Applications of an Animal Model in the United States Beef Cattle Industry

Applications of an Animal Model in the United States Beef Cattle Industry L. L. BENVSHEK, M. H. JOHNSON, D. E. LITTLE, J. K. BERTRAND. and L. A. KRIESE Animal and Dairy Science Department The University of Georgia

Athens 30602 Montana). In 1955, the first Beef Cattle Improvement Association was founded in Virginia and Performance Registry International was initiated. In 1959, beef cattle breed registry associations began to formalize collection of records by their members. Performance programs were nurtured in the 1960's and began to flourish, providing objective information that breeders could use in making selection decisions. In 1968, the Beef Improvement Federation (BIF) was formed. Thereafter, it began to provide the framework for the standardized and systematic procedures the beef cattle performance movement desperately needed. The B/F Guidelines became the perform~ ance standard reference for the US beef industry. One of the working committees established within BIF during that first meeting was to address National Sire Evaluation (NSE). Guidelines were approved by the BIF board in 1971 and published in 1972. In 1972 the American Simmental Association published the first national sire summary. Bulls were compared across herds, across generations, or across herds and generations, and beef cattle breeding had entered the twentieth century. Early sire summaries were based on a contemporary group-sire model. This model required several practical assumptions: I) contemporary groups are fixed environmental effects with groups defined as animals that arc of similar age, same sex, and each having equal opportunity to perform, i.e .. same herd environment, year, 2) sire effects are random with mean zero and variance a;, 3) genetic trend is not existent or unimportant, 4) sires arc mated to comparable cows, and 5) progeny are treated similarly within contemporary groups. Proliferation and implementation of technology for beef sire evaluation was rapid. C. R. Hender· son presented an invited paper at the 1972 Amer~ ican Society of Animal Science Annual Meeting, which formalized his mixed model procedures providing BLUP of breeding value (BY). Best linear unbiased prediction was soon part of beef national sire evaluation guidelines and a part of the vocabulary of serious beef breeders.

ABSTRACT

The theory of mixed linear models is finding widespread application in the United States beef cattle industry. At least 15 beef breeds have developed or are in the process of developing national genetic improvement

programs based on best linear unbiased prediction procedures and the animal model (or reduced animal model). These 15 breeds represent over 600,000 new registrations each year. The commercial industry is may· iog rapidly toward acceptance of genetic values on yearling bulls from these pro· grams. Both single trait and multiple trait analyses are conducted depending on breed and traits analyzed. All breeds have developed models for maternally influenced traits. At present. primary emphasis is on growth; however, some breeds have in~ cluded such traits as calving ease and hip height. Interest is developing among breeders for genetic evaluations of carcass traits. Procedures have been developed for gener~ tHing genetic values on a daily basis for young animals that are not included in the major analysis due to the time of year their records were obtained. These interim ge~ netic values provide information between major analyses. INTRODUCTION Brief History of Genetic Prediction in the US Beef Industry

The history of genetic prediction in the US beef industry begins with the chronology of beef cattle performance testing in the United States (I, 2). Research began in the 1930's with work at the US Livestock Range Research Station, Miles City, MT. Research continued through the 1940's with large regional programs (W-I, NCI, and S-IO). Bull test stations that appeared in the 1940's were the first attempt to provide across~herd information to beef producers. In the late 1940's and early 1950's beef cattle improvement programs began in several states (California, New Mexico. and 35

36

BENYSHEK ET AL.

Artificial insemination in the beef industry provided a data structure that lends itself to sophisticated models. Increased sophistication of mathematical models used in NSE has paralleled the improvements in computer hardware. Introduction of large·scale scientific supercomputers has opened the door to application of models not thought possible only a few years ago. In the decade from 1975 to 1985, many changes took place in sire evaluation technology. Mathematical models used in the analyses began to account for more and more of the factors that

could possibly bias predicted genetic values. Incorporation of the inverse of Wright's numerator relationship matrix (A-inverse) to enhance the accuracy of genetic prediction was documented in 1973 (14). The relationship matrix provided the means to incorporate pedigree information in the analyical procedure and a method to account for genetic trend. By 1983, the relationship matrix was incorporated into NSE programs of the US beef industry. Even with improvements in models, breeders and researchers alike continued to question effects of nonrandom mating of dams to sires on sire evaluations. At the same time (late 1970s and early 1980s) computer hardware was improving at a phenomenal rate. In 1984, a dam effect was included in the basic sire evaluation model for Hereford, Angus, and Limousin. In 1984, model dependency on difficult-to-verify assumptions was becoming less and less a problem in sire evalua· tion. Incorporation of dams into the model along with the A-inverse provided breeders the most accurate prediction of BY to date. Another problem that continued to burden breeders and researchers alike was the older age at which bulls were entering national sire summaries. Scientists were concerned because the generation interval increases with the age of the parents in a population, and this may result in reduced genetic change per year unless the accuracy of selection is substantially improved with the testing procedure. Breeders like to use young bulls in an attempt to move ahead of their competitors; therefore, they were making selection decisions based on information other than that contained in beef sire summaries, such as actual weights or show ring results. Most researchers in beef genetics had con· tended that NSE was a means to an end rather than the ultimate in genetic improvement of performance. It was generally recognized that unless

NSE was merged with on-farm and ranch testing programs, genetic progress would be slow, particularly in commercial herds (26, 27) since most commercial herds are not able to use AI. Methods for BLUP of BY utilizing records of relatives as well as the individual's own record were described in 1976 (16). The mathematical model termed the "animal model" (21, 22) was less dependent on hard-to-verify assumptions such as random mating of dams to sires and the absence of genetic trend in the population. The procedures merged NSE and on·farm testing programs into a National Cattle Evaluation (NCE) program. Genetic values are computed in the form of breeding values on sires, dams, and young animals (males and females) not yet producing progeny. The procedure computes BY, but the industry has elected to report and utilize expected progeny differences (EPD), which are equal to one-half the BY. The procedure adjusts for the merit of the mates of an individual, reducing substantially if not totally eliminating the effects of nonrandom mating. The animal model provides simultaneous BY (or EPD) for direct growth and maternal ability for those traits that are maternally influenced. Genetic trend is accounted for in the analysis, thereby providing more precise comparisons of old versus young animals. The animal model and data structure the purebred beef industry had established after JO yr of AI and NSE seemed to provide the ultimate in genetic prediction technology for beef can!e across-herd and generation evaluations of all individuals (male and female) in the population (breed). Computing problems associated with the animal model were reduced (22) by developing an equivalent model referred to as the reduced animal model (RAM). The RAM was less of a computational nightmare but also seemed beyond computing strategy and hardware of the early 1980's for breed-wide analysis. However, large scale scientific computers became readily available and experience gained in developing computing strategy for the sire-dam model in 1983 to 1984 encouraged application of the reduced animal model. In late 1984, RAM was applied in the Limousin and Brangus breeds. The Horned Hereford, Angus, Gelbvieh, and Red Angus breeds developed analyses based on the reduced animal model in 1985 to 1986. The RAM technology for prediction of genetic values is rapidly being adopted across the beef cattle industry because now commercial herds can

ANIMAL MODEL-BEEF

share directly and much earlier in the purebred industry's genetic progress. An example of genetic progres is shown in Figure 1. Regression coefficients for average BY (kg) on birth year are birth weight, .07; weaning direct, 1.25; weaning maternal (expre sed as kilograms of weaned calf), .28; and yearling weight, 2.13. Trends for weaning and yearling weight are probably half of what could be accomplished with increased AI and utilization of information in the breed sire summary. Until the mid-1980s, the show ring continued to have major influences on the purebred industry, which has hindered genetic change for performance characteri tic . It remains to be seen whether the application of RAM beginning in 1985 will increase the rate of change. It can be speculated that the rate will increase, if for no other rea on, because of commercial producer interest in EPD which will automatically force the purebred industry to place emphasis on NCE programs. Similar genetic trend can be shown in several other breeds with national programs. Fifteen beef breed in the United State currently have national genetic evaluation programs or are in the process of developing them. These programs have the potential to provide genetic values on over 600,000 registered beef animals

37

each year. Commercial beef producers in the US have little excuse for purchasing bulls that will not produce progeny with increased performance in growth and milking ability because the purebred industry makes public the genetic predictions on all bulls. In addition to growth and milk, some breeds are providing information on traits such as calving ease, scrotal circumference, and hip height. Female evaluation are made available to owners. Some breeds produce female lists or summaries each year. Specific matings based on NCE results are becoming more prevalent in the purebred beef industry. At least two breeds are providing EPD trends to breeders which allows them to monitor their genetic progress. Environmental trends are not utilized by the beef industry at the present time. Some breeds provide a computer sorting and listing service for bulls. This allows purebred or commercial producers the opportunity to access all of the EPD available through NCE. CURRENT METHODOLOGY

Historical information concerning genetic prediction procedures and the evolution of mathematical models is given in (3, 6). At present, most

30 25 (/)

~ --l

20

>

15


0

Z

is w w

([

CO

10 5 0

-5

L..---+---'---t-"---'----j---'-----t---'---t--L..--+--'---+------''---t---'

1972

1976

1978

1980

1982

1984

1986

BIRTH YEAR -.-. BWT

.. t:;, ..

WW

--0-- YW

-+

MA TERr'~AL

Figurc I. Hereford genetic trend average breeding valuc per birth year (kg). BWT = Birthweighl. WW = weaning weight. and YW = yearly wcight.

BE YSHEK ET AL.

38

US beef breeds utilize the reduced animal model (4,21). One breed uses the sire-maternal grandsire model. Both models are used in multiple-trait and single-trait applications. In matrix notation the animal model is: Y = Xb

+ Zu + e

where X and Z are incidence matrice relating the fixed and random effects band u to the vector of records Y. Fixed effects are usually contemporary group effects and random effect are breeding values of animals under evaluation. Records for traits such as weaning weight, yearling weight and hip heights are adjusted prior to analysis for known sources of variation such as age of dam and age of calf. The model specifications are: E Y u

Xb

=

e

0 0

and:

and: IX

= a';/a;, the ratio of the re idual vari-

A

=

ance to the additive genetic variance. numerator relationship matrix for animals in u.

COMPUTATIONAL CONSIDERATIONS

Analyses for national beef genetic evaluation programs are pre ently being run at Colorado State University, Cornell University, Iowa State University, and Univer ity of Georgia (UGA). These universitie u e everal different computers. For example, at Colorado State University, a CDC 205 supercomputer is utilized, whereas UGA conducts analyses on a IBM 3090 series y tem. Because of the different computing environments, several computing strategies have evolved. Each strategy is omewhat specific for the computer system available. The IBM system at UGA has exceptionally fast input/output I/O; thus, the strategy takes advantage of torage out of core. However, the CDC 205 at Colorado State University has almost unlimited core, so the strategy there is to move the entire data set into the core and build and olve the RAM equations internally. As an example, let us look at the computing needs for analysis of data from the American Angus Association using the IBM 3090 series computer at Georgia. The Angus data set is the largest analyzed to date in the US with RAM. In the most current analy is this data set contains 1,254,383 weaning records, resulting in 1,54],678 RAM equations. Weaning weight for the Angus breed is analyzed as a single maternally influenced trait. Table ] also provides information on run times and core requirement . Table 2 provide information for a multipletrait (weaning weight and postweaning gain) analysis of the Limou in data set. This analysis was conducted on the UGA IBM 3090. The Limou in data set represents the largest data set analyzed using a multiple trait RAM. All programs involved in editing and building equations are written in

The reduction in the animal model to RAM is accomplished by representing the breeding value of a nonparent individual, say i, as follows: u, = 1/2u'.

+

1/2u~

+ cP,

where super cripts sand d refer to the ire and dam of the ith individual. The cP, represents a Mendelian sampling effect. Step leading to the RAM equations are given in (4,21,22) Appendix 1 details both the animal model and RAM for a maternally influenced trait uch a weaning weight in a single trait analysis. Appendix I also provides the steps for reduction in a multiple trait analysis where one trait is maternally influenced.

TABLE I. Central processing unit (CPU) time and core requirements for single-trait analysis (weaning weight) of the Angus breed' (IBM 3090 series computer).

Edits Building equations Solutions Total

CPU Time (min)

Maximum core (K)

17.85 23.25 75.00 116.10

1000 816 6472

'Total weaning records = equations = 1.541,67R.

1.254.383. Total number of

39

ANIMAL MODEL-BEEF TABLE 2. Central processing unit (CPU) lime and core requirements for multiple-trait analysis (weaning weight and gain) of the Limousin breed ' (IBM 3090 series com pUler).

Edits Building equations Solulions Total

CPU Time (min)

Maximum core (K)

24.95 9.42 20.50 34.87

1504 412 2976

ITou.! weaning records = 274.145. TOI,.I number of equalions = 435,825.

COBOL, and the iterative solution program is written in PUI; bOlh have rapid I/O. The other three institutions primarily use FORTRAN. The editing procedures a1 UGA provide a series of checks to ensure the integrity of the data. The data provided by the breed associations are usually adjusted for factors such as age of dam and age of calf. Edits are as follows: 1. Check for proper contemporary grouping. An· imals must be grouped according to date of measure. herd, management code (creep or noncreep fed), age, sex, and percentage of breed if crossbreds are available in so-called upgrading programs. Single record contemporary groups are deleted to reduce overall num· bers of equations. 2. Outliers within contemporary group ratios are computed and those animals with ratios below 60 and above 140 are deleted. 3. Connectedness of sires is checked by absorbing the contemporary group equations into the sire equations and then by comparing off-diagonal elements of the resulting coefficient matrix. Disconnected sires are deleted from breeds with small numbers that may have few relationship ties. Periodically new genetic parameters are esti· mated for each breed. Present heritabilities for the breeds at UGA range from .24 to .33 for birth weight direct. whereas birth weight maternal ranges from .06 to .15. Weaning weight direct and maternal heritabilities range from .16 to .28 and .13 to .26. respectively. Estimates of 160 d postweaning gain heritability range from .15 to .20. Hip height is reported in only one of the UGA breeds with a heritability of .33. Genetic correlations between weaning weight direct and maternal have been estimated from - .30 to O. Genetic

correlations for weaning direct and 160 d postweaning gain direct have a narrow range from .30 to .35. Residual error variance ranges for birth weight. weaning weight and gain are 6.8 to 12.2 kg'. 257.0 to 377.7 kg', and 248.6 to 370.1 kg', respectively. An accuracy value is computed for each EPD. Accuracy in NCE programs is given by the following expression:

1-

Prediction Error Variance Additive Genetic Variance

The prediction error variance must be approximated because the actual inverse of the coefficient matrix is not obtained during the computation of the EPD. Approximate diagonals for the inverse of the coefficient matrix can be obtained at considerable computing cost. This has been the method used at Cornell. At UGA a simple system of developing accuracy values has been developed which probably requires somewhat less computing time than taking an approximate inverse. The procedure at UGA develops a lead diagonal element for each sire and dam by absorbing the contemporary group equations into the sire and dam equations. These diagonal elements are then used with diagonal elements from the A-inverse to compute the prediction error variance. This prediction error variance is probably more appropriate for a sire·dam model; however, in RAM analyses of small data sets where the actual inverse was available the approximation is reasonably good. Accuracies for nonparent EPD are computed as a linear combination of the parental accuracies. Some insight into a new computing rationale for the animal model is given by Schaeffer and Wilton (23). This strategy will probably be adopted because it does not require building the mixed model equations. APPLICATIONS RESEARCH

Comparison of Evaluations from Sire Models and the Reduced Animal Model

As the purebred beef industry prepared to change genetic evaluation procedures from sire models to animal models, there was considerable concern about changes in published ran kings of sires. Theoretically. the animal model provided for more accurate evaluations, so the industry

40

BENYSHEK ET AL.

never faltered in moving to the new procedures. A small simulation study in 1984 at UGA provided some insight to purebred breeders about the increased accuracy of animal model predictions and changes to be expected. The simulated data set for weaning weight contained only 61 sires but was of the size that could be analyzed easily. Genetic predictions for weaning direct were computed for the 61 sires using five methods: RAM, sire-dam model with A-inverse, sire model with A-inverse, sire model without A-inverse, and sire progeny means. Rank correlations between predictions from the above mentioned procedures and

a portion of weaning direct as well as maternal and was part of the reason for the low correlation between the 1984 and 1985 values. Comparison of Consecutive Years' Analyses

Generally rank correlations between BV or EPD from consecutive years are high. Table 3 shows rank correlations between consecutive analyses for sires of five breeds of beef cattle analyzed at UGA. All correlations are above .9 except for those of Shorthorns and postweaning gain for Brangus. The 1988 analysis of data from Shorthorn represents the 2nd yr of their NeE program. These correlations are smaller than expected based on consecutive years' analyses from other breeds analyzed at UGA. Observation of the two data sets, 1987 versus 1988, shows that numbers for Shorthorns, although small compared with the other breeds in Table 4, almost doubled from 1987 to 1988. This increase resulted from submission of much old data to the association after the publication of the 1987 Shorthorn Sire Summary. This back data (as many as 1000 records from one herd) resulted in changes in the base for the breed as well as numerous changes in pedigree infor· mation. Quantitating expected changes under these circumstances using simulated data has not been done. The smaller correlation for Brangus postweaning gain is the result of changing from single~trait to multiple-trait analyses in the current year.

true breeding values were .88, .84, .74, .66, and .66, respectively. This was not conclusive evidence of potential changes, but it was enough for two breeds to move immediately to RAM. The Limousin breed was the first US breed to apply RAM in 1985. In 1984, the sire-dam model was used in the genetic prediction procedure for the Limousin breed. Rank correlation between the 1984 and 1985 predictions for weaning direct EPD was .84, but the correlation between mater~ nal EPD was only .22. This latter change caused much concern among Limousin breeders; how~ ever, there was a general consensus that RAM values were more accurate and followed more closely observations in the field. Maternal EPD prior to 1985 were computed using a sire model with weaning weight of the calf t.aken as a trait of the dam. These sire model predictions contained

TABLE 3. Rank correlalions (Corr) bel ween expected progeny differences for sires from conseculive year's analyses. Weaning weight

Birth weight Oreed~

Angus Brangus Homed Hereford Umousin Shorthorn

Corr

.994 .901 .992 .%8 .686

Number! sires

23.992 22.459 2224 1610 9180

8613 8168 6786 762

482

Corr

Weaning mate mal

Number sires

Corr

Postweaning gain

Number sires

Corr

.997

36.333 34.609

.983

36.333 34,609

.995

.957

3475 2844

.907

3475 2844

.787

.997

25,295 24528

991

25.295 24528

.923

5510 4884

.976 .797

5510

4884 742

491

.698

742 491

Number sires

20.386

Yearling weight Corr

Hip height

Number sires

.998

20.313 \9,960

3475 1038

.932

3475 1038

.9%

16.661 16.485

.998

16.661 16.485

.982

5510 4884

.754

20.033

742 491

.979 .794

INumber sires = TOlal sires analyzed. top enlry = current year. Doltom enlry = previous year. lAngus and Horned Hereford analyzed biannually; Brangus, Limousin. and Shorthorn analyzed annually.

5510

4884 742 49\

Corr

.978

Number sires

5360 5265

41

ANIMAL MODEL-BEEF TABLE 4. Mating scheme for simulated herds under selection. Herd

Sires l

Mating scheme 2

1

HAl, LAl, 21-11-1, LH LAI. HAl, LH, 2HH 2HH, LH, HAl, LAI tH. 21-11-1. LAI, HAl HAl, 2HI-I. LH, LAI LAI. LH, 21-11-1, HAl HAL LAL LH, 2HH Sons of HAl and LAI

HAl x highest dams, other malings random LAI X highest dams, other matings random one HH x highest dams, other matings random LH x highest dams. other matings random HAl x lowest dams, other matings random LAI x lowest dams. other matings random All malings random All malings random

2 3 4

5 6 7

8

IHAI == The AI sire selected on highest actual breeding values for weaning direct and maternaL LAI = AI sire selected on lowest actual breeding values for weaning direct and maternal. HI-! = Within-herd sires seleclCd on highest llCtUlil breeding values for weaning direct and maternal. LH = Within-herd sires selected on lowest ilctual breeding values for weaning direct and maternal. 1Dams were retained with above average weaning ralios such that each herd maintained 50 breeding females. Highest dams included all above average heifers, based on actual direct and maternal breeding values. Lowest dams were females clOSCSI to the average weaning mlio of 100.

Commercial and purebred beef breeders in the US are beginning to pay more attention to ex· pected progeny differences on yearling bulls. Thus, a question of importance is reliability of genetic values computed for young animals without progeny. A study on this question has been conducted at UGA with Limousin and Hereford data using 160 d postweaning gain (weight gain from weaning to yearling). The study involved 71 Limousin and 138 Hereford bulls. all of which had legitimate individual postweaning records and were part of a legitimate contemporary group. In addition to having an individual record, the bulls had to have a specified number of progeny (Limousin. a minimum of 10, and Herefords, a minimum of 30 progeny). Expected progeny differences were computed using RAM, first. based on their own record plus pedigree (omitting progeny records) and. second, based only on their progeny plus pedigree (without their individual records). Rank correlations between these two sets of EPO were .59 and .58 for Limousin and Hereford. respectively. This contrasts to correlations for within-contemporary group 160 d postweaning gain ralios for these bulls and their EPO based on progeny of .17 and .20 for the Limousin and Hereford, respectively. This does not prove conclusively that nonparent EPO are the best pred· ictors of breeding worth, but it does show that basing selection decisions on performance ratios may not cause retention of the bulls which will have the better EPO based on progeny. These correlations point out that commercial producers

can select young bulls for natural service based on EPO with confidence that they are selecting bulls that would have superior EPO based on progeny had those bulls been progeny tested in purebred herds. This is important. because commercial producers seldom obtain more information on these bulls since progeny data from commercial herds are not used in the NeE programs. In beef cattle, maternally influenced traits make up an important part of the normal produc· tion cycle. Studies such as (13), which utilized a diallel mating system, have shown maternal effects to be important in beef cattle. Heritabilities for weaning weight maternal were .15 and .20 for Limousin and Brangus, respectively (7). Maternal heritabilities were greater than additive direct heritabilities for Hereford and Angus (24). In Limousin and Brangus the genetic correlation between direct and maternal is negative for weaning weight. A preliminary simulation study was conducted to demonstrate the effect of three levels of covar· iance between direct and maternal breeding values on genetic predictions in a simulated population under selection (17). This experiment was designed to investigate effects of intense selection in the presence of covariance between direct and maternal weaning weight breeding values as well as effects of using improper genetic covariances in RAM analyses. In order to study the effects of selection, two simulated data sets were generated using a beef cattle simulation program (28). Simulated were a

42

BENYSHEK ET AL.

random mating population and another where intense selection was practiced for a combination of weaning direct and maternal. Both populations consisted of eight herds with SO dams and 5 sires

(2 AI and 3 natural service) per herd. Sires were each bred to 10 dams. Eight calf crops were generated. Herds and sires were directly connected through use of AI, except for one herd where only sons of AI sires were used. This herd was connected only through the relationship matrix, which is similar to some herds in the purebred beef industry. The random mating population consisted of 3037 records from 92 sires and 883 dams representing 128 contemporary groups. To ensure ties in the population, sons of Al sires were used within a herd to replace old herd sires. The selected population consisted of 3050 records from 126 sires and 1157 dams representing 128 contemporary groups. More individuals became parents in this population than the random mating population, since there was active selection and replacement with selected animals. Replacement occurred in the random mating population mainly due to age and death loss. In the selected population, all initial selections of heifers and young bulls were based on indepen· dent culling levels for actual direct and maternal BV. Heifers had to be above average for both BV. Bulls were selected for both above average (high) and below average (low) combined BV. Each herd consisted of a high AI bull and a low Al bull that were selected at the beginning of the project and were used for the duration of the simulation. The remaining three sires ill each herd were within herd sires and two were high bulls and one was low. They were replaced by a comparable young bull after three calf crops or death. Mating schemes were consistent within herds with several combinations of assortive matings to simulate breeding programs in the beef industry. Replace· menl heifers were considered to be the highest value dams (see Table 4) when matings were made. Dams that had produced progeny were considered for matings based on the average of their progeny weaning ratios. They had met the selection criteria as heifers and then were retained on above average performance with each herd maintaining 50 breeding females. Table 4 shows the various matings made in the herds. The reason for the assortment of mating schemes is that the purebred beef industry uses many traits including visual appraisal traits in

selection programs. Thus, purebred breeders may select bulls have low BV or EPD for weights. Three data sets were generated for each ran· darn mating and selection population. Data sets were identical except for the correlation between direct and maternal weaning weight BV. The control data set had a genetic correlation (rll ) of zero. The negative correlation data set had a -.3 rg whereas a .3 rll was simulated in the positive correlation data set. Results showed that the random mating popu· lation retained correlations as originally input, but selection practiced on the other population even· tually generated a positive correlation between direct and maternal weaning weight breeding value even when a negative correlation was used in the simulation (see Table 5). The three data sets from each population were analyzed using mixed model procedures and RAM. Each data set was subjected to three analyses: first, with no covariance between direct and maternal; second, with a negative covariance equal to rll of - .3; and third with a positive covariance equal to rll of .3. Thus, each data set was analyzed once with the proper correlation and twice with improper covariances. Table 6 provides a legend for the 18 analyses conducted. Table 7 shows rank correlations between predicted and true BV for the random versus selection data sets by sires. dams, and nonparents. Accuracy of predicted BV for sires was enhanced by selection. This may be due to an increase in direct ties for sires since their daughters were also selected. There was no inbreeding depression built into the simulation model. Results may also have been influenced by the high-low selection of the sires, which split the sires into two groups and

TABLE 5. Correlations between simulated direct and malCrnal breeding values found in Inc data sets at tne end of calf crop 8. Random mating Control data set (initial r, = U)I Negative correlation data set (initial r_ "" - .3) Positive correlation data sct (initial r, "" .3) Ir, ""

Genetic correlation.

Selection

.07

.47

-.25

.28

.36

.60

43

ANIMAL MODEL-BEEF TABLE 6. Legend for the various analyses conducted. l Random mating population

Selection population

Control OS

Neg corr OS

Pas corr OS

Control OS

Neg corr OS

Pas corr OS

Control analysis T, = 0

CO

NC

PC

CC

NC

PC

Neg corr analysis

CN

NN

PN

CN

NN

I'N

CP

NP

PI'

CI'

NI'

PI'

T, =

-.3

Pas corr analysis T, = .3

IT, = Genelic correlation. neg = negative. corr = correlalion. pos = positive. OS = Dala sct. lFirsl [eller designates level of correlation used to generate the data sct. Second letter designates level of correlation used in the analysis of the data set. e.g., CC generated with T, = 0 and analyzed with T, = O.

possibly making it easier to predict true rank. Genetic trend, accounted for by the inverse of the relationship matrix, may have split true rankings even morc. This might have caused larger differences between sires. which could more easily be predicted. Solutions for dams were unaffected by the mating scheme. Nonparents' prediction accuracies were enhanced by selection in part for the same reasons as sires and due to the increased accuracy of prediction of their sires. Table 8 shows rank correlations between predicted and true BV for the control data set (zero correlation) under random mating. Predictions of direct weaning weight BV for sires, dams, and

non parents were not affected by the presence of a covariance. Accuracy of maternal BV predictions for dams and nonparel1ts appeared unaffected by the positive and negative covariances. Sire maternal BV predictions were most affected by the use of an improper covariance. Use of a negative correlation when a correlation did not exist resulted in the lowest accuracy of prediction for sires. This supports using a zero covariance if accurate estimates of the true value are not available.

TABLE 8. Rank correlations between predicted and true brecding values of weaning weight (WW) for the control random mating data set :malyses. TABLE 7. Rank correlations bctwecn predicted and true breeding values of weaning weights (WW) comparing random mating ilnd selection populations. Random mating

Selection

Sires Direct WW M~lIernal WW

.58 .55

.82 .75

Dams Direct WW M~I.ern~lJ WW

.52 .69

.52 .69

Nonpilrents Direct WW Maternal WW

.54 .39

.74 .65

CC'

CN

CP

Sires. n '= 52 Direct WW Maternal WW

.58 .55

.55 .46

.6\ .62

Darns. n '= 491 Direct WW Maternal WW

.52 .69

.50 .69

.5\ .69

Nonparcnls. n = 2.494 Direct WW Maternal WW

.54 .39

.53 .37

.53 .39

1 First letter designatcs level of correlation used to generate the data set. Second letter dcsignalCs level of correlation used in the analysis of the data set. e.g .. CC generated with r, = 0 ,wei ~walyzed with r, '= O.

44

BENYSHEK ET AL.

Table 9 provides the rank correlations between predicted and true BY for the control data set (no covariance) with assortive mating. Weaning direct BY predictions were little affected by the covariance. Maternal BY predictions were most affected by the use of the negative correlation. In these analyses the most correct T, is .3, since the mating scheme resulted in a .47 rI between direct and maternal. This is partially revealed in the higher rank correlations for maternal in that analysis (CP). Dams are probably less affected than are sires and non parents by the improper covariance, since they actually have a record for maternal. Table 10 gives rank correlations for the random mating data set developed with a -.3 Til between direct and maternal. As seen in Table 5, there was a negative .25 correlation between direct and maternal in this data set. Again, direct BV pred· ictions were little affected by the covariance used. The use of the negative covariance did not enhance the accuracy of prediction and in fact provided the least accuracy for sire maternal BY. The reason for this is not readily apparent, although it may simply be an artifact of the analysis. Assumption of no correlation between maternal and direct was not detrimental. Table 11 shows the analysis of the negative correlation data set under selection. Direct BV predictions were again not affected by the covariance used in the analysis. Because the mating scheme resulted in a .28 rg between direct and maternal, the most accurate analysis for sire and

TABLE 9. Rank correlations betwccn predictcd and true brceding values of weaning weight (WW) for thc control selection data set analyses.

CC' Sires. n = 86 Direct ww Maternal WW Dams. n =:< 762 Direct WW Maternal WW Nonparents, n = 2202 Direct WW Maternal WW

CN

CP

TABLE 10. Rank correlations between predicted and true breeding values of weaning weight (WW) for analyses of the random mating data set with negative genetic correlations. I

Sires. n =:< 52 Direct WW Maternal WW Dams. n =:< 491 Direct WW Maternal WW Nonparents. n =:< 2494 Direct WW Maternal WW

NC'

NN

NP

.58 .50

.56 .44

.61 .55

.45

.47 .65

.42 .64

.65 .51 .36

.52

.50

.36

.34

IGenetic correlations between direct and maternal weaning weight =:< - .3. 2Firstletter designates level of correlation used to generate the data set. Second letter designates level of correlation used in the analysis of the data set. e.g., CC generated with r, = 0 and analyzed with r, = O.

nonparent maternal was the one using rg equal .3. Use of -.3 was detrimental to the accuracy of sire and nonparent maternal predictions while the assumption of no covariance provided fairly good predictions. Tables 12 and 13 show rank correlations for the random mating and selection data set generated with a .3 r8 between direct and maternal. Actual

TABLE II. Rank correlations between predicted and true breeding values of weaning weight (WW) for analyses of the selection data set with negative genetic correlations. I

NC'

NN

NP

Sires. n = 86 Direct WW Maternal WW

.82 .73

.82 .54

.80 .S2

.82

.83

.75

.56

.81 .86

Dams. n =:< 762 Direct WW Maternal WW

.49 .67

.49 65

.47 .68

.52 .69

.51 .66

.52 .71

Nonparents. n = 2202 Direct WW Maternal WW

.73 .62

.73 .51

.73 .67

.74 .65

.73 .53

.74 .71

IFirst letter designates levcl of correlation used 10 generate the data sct. Sccond leller designates level of correlation uscd in the analysis of the data set. e.g .. CC generated with r~ =:< 0 and analyzed with r, =:< O.

IGenetic correlations between direci and maternal weaning weight = -.3 :lFirstlellerdcsignatcs level of correlation used to generate the data set. Second letter designates level of correlation used in the analysis of the dma set. e.g.. CC generated with r, = 0 and analyzed with r, = O.

ANIMAL MODEL-BEEF TABLE 12, Rank correlations between predicted and true breeding values of weaning weight (WW) for analyses of the random mating data SCI with positive genetic correlations. l

PC'

PN

PP

.58

.56 .46

.64 .68

.58

.53

.59

.72

.72

.72

.56 .45

.55 .42

.56 .47

Sires. n ; ; ; 52 Direct WW Maternal WW Dams, n = 491 Direct WW Maternal WW

Nonparcllts. n = 2494 Direct WW Maternal WW

.6D

'Genetic correlations between direct and maternal weaning weight = -.3

lFirst lettcr designates level of correlation used to generate the data set. Second letter designates level of correlation used in thc analysis of Ihc data sct, e.g .. CC generated with r~ = 0 and analyzed with r~ = O.

correlations were .36 and .60 for the data sets in Tables 12 and 13, respectively. As was the case throughout these analyses, weaning direct was not greatly affected by the covariance used in the analysis. Use of a negative correlation between direct and maternal resulted in lower accuracies for sires and nonparenl maternal in both data sets. Use of the proper positive covariance provided the most precise predictions of maternal BV for

TABLE 13. Rank correlations between predicted and Irue breeding values of wcaning wcight (WW) for analyses of the selection daw sel with positive genetic correlations, I PC 2

PN

PP

83

Sires, n = 86 Direel WW Maternal WW

.77

.83 .58

.82 .86

Dams, n = 762 Direct WW Maternal WW

.55 .70

52 .67

.72

Nonparents. 11 = 2202 Direct WW Maternal WW

.75 .6R

.74 .54

.75 .74

.56

IGenetic correlations between direct and malernlll wellning weight = -.3 :!First lettcrdesignates level of correlation used 10 generate the dllta set. Second letter designlllcs level of correlation used in the
45

sires and nonparents. In both data sets, the use of zero covariance would provide reasonably good predictions. Individual performance records of embryo transfer (ET) calves are routinely deleted from national sire and national cattle evaluation analyses because the calves are raised on surrogate dams. Usually the surrogate dams are of another breed and little information from them is available. This represents a sizable loss of information on ET calves, since selection decisions using EPD must be postponed until these calves become parents. In some breeds ET make up 10% of the registrations. A study was conducted at the Uni· versity of Georgia to determine the usefulness of ET records for prediction of 160 d postweaning gain EPD (19), Postweaning gain is the first record obtained after weaning and should be less affected by the maternal environment of the surrogate dam than weaning weight. Fifty-five bulls in the 1986 Limousin sire summary, having 10 or more progeny and postweaning gain records of their own, had ET calves themselves. Postweaning gain records of these 55 bulls and their ET contemporar· ies were added to the 1986 Limousin data set, while the progeny of these 55 bulls were deleted. Expected progeny differences were computed from this new data set using RAM and correlated with the 1986 published values based only on progeny. The rank correlation was found to be .14. Correlation of expected progeny differences based on pedigree alone for the 55 bulls with published EPD was .28. Within contemporary group performance ratios and actual gain were correlated with the published EPD based on progeny and found to be -.24 and - .02, respec· tively. This is in contrast to the results reported earlier in this paper showing that record plus pedigree yields EPD, which arc correlated around .6 with later EPD based on progeny. This indicates that there may be major problems in using indi· vidual performance records of ET calves for genetic evaluation. These low correlations compared with calves raised on natural dams may have resulted from improper contemporary group· ings since breed of surrogate dam was unknown . Surrogate dam effects may carryover into the post weaning phase of the animal's life. A method for computing genetic values in the form of EPD all a daily basis as new data become available has been developed (29). Appendix 2 shows the computational procedures. These interim procedures provide an excellent method of

46

BENYSHEK ET AL.

generating information on young animals at a low cost to breed associations. Such values appear to be far superior to performance ratios and estimated BV computed by selection index methods. Values are computed daily by breed associations and replaced when major analyses are done once or twice per year. In cooperative work with the Brangus Association, we found weaning direct and yearling weight EPD to be highly correlated (.99) with those eventually computed in the major RAM analyses. Maternal EPD correlated at .97. Results with Angus cattle were similar (29). Vanderwert (personal communication), working with the Limousin breed, also found that this interim procedure provided excellent early in for· mati on for those animals that had not made records at the time of the previous major reduced animal model analysis.

FUTURE CONSIDERATIONS

The US beef industry is beginning to explore the possibility of incorporating new traits into national genetic improvement programs. One breed is now publishing EPO for scrotal circum· ference, the first attempt to consider reproductive efficiency. Performance testing in beef begins with birth of a calf for most operations; thus, gathering reliable field data for the reproductive trait com· plex is very difficult. Calving interval and calving date as a trait of the cow within contemporary group have been suggested as possible traits. This assumes that cows having a shorter calving interval and calving earlier in the season are more repro· ductively fit. Management can have a large effect on characteristics of this nature, such as AI versus natural service in the same contemporary group. There is certainly much concern among producers with respect to reproductive efficiency; however, widespread incorporation of reproductive traits does not seem feasible in the near future. The US beef industry has become more concerned about carcass characteristics in recent months. Some firms in the packing industry have indicated that they might consider paying a pre· mium for carcass merit. An antiquated marketing and grading system will not allow much progress in this area; however. considerable research will probably be initiated concerning selection for carcass merit. To examine the feasibility of incorporating carcass characteristics into a multiple trait RAM

analysis, a preliminary simulation study was con· ducted at the University of Georgia (18). Data were generated using the beef cattle genetic simulation program (28). Data consisted of 4696 weaning weight and feedlot gain observations and 999 carcass product observations from II herds over nine calf crops. Weaning and gain records were from progeny produced by III sires and 1183 dams. Only 80 sires and 484 dams produced progeny with carcass information. Initial AI bull selection was based on above average actual yearling weight breeding value; however, the best bulls were intentionally not selected so the population mean did not increase quickly. Subsequent choices of new Al bulls, herd bulls. and replacement heifers was based on above average yearling weight estimated BY computed by the program using selection index methods. This is similar to selection schemes practiced in the industry at the present time. Artificial insemination bulls were used across 10 herds to connect the data set. Sons of these AI bulls were used in the II th herd. Three AI bulls were initially selected. One bull was used across all 10 herds and replaced with a son after four calf crops. The other two were each lIsed in a different subset of five herds for two calf crops. They were thcn exchanged for one calf crop. At this time they were rcplaced with sons who were used for two calf crops. Sons were then switched to the herds in which their sires were initially used for a calf crop and then replaced by sons. Each herd consisted of two AI sires, two herd bulls, and 50 cows. Base generation cows were replaced as quickly as possible. Most replacements were allowed to remain until the end of the simulation, giving an average of four progeny with weaning and gain records and two progeny with carcass information per dam. Two different slaughtering schemes were uscd. Progeny in six herds were slaughtered randomly, bUI in the other five herds offspring of cows with below average yearling weight estimated BY were slaughtered. Most genetic parametcrs used to simulate the data were unchanged from the original simulation program. These included the rIC between weaning weight direct and feedlot gain direct of .25. However. the program was modificd to include a genetic correlation of - .30 between weaning weight direct and weaning weight maternal. Three different genetic correlations between feedlot gain and carcass product were used: .15 .. 30. and .50.

47

ANIMAL MODEL-BEEF

After all of the data were simulated. three populations were identical except for carcass prod· uet. Three data sets for each level of gain and carcass correlation were derived for analysis. Data set J (DSl) contained all of the data. Data set 2 (OS2) contained carcass information on those animals with below average feedlot gain since those with above average gain were retained for breeding and could not produce a carcass record. Individuals in data set 3 (OS3) were selected at weaning. Those in the upper 75% of the population went on to feedlot gain and carcass records, whereas the lower 25% were culled. All relevant single-trait and multiple-trait (two and three trails) reduced animal model analyses were performed on each data set for each degree of gain-carcass correlation. Animals always had weaning weight reported. If they had a carcass record, they also had a feedlol gain record. This hierarchical arrangement simplifies the two-trait and three-trait multiple-trait RAM analysis. Weaning weight direct, weaning maternal, and feedlot gain predictions were little affected by type of analysis (single versus multiple trait). selection for slaughter scheme. or degree of rJl. between gain and carcass product. Table 14 contains the rank correlations between carcass predictions and true BV for sires. For lower rl." single-trait analysis produced predictions with accuracy similar to multiple-trait analysis for sires with progeny. However. with the higher genetic correlation of .5. the

multiple-trait analysis was superior in accuracy. particularly when selection practiced was on the basis of the correlated trait (DS2). Even predictions for sires whose progeny did not have carcass records were more accurate than those from the single-trait analysis. An additional consideration concerns the effects of genotype x environment interactions on BV prediction and use. Several studies (9, II, 12. 20. 25) have examined the importance of sire x environment interactions in beef cattle field data. Sire by breed-of-dam interactions have also been shown to exist in such data (5). The general conclusion was that interactions were of a magnitude to indicate some rcranking of sire progeny performance occurs across environments. Sire x environment interactions in field data may be due in part to assortative mating practices and could be reduced by including both parents in the estimation procedures (10). However. including all parents and the relationship matrix will nol account for interactions that are truly biological in nature. Sire x contemporary group effects. as suggested by Henderson (15), should be included in mixed model analyses of field data to reduce the contribution of any single sire contemporary group. This forces sires to be used across many herds to achieve a high accuracy of prediction. Separate sire evaluations for some regions of the country may be necessary to identify sires that perform well in regions where adaptation to ex-

TABLE 14. Carcass product rank correlation with true expected progeny differences. Sires +.15

STC~

MTG-C~

MTW-G-C Wifh progeny MTG-C MTW-G-C Without progeny MTG-C MTW-G-C

+.50

+ .30

OSI)

OS2

OS3

OS]

OS2

OS3

OSi

OS2

OS3

.73 .62 .63

53 .'8 .5U

6(,

.70 .64 .65

.S2 .50 .52

.63 .57 .59

.64

.5S .58

.71

.39 .58 .62

.62 .68 .69

n=HO

n=77

n =: 76

n=~O

n=77

n=76

n=80

n=77

n=76

.72 .72

.52 .54

.6'

.68 .69

.51 .53

.64

.68

.68

.65

.71

.5U .56

.69 .72

n=31

n=34

n= 35

n=31

n=3.\

n=35

n=31

n=34

n=35

AI .42

.35

.37 .39

.4(l

.37

.,'

.32 .30

.35 .37

.62 .63

.48 .50

.50 .51

.69

ISec tcxl for descriplioll of OS!. OS2. and OS3. ~ST

= Single lrait. MT = multiple frait. C = carcass product. G = gain. and W = we,ming weight.

48

BE YSHEK ET AL.

treme temperature, and humidity is essential for efficient production. Beef cattle national genetic improvement programs are dynamic; thus, improved technology will continue to be applied and certainly new trait will be added to program.

AN EXAMPLE OF COOPERATION

Rapid development of national genetic improvement programs by the US beef industry in recent years has resulted from cooperation between industry and Land-Grant universities. Industry has the responsibility to gather the data, ensure its validity and disseminate results of analy e . Land-Grant univer ities have responsibility for re earch and development. The two groups share the cost of development and both groups provide educational expertise to commercial and purebred producers. The system seems to be working very well. The theory of mixed linear models ha found widespread application in national beef cattle genetic evaluation program. The reduced animal model, along with enhanced computer technology, is providing the US beef cattle industry more accurate information for selection decisions than thought po ible only a few years ago. Extension of beef cattle performance testing programs into National Cattle Evaluation programs is helping to provide the basis for a genetically sound beef cattle industry.

B. Permanent environmental factors affecting the dam's milking ability (e.g.. loss of a quarter to mastitis) IV. Fixed factors A. Contemporary group environment (groups are defined as animals of similar age, same breed, same sex, given equal opportunity to perform, i.e., same management, same year,) B. Age of calf, adjusted to 205 d of age prior to analysis C. Age of dam, additive adjustment prior to analysis D. Others, may be unknown or considered part of the contemporary group A model accounting for the factors in the above outline is: Record of the individual = fixed contemporary group effect + breeding value of the individual + maternal breeding value of the dam + permanent environment affecting the dam + error. In matrix notation the model is:

where X and Z are incidence matrices relating the fixed effects b and the random factors (u d , direct breeding value; Urn' maternal BV, and upe, permanent environment) to the vector of records Y. The variance-covariance matrix for the random effect in the model is: Var

APPENDIX 1

I. Gene received from the individual's ire II. Genes received from the individual's dam III. Milking ability of the individual's dam A. Dam' genotype for milk I) Genes received from her sire for milking ability (maternal grandsire of the individual) 2) Genes received from her dam for milking ability (maternal granddam of the individual)

gilA g22A

Symmetric

U,'" e

Current Mixed Model Methodology used in the US Beef Industry

The factors affecting weaning weight, a maternally influenced trait in beef cattle, can be outlined as follows:

gilA

Ud Um

0 0 gJJI

0 0 0

aD

where: A = Wright's Numerator Relationship matrix, gil = additive genetic variance direct, 0:;; g22 = additive genetic variance maternal, 0;;,; g,2 = additive genetic covariance between direct and maternal, a•. m , and gJ' = 0;.. The following occurs because sent the same animal.

varl I Ud

um

=

Ig,1 g,2118) A gZI

g22

Ud

and u'" repre-

=

G., 18) A

49

ANIMAL MODEL-BEEF

u"'da", U''''d'"' represents the where y, - 6, contribution of the individual's own record; .~. a'Ja,u d, is the contribution of the individual's

therefore:

J"

Taking the inverse of Go and post multiplying by gives the following:

cr.

relatives and adjustment for mates. The adjustment of the individual's direct breeding value for the relationship between growth and milk is given by L a'Ja1u",j' J

and the mixed model equations for a maternally influenced trait become:

X'X X'Zd Z~Zd

X'Zm

+ A-'a,

+ A-la, Z~,Zm + A-'a) Z~Zm

X'Z... Z~Z... Z~Zpc Z~Zp<

a, =

where

(12

0-; *g",

= 0"; *gI2'

and

0'3

=

+ la,

b

X'Y

ud U'"

Z~y

u""

Z;",Y

Z~y

(T~ *g22l

o-;Icr""

a4 =

The prediction of direct breeding value for the i'h animal i :

Ulli

=

X~Xp

+ X~R"X"

X~

+ ~X~R"P

Z~Zp

The prediction of maternal breeding value for the i'h individual is:

X~Zmp

The first line in the case of a female represents the contribution of the dam's calves' records (k) taken a a trait of the dam (her calve' weaning weight indicate her milking ability). The second line represents relative' contribution and the last line adjusts for the relationship between milk and growth. The animal model equations for a maternally influenced trait can be reduced as shown by Quaas and Pollak (22). Bertrand et at. (7) discuss how to build the RAM equations for a maternally influenced trait. The RAM equations are as follow:

+ X~R"Zmp

+ X~R"Zp<

X~Zp<

+ tp'R"P + A,;;,'a, Z~Zmp + !P'R"Zmp + A,;;, 'a, Z~Z,>< + !P'R"Zp< Z~",Zm"

Symmetric

+

Z~,:R"Z:'p

+

Ap~'aJ Z~\pZp< Z~Zp

X~Yp

*

u d

u

m

up< parent· where R12 is defined as:

+

Z~,:R22Z~

+ Z~*R"Z~ + la,

+ X~R"Ya

where • indicates Z matrices relating nonparent records to Z~,pYp + Z~,:R"Z:'pY" parents' maternal breeding values Z~Yp + Z~·R"Z~Y" or permanent environment effect.

Yp + !P'R"Y"

The value of D, is l/2 or 3/4 depending on whether one or both parents are known. The a values are a previously defined. Backsolutions for non parents are given by:

U", = Il2u""oc

1+ O,a,-'

+ 1I2u""a", + I +

~

"

0

,(Y, -

,

6,

- u"'''''''' - u""""" - 1I2u""," - I12u"d'''')

50

BE YSHEK ET AL.

where:

and:

where Ud' is direct BY for growth and um, is maternal BY. The value of a" = O"~/a~, a'2 = O"~/ O",.m, and the value of D, = 1/2 or 3/4. Multiple-trait mixed model analysis considers the relation hip between two or more traits to enhance the accuracy of prediction. The use of multiple trait analyses can correct for election bias such as occurs in beef cattle data when some individuals are culled prior to a test period. An example i the effect of selection at weaning on postweaning gain te t. The following multiple-trait model is for a maternally influenced trait like weaning weight and a second trait postweaning gain:

gil = o;w = additive genetic variance weaning direct, g'2 = O"uw.m = additive genetic covariance between weaning direct and maternal ability, g'2 = O",w.", = additive genetic covariance between weaning direct and postweaning gain, g22 = O"~, = additive genetic variance for maternal ability, g23 = O"m.,g = additive genetic covariance between maternal ability and postweaning gain, g33 = o;g = additive genetic variance for postweaning gain, g..j = O"~ = permanent environmental variance.

Quaas and Pollak (22) show the multiple-trait mixed model equations for the full animal model. Given the following: where Ywand Yg are vectors of weaning weight and postweaning gain records. The X's, b's, Z's, u's. and e's are the same as previously defined with the subscript g indicating postweaning gain. The variance-covariance matrix for the random effects in the above model are: Uw

um

ug u"" ew eg

gilA g'2 A glJA 0 g22 A g2JA 0 g33A 0 Symmetric g.... 1

0 0 0 0 U;wl

0 X:R"Zw X;R2ZX. 0 Z:R"X w 0 Z:R"Zw + A -'gil Z;',R"X w 0 Z;',R"Zw + A-'g'2 o Z;R2ZXg A-'glJ Z;",R"X w 0 Z~R"Zg

X:R"X w

o

and

G; I

0 0 0 0 0 u;2gl

=

gil g02 glJ g21 g22 g23 g" g32 g33

u;w

Un",.", U nw ,a8-

U n ...... m

0"~1

-I

U m . ag ?

O"(\w.:I8o U I1l . u!t a~g

and if it is a sumed that O"cw.c. = 0 and O"m.". = 0, then the full mixed model equations appear as:

0 X:R"Zpe X;R22Z. 0 Z:R"Z", + A -'g'2 A -'g'3 Z:R"Z"" Z~R"Z", + A- 1g22 A-'go.' Z;',R"Z"" A-'g23 Z;R2ZZg +A-'g33 0 Z;",R"Z", 0 Z~cR"Zpc + ('/0";;"

X:R"Zm

0

b b

w•

w

* U'"

fi m

U.

u

pe

X:.R"Y w X;R20Y g Z:R"Yw Z;l1 R"Y . . . R" Roo Z;R 22 Yg Z~R"Yw

=

I'/O"~w

= I'/O"~g

51

A IMAL MODEL-BEEF

Solving the full mixed model equation is formidable for a multiple-trait analysis in most beef cattle population . The equivalent reduced animal model decreases the number of equations to be solved in a multiple-trait analy i and has been put into practice by several beef cattle breeds in the US. The reduction of the multiple-trait animal model as in the ingle trait previously discussed takes advantage of restating a nonparent record as the average of parental breeding values plus a Mendelian ampling effect. In matrix notation this can be written a follow:

where d = 1/2 if both parents are known or d = 3/4 if only one parent is known. Taking the inver e of R:

where

aL

u:

g

u,~.

= weaning weight residual, = gain residual,

= weaning weight additive genetic variance,

U;g = gain additive genetic variance,

covariance between weaning weight and gain and d; = 1/2 or 3/4. u"w.".

=

The error structure for nonparent records is:

ewn + cJ>wn I = Ieg" + cJ>g"

II~w + dU;w

dU;w.ng

dUaw."g

I~.

+ dU;.

I= R

provide the adju tments neces ary to write the RAM multiple-trait equations. The RAM multiple-trait equations are:

X:R"X w+ !X~.R;'P X:R"X m+ X:.R;'Zm. X~.R;'X •• X; R"Xg + X;.R;;'Xg• !X;.~'P X;n~112Zmn Z:R"X w+ ~P'R;'X •• 2 PR;2X,. Z:R"Z•. + !P'R;'P + Ap;'g" Z~R"Zm + !P'R;'Z",. + Ap;'gl2 Z.:lR"X w + Z~lI1R~IXwn Z~nR~2Xgn Z;,R"Zw + !Z~.R~,'P + A,;;,'g" Z~R"Zm + Z~.R;'Zm. + A,;;, 'g" !P'R;'Z",. + A,;;,'g2.1 W'R;'X•• Z;R"Xg + !P'R;'X,. tp'R~'P + Ap;'g'J

+ X~.R~'X~.

X~R"Xw

X;nR~2X;n

!X~.R~'P

b. b,

X:R"Z"" + X:.R"Z"". X;R22Z, + !X;.R;2p X;.RI2Z"". tP'R;'P + A,;;,'gIJ Z~.R"Z"" + !P'R;'Z", !Z;,.R;'P + A,;;, 'g2.1 Z~,R"Z,,, + Z.R~,'Z"". Z;R;'Zg + 4P'R;'P + A,;;,'gJJ !Z~nR;'P

II•.

11 m II,

+ Zpe.R~'Z",. + I'/er,.. llpe App = inver e relationship X~.R"Y. + X~"R;'Y", + X: mRl2y,. matrix among the parent . X;R"Y, + X;.R;'Yg• + X;.R;'Y•• Z:R"Y w+ !P'R;'Y w• + !P'R;'Yg, Subscript n denotes Z~R"Z""

Z~R" Yw+ Z;/nR;' Y", + Z~"R;'Y" Z;R"Y, + !P'R;'Y,. + !P'R;'Y•• Z~R22Y w+ Z~,R;'Y •• + Z~,R;'Yg.

The backsolution for nonparents is given by:

nonparent matrices, matrices without subscripts denotes parents.

where j = sire, k = dam B" = (R,7' + d,-'G;')-' * R,7',

U W1

= B.~

u""

l/u~w

Y., -

6w '

Y g,

6

-

g, -

-

u ml

-

1/2u Ugj

up• l

o -

-

1/2u wj

-

1/2u

R,7'

w,

o o

0

o

0 lla-;, 0 l/u;g

l/2u..

+

l/2u w , + 1/2u w, l/2u m , + 1/2u m , 1/2ug , + 1/2u,

O:w GO' =

u a ..... 1ll ,

O"a ...... Ig.

if,lw.nl

a~l

um.ag.

all'\\',
anl.;,~

o:~

,

and d,

=

1/2 or 3/4

52

BENYSHEK ET AL. APPENDIX 2

Y = Ic

+ 1/2Pu + cf> + e

where: Interim Expected Progeny Difference Procedures

The following is taken from work by Wilson and Willham (29): Y = JL

+ cj + 1I2BV' + 1I2BVd + cf>i + e,;

where: Y JL

c; BV' BV"

cf>

record of performance, a common mean, a contemporary group fixed effect, breeding value of the sire of the i'h calf, breeding value of the dam of the ith calf, Mendelian sampling effect of the ith calf, NID (0, a;)

and e t, = a residual error effect, NID (0, cr.). The BV of the i'h calf can be expressed as the sum of the additive genetic contribution from both parents and its Mendelian sampling effect as: BV i = 1I2BV' + 1/2BV" + cf>t' The EPO for an animal is half the breeding value of the animal. Therefore, the EPO of the i'h calf given in (I) i : EPO, = 1I2EPD'

Y 1

c = P = u =

cf> = e =

The Var (cf» is given by G, equal to la;, and Var (e) i represented by the diagonal matrix R. The residual error i a umed to contain the genetic contributions of the parents for ca es whenever one or both parent EPDs are unknown. Therefore, a;, is equal to a~, 1/4a; + a; or 1I2a; + a~ for ca es with both parent EPOs known, one parent EPO unknown or both parent EPDs unknown, respectively, and a; i the additive genetic variance for the trait being analyzed. The Mendelian sampling variance, is equal to half the additive genetic variance a;. Solutions for the contemporary group fixed effect, e. and Mendelian sampling effect, «>, are obtained by olving the following mixed-model equations as:

a;,

JR-'IIR-' R-' + G-'

IR-'l

+ 1I2EPOd + 1I2cf>,.

The EPO for both sire and dam can be obtained from a previous National Cattle valuation for most young animal for which interim EPOs are desired, leaving the predictor of the Mendelian ampling effect, cf>i to be determined. Thi predictor can be obtained by deviating the performance record from an estimate of the effect of the contemporary group in which the calf was reared and regressing the deviation according to the heritability of the trait. The procedure estimates the common mean and fixed effect for each contemporary group. The estimate is determined from all the performance records of calve in the contemporary group. The procedure for determining contemporary group fixed effect estimates represented in matrix notation is as follows:

vector of BW records, an n x 1 vector of 1's, where n is the number of calve in a contemporary group, an unknown contemporary group fixed effect, parent incidence matrix, vector of previously predicted parent breeding values, vector of unknown random Mendelian sampling effects and vector of residual errors.

Ilel (p

where: Y* = Y - 1I2PfJ. In computing Y* for young animal in the contemporary group with one or both parent PO unknown, unknown parent EPO are assumed to equal zero. It can be shown that:

c= and:

~ (I/cr.,)Y,* ~ (I/a~;)

ANIMAL MODEL-BEEF

where:


=

the Mendelian sampling effect for the i'h animal.

The EPD [or the i'h animal is then obtained from: EPO,

=

1/2EPO'

+ 1/2EPO' + 1/24>,.

In computing interim EPD for direct weaning weight, the 20Sd record must be additionally adjusted [or the maternal influence of the dam before it can be used to obtain the contemporary group estimate. The total adjustment subtracted from the 20Sd weaning weight record is equal to half the sire and dam EPD for direct weaning weight plus two times the EPD for maternal WW (MWW) of the dam plus the maternal permanent environmental (PE) effect of the dam. The wean· ing weight (WW) adjustment is expressed as: Yi(WW1*

=

Y,(WW)

-

-

l/2EPD~.w

2EPD~lww

- l/2EPD~w

- PEd

REFERENCES 1 Baker. F. H. 1975. The Beef Improvement Federation. World Rev, Anim. Prod. II:SepI.IO Dec. 2 Baker. F. H. 1967. Hislory and developmenl of beef and dairy pcrformance programs in lhe United SillIes. J. Anim. Sci. 26: 1261. 3 Benyshek. L. 19R6. Sire cvalualion-where we've come from. Proc. Beef lmprov. Fed. Res. Symp. Annu. Mtg. Lexington, KY. 4 Benyshek. L. 1987. Reduced animal model prcdictions and backsoluliuns-an O\'crview of cUTTenlly used methodology for genctic prediction. Prediction of genetic value for beef callie. Proc. Workshop II. Winrock Int. Kansas City. MO. 5 Benyshck. L. L. 1979. Sire by breed of dam interaclion for weaning weight in Limousin sire cvaluation. J. Anim. Sci, 4lJ:63. 6 Berger. P. J. 19R3. Current sire evalu
53

of sire progeny performance across regions in dam-adjusted lield data. J. Anim. Sci. 64:77. 11 Buchanan. D. S.. and M. K. Nielsen. 1979. Sire by environment interactions in beef callie lield data. J. Anim. Sci,48:307. 12 Burfcning. P. J .. D. D. Kress. and R. L. Friedrich. 1982. Sire x region of the United States and herd interactions for calving case and birth weigh\. J. Anim. Sci. 55:765. 13 Comerford. J. W.. L. L. Benyshek. J. K. Bertrand. and M. H. Johnson, 1988. Evaluation of pcrformance charactcrislics in a diallel among Simmenta1. Lirnousin. Polled Hereford and Brahman beef callie. I. Growth. hip height and pelvic size. J. Anim. Sci. 66:293. [4 Henderson. C. R. IlJ73, Sire evaluation and genetic lrends. Proc. Anim. Breed. Genel. Syrnp. in Honor of Dr. J. L. Lush. Am. Dairy Sci. Assoc. and Am. Soc. Anim. Sci .. Champaign.lL. 15 Henderson. C. R, [974. Gcneral flexibility of linear model techniques for sire evaluation. J. Dairy Sci. 57:963, 16 Henderson. C. R., and R. L. Quaas. 1976. Multiple trait evaluation using relatives· records. J. Anim. Sci. 43: 1188. 17 Johnson. M. 1-1 .• and L. L. Benyshek. 1986. The effect of selection ancl covariance between direct and maternal breeding value on genetic prediclions using the rcduced animal model. J. Anim. Sci. 63(Suppl. 1):179. (Abstr.) lR Johnson. M. H.. L. L. Benyshek. and J. K. Bertrand. 1988. Comparison of single trait reduccd animal models with multiple trail models for weaning weight. postweaning gain and carcass product using simulation data. J. Anim. Sci. 67(Suppl. 1):13, (Abstr.) 19 Lillie. D. E .. M, H. Johnson. and L. L. Bcnyshek, 1986. The incorporalion of lhe individua['s record into the computation of postweaning gain EPD's for embryo lransferC:.Jlves. J. Anim. Sci. 63(Suppl. 1):179. (Abstr.) 20 Nunn. 1'. R.. D. D. Kress. P. J. Burfening. and D. Vaniman. 1978. Rcgion by sire inleraetions for reproductive trails on beef cattle, J. Anim. Sci. 46:957. 21 Pollak. E. J .. and R. L. Quaas. 1983. Genetic evaluation of beef cattle from performance test data. Prediction of genetic values for beef callie. Proc. Workshop. Winrock. Inl. Morrilton. AR. 22 Quaas. R. L.. and E, J, Pollak. 1980. Mixed model methodology for farm and ranch beef callie testing programs. J. Anim. Sci. 51:1277. 23 Schaeffer, L. R.. and J. W. Wilton. 19R7. RAM commputing strategies and multiple traits. Prediction of genetic value for beef callie. Proc. Workshop II. Winrock Inl. Kansas City. MO. 24 Skaar, B. R. 19R5. Direct genetic and maternal variances ,lOci covariance component estimates from Angus and Hereford field data. Ph.D. Diss .. Iowa State Univ.. Ames. 25 Tess. M. W.. D. D. Kress. P. 1. Burfening. and R. L. Griedrich. 1(71). Sirc by environment interactions in Simmental breed calves. J. Anim. Sci. 49:964. 26 Willhalll. R. L. [979. Evaluation and direction of beef sire evaluation programs. J. Anim. Sci. 49:592. 27 Willham. R. L. 1982. Genetic improvemenl of beef callie in the Uniled States: Callie. people and lheir interaction. J. Anim. Sci. 54:659. 2X WillhalTl. R. L.. and G. Thomson. 1970. Instructions for usc of the beef callie simulalion program. Mimeo. Iowa State Univ.. Ames. 29 Wilson. D. E ..