomly sampled seeds. are shown in Table 24, A description of the data sets The distribution of sires by number of herds and number of daughters for each sample are included in Appendix D. Table 24. Data Set Sires Total Herds 1 2 3 4 5 150 150 150 150 150 9,441 9,147 9,532 8,975 9,688 Descriptions of Sampled Data Sets Herds with Paired Data 1,433 1,268 1,547 1,332 1,466 Total Records Paired Records 60,008 51,651 65,264 50,472 69,087 4,882 3,749 6,416 3,960 5,550 Percent Paired 8.14 7.26 9.83 7.85 8.03 The same data base of 64,875 Holstein cows described earlier was used in the investigation of genetic parameters while jointly considering milk production and the linear type score. Each lacta­ tion record was identified by DHIA herd number and dam, sire and cow numbers. Cow's age, parity number and the date of calving which initiated the lactation were also recorded. 68 III.2.2 A priori adjustments and assumptions The scores of the 15 linearly scored type traits for each cow were adjusted for differences due to stage of lactation and age within lactation number using adjustment factors supplied by the association. The milk production records supplied by the Wisconsin and Michigan DHIA were adjusted for lactation length, times per day milking and age and season at calving (Norman et al, 1980 and Wig­ gins and Powell, 1980). Age and season at calving differences were adjusted on a within lactation basis assuming that the parity by age effect is negligible. milking. Records were standardized to a twice a day Incomplete records that were less than 305 days in length and not coded a normal termination were extended to 305 days. ' The production data covered 3 years, 1982 through 1984, but an assump­ tion was made that the effects of year were negligible. The assump­ tion that all adjustment factors are perfect and any interaction of factors in the model with those of a priori adjustment are nil is also necessary. III.2.2.1 Single trait model The equation is **• where, III,5 is the observation vector of the ith trait; the trait is one of the 15 primary type traits or milk production; is the overall constant; 1 Is a column vector of ones; 69 hj is a vector of length ra^ containing the unknown fixed con­ stants pertaining to herd; is an n^xm^ incidence matrix pertaining to herds, where and depend on the data set sampled; is a vector of length 10 containing the unknown fixed con­ stants pertaining to sire groups; 6^ is an n^xk incidence matrix pertaining to sire groups, where k—10; is a vector of length 150 containing the unknown random effects of sires; is an n^xP incidence matrix pertaining to sires, where P-150; and is an njxl vector of nonobservable random residuals corre­ sponding to y^. The expectations are: EtyJ - W±1 + +0^ E[Bt ] - 0 E [3±] - 0 The corresponding variance-covariance structure is: yi Var s± ei where VR - S±S I Vn - S* 2 Siai i IpoJ l ace 2 Xn " \ 0 0 n»12 * « W 2*2,>»2t * «t40ltt.10*10»T10 (I 21*q21,21)y2i ♦ (X^i, t?21,12) r 1g__________________ III. 7 tt1'a«o,*'ia)»w * tzil*o«*at)y21 * tt*Q«,io*io>Tio *^1,fl21*a,»fia * «ii,"21,ia>»« 77 Tke S Priori values used for the genetic and residual variancecovariance matrices were obtained by the single trait estimates from the same sample of data. These values can be found in the discus­ sion of single trait estimates of milk and type (Section III.2.2.1), Estimates of the residual covariance, q^j, were obtained as­ suming a residual correlation of .01 and the formula: ‘kj " a ij/aiaj Estimates of the genetic covariance, w^j, between traits 1 and j, where I-J, was assumed to be 0.0 which corresponds to a genetic correlation of 0.0 between milk and type. The arrangement of factors within traits forms nondiagonal block matrices for fixed and random effects. process of absorption of fixed effects. This complicates the The complication is due to the assumption of nonzero residual covariances. This characteristic makes loop absorption one trait at a time impossible. Thus, a transformation of the data to possess zero residual covariance was performed. III.2.2.2.1 Triangular transformation of MTMME The method of triangularization is described by Schaeffer (1985) and Pollack and Quass (1982) as cited by Van Den Werf (1983). This method requires a specific data structure and model: 1. The random effects must be the same for all traits; 2. Fixed effects may be different for different traits; 3. Data may be missing on some traits, but with restrictions on the missing traits as follows: If y^ contains t traits and trait j is missing then, 78 a. b. traits 1 to j-1 must be present traits j to t must all be missing These data and model meet all of the above criteria. to find a transformation matrix P such that Var(Pe) - I. We wish To obtain this assume Var(Pe) - PVar(e)P* - PRP*. It is known that R. is symmetric and may be broken down into QQ' i where Q is a lower triangular matrix formed by a Cholesky decomposi­ tion: Qll 0 0 0 Qn 0 0 Ql2 Q22 Q - I—I 1 O’ PQQ'P' is equal to I if P - Assume that 0 0 0 It11 0 0 It12 It11 P - T"1 - ft ro to n and t11 0 r 1 r 0 CM IO t u CM CM 4J T « 1—1 where It22_ Furthermore, XT’ - R11 R12 R 21 r22 and III. 8 where PQQ'P' - IT11 0 0 0 IT11 0 0 IT12 IT22 and PQQ'P' - I if P - Q -1 Also noted is the fact that PX - XT"^ and PZ - ZT~^. The transfor­ mation of y is: * y “ * yio * yi2 * y2i n o T yi2r 11 XI 19 yi2T 99 + y2iT The equation can now be expressed as: Py - y - PXb + PZu + Pe - XT”^b + ZT + Pe - Xb* + Zu* + Pe where Var(Py) - P(ZGZ' + R)P' - PZGZ'P' + PRP* - ZT"1GT'1,Z' + PRP' - ZG*Z* + I The transformation is complete with the new variance-covariance matrix of random factors expressed as G and a residual variance- so covariance matrix expressed as I. The advantage of the transformed equations la that in the case where the residual covariance is assumed to be nonzero, the transformed equation may have factors absorbed one trait at a time by loop absorption processes due to the nature of the transformed residual variance-covariance structure. The transfomed MTMME are: 0 *12*12 ♦ *10*10 0 j **1*21 ! *12*12 ♦ *10*10 0 0 *21*21 4 I.*13 4 *12*12 ♦ *io*io 0 *21*21 > III.2.2.2.2 Absorption of herds 8 | *iV« * *i’o*io * **"11 *21*21 * *****. *«*” *10**0 * *12**2 m *21X21 III.9 *10**0 * *12*12 L4. . *«*& . The herd equations were absorbed one trait at a time into group and sire equations for both milk and type by a loop absorption procedure. The data were first sorted by herd and a transformed by the P matrix. The transformed sum of squares, crossproducts herd counter for each herd were stored. a This process continued until all herds were absorbed. The loop absorption, as described in the section on single trait analysis (Section I1I.4.1), was carried out for each trait before they ware combined to form the reduced MTMME shown below: ri2Atzia**iV2rio 8 a *t2tt*12»*10*2*10 * *i,zMia»*ra‘2'w o a H-1* Zt^A1Z1Z♦liol2^10*I**1, t;,A322|*I«•22 wh*r* ■ x - *i2s' ‘*ia0 *3 ‘ ITOA2TlVX12A1I*2 *1* T_! 1* Z1tM ond Xg] n p rM M t tbo bord parttao o f tbo flood ofroata of pot rod >11It, unpolrod i l l l t ond typo roopootlvoly. •T °2 *21*3*ll *lW?0**1*2*lXf2 *21*3*21 III.10 81 111.2.2.2,3 Variance component estimation Restricted maximum likelihood (REML) by the expectation maximi­ zation (EM) algorithm (Dempster et al., 1977) was chosen for estima­ tion of variance components since convergence of estimates to non­ negative from positive priors is guaranteed (Henderson, 1985 and Taylor et al., 1985). Additionally, all the properties of single trait REML will also hold true for multiple trait analysis. The REML estimators are shown below (Mao, 1982). By “ + tr(C^))/q where i can be estimated by: a* e10 yio ■ xio^i ■ zio“i a* 12 - yi2 * X12^1 • Z12-i 21 where y yJi ■ ^i^l ■ z2ii4 - Py b* - T -1b u * - T “^ u and although not noted, the effects of b and u are adjusted by the 83 absorption of herd effects. The vector y , however, effects which must be removed. retains herd Let e21A3e21 “ ^ 2 1 ' * 2 1 4 ' Z2l'4'>'A3’* *22 z21A3y2i The estimator of the residual sum of squares for milk contains 85 paired as well as unpaired records. This estimator is in the form of: e10A2e10 + e12Ale12 ” yio^yio + y 12*172 3 2 [bJ' uj'] xioA2yio + x i2Aiyi2 zioA2yio + zi2Aiyi2 [if uf] X 10A2X10+X12A1X 12 X10A2Z10+X12A1Z1C "k * bl Z10A2X10+Z12A1X12 Z10A2Z10+Z12a1Z12 (if where Aj_ - I - xi2H^X12HX12H^ X 12H *2 " 1 ' X10H X10H- The addition of the sire variance-covariance structure to coefficient matrix allows it the to be equated to the right handsides for paired and unpaired milk production records as is shown below: X10A2X10+X12A1X12 0 X10A2Z10+X12A1Z10 bi 0 0 0 Z10A2X10+Z12A1X12 0 Z10A2Z10+Z12A1Z12+IS 0 0 0 K* 2 ^* "1 ** _u2 _ t I *12 ig*12 0 x ioA2yio+xi2Aiyi2 0 0 uflg*11+0^ 1g*12 Zl'oA2yiO+Z12A l A 2 0 0 86 The estimator of the residual milk sum of squares becomes ®fo*A2®io + ei2'Aiei2 “ yio’A2yi2 + yi2'Aiyi2 ■ b*’ u* ujujg*11 - uju|g*12 x ioA2yio + x i2Aiyio zioA2yio + zi2Aiyi2 The estimator of residual crossproducts is defined as: ®12'A4e21 " < uijk2>/150> ^ « “ ijkl ■ « Uijkl>2/150))*( u ljk2 - « uljk2)2/150)))°-5 ' 1 IV. IV.1 Results and Discussion Heritability and genetic and phenotypic correlations of linearly scored type traits IV.1.1 Heritabillty estimates The estimated sire and error components of variance and heritability values are presented in Table 26 for the 15 primary linear type traits. The most highly heritable trait was stature (.39). This is in agreement with Thompson et al. (1983) and Hay et al. (1983) who also reported stature as the most highly heritable type trait. The most lowly heritable trait was udder support (.10). This estimate agrees closely with Thompson et al. (1983) also, as they reported a heritabillty of .12 for suspensory ligament. Hay et al. (1983) found that the variance component estimate of dominance was greater than that of additive in affecting udder support. This relationship would confirm the observed low heritabillty as large nonadditive effects would lower heritabillty in the narrow sense. The heritabillty of rear leg side view was also small (.17) and agrees with research by Thompson et al. (1983) and Thompson et al. (1980). In general, traits that are linear scores of the entire body such as stature, strength, body depth and the rump traits were more highly heritable than those of udder or feet and legs. These find­ ings are supported by the work of Thompson et al. (1981) using linear scores from the Mating Appraisal for Profit program. The general magnitude of the heritabillty estimates are similar to corresponding estimates obtained from type data measured on a 90 Table 26. Trait Estimated sire and error variance components and heritability values for primary linear type scores Sire Variance Error Variance Heritability Standard Error of Heritability Stature Strength Body depth Angularity 4.7513 2.2710 2.7382 2.2364 44.2602 39.9747 36.2065 46.2997 .3878 .2150 .2812 .1843 .0031 .0019 .0235 .0017 Rump angle Rump length Rump width 1.6127 1.3550 2.5437 25.8492 23.0810 35.3424 .2349 .2218 .2686 .0020 .0017 .0023 Rear leg side veiw Foot angle 1.7810 2.7284 39.6683 36.9082 .1719 .2753 .0016 .0023 Fore udder attachment Rear udder height Rear udder width Udder support Udder depth Teat placement rear view 2.5516 2.5749 2.0166 1.4395 1.6139 1.8846 47.9603 43.0926 44.8741 40.0301 22.6335 36.5244 .2021 .2255 .1720 .0999 .2662 .1963 .0324 .0019 .0016 .0013 .0022 .0017 92 descriptive scale of one through six (Cassell et al., 1973 and Hay et al.. 1983), Thus, the scoring of type traits on a 50-point scale appears to have little effect on the heritability values when com­ pared to estimates of type traits scored one through six. IV.1.2 Phenotypic correlations Estimates of phenotypic correlations between the 15 primary linear type traits are presented in Table 27. All correlations are positive and greater than .30 with the exception of correlations between angularity and udder depth, rear leg side view and foot angle, rear leg side view and udder depth and rear udder height and rear udder width. All correlations are significant (PC.05). These results disagree with the work of Thompson et al. (1981) which showed mostly small and negative phenotypic correlations between linear type scores. Udder traits were more highly correlated among themselves than with other type traits. In the present study, the phenotypic rela­ tionships between the udder traits were greater than .50 with the exception of that between rear udder width and rear udder height (.09) and between udder depth and rear udder width (.47). Thompson et al. (1981) reported the similar tendency and that 11 out of the 15 phenotypic correlations among udder traits were greater than .20. The rear udder height of Holstein cattle appears to be rela­ tively independent of the rear udder width. This could additionally be explained by the fact that a highly attached udder may visually appear more narrow than an udder more lowly attached. Teat placement rear view was highly correlated with udder support (.94) as expected since the support of the suspensory liga- Table 27. Trait ( 1) ( 2) ( 3) ( 4) ( 5) ( 6) ( 7) ( 8) ( 9) (10) (11) (12) (13) (14) (15) Stature Strength Body depth Angularity Rump angle Rump length Rump Width Rear leg side view Foot angle Fore udder att. Rear udder hgt. Rear udder wth. Udder support Udder depth Teat placement rear view Phenotypic correlations among the fifteen linear type traits ( 1) ( 2) ( 3) ( 4) ( 5) ( 6) ( 7) ( 8) ( 9) .50 .61 .59 .41 .86 .76 .34 .50 .57 .53 .58 .47 .46 .44 .74 .34 .36 .76 .84 .32 .58 .62 .60 .69 .49 .34 .47 .56 .39 .83 .86 .39 .57 .63 .62 .70 .52 .32 .49 .33 .41 .40 .57 .35 .49 .53 .56 .56 .24 .49 .46 .46 .51 .44 .48 .43 .50 .48 .33 .46 1.00 .57 .63 .75 .72 .53 .65 .50 .61 .44 .57 .62 .63 .73 .53 .39 .49 .23 .43 .38 .39 .48 .29 .45 .63 .60 .63 .54 .89 .50 (10) (11) (12) (13) (14) .88 .87 .76 .76 .82 .09 .73 .53 .67 .75 .47 .67 .67 .94 .90 94 raent would influence the placement of the teats. The correlation between rump width and rump length was 1.00. The measurements among those traits influenced by size and scale should change proportionately. Rump length and width were highly corre­ lated with stature, strength and body depth. The correlations between these traits exceeded .75. Cattle that were stronger and deeper bodied tended to have udders that were stronger in the fore attachment, more highly at­ tached and wider in the rear udder. Phenotypic correlations between rear leg side view and foot angle indicated that cattle with more sec to the hock tended to be deeper heeled. This relationship, however, is illogical since addi­ tional angularity in the set of the rear leg should place more weight and wear on the heel. Additionally, cattle which were taller tended to have more set to the rear leg. The height of a cow may be altered by a change in either the length of the bone or angle of the attachment.This phenotypic relationship suggests that the skeletal structure is elongated while the angle of the hock becomes more acute. IV.1.3 Genetic correlations Genetic correlations between the 15 primary linear type traits are presented in Table 28 and all are significant (P<.05), The genetic correlation estimates are generally smaller Chan the corre­ sponding phenotypic correlation values. This contradicts the work of Thompson et al. (1981) and Thompson at al. (1980). The genetic associations between stature, strength and body depth are high. The estimated correlation between stature and Table 28. Genetic correlations among the fifteen linear type traits Trait ( 1) ( 2) ( 3) ( 4) ( 5) ( 6) ( 7) ( 8) ( 9) (10) (11) (12) (13) (14) (15) Stature Strength Body depth Angularity Rump angle Rump length Rump Width Rear leg side view Foot angle Fore udder att. Rear udder hgt. Rear udder wth. Udder support Udder depth Teat placement rear view ( 1) ( 2) ( 3) ( 4) ( 5) ( 6) ( 7) ( 8) ( 9) (10) (11) (12) (13) (14) .68 .76 .13 .11 .88 .54 -.20 .13 .29 .12 .15 .13 .36 .13 .93 -.24 .03 .62 .55 -.34 .04 .14 .10 .21 .15 .02 .02 .03 .01 .72 .58 -.24 -.01 .15 .12 .23 .17 .02 .02 .11 .20 .02 .01 -.01 .38 -.00 -.34 -.35 -.02 -.27 -.01 . -.35 .03 -.32 .14 -.25 -.09 -.14 .18 -.13 .68 -.07 -.10 .25 .11 .17 .18 .30 .21 -.11 -.05 .10 .07 .20 .05 .07 .06 -.57 -.17 -.35 -.33 -.07 -.15 .03 -.08 -.11 -.12 -.13 -.10 -.19 .58 .54 .53 .83 .63 .93 .37 .35 .28 .41 .26 .35 .47 .77 .52 96 strength (.68) is very similar to that reported by Thompson et al. (1981). The daughters of bulls which are stronger, taller and deeper bodied tend to have less set to the rear leg, have longer and wider rumps and have deeper udders. These relationships also suggest that selection for taller cows would lead to elongation of the skeletal structure and additional height due to more posty rear legs and deeper heels. The genetic correlations between udder traits were positive and ranged from .26 to .93. Thompson et al. (1981) also reported posi­ tive genetic correlations between udder traits. Therefore, selec­ tion for any udder trait would tend to enhance other udder scores. Rear udder height and width had the highest genetic correlation (.93) which agrees with the results by Thompson et al. (1981). Udder traits did appear to be negatively associated genetically with feet and leg traits* Therefore, cattle selected for desirable udder characteristics would generally be straighter in the rear leg and more shallow heeled. However, daughters of bulls which are taller, stronger and deeper bodied tend to have more desirable udders. The negative genetic correlations between feet and leg traits and the majority of other linear type traits agree with the work by Thompson et al. (1981) on Hosteins and Norman et al. (1983) on Ayrshire, Guernsey, Jersey and Milking Shorthorn cattle. Selection programs designed to Improve the average udder traits would result in a more posty rear leg and more shallow heel. 97 IV.1.4 Environmental correlations Searle (1961) reported that the phenotypic correlation may be expressed as: rp - tg(h1h2)"5 + r ^ a - l i ^ a - h j ) ] * 5 where rp is the phenotypic correlation. rg is the genetic correlation. r_ is the environmental correlation, h^ is the heritability of trait one. h2 Is the heritability of trait two. Thus, the phenotypic correlation is a function of the joint genetic and environmental variation between two traits. Addition­ ally he notes that the phenotypic correlation between two traits exceeds the genetic correlation if the ratio of the environmental correlation to the genetic correlation exceeds the value [1- (h^gJ^l/Ul-hjKl-hg)]*5. Hence, if the genetic and phenotypic correlations are opposite in signs, the environmental correlation has the sign of the phenoty­ pic correlation. If the phenotypic and genetic correlations share the same sign, the environmental correlation is positive if the ratio of phenotypic to genetic correlation is greater than the geometric mean of the heritabilities of the two traits. Therefore, the genetic and phenotypic correlations in this study seem to suggest a large positive environmental correlation. The factors contributing to this environmental influence were not investigated in this research. 98 IV.2 Heritability and genetic and phenotypic correlations of milk production and linearly scored type traits The estimation of genetic parameters of type characteristics of Holstein dairy cattle has progressed over many years and many clas­ sification systems. Yet,, it has been hypothesized that the animals scored for type may represent a superior population since few dairy cows are scored for type. Selection pressure for milk production may additionally lower the probability that an animal receives a type score by culling animals for low production. Henderson (1975) reports that under normality, with selection decisions invariant to the fixed effects and with data upon which the selection decisions were made included in the analysis, that Best Linear Unbiased Prediction (BLUP) with selection is computed as BLUP with selection. Thus, the inclusion of milk records in the model with type may reduce the effects of selection. Walter and Mao (1985) reported that under selection, a multiple trait algorithm was superior to single trait estimates in improving the accuracy of estimated sire and error variance components. The milk record population is less selected than those cows scored for type. The simultaneous consideration of milk with type traits may reduce any selection bias inherent to the population scored for type. This simultaneous consideration is accomplished by the variance and covariance structure of the random factors in the multiple trait mixed model equations. The 15 primary linear type traits and milk yield were first analyzed by a single trait mixed model (Equation III.l), which is henceforth referred to as single trait analysis (ST); The resulting variance estimates were then used as the a priori values in a multi- 59 pie trait (MT) analysis of milk with each of the type traits. The milk yield and one of the 15 primary linear type traits were ana­ lyzed in each of the MT analysis. IV.2.1 Single trait MME methods IV.2.1.1 Heritabillty The estimates of sire and error variance components obtained by ST REML are presented in Table 29 and Table 30. The heritability values estimated from the variance components are in Table 31 and are significant (P<.05), The mean estimates of the heritability values of linear type traits, averaged over the five data sets, correspond closely to the estimates obtained in the analysis of type traits alone. The ST estimates of heritability for rump length and rump width appear to be the most variable, while strength and rear udder width were the least variable across data sets. Stature was the most highly heritable type trait (.35) and rear leg side view the least (.15). The greatest difference between single and multiple trait estimated heritabilities was the larger estimate by MT for udder support. The estimate increased from .09 with a single estimate on a relatively large data set (41,834 obser­ vations pertaining to 299 sires) to .14 across five data sets of 150 sires each. However, the average heritabillty was different from zero (P<,05) for all linear traits studied. IV.2.2 Multiple trait IV.2.2.1 Heritability Estimates of heritabillty and phenotypic and genetic correla­ tions for milk production and linear type traits from MTMME method Table 29. Estimated alra variance components of milk and linear type traits obtained through single trait methodology D ata S e t T rait 1 2 3 4 5 H ean S tan d ard D ev iatio n H llk S tatu re S tren g th Body d ep th A n g u larity Bump a n g le Hump l e n g t h Bump w i d t h B ear le g s id e view F oot an g le F ore udder attach m en t Bear udder h eig h t R ear ud der w id th Udder su p p o rt U dder d ep th T e a t p la c e m e n t r e a r view 3 2 4 1 5 4 .0 6 4 .7 5 2 .0 0 2 .6 9 2 .2 2 ,6B 2 .0 3 3 .5 0 1 .9 3 1 .9 3 3 .0 3 2 .9 8 2 .1 0 1 .7 6 1 .5 7 2 .2 1 3 6 2 5 9 8 .2 7 4 .3 8 2 .5 7 2 .5 6 .6 2 2 .5 1 .3 1 2 .5 2 1 .8 7 1 .3 0 3 .2 2 2 .5 5 2 .7 7 2 .6 9 1 .61 2 .3 9 4 6 2 1 0 0 .3 5 3 .1 7 2 .2 8 1 .8 3 3 .0 0 1 .9 5 1 .4 9 4 .5 7 1 .6 3 .53 2 .6 3 1 .9 2 2 .2 2 .6 5 2 .0 6 1 .6 0 3 7 9 4 5 9 .1 7 4 .3 3 2 .6 1 3 .6 7 3 .1 3 1 .4 6 .7 7 1 .04 1 .11 .77 3 .0 8 1 .3 6 2 .0 2 .78 .7 5 1 .7 2 3 2 9 7 9 6 .4 8 4 .0 8 1 .8 5 2 .1 6 1 .8 5 2 .0 8 1 .2 8 2 .4 9 1 .4 2 1 .3 0 2 .1 3 1 .1 4 1 .8 6 1 .7 7 1 .0 0 1 .4 7 3 7 1 6 2 1 .6 7 4 .1 4 2 .2 6 2 .5 8 2 .1 7 1 .7 3 1 .1 8 2 .8 2 1 .5 9 1 .1 7 2 .8 2 1 .9 9 2 .1 9 1 .5 3 1 .4 0 1 .8 8 5 5 5 2 4 .2 3 .5 9 .3 4 .70 1 .0 1 .7 0 .66 1.3 1 .34 .5 4 .4 4 .7 8 .35 .8 4 .52 .40 Table 30. Estimated error variance components of milk and linear typo tralta obtained through single trait methodology Data Set Trait Hllk Stature Strength Body depth gngutarlty Rump angle Ruep length Rump uldth Hear leg side view Foot angle Fore udder attaolueent Near udder height Rear udder uldth Udder support Udder depth Teat placement rear view 1 2 3 9 9,517,600.12 85.17 39.32 35.19 50.81 25.89 22.50 36.53 99.31 38.52 96.33 90.80 92.99 92.67 23.09 37.78 9,929,236.07 99.65 37.21 33.27 95.29 26.53 23.29 39.13 38.59 35.92 97.75 90.89 93.36 90.99 22.53 39.36 9,588,083.17 90.60 38.59 39.53 85.16 28.12 21.86 35.77 37.93 37.99 50.17 85.89 87.16 91.65 23.61 38.85 9,682,990.55 83.97 91.32 37.05 97.05 29.53 23.13 36.77 93.81 36.72 89.28 82.39 99.98 37.69 21.66 33.53 5 9,965,815.29 98.36 39.72 36.86 86.2} 26.99 22.66 35.71 91.63 80.18 89.00 93.80 85.93 81.65 23.91 38.75 Mean 9.635.751.03 83.69 39.23 35.37 96.90 26.36 22.69 35.78 91.15 37.76 97.50 82.79 88.77 80.96 22.96 36.57 Standard Deviation 100,652.71 1.01 1.51 1.60 2.31 1.83 .57 1.0J 3.07 1.01 2.32 2.16 1.77 1.93 .90 2.88 Table 31* Estimated heritabilities for milk and linear type traits obtained through single trait methodology Data Set Trait 1 2 3 4 5 Milk Stature Strength Body depth Angularity Rump angle Rump length Rump width Rear leg side view Foot angle Fore udder attachment Rear udder height Rear udder width Udder support Udder depth Teat placement rear view .13 .38 .19 .29 .17 .10 .33 .35 .17 .19 .25 .27 .19 .16 .25 .22 .14 .36 .26 .29 .05 .35 .05 .27 .19 .14 .25 .23 .24 .25 .27 .26 .18 .29 .22 .20 .25 .26 .26 .45 .17 .06 .20 .16 .18 .06 .32 .16 .15 .36 .24 .36 .25 .23 .13 .11 .10 .08 .26 .12 .17 .08 .13 .19 .13 .34 .18 .22 .15 .28 .21 .26 .13 .12 .17 .10 .16 .16 .16 .15 Mean .15 .35 .22 .27 .18 .24 .20 .29 .15 .12 .22 .18 .19 .14 .23 .20 Standard Deviation .02 .04 .03 .06 .08 .09 .11 .13 .04 .05 .04 .07 .03 .07 .08 .05 103 are shown In Table 32 through Table 46. The heritability of milk yield increased slightly from .15 by ST methodology to .16 by MT methods. This difference is not statis­ tically significant since the standard deviations overlap consider­ ably. However, the standard deviations of the heritability esti­ mates from both ST and MT analyses are approximately the same. The additional information on type had little effect on the estimates of heritability for milk yield. The estimated heritabilities of linear type traits obtained via MT analysis were marginally less than or equal to the corresponding ST estimates. The exception to this was udder support and angular­ ity which had a .PN116 .OP slightly larger average estimate by MT analysis. The traits most affected by method of analysis were stature and foot angle as the MT estimate was 4 points smaller chan the corresponding ST estimate. Multiple trait analysis seems to offer no great advantage for improving the precision of heritability estimates since the standard deviations of the estimates are similar to those obtained from ST analysis. Schaeffer (1984) stated that the correlation between error ef­ fects for different traits has a direct effect on the interchanging contributions that one trait will have upon another. He also notes that as the number of observations on trait i increases the contri­ bution of trait j would tend to have no influence. Therefore, if the relationships between milk yield and type characteristics are small and the number of progeny large, the contribution of milk yield information to improve genetic estimates of type would be expected to be small. This could possibly explain the small or negligible changes in genetic parameters for type when Table 32. Data set 1 2 3 4 5 Average Std. deviation Total number of records 60,008 51,651 65,264 50,472 69,078 Estimated genetic parameters between milk and stature Number of paired records 4,882 3,749 6,416 3,960 5,550 aEstimates are significant (P<«05) Heritability Correlation ----------------------- ■ -------------------------------------- Milk Stature .15 .14 .19 .16 .14 .16 .02 .31 .38 .26 .32 .31 .31 .04 Phenotypic .03 .02 .02 .01 .06 .03a .02 Genetic -.41 -.18 -.16 -.19 .06 -.16 .17 Table 33. Data set 1 2 3 4 5 Average Std. deviation Total number of records 60t008 51,651 65*264 50,472 69,078 Estimated genetic parameters between milk and strength Number Heritabillty Correlation of p a i r e d ------------------------ ------------records Milk Strength Phenotypic Genetic 4,882 3,749 6,416 3,960 5,550 .19 .14 .15 .16 .14 .16 .02 .22 .17 .26 .24 .17 .21 .04 -.00 -.04 -.00 -.03 -.02 -.02 .02 .03 -.36 -.14 -.17 -.01 -.13 .16 Table 34. Data set 1 2 3 4 5 Average Std. deviation Estimated genetic parameters between milk and body depth Total number of records Humber of paired records 60,008 51,651 65,264 50,472 69,078 4,882 3,749 6,416 3,960 5,550 aEstimates are significant (PC.05) Heritability Correlation --- -------------- ------ Milk Body Depth .15 .14 .19 .16 .14 .16 .02 .26 .26 .19 .36 .20 .25 .07 Phenotypic .07 .02 .04 .01 .04 .04a .02 Genetic -.22 -.30 .02 -.09 -.21 — .16 .13 Table 35. Data set 1 2 3 4 5 Average Std. deviation Estimated genetic parameters between milk and angularity Total number of records Number of paired records 60,008 51.651 65,264 50,472 69,078 4,882 3,749 6,416 3,960 5,550 aEstimates are significant (P<.05) Heritability Correlation ------ ----- ---- ------ Milk Angularity .14 .15 .19 .16 .14 .15 .02 .19 .05 .22 .31 .23 .20 .09 Phenotypic .36 .35 .30 .34 .34 ,34a .02 Genetic .20 -.11 .15 .56 .07 .17 .24 Table 36. Data set 1 2 3 5 Average Std. deviation Estimated genetic parameters between milk and rump angle Total number of records 60,008 51,651 65,26*1 50,472 69,078 Number Heritability Correlation records Hilk Rump Angle 4,882 3,749 6,416 3,960 5,550 .16 .14 .15 .19 .14 .16 .02 .19 .10 .33 .26 .29 .23 .09 aEstimates are significant (P<.05) Phenotypic .06 .01 .01 .01 .04 .03a .02 Genetic .23 .22 .28 .17 .05 .19a .09 Table 37. Data set 1 2 3 4 5 Average Std. deviation Estimated genetic parameters between milk and rump length Total number of records Number of paired records 60,008 51,651 65,264 50,472 69,078 4,882 3,749 6,416 3,960 5,550 Heritability Correlation ------- ---- ---- ------- ------ -------Hilk Rump Length Phenotypic Genetic .14 .14 .15 .19 .16 .16 .02 .20 .32 .05 .26 .13 .19 .11 .05 .00 .05 .00 .01 .02 .03 .05 -.26 -.23 -.33 -.55 -.26 .21 Table 38. Data set 1 2 3 4 5 Average Std. deviation Estimated genetic parameters between milk and rump width Total number of records 60,008 51,651 65,264 50,472 69,078 Number of paired records 4,882 3,749 6,416 3,960 5,550 aEstimates are significant (P<.05) Heritability Correlation ------------------------- Milk Rump Width Phenotypic .15 .14 .19 .16 .14 .15 .02 .27 .35 .46 .11 .25 .29 .13 -.00 .02 .01 .01 .03 .01 .01 Genetic -.22 -.32 -.33 -.40 .03 -.25a .17 Table 39. set 1 2 3 4 5 Average Std. deviation Estimated genetic parameters between milk and rear leg side view Total Number records records Milk 4,882 3,749 6,416 3,960 5,550 .14 .15 .19 .16 .14 .16 .02 60,008 51,651 65,264 50,472 69,078 aEstiraates are significant (P<.05) Heritability Correlation Rear leg side view .17 .18 .16 .09 .12 .15 .04 Phenotypic .04 .05 .02 .04 .01 .03a .02 Genetic .19 -.02 .13 -.18 -.13 .05 .15 Table 40. Data set 1 2 3 4 5 Average Std. deviation Total number of records Estimated genetic parameters between milk and foot angle Humber of paired records 60.008 51,651 65,264 50,472 69,078 4,882 3,749 6,416 3,960 5,550 4 Heritablllty -------Milk Foot Angle .14 .14 .15 .16 .19 .16 .02 .12 .18 .13 .07 .06 .11 .05 Correlation --------- ------------Phenotypic Genetic .01 -.02 -.01 .01 .01 .01 .01 -.19 -.14 .45 .12 .10 .07 .25 Table 41. set 1 2 3 4 5 Average Std. deviation Estimated genetic parameters between milk and fore udder attachment Total Number records records Hilk Fore udder attachment 4,882 3,749 6,416 3,960 5,550 .14 .15 .19 .16 .14 .16 .02 .24 .25 .19 .28 .15 .22 .05 60,008 51,651 65,264 50,472 69,078 aEstimates are significant (P<.05) Heritability Correlation Phenotypic -.04 -.02 -.04 -.06 -.05 -.04a .01 Genetic -.36 .08 -.34 -.57 -.26 -.29 .24 Table 42. Data set 1 2 3 4 5 Average Std. deviation Estimated genetic parameters between milk and rear udder height Total number of records 60,008 51,651 65,264 50,472 69,078 Number of paired records 4,882 3,749 6,416 3,960 5,550 aEstlmates are significant (P<.05) Heritability ------------ ------- ---Milk Rear udder height .19 .14 .15 .16 .14 .16 .02 .15 .29 .22 .12 .10 .18 .08 Correlation ---------------------Phenotypic Genetic .08 .08 .09 .08 .07 ,08a .01 -.33 .07 -.30 -.17 .01 -.14 .18 Table 43. Data set 1 2 3 4 5 Average Std. deviation Estimated genetic parameters between milk and rear udder width Total number of records Number of paired records 60,008 51,651 65,264 50,472 69.078 4,882 3,749 6,416 3,960 5,550 aEstimates are significant (PC.05) Heritability Correlation ----------------------- — Milk Rear udder width .14 .15 .19 .16 .14 .16 .02 .22 .23 .18 .18 .14 .19 .04 Phenotypic .09 .12 .11 .12 .10 .11a .01 ------- — — — Genetic -.51 .13 -.10 -.14 -.05 -.01 .20 Table 44. Data set 1 2 3 4 5 Average Std. deviation Estimated genetic parameters between milk and udder support Number Heritability Correlation Total number of records records Milk Udder support 60»00B 51,651 65,264 50,472 69,078 4,882 3,749 6,416 3,960 5,550 .14 .15 .19 .16 .14 .16 .02 .17 .26 .06 .08 .16 .15 .08 aE3timates are significant (P<,05) Phenotypic .08 .10 .08 .07 .05 .08a .02 Genetic -.15 -.21 .42 .02 -.39 -.06 .31 Table 45. Data set 1 2 3 4 5 Average Std. deviation Estimated genetic parameters between milk and udder depth Total number of records Number of paired records 60(008 51,651 65,264 50,472 69,078 4,882 3,749 6,416 3,960 5,550 aEstimates are significant (P<.05) Heritability Correlation Milk Udder depth .14 .15 .19 .16 .14 .16 .02 .23 .25 .33 .14 .21 .23 .07 Phenotypic -.15 -.11 -.14 -.16 -.17 -.15a .02 Genetic -.42 .16 -.13 -.45 -.00 -.17 .26 Table 46. Data set 1 2 3 4 5 Average Std. deviation Estimated genetic parameters between milk and teat placement rear view Total number of records 60,008 51,651 65,264 50,472 69,078 Number of paired records 4,882 3,749 6,416 3,960 5,550 aEstimates are significant (P<.05) — Heritability ------ ----- --------Milk Teat placement rear view .16 .14 .15 .19 .14 .16 .02 .18 .22 .26 .15 .13 .19 .05 Correlation ---------------------Phenotypic Cenetlc .01 .05 .03 .02 .00 .02 .02 -.18 -.25 -.06 -.36 -.28 -.22 .11 119 MT analysis was applied. IV.2.2.2 Phenotypic correlations Phenotypic correlations between milk yield and linear type traits estimated from MTMME methodology are also presented in Table 32 through Table 46. and positive. In general, phenotypic correlations were small This relationship indicates that cattle which were more desirable in type had a tendency to also produce more milk. Norman and Van Vleck (1972c), using Holstein data collected In the New York Type Appraisal Program, reported that most of the phenoty­ pic correlations between milk yield and type score were positive. The phenotypic correlations between milk yield and type traits which measure the overall physical characteristics of the body such as stature, strength, body depth and angularity were generally positive and small. The exceptions were strength, which was nega­ tively related to milk yield, and angularity which exhibited the largest positive phenotypic relationship with milk yield. The cor­ relations between milk yield and overall body measurements were significant (PC.05), with the exception of the correlation between milk yield and strength. This suggests that taller, deeper bodied cows that were more angular in their physical attributes have a tendency to produce more milk. Carter et al. (1965) using descriptively scored Holsteins, com­ pared to the ideal breed type, suggested that the phenotypic rela­ tionship between dairy character and milk production was the highest (.29) among all type traits studied. Although angularity and dairy character differ in the choice of scale (linear versus ordinal), the same characteristics should prove 120 to be desirable In both traits. Traits describing the rump structure of a cow such as rump angle, rump length and rump width were essentially independent of the cow's milk yield. Although the correlation between milk yield with rump angle was significant (PC.05) the estimated value was only .03. The phenotypic correlations between rear leg side view and foot angle with milk yield were also practically zero. Thus, any pheno­ typic association between milk yield and the desirability of the rear leg from the side view and the angle of the foot would be minimal. The udder traits were generally correlated positively with milk yield and were significantly different from zero (PC.05) with the exception of teat placement rear view. The width of the rear udder exhibited the highest positive correlation with milk yield (.11). Ocher udder traits that correlate positively with milk yield are rear udder height (.08) and udder support (.08). The depth of the udder was negatively associated with milk yield (-.15) as was the fore udder attachment (-.04). The two type traits most highly related phenotypically to milk yield were the depth of the udder and angularity. Norman and Van Vleck (1972) reported the depth of the udder and sharpness to be the best predictor of first lactation production. Burnside et al. (1963) also reports a positive relationship between the depth of the udder and milk yield. Dairy cattle which gave more milk tended to be deeper and wider in the udder and were more angular in their appearance. Cows with a higher milk yield on the average would be taller, deeper bodied and 121 be looser In the fore udder, more highly attached in the rear udder and have more udder support. IV.2.2.3 Genetic correlations Genetic correlations between milk yield and type traits ob­ tained by MT analysis are also presented In Table 32 through Table 46. The genetic relationships between the majority of type traits with milk yield was negative. The only positive correlations with milk were recorded for angularity, rump angle, rear leg side view and foot angle. The variability of estimates of genetic correlations among data setts was much greater than those of the corresponding phenotypic correlation estimates. The coefficients of variation of the mean estimates ranged from 47% to 517% for rump angle and udder support, respectively. Grantham et al. (1974) and White (1974) reported all descrip­ tively measured type traits except dairy character were negatively genetically associated with milk yield. The antagonistic relation­ ships would result in poorer milk yield if selection were placed on type characteristics In the dairy cattle population. In this study, the estimated genetic correlations between milk yield and the traits which measure the entire body, stature, strength, body depth and angularity, were not different from zero (P>.05). None the less, the estimates obtained were negative for the correlation between milk yield and stature, strength and body depth. A great deal of variation was exhibited across sample data sets with a majority of estimates being negative. The average genetic correlation between angularity and milk yield was positive 122 and moderate in magnitude (.17). However, estimates ranged from - .11 to .56 and thus the estimate was not (P>.05). different from zero The linearly scored type trait of angularity measures the similar attributes as the old descriptive trait dairy character. This suggests that sires which produce more angular daughters also have daughters which, on the average, produce more pounds of milk. The traits describing the rump structure of the dairy cow were mixed in their genetic relationship with milk yield. The correla­ tion between milk yield and rump angle was positive. Selection programs developed for milk yield would also produce progeny which would be lower at the pins. Rump length and rump width were moderately, but negatively correlated with milk yield as the estimates were -.26 and -.25, respectively. The estimate between milk yield and rump width was significant (P<.05). These traits were among the greatest in their average genetic association with milk yield. It would seem logical that if the correlations between milk yield and stature, strength or body depth are negative, rump length and rump width would correlate with milk in a similar manner. This is expected since taller and deeper bodied animals should also be longer rumped and wider rumped. The genetic relationship between milk and rear leg side view or foot angle appeared to be small, as the estiamtes were .05 and .12, respectively. However, the standard error among estimates across data sets was large. The estimated genetic correlations ranged from -.19 to .45 for foot angle and milk, All udder traits were negatively correlated genetically with milk yield. The two largest correlations were between milk and fore 123 udder attachment (-.29) and between milk and teat placement rear view (-.22). However, teat placement rear view was the only signif­ icant correlation (P<.05)> among the udder traits. It appears that selection for milk yield would eventually change the population to be more broken in the fore udder attachment and have teats that are more widely spaced and not parallel in their structure. The estimated genetic correlations between udder traits and milk yield varied from data set to data set more than other esti­ mated correlations. The variation in estimates was the greatest for estimates involving udder support and udder depth. The implication of negative genetic correlations between milk yield and udder traits is that a sire that produces daughters that excel in milk yield would also sire daughters that are more broken in fore udder, nar­ rower in the width of the rear udder and lower at the rear udder attachment. Furthermore, these daughters would have less udder support, more udder depth and have a wider teat placement. Genetic correlation estimates indicated that the traits which measure the angles of the body are most likely to be positively re­ lated to milk yield genetically. These traits such as angularity, rump angle, rear leg side view and foot angle may reflect the gen­ eral dairyness of the cow. IV.2.3 Correlations of sire solutions from single and multiple trait methodology Multiple trait mixed model methods can improve the accuracy of sire ranking for type traits by incorporating large milk yield data bases. This improvement would be available if only selected subpop­ ulations contribute type information. 124 If MT methodology is successful in increasing the accuracy of sire ranking for type, the BLUP results from ST may be different from those from MT methodology. The rank correlations between ST sire solutions from (Equation III.5) and MT sire solutions (Equation III.6) were computed and presented in Table 47 and Table 48, respec­ tively. The average rank correlations range from .955 for strength to .675 for angularity. Product moment correlations between ST and MT methodologies follow similar patterns for all traits but are margin­ ally higher in magnitude. The ranking of the sire solutions for stature, strength, body depth, rear leg side view and rump angle changed little from analy­ sis by ST or by MT methods, as the average rank and product moment correlations were all above .90. These results seem to suggest little additional accuracy is gained by MT analysis over a more simple ST method. Rump length, rump width, foot angle and all traits associated with the udder had rank correlations greater chan .80 but less than .90. The sire solutions of these traits are more influenced by the method of analysis. However, no noticeable trend in the estimated genetic or phenotypic correlations was discovered between the traits that had sire solutions correlated above .90 and those correlated between .81 and .89. Angularity was most affected by the method of analysis. The rank and product moment correlations between ST and MT methodology were .675 and .710, respectively. two was .246. The rank correlation for data set The removal of this estimate raises the average to .782 which is still slightly below other traits. Table 47. Rank correlations between sire solutions for single and multiple trait analysis Data set Trait Stature Strength Body depth Angularity Rump angle Rump length Rump width Rear leg aide view Foot angle Fore udder attachment Rear udder height Rear udder width Udder support Udder depth Teat placement rear view 1 2 3 4 5 Average Std. Dev, .97 .86 .88 .76 .88 .94 .89 .95 .94 .88 .82 .69 .90 .94 .93 .85 .97 .86 .25 .92 .60 .93 .98 .96 .97 .99 .98 .86 .87 .88 .96 .99 .99 .81 .96 .88 .93 .96 .58 .86 .74 .85 .72 .96 .98 .96 .96 .98 .80 .93 .64 .66 .79 .95 .77 .80 .87 .92 .81 .76 .99 .99 .88 .78 .99 .99 .99 .94 .98 .93 .97 .90 .72 .90 .84 .95 .96 .92 .67 .94 .81 .88 .92 .89 .88 .86 .86 .82 .90 .88 .06 .06 .07 .24 .04 .18 .13 .08 .17 .08 .11 .11 .10 .06 .09 Table 48. Product moment correlations between sire solutions for single and multiple trait analysis Data set Trait Stature Strength Body depth Angularity Rump angle Rump length Rump width Rear leg side view Foot angle Fore udder attachment Rear udder height Rear udder width Udder support Udder depth Teat placement rear view 1 2 3 4 5 Average Std. Dev. .98 .91 .93 .77 .9*1 .96 .94 .98 .98 .93 .89 .77 .93 .94 .95 .86 .98 .92 .29 .95 .73 .96 .99 .9B .99 .99 .99 .91 .91 .93 .98 .99 .99 .83 .98 .91 .93 .98 .66 .90 .81 .91 .81 .98 .99 .96 .98 .99 .88 .96 .70 .74 .89 .97 .79 .86 .89 .96 .88 .83 .99 .99 .94 .78 .99 .99 .99 .97 .99 .96 .98 .94 .83 .92 .91 .97 .96 .95 .71 .96 .86 .91 .96 .91 .91 .91 .90 .B9 .92 .92 .05 .03 .04 .24 .02 .14 .10 .04 .15 .08 .08 .08 .07 .03 .06 127 Low correlations were also found in one of the five data sets for foot angle, rump length and rump angle. Coincidentally, the estimated sire variance components from single trait analysis were relatively small for these traits. Thus, sampling error would probably be relatively great for these traits. The standard deviations of sire solutions of linear type scores obtained by single and by multiple trait analysis are shown in Table 49. The estimates from MT methodology were generally more variable within data set across all samples. It seems that MT analysis would result in greater relative differences between sires. The standard deviations of sire solutions from the five data sets show that results from MT analysis tend to be more variable. However, data set five had only five of the 15 traits more variable in the MT estimates than ST estimates. Udder support and udder depth were the only traits consistent in variability among solutions. Multiple trait analysis separated more of the sire differences across all five randomly sampled data sets. Table 49. Haan standard deviation of aire estimates for type tralta analyzed by single and aultlple trait nachodology 1 Trait Stature Strength Body dtpth Angularity Buap angle Rump length Buap width Bear leg aide view Foot angle Fare udder attach. Rear udder height Rear udder width Udder support Udder depth Teat placeuent rear view ST 1.246 .665 .860 .673 .323 .786 1.044 .637 .652 ,88B .904 .684 .603 .634 .736 2 KT 1.272 .666 .877 .790 .326 .794 1.111 .647 .653 .934 1.079 1.023 .671 .610 .785 ST 1.010 .793 .806 .231 .84B .161 .797 .614 .462 .881 .758 .804 .799 .628 .764 Data Set 4 3 HT 1.138 .802 .829 .521 .853 .200 .812 .604 .454 .880 .728 .777 .925 .653 .828 ST .859 .686 .585 .816 .666 .579 1.195 .528 .212 .700 .560 .635 .240 .726 .512 KT .830 .685 .571 .784 .692 ,65S 1.304 .530 .333 .759 .690 .700 .272 .752 .488 ST 1.006 .701 .942 .780 .505 .308 .339 .339 .266 .784 .404 .561 .266 .307 .523 HT .947 .723 .947 .892 .453 .474 .453 .375 .259 1.029 .480 .667 .267 .336 .583 S ST 1.100 .623 .714 .597 .762 .543 .801 ' .499 .469 .654 .413 .599 .601 .444 .524 Avg. HT 1.053 .615 .709 .923 .765 .532 .777 .495 .462 .642 .407 .577 .722 .582 .533 ST 1.044 .694 .781 .619 .621 .475 .835 .523 .412 .781 .608 .657 .502 .548 .612 Std. ,MT ST MT 1.480 .698 .787 .782 .618 .531 .891 .530 .432 .664 .677 .749 .571 .587 .643 .142 .063 .138 .234 .210 .244 .325 .118 .176 .105 .219 .094 .241 .169 .127 .170 .070 .148 .15B .221 .222 .328 .106 .150 .333 .263 .169 .291 .154 .153 V. Summary and Conclusions Genetic selection for some body conformation characteristics, with various degrees of relative emphasis and accuracy, has been practiced by Holstein dairymen. Only a subpopulation of Holstein cows have contributed information for the genetic evaluation of bulls and for estimation of genetic parameters involving type traits. This subpopulation may not represent a random sample of the total milk recorded population in which genetic selection for type has been of interest. If not, the bull ranking for type and the relationship estimates between type and production from this subpop­ ulation may be inaccurate for the total population. A new linear scoring system was implemented by the HFAA in January of 1983. The infancy of this new system may further re­ strict the subpopulation which provides the database. A recently developed statistical procedure, multiple trait analysis, can be used to remove such possible inaccuracies by a joint analysis of type and milk production. Type data is from a subpopulation which may not be random, while the more abundant production data is more likely to randomly represent the entire population. The purposes of this study were to estimate heritabilities and genetic and phenotypic correlations among the linear type traits, and the phenotypic and genetic correlations between type and produc­ tion for the entire population in which genetic selection for both milk and type is of interest. The goal was to establish the dif­ ferences, if any, in the genetic parameters and bull ranking between the small population which provides the linear type scores and the 129 130 larger populacion. The 305-day 2X-ME lactation records were provided by Michigan and Wisconsin DHIA and the first linear scores were provided by HFAA. The most highly heritable type trait in the subpopulation was stature, while the least heritable was udder support. The scores encompassing the entire body such as stature, strength, body depth and the rump traits were more highly heritable than those of the udder or the feet and leg traits. The phenotypic correlations among the 15 primary type traits were generally large and all were positive. greater than .90 were: Phenotypic correlations rump length and rump width; udder support and teat placement rear view; and udder depth and teat placement rear view. The traits that were least associated with each other phenotypically were: udder depth and angularity, rear leg side view and foot angle, udder depth and rear leg side view, and rear udder height and rear udder width. Genetic correlations among the 15 linear type traits were generally smaller than their corresponding phenotypic correlations. Rump angle, foot angle and rear leg side view were negatively asso­ ciated genetically with most of the other type traits. The largest genetic correlations were between stature, strength and body depth. The udder traits were also highly genetically asso­ ciated among themselves. Selection programs designed to improve the udder characteris­ tics would also tend to produce taller, stronger, deeper bodied cattle that were lower at the pins and more posty in the rear leg. Heritability estimates from the subpopulation using single 131 trait (ST) methodology and for the larger population using multiple trait (HT) methodology were similar. The trait exhibiting the largest heritability was stature, regardless of methodology. The traits with the greatest change in estimated heritability between methods were stature and foot angle as both were smaller from MT methods than those from ST. In general, MT methodology seems to offer no great change In estimating heritability of linear type traits. The phenotypic correlations between milk yield and linear type traits from MT for the larger population were generally small and positive. Milk yield was significantly (PC.05) correlated with sta­ ture, body depth, angularity, rump angle, rear leg side view, fore udder attachment, rear udder height, rear udder width, udder support and udder depth. The strongest phenotypic correlations were between milk yield and angularity (.34) and milk yield and udder depth (-.15). Dairy cattle which gave more milk tended to be deeper and wider in the udder and more angular in their appearance. Cows with a higher milk yield, on the average, would be taller, deeper bodied and looser in the fore udder, more highly attached in the rear udder and have more udder support. The genetic correlations between milk yield and the 15 linear type traits were generally negative from MT for the larger popula­ tion. The only traits positively correlated with milk yield were angularity, rump angle, rear leg side view and foot angle. The variances of genetic correlation estimates were much greater than those of the corresponding phenotypic correlation esti­ mates. In fact, the genetic correlations between milk and 12 of the 132 15 type traits were not signficantly different from zero. Only those between milk and rump angle, rump width and teat placement rear view were significantly different from zero (P<,05). Traits which measure body angles are most likely to be posi­ tively related to milk yield, while milk production seems to have little genetic association or is negatively related with the remain­ ing type traits. Valter and Mao (1985), using simulated data, found the dif­ ferences between single and multiple trait analysis with zero re­ sidual covariance and full multiple trait analysis to be influenced by the amount of selection and the magnitude of the genetic and residual covariances. Full multiple trait analysis removed the effects of selection regardless of either the level of selection or the magnitude of the correlations. The results of the present study would suggest that the cattle scored for type do randomly represent the total milk recorded popu­ lation. This conclusion is based on the fact that single and multi­ ple trait results differ very little. The rank and product moment correlations between best linear unbiased prediction (BLUP) results from ST and those from MT methods revealed little difference between the ranking of sires based on the subpopulation and from the larger population. The average rank correlations ranged from .955 for strength to .675 for angularity. The standard deviations of sire solutions of the linear type scores from MT methodology were generally greater than those from ST, suggesting that MT analysis produces greater relative differ­ ences between sires. For MT analysis, the entire data set available was not used. 133 Rather, five samples of 150 sires and their daughters' data sets were randomly sampled with replacement. Possibly, a stratified sampling strategy which divides the sires into classes by the number of daughters would aid in the prevention of selection of sires which have an enormous number of daughters with milk records and very sparse type Information. This would prevent the saturation of the data set with milk records. A sampling procedure which chooses the 150 sires with the highest percent of paired records may indicate the need of quality data structure. This would prove to be interesting work particular­ ly in the evaluation of milk and type since heritabilities and genetic and phenotypic correlations between the traits can be low. The general framework in the application of the triangular transformation to achieve zero residual covariances in MT has been described in the literature. However, the methods which were used to calculate residuals and the algorithms used to estimate the variance components have not been used in simulation to confirm their efficiency or convergence characteristics. Such comparisons among alternative algorithms should be most useful in practice and probably can be done most effectively by the simulation approach. APPENDICES 134 Table A. 1 The Holstein Association Linear Classification Program PLEASE NOTE: C opyrighted m ate ria ls in this docum ent h av e not b e e n film ed a t th e r e q u e s t of th e au thor. T hey a r e available for c o n su ltatio n , h o w ev er, in th e a u th o r's university library. T h e se co n sist of p a g e s : LINEAR H o l s t e i n A s s o c i a t i o n Linear C l a s s i f i c a t i o n Program University Microfilms International 300 N Z eeb R d., Ann Arbor, Ml 48106 (313) 761-4700 135 Table B.l Description of the linear type data Item Michigan Wisconsin Grade cows Registered cows Canadian sires United States sires Stage of lactation dry springing milking Number of classifiers Number of Observations 14,587 50,288 2,899 61,976 1,378 63,497 3,286 274 61,515 25 136 Table B.2 Distribution of cows by parity Parity 0 1 2 3 4 5 6 7 a 9 10 >11 Counts 3,715 23,743 17,017 11,482 5,619 1,782 781 368 183 92 57 36 137 Table C.l .Lactation number distribution Lactation Number 1 2 3 4 5 6 7 8 9 10 >11 Count Michigan Wisconsin 193665 142998 100317 66966 42054 24445 13030 6454 3026 1249 835 324771 226589 159553 109048 70794 42825 23479 12148 5969 2708 1796 138 Table C.2 Month January February March April May June July August September October November December Distribution of month of last calf Count Michigan Wisconsin 45877 40971 49937 45460 46177 48818 54984 55772 52608 51167 51633 50638 82283 80852 96519 81399 81058 46031 73971 74620 82672 83264 83444 83444 Table D.1 Distribution of sires by number of daughters and herdsJ Data set 1 Number of Herds II 16 21 26 31 11 51 61 71 81 91 101 201 301 1D1 501 IS 20 25 30 10 50 60 70 BO 90 100 200 300 400 500 650 11 12 13 11 15 16 4 0 16 0 0 0 0 0 0 1 0 0 0 0 0 11 17 11 T~ 3 o 0 1 0 10 2 1 0 0 0 8 4 2 0 0 a i 0 0 14 3 2 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 11 0 0 ,0 0 0 4 0 0 0 31 01 01 -I- 0 0 0 0 0 0 0 0 0 0 0 0 4 11 IB 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 01 01 01 01 01 0 0 0 0 0 _J 11 I I 31 Table D.2 Distribution of alres by nuaber of daughters and herdsi Umber II 15 Class Coda I u H B E I 3 2 4 5 1 2 0 0 6 7 9 10 *11 D 1 U a u T f E S 12 13 14 15 16 17 IB 0 0 0 0 0 0 0 0 0 0 0 SI 60 61 70 71 BO T I B 0 F 16 21 26 31 41 20 25 30 40 50 2 2 0 0 0 11 0 2 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 or Hards B1 90 91 100 101 200 201 300 10 11 12 13 301 400 401 500 SOI 650 W 15 16 651 B01 Total BOO 9999 Sires 17 IB I I I I I -II 10 0 0 0 0 0 Data sat 2 4 0 0 0 0| 3 0 19 0 0 0 0 0 0 -I01 0| 01 01 01 0| 0 0 0 0 0 0 2 0 0 0 0 0 1 II II B 0 0 0 0 0 5 1 0 0 0 a 0 6 0 0 17 6 17 _l Total Sires 13 IB 12 I I 21 I 21 150 141 *O» U H •» £ c— e™ S 1s m © Data set 3 in i S — and herds] CM O O CM *S tn IM O O O CM -I 0 o © o o ii 0 N O O O Q O ►* i8 CM m o o o o © o fn .8 CM O o o o o o o CM « • © o o o o o o cn 5 1 0 0 of sires by nuaber, of daughters Distribution Table D.3 o o I in in 0 o o o o o o 0 in *- o o o o o o o o o 0 CM o o o o o o o o o o 0 o o o o o o o o o o o o o o o o o a o o o o 0 — 0 0 0 o o o o o o Ol 0 O I 01 1 m s *s — It o« • - o in i m 3 » iR S is iS I R 0 OS •* o ** o m «*• m o o 8 CM i SQ O