University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Faculty Papers and Publications in Animal Science Animal Science Department January 1979 GROWTH RATE OF THOROUGHBREDS. EFFECT OF AGE OF DAM, YEAR AND MONTH OF BIRTH, AND SEX OF FOAL R. L. Hintz Oklahoma State University, Stillwater H. F. Hintz Cornell University L. Dale Van Vleck University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/animalscifacpub Part of the Animal Sciences Commons Hintz, R. L.; Hintz, H. F.; and Van Vleck, L. Dale, "GROWTH RATE OF THOROUGHBREDS. EFFECT OF AGE OF DAM, YEAR AND MONTH OF BIRTH, AND SEX OF FOAL" (1979). Faculty Papers and Publications in Animal Science. 338. https://digitalcommons.unl.edu/animalscifacpub/338 This Article is brought to you for free and open access by the Animal Science Department at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Papers and Publications in Animal Science by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. GROWTH RATE OF THOROUGHBREDS. EFFECT OF AGE OF DAM, YEAR AND MONTH OF BIRTH, AND SEX OF FOAL H. F. Hintz 1 , R. L. Hintz 2 and L. D. Van Vleck I Cornell University, Ithaca, NY 14853 SU MM A R Y about the 15th of each month. A total of Weight, height, and cannon bone measure- 19,883 records on 1,992 foals out of 813 dams ments were obtained on 1,992 Thoroughbred and by 365 sires was collected from January foals. Colts were heavier than fillies at birth and 1958 to June 1976. The records were classified the differences increased with age. Dams under into 47 age groups (table 1). The 47 age groups 7 years of age and older than 11 years had foals were divided arbitrarily into nine sections for of lighter weight at birth than mares 7 to 11 the estimation of variances which were then years of age and the differences persisted at 510 assumed to be homogeneous for all ages within days of age. Foals born in April, May, or a section of the data. June were heavier than foals born in January, The following linear model was assumed for February, or March. Year of birth also influ- each growth measurement (weight, height, and enced body weight. The trends for height at front cannon bone circumference): withers and cannon circumference were similar to those of body weight. Y=X/3+Zu+e (Key Words: Growth, Horses, Thoroughbreds.) where Y is the vector of records;/3 is a vector of INTRODUCTION sex of foal effects, age of dam effects, month- year of birth of foal effects, age group effects Few studies are available in which the and population mean; X is a known design growth rates of a large number of horses have matrix; u is a vector of one-half the additive been examined. For example, growth curves are genetic effects of the sires having a multivariate presented in the NRC (1973) publication on distribution with mean zero and nonsingular horse nutrition but with the apology, "The variance-covariance matrix G; Z is a known curves are presented as examples rather than as design matrix; e is a vector of residual effects models because they are based on limited including environmental and other genetic data." Furthermore, the effects of many factors effects having a multivariate distribution on growth rate have not been determined. with mean zero and variance-covariance matrix Therefore, analysis of the data collected by R; and u and e are mutually uncorrelated. Windfields Farm 3 was made to estimate growth For the class of linear models assumed, the rates of Thoroughbreds and to examine the solutions to the equations: effects of age of dam, sex of foal, and month and year of birth on measurements of growth. x'~-'x X'R-lZ 7 pt = [X'~-ly7 MATERIALS AND METHODS 7.,.-,x Lz,.-,yj Every foal at Windfields Farm is weighed and height at withers and front cannon bone circumference at the midpoint is measured on namely, /3 and u are generalized least squares (GLS) solutions of functions of the fixed effects (Henderson et al., 1959, 1973) and best linear unbiased prediction (BLUP) of the xDepartment of Animal Science. random effects (Henderson, 1963, 1973), 2Present address: Department of Animal Science, respectively. Oklahoma State University, Stillwater. 3 The cooperation of Windfields Farms, Oshawa, For this investigation, the vector u was Ontario, Can. in supplying the data is greatly appreci- expanded to include one-half the additive ated. 480genetic effects of all 4,214 animals which JOURNAL OF ANIMAL SCIENCE, Vol. 48, No. 3 (1979) GROWTI 1 OF TI IOROUGI IBREDS 481 TABLE 1. ESTIMATES OF GROWTH defined to be A882 a~, where A is the numer- MEASUREMENTS OF FOALS ator relationship matrix of all animals with ADJUSTED TO THE BASIS order 4,214; h 2 is heritability; and Oy2 is the OF 8-YEAR-OLD MARES THAT FOALED IN total variance of records. Estimates of heritabil- MARCH OF 1958 ity obtained by Hintz et al. (1978) were used. It was assumed that R = lOe2 = l(1--88 Age of Weight Height Cannon bone where I is an identity matrix with order equal foals Colts Fillies Colts Fillies Colts Fillies to the number of records which implies that the e's are uncorrelated and that all records have days ~ kg cm common variance, ~ 2 The assumption of a common variance may not be a.ppropriate but is 2 55 54 100.6 100.1 12.5 12.3 7 63 62 102.3 101.9 12.6 12.4 convenient from a computing standpoint, and 12 71 71 104.6 104.1 12.9 12.7 any deviation from equality of variance was not 17 79 79 106.5 106.1 13.0 12.9 considered an important source of error. The 22 86 85 107.8 107.4 13.3 13.1 equations now become: 27 91 90 109.2 108.8 13.4 13.2 32 98 97 110.8 110.4 13.7 13.4 37 103 102 112.0 111.6 13.8 13.6 42 110 109 113.3 112.9 14.0 13.8 47 121 120 116.0 115.7 14.2 13.9 'X Z,Z+A-1 4 LZyj 52 128 127 117.6 117.3 14.5 14.3 57 132 131 118.5 118.2 14.6 14.4 62 137 135 119.6 119.3 14.8 14.5 The inverse of A is easily obtained using the 67 144 143 120.6 120.3 15.0 14.7 rapid procedure developed by Henderson 72 148 147 12019 120.6 15.0 14.7 (1975). 77 154 153 122.1 121.8 15.3 15.0 82 162 160 123.4 123.1 15.4 15.2 An iterative solution was obtained since a 87 165 163 124.4 124.0 15.5 15.2 direct solution to the full set of equations is 97 170 166 125.2 124.4 15.5 15.2 impossible because of the large number of 112 185 182 127.2 126.4 15.8 15.5 equations. Estimable functions of interest to 127 195 192 128.9 128.0 15.8 15.5 this investigation were the differences between 142 207 204 130.3 129.4 15.9 15.6 157 221 212 131.6 130.3 16.5 16.1 levels of the fixed effects such as the difference 172 235 227 133.4 132.0 16.6 16.2 between the effects of two ages of dam. The 187 245 236 134.6 133.2 16.8 16.4 inverse of the coefficient matrix needed for 202 258 250 135.8 134.5 16.9 16.5 computing variances of estimable functions was 217 270 260 137.1 135.7 18.1 17.7 232 283 272 138.5 137.1 18.3 17.9 not obtained since the equations were solved 247 297 280 139.5 138.1 18.4 18.0 iteratively. However, approximate variances of 262 301 290 140.7 139.3 18.5 18.1 differences were estimated using the following 277 310 296 141.8 140.4 18.6 18.1 equation: 292 318 304 142.6 141.3 18.8 18.3 307 325 311 143.6 142.2 18.9 18.4 Estimated variance of differences 322 334 320 144.4 143.1 19.0 18.5 337 336 320 145.1 143.4 19.2 18.6 ~ + 11 (TSS--RED)/(N--S) 352 345 329 145.9 144.2 19.4 18.9 n 374 359 343 147.2 145.5 19.6 19.1 404 373 355 148.8 146.8 20.1 19.5 434 392 375 150.2 148.3 20.4 19.9 where n 1 andn2 are the number of observations 464 415 392 151.8 149.8 20.7 20.1 containing the levels of the fixed effects in- 494 428 406 152.8 150.7 20.9 20.3 524 440 417 153.8 151.7 21.0 20.4 volved in the difference; TSS is the total sum of 554 446 424 154.5 152.4 21.2 20.6 squares; RED is the reduction in sum of squares 584 454 432 155.4 153.3 21.3 20.7 due to fitting the complete model; N is the 614 461 439 156.1 154.0 21.3 20.7 644 470 448 156.5 154.5 21.4 20.8 total number of observations; and S is the rank 674 482 459 156.0 154.9 21.4 20.8 of X.