Prediction of Average Daughter Performance from Sire Proofs for Use in Linear Programming Sire Profit Models

When linear programming is used to rank sires on daughter profits, coefficients of input are required for representative daughters of each sire. Within herdyear-season regressions of daughter's actual 305-day milk, fat percent, days open, 2-min milk yield adjusted for total yield, total milking time, and body weight at birth and first calving on sire's proofs for production, conformation, milking speed, and nonreturn rate were computed from progeny data from 71 Canadian Holstein-Friesian artificial insemination sires, to provide these coefficients. Coefficients of determination for prediction equations were .23 to .71. A production function was fitted for milk production and days open. First lactation 305-day milk was predicted from sire's milk rating and linear and quadratic terms of size ratings. Fat percent proof and its squared term predicted daughter's fat percent. Days open was predicted by milk and fat proofs. Milk yield in the first 2-min of milking, adjusted for milking yield, was predicted by proofs for milking speed and the quadratic term for fat percent. Total milking time was obtained from 2-min yield by regression ( .3837) of total milking time on 2-rain yield. Daughter's body weight at first calving was predicted from sire's size proof, as was birth weight. Milk yield was curvilinearly associated with days open. Received December 6, 1982. ~Animal Production Division, Malaysian Agricultural Research and Development Institute, P. O. Box 12301, General Post Office, Kuala Lumpur, Malaysia. This paper is based on the Ph.D. thesis of the first author, which was filed with the University of Guelph in 1979. Incidence of mastiffs was derived indirectly from regression (.00172) on sire's milk proof for milk. I N T R O D U C T I O N Proven artificial insemination (AI) dairy sires are rated in Canada for traits by best linear unbiased prediction (BLUP), estimated transmitting ability (ETA), and these have widespread use and acceptance by industry. In addition, since 1964 dairy sires have been rated on an approximation of dairy profit, referred to as a production dollar difference. This approximation is under review, and one alternative is a dairy farm linear programming model to rank sires on profitability of an average daughter. Because sire evaluations are independent for each trait, little is known about the correlated effect of a sire's merit for a number of traits on daughter's performance for any single trait or for total dairy merit. The merit of a sire for a single trait, measured on his daughters, may be defined as a function of the sire's ETA for a number of measurable traits that may affect the trait in question. Therefore, for estimating average daughter performance for linear programming models to rate sires on profitability, development of prediction equations should consider all available ETA of each sire. Although the sire's E T A is defined as an estimate of the relative mean of an infinite number of future daughers, the relationship between a sire's ETA for production, type, milking speed, and reproductive traits and his daughter's actual performance for milk yield, fat percent, days open, birth weight, body weight, and milking speed has not been the subject of study. One study that compared profitability of cows of high, medium, or low ETA for milk (1) revealed a linear relationship between ETA for milk and gross returns, but ETA for milk had a curvilinear relationship with days dry and days open. 1984 J Dairy Sci 67:3008--3014 3008 PREDICTION OF PRODUCTION COEFFICIENTS 3009 Thus, high milk proofs need not mean necessarily favorable production for other traits, and high milk yield among daughters need not be influenced necessarily by sire's superiority for milk alone but also may be influenced indirectly by sire's proofs for other characteristics. Our purpose was to measure the magnitude and direction of the effect of sire proofs for a number of important traits on their daughters' performance for economic traits taken singly in the form of prediction equations. Equations derived in this fashion are also useful in economic modeling. MATERIALS AND METHODS Seventy-one Canadian Holstein-Friesian sires had official proofs for type traits, production traits, and milking speed with 55% or higher repeatability based on daughters in five or more herds and nonreturn rates for a minimum of 20 daughters in at least 10 herds. Production records consisting of 305-day milk yield in first lactation, fat percent, and days open following calving between 1968 and 1978 were drawn from Canadian Holstein-Friesian Records of Performance (ROP) herd files. Daughter records in first lactation of the 71 sires were chosen randomly to have approximately equal numbers of observations per sire by our drawing records at more frequent intervals for sires with fewer daughters than for sires with larger numbers of daughters. Daughters of each sire were chosen randomly so that an average of 800 records was obtained per sire from a data set containing 98,118 records, irrespective of the herd in which the record was made. These records included more recent daughter records gathered after sires were proven. From the resulting data set of 56,800 daugher records, those having lactation lengths less than 100 days and first calving age less than 15 mo or greater than 36 mo were removed, reducing the data to 44,196 records. Days open is not recorded routinely in ROP records but is computed indirectly by subtracting a standard 283-day gestation from the interval between first and second calvings. For the analysis involving days open, only approximately one-half of the 44,196 heifer records had days open available, because remaining heifers had not had their second lactations entered into the file. With these restrictions, 22,392 daughter records of days open were available for analysis. Body weight records in first lactation of 7,672 daughters of the 71 sires obtained from Dairy Herd Improvement files; 582 birth weight records of all parities from the Elora Dairy Research Centre, University of Guelph files; 1,281 2-min milk yield records and 392 2-min and total milking time records from field data files collected by the University of Guelph were also available. The sire's average daughter 305-day milk yield, fat percent, and days open were predicted in separate analyses by the following model from sire proofs for production traits, type traits, milking speed, and nonreturn rates free of environmental variations common to individual herds: n Yij = a + h i +t=Z1 b t xti j + eij