Prediction of Sire Transmitting Abilities for Herd Life from Transmitting Abilities for Linear Type Traits1

Prediction of Sire Transmitting Abilities for Herd Life from Transmitting Abilities for Linear Type Traits1 K. G. BOLDMAN,2 A. E. FREEMAN, and B. L. HARRIS Department of Animal ScIence Iowa State University Ames 50011 A. L. KUCK 21 st Century Genetics

Shawano, WI 54166 ABSTRACT

of herd life from type had a maximum reliability (squared correlation of predicted and true transmitting ability) of .56, but it was more reliable than direct prediction with 75 or fewer effective progeny. Additionally. linear type data are available earlier than herd life data. (Key words: herd life. type traits. genetic evaluation)

Use of sire linear type trait transmitting abilities as indirect predictors of herd life transmitting abilities was investigated. Data consisted of 53.830 grade Holstein daughters of 617 sires evaluated during first lactation for 18 type traits and having the opportunity to survive to 72 mo. Two measures of herd life were used; true herd life was not adjusted for yield, and functional herd life was linearly adjusted for the cow's last lactation yield relative to that of herdmates. (Co)variances among the 20 traits were estimated via a multiple-trait REML algorithm. Heritabilities for linear traits ranged from .08 to .41. Heritability estimates for both herd life traits were .03. The genetic correlation between the two measures of herd life was .84. Weights to predict herd life from linear traits. estimated as a function of the sire (co)variance matrix among herd life measures and linear traits, were different for true and for functional herd life. Predictions of herd life from the weights are equivalent to those from a multipletrait BLUP model with herd life as a correlated but WIobserved trait. For the estimated parameters. indirect prediction

Abbreviation key: HLF = functional herd life, HLT = true herd life, MME = mixed model equations. INTRODUCTION

Received June 28, 1991. Accepted September 6, 1991. lJoumal Paper Number J-14543 of the Iowa Agriculture and Home Economics Experiment Station, Ames. Pro.iect Number 1053. "2Current address: USDA-ARS, R. L. Hruska US Meat Animal Research Center, University of Nebraska, Lincoln 68583-
In the US dairy cattle population, primary selection traits are milk. fat. and protein yields and other traits such as conformation. Increased herd life also contributes to the profitability of dairy yield by decreasing replacement costs and by increasing the percentage of cows producing at mature levels. The productive life of dairy cows averages about 3.5 yr (13). which is much less than their biological potential. Bumside et al. (2) concluded from simulation studies that milk yield is economically twice as important as herd life WIder present conditions. More recently, Burnside (1) has suggested that higher milk yields resulting from the use of bovine growth hormone could lead to greater stress on cows and, thus, increase the relative importance of herd life. A term commonly used to characterize herd life is stayability (6), which is a binomial trait, i.e.. a cow either survives or does not survive to a given age. Sires used for AI are routinely evaluated for stayability of their daughters in the northeastem US (5). Stayability to a fixed age is not an ideal measure of herd life. however. because of the binomial nature of the

552

553

PREDICIlON OF SIRE HERD LIFE FROM LINEAR TYPE

data and because of the limited number of records available (7). A continuous measure of herd life would be preferable, but waiting until all cows have completed their herd life is not feasible. Recently, several methods have been presented that utilize censored data, i.e., information on cows alive at the time of analysis (4, 16). Theoretically, these methods permit evaluation of a sire for herd life of his daughters before the sire is used extensively throughout the cow population. Smith and Quaas (16) warned that, even though the use of censored records increases the information available, it is unlikely that sires could be evaluated early enough for direct selection on herd life. In addition, the procedures use complex nonlinear models having greater computational requirements than linear models commonly used for genetic evaluation. An alternative to direct evaluation of sires for herd life is indirect prediction from genetically correlated traits that can be measured during first lactation. Sire evaluations for linear type traits are routinely calculated independently of yield traits by several AI organizations and breed associations and are available at the same time as initial yield evaluations. Burnside et al. (2) reviewed the literature and concluded that first lactation yield is a useful indicator of herd life, but the role of conformation is unclear and requires further research. The influence of type traits on herd life seems to differ between registered and grade cattle (3, 15), but stature and traits that measure udder characteristics have been found to affect the herd life of commereial dairy cows (9, 15). Several studies (15, 17) have used linear regression analyses to estimate coefficients to predict herd life from sire evaluations for individual type traits. The weights obtained via this least squares method do not properly account for the genetic covariances among the different type traits and can also be inaccurate if type evaluations are based on many more records than herd life evaluations; i.e., the herd life predictions from BLUP procedures would be further regressed toward the mean than the type predictions. A preferable approach would be to estimate the weights while considering the genetic relationships among the type traits and their genetic relationship to herd life. Most studies on the relationship of type traits and herd life have used stayability or

length of productive life as measures of herd life. These measures reflect both voluntary and involuntary reasons for culling. Ducrocq et al. (4) defined two types of herd life: functional herd life (HLF) is the ability to delay involuntary culling, whereas true herd life (HL T) is the ability to delay both voluntary and involuntary culling. Sires were evaluated by Ducrocq et a1 (4) for HLT and for 1ll.F, adjusting for low milk yield, the major reason for voluntary culling. Results indicated that Ill.F and HLT are different traits and that milk yield has a positive effect on HLT but a negative effect on 1ll.F. Van Arendonk (18) concluded from a simulation study that, to increase profits, selection should be directed toward a decrease in involuntary disposal rather than toward increasing average herd life. The effect of linear type traits on herd life may differ for HLT and 1ll.F. The objective of this study was to derive weighting factors to predict average herd life of sires' daughter by using linearly scored type traits from daughters of the same sires and to determine the reliability of indirect prediction. MATERIALS AND METHODS Prediction of Transmitting Abilities for a Trait Not In the Model Observation Vector

Henderson (10) presented several methods for computing BLUP of genetic values for animals without records. One method involved expanding the mixed model equations (MME) to include animals without records. This procedure has been widely used in practice, e.g., in animal models utilizing the complete relationship matrix. A second method involves taking linear functions of BLUP genetic values of animals with records. Either method can be extended to the multiple-trait situation in which records are available for traits that are correlated with a trait not observed, e.g., cows in first lactation that have linear trait scores but no measure of herd life. Assume that c cows are scored for each of t linear traits and that these data are used to predict their q sire's PTA for the t linear traits from the multiple-trait model y

= (It

@

X)

Ii +

(I,

@

Z)s + e

[1]

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554

BOlDMAN ET AL.

where y is a tc by 1 vector of observations for the t traits on each of c cows ordered cow within trait, It is an identity matrix of order t, 13 is a tf by 1 vector of fixed effects with f levels for each of the t traits, S is a tq by 1 vector of random sire effects, X and Z are known incidence matrices, @ denotes the direct product operation, and e is a tc by 1 vector of random residuals. In addition, E(y) = (II @ X) 13, E(s) = 0, E(e) = 0, Var(y) = G @ ZAZ' + R Var(s) = G @ A, and Var(e) = R @ Ie,

@

Ie.

where G and R are (co)variance matrices of the t traits for the sire effects and the residual, respectively, and A is the numerator relationship matrix for sires. The MME corresponding to [1] after absorption of 13 are [R-l

@

Z'MZ + G-l @ A-I] g (R-I @ Z'M)y

= [2]

where M = Ie - X(X'X)-X ' is a c by c matrix. Because all t traits are measured on all cows and because identical models are used, a canonical transformation can be used to reduce the tq by tq system of multipl~trait equations in [2] to a system of t independent q by q independent blocks and thus greatly reduce computational requirements to obtain PI'A for sires (11). If the t observed type traits are genetically correlated with one or more unobserved traits, e.g., herd life, then the linear trait data can be used to predict sire PI'A for the unobserved trait(s). One method for computing Sa. the vector of sire PfA for the unobserved trait(s), is to augment the equations in [2] as follows:

Journal of Dairy Science Vol. 75. No. 2, 1992

[r-

I

@

Z'M)Y ]

[3]

where G+ is the t + 1 by t + 1 sire (co)variance matrix for the t type traits and for herd life, i.e.,

[

G

:]

where gin is the t by 1 vector of sire covariances between the t observed traits and the unobserved trait, and goo is the sire variance for the unobserved trait One disadvantage of this approach is that a canonical transformation cannot be used because the X and Z incidence matrices for herd life are null and thus different from those for the linear traits. The same predictions of Sn can be obtained, however, as a linear function of g, the sire PI'A for the t observed traits, from

Sn = Cov(Sn,s)' [Var(s)]-I ~ Sn = (gin @ A)'(G-l @ A-l)§.

[4]

The advantage of this approach is that ~ can he obtained from the MME in [2] using a canonical transformation of the multiple-trait MME. Reliability of Indirect Prediction. Even though indirect predictions of genetic values are often available earlier than direct predictions in an animal's life, their usefulness for selection also depends on their relative reliability, i.e., the squared correlation between true and predicted transmitting ability. If Sn is obtained from the augmented equations in [3], then reliability of the prediction for either the observed or the unobserved trait of a sire can be calculated as 1 - Cg'gjio where Cjj is the diagonal element of the inverse of the absorbed coefficient matrix corresponding to sire j for trait i. Because the MME are usually solved iteratively, inverse elements are not available and must be approximated. In univariate models. inverse elements are commonly approximated by the reciprocal of the diagonal elements of Z'MZ, i.e., the reciprocals of the effective number of progeny for a sire. In this study, to approximate the reliability of indirect

555

PREDICI10N OF SIRE HERD LIFE FROM LINEAR TYPE

prediction of herd life for different effective progeny numbers, the element of c corresponding to herd life was calculated as the last element of the t + 1 by t + 1 matrix

t

= [ [ :-. I,

X

p)

o o

JG-1JI +

[5]

where the scalar p is the specific effective progeny number. This selection index approximation, which considers neither off-diagonal elements of Z'MZ nor relationships among sires, tends to overestimate reliability but is computationally feasible and allows comparison of reliabilities for a wide range of effective progeny values. The maximum reliability of indirect selection would result if the true values of·s were known. H they were, reliability could be calculated as r 2 = Cov(Sn,s)'[Var(sr1] 58 Cov(Sn,s)[Var( sJ-1].

[6]

Because s is never known without error, this value represents an upper limit of the reliability of indirect prediction. Nwnerical Example. A numerical example will be used to illustrate the equivalency of the

solutions for ~ obtained via the two methods and the calculation of the reliability of indirect prediction. The data are modified from those presented in Jensen and Mao (11) and consist of two traits (t = 2) recorded on 23 cows (c = 23), daughters of three sires (q = 3) in three herds. The two traits are genetically correlated with a third unobserved trait. The assumed (co)variance matrices for the three traits are

G+

=[

12

9

9

10

-25

-15

R= [16075

-25 ] -15 100

75

140

],

which result in a genetic correlation of -.72 and -.47 between the unobserved trait and the first and second observed traits, respectively. The sires are assumed to be related according to the following relationship matrix:

A

=

.25 .25 1.00 .25 .50

1.00 [

.25 ] .50 1.00 .

The multiple-trait MME from [2] for the two observed traits after absorption of the three fixed herd effects are

-.0522 -.1844 .3764 .0449 .1582 -.3290

.3034 -.0647 .0647 .3889 -.0522 -.1844 -.2644 .0516 .0516 -.3357 .0449 .1582

-.2644 .0516 .0449 .3627 -.0766 -.0623

.0516 -.3357 .1582 -.0766 .4645 -.2200

.0449

.1582 -.3290 -.0623 -.2200 .4502

=

-.1749 -.0534 .2282 -.1825 .0366 .1459

with solutions

f'

= [-2.2024

.5212 2.4153 -2.0021

.5511

2.1183]

where ~ij is the solution for sire j for trait i. The sire solutions for the unobserved trait(s), ~, can be obtained from the augmented equations in [3]. For the example data, the right-hand sides are the same as those just given with the addition of three zeros at the end of the vector

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BOLDMAN ET AL.

corresponding to the unobserved trait The augmented left-hand sides of the MME in [3] ordered sire within trait are

.5210 -.1010 -.1010 .6610 -.0885 -.3113 -.3496 .0658 .0658 -.4422 .0591 .2079 .0738 -.0123 -.0123 .0922 -.0123 -.0430

-.0885 -.3113 .6484 .0591 .2C179 -.4355 -.0123 -.0430 .0922

-.3496 .0658 .0591 .0738 -.0123 -.0123 .0658 -.4422 .2C179 -.0123 .0922 -.0430 .0591 .2C179 -.4355 -.0123 -.0430 .0922 .3960 -.0822 -.0679 -.0289 .0048 .0048 -.0822 .5061 -.2395 .0048 -.0361 .0168 -.0679 -.2395 .4918 .0048 .0168 -.0361 -.0289 .0048 .0048 .0250 -.0042 -.0042 .0048 -.0361 .0168 -.0042 .0313 -.0146 .0048 .0168 -.0361 -.0042 -.0146 .0313

§ll g12 g13 §21 §22 §23 g31 ~32

g33

with solutions (g §xJ' = [-2.2024 .5212 2.4153 -2.0021

.5511 2.1183 4.1841 -.9011 -4.6777].

The reliability of §3j is calculated from 1 - cjjll00, where Cjj is the inverse element of the coefficient matrix of the MME corresponding to sire j for trait 3, and 100 is the sire variance for the third trait. For the example data, the reliability values are .049, .057, and .038 for sires 1 through 3, which have 2.83, 4.71, and 3.21 effective progeny, respectively. Alternatively, the solutions for ~ can be obtained from g in [2] by using [4]. For the example data, this solution is [4]

_ [ [-25] ® [1.00 .25 .25] ] ' [ [12 9 .25 1.00 .50 9 10 -15 .25 .50 1.00

~n -

§n =

gn

-2.9487 0 0 -2.9487 [ o 0

=[

0 0 2.9487

1.1538

o

o

]-1

o 1.1538

o

® [1.00 .25

.25 .25 1.00.50 .25 .50 1.00

o o 1.1538

]

]-1]

~

-2.2024 .5212 2.4153 -2.0021 .5511 2.1183

4.1841 ] -.9011 -4.6777

which are the same solutions as those obtained with the MME in [3] augmented for the unobserved trait.

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PREDICTION OF SIRE HERD LIFE FROM LINEAR TYPE

Because all cows are measured for the same traits, the same linear ftmction -2.9487 ~1j + 1.1538 ~2j can be used to predict ~3j for each sire j even though the sires have different numbers of daughters. This t by 1 vector of weights, denoted w.. can also be obtained from , 1 gllP- = (wr) = (WI W2) = (-2.9487 1.1538); Le., with equal incidence matrices for the 0bserved traits, equation [4] can be rewritten as ~

= (gtn @

~

=

A)'{G-I @ A-1)~ [(g~G-I)J @ I q §

~ = Wt @

[4]

Iq ~

[4aJ

so that the relationship matrix A among sires is not used to determine Wt. Therefore, in the equal information example, the appropriate weights to calculate PTA for an unobserved trait from PTA for observed traits are the same for all sires even though they have different numbers of effective progeny, and the weights can be calculated as a simple ftmction of the sire (co)variance matrix among traits. Because the number of daughters for each sire and the structure of the relationship matrix have already been accounted for in the MME used to predict ~, this information is not needed for prediction of ~ from ~. The approximate prediction error variance used to calculate the reliability of ~ for each sire calculated from [5J is a ftmction of the sire's effective progeny number and the (co)variance matrices among the traits. For the example, the approximation for sire I with 2.83 effective progeny is

t

9.71 =

7.06

7.06 8.12 [ -20.48 -11.45

-20.48 -11.45 90.76

]

This results in an approximate reliability of 1 ell/gun = (1 - 90.76/1(0) = .092, which is greater than the true reliability estimated from the augmented MME when parameters are known. For the sire (co)variance matrix among traits used in the example, the maximum reliability for ~ that could be obtained from indirect prediction is .563, which is calculated using [6]. This value would be approached for sires with many recorded daughters, i.e., for a large effective progeny number.

557

Data

Estimation of the weights to predict herd life derived in the previous section requires an estimate of G+> the sire (co)varial.1.ce matrix among the traits used for prediction and the trait to be predicted. Because linear traits and hero life are affected by different fixed effects, the traits were preadjusted for fixed effects, as will be described later. The REML estimates of (co)variance components among linear type and herd life were then estimated from the precorrected data in a multiple-trait mixed model utilizing a canonical transformation. Compared with REML estimation in a multiple-trait model with unequal design matrices, this procedure greatly reduced computational requirements and is suitable to account for fixed effects with few degrees of freedom (19). Linear Type Data. Linear type scores were from grade Holstein cows in herds in the north central US evaluated between September 1979 and December 1988 in the Mating Appraisal for Profit Program of 21st Century Genetics Cooperative. Each cow was evaluated during first lactation for 18 linear traits; 16 type traits were scored by evaluators from 21st Century Genetics, whereas 2 management traits (disposition and milkout) were scored by the herd owner. All traits were scored on a 1- to 50-point scale, except disposition and millrout, which were scored on a scale of 1 to 4 and 1 to 5, respectively, in 1979 and 1980. To equate mean and variance between the two different scales, disposition and milkout scores from 1979 and 1980 were transformed as described by Foster et at (8). Matching production data for the cows were obtained from Wisconsin DID, Minnesota DID, and the Mid-States Regional Processing Center to permit calculation of ages of cows. After preliminary edits, the matched type and Dill data included 113,305 grade cows, daughters of 665 sires. Raw scores for the 18 traits were preadjusted for days of age at first freshening and stage of lactation (8) using adjustment factors estimated from a multiple-trait mixed model. The assumed model of analysis was Ytijkmn

= b ti + gtj + 8tjk + l~ + btl(3tijkmn -1) + ba(3tijkmn - 1) + Ctijkmn

[7J

10urnal of Dairy Science Vol. 75, No.2, 1992

558

BOLDMAN ET AL.

where is the record for trait t (t = 1, .•. , 18) on daughter n of sire k in group j in herd-year i, stage of lactation m, and age ati"kmn; hti is the fixed effect of herd-year of evaluation i for trait t; gtj is the fIXed effect of genetic group j (j = 1, ... , 14) for trait t; stjk is the random effect of sire k in group j for trait t; 1tm is the fIXed effect of stage of lactation m (m = 1, ... , 12) for trait t; ~jkmn is the age at first calving associated with Ytijkmn; '[ is the average age in days at scoring; btl, ba are the linear and quadratic regression coefficients, respectively, of trait t on age at scoring; and ~jkmn is the random residual. Ytijkmn

Sires were assumed to be unrelated and were assigned to genetic groups by year of birth. Best linear unbiased procedure estimates of stage effects and age regression coefficients were obtained at convergence of a multipletrait expectation-maximization-like REML algorithm described by Meyer (12). In this procedure, all fixed effects are absorbed, and the absorbed sire coefficient matrix is tridiagonalized, and the equal incidence matrices for all traits allow a transformation to canonical scale. Convergence was assumed when the change in each of the (co)variance estimates from the previous round was smaller than .1%. After convergence, solutions for all fixed effects except herd-year were obtained by back-solution. Herd Life Data. Cows used in the analysis of herd life were a subset of those used in the type analysis and consisted of those cows that had left the herd or had the opportunity to survive to 72 mo. The criteria used to determine whether a cow had left the herd were those used by Foster et al. (9) in a previous study with a subset of the data: 1) presence of a valid DHI code indicating that the cow was culled for purposes other than dairy or 2) failure to calve by 540 d after the date of last calving. Data consisted of 53,830 grade cows, daughters of 617 sires, and herd life was meaJoumal of Dairy Science Vol. 75, No.2, 1992

sured in terms of days from birth. Twenty-one percent of the cows were still in the herd at 72 mo and were assigned a herd-life value of 2190 d. Herd-life values were preadjusted for age in months at fIrst calving (3) using linear and quadratic regression coefficients estimated from the following univariate mixed model:

where Yijkl is the herd life of daughter I of sire k in group j in herd-year i at age ~jkl;

hi is the fixed effect of herd-year of birth i; gj is the fixed effect of genetic group j (j = 1, ... , 14); Sjk is the random effect of sire k in group j; aijkl is the age at first calving associated with Yijkl; '[ is the average age in months at flrst calving; b.. ~ are the linear and quadratic regression coefficients, respectively, of herd life on age at first calving; and eijkl is the random residual. Best linear unbiased procedure estimates of the regression coefficients were obtained after convergence of the REML algorithm. Herd life values obtained after correction for age at first calving reflect both voluntary and involuntary culling; i.e., they measure HLT rather than HLF. To determine whether the effects of linear type traits are different for these two measures of herd life, an estimate of HLF is required. In an attempt to measure HLF, Ducrocq et al. (4) accounted for a cow's level of yield in each lactation before culling. They suggested that an adjustment based on relative milk yield within a herd would more adequately reflect voluntary culling than would simply fitting absolute yield. Therefore, to obtain an approximate measure of HLF, a second univariate mixed model for herd life was used. This univariate model included a linear covari-

559

PREDICI10N OF SIRE HERD LIFE FROM LINEAR TYPE

ate for the rank of a cow's yield relative to that of her herdmates. For each year of the data, all cows in each herd, including both cows with and cows without type and herd life measures, were assigned to percentiles from high to low based on their daily mature equivalent milk yield. A regression coefficient for each cow's percentile in her last lactation (which was the first lactation for cows culled in first lactation) was then added to model [8] to obtain an estimate of the linear effect of relative milk yield on herd life. The product of this estimated covariate coefficient and the relative rank of a cow was then subtracted from the cow's lfi.,T measure to give an approximation of HLF, i.e., herd life independent of the influence of the cow's last production record, which likely accounted for a large part of the reason for culling. Alternatively, instead of last lactation, herd life could have been corrected for first lactation yield, which might be less affected by health problems. The cow's rank in last lactation was used in this study because a cow is culled on the basis of her yield relative to others in the herd at the same time; therefore, yield rank in last lactation is the criterion for voluntary culling. Further study is needed to determine which procedure gives a better estimate of lfi.,F. RESULTS AND DISCUSSION Estimation of Functional Herd Life

The average herd life of the 53,830 cows after adjustment for age at first calving was 1718 d. This value underestimates actual lfi.,T because longer herd lives were possible for those 21 % of cows assigned a value of 2190 d. Dentine et al. (3) reported an average herd life of 1821 d for grade Holstein cows in an analysis with an upper limit of six calvings. The .HLP was calculated by subtracting from lfi.,T the estimate of the linear effect of percentile rank of the last actual record. The value of this linear coefficient was 5.08, which, as previously reported by Ducrocq et al. (4), indicates a positive relation between milk yield rank and lfi.,T. The HLP for each cow was calculated as HLT minus 5.08 times the cow's relative yield rank. so the estimate of HLP was greater than that of HLT for a cow ranking in the lower half of the herd. This

TABLE 1. Heritabilities of linear lraits and two measures of herd life for grade Holstein cows. Trait

Heritability

Basic fonn Strength of body

.40 .24

Dairyness Stature Body depth Rump, side view

.23 .41 .27 .26 .12

Rear legs, side view Foot angle Fore udder attachment Udder depth Ramp width Rear legs, rear view Rear udder height Rear udder width

Suspensory ligament Fore and rear teat placement Disposition Milkout True herd life

Functional herd life

.08 .14 .22

.20 .10

.19 .15 .15 .20

.09 .12 .03 .03

adjustment is an attempt to estimate herd life free of the effect of culling for low milk yield, a primary reason for voluntary disposal. Estimates of Genetic Parameters

In multiple-trait models, data from all correlated traits are used to estimate PI'A for a sire. Multiple-trait models are most useful when traits of low heritability are highly correlated to more heritable traits and when phenotypic correlations are very different from genetic correlations (20). Heritability. Heritability estimates for the 18 linear traits and for the two measures of herd life are in Table 1. Heritability estimates for linear traits were moderate, ranging from .41 for stature to .08 for foot angle, and did not differ greatly from previous estimates for registered Holsteins calculated by multiple-trait REML [e.g., (20)]. Heritability estimates for both measures of herd life were .03. These estimates indicate the need for large numbers of daughter records for accurate evaluation of sires for herd life PI'A. Dentine et al. (3) also reported a heritability estimate of .03 for age at last record uncorrected for yield, i.e., HLT, for grade Holstein cows. Ducrocq et al. (4) obtained an empirical Bayes estimate of sire variance in a Weibull model and reported a "pseuJournal of Dairy Science Vol. 75, No.2, 1992

560

BOlDMAN ET AL.

TABLE 2. Genetic (G) and phenotypic (P) correlations between true and functional herd life and linear traits for grade Holstein cows. True herd life

TABLE 3. Weights to predict sire transmitting abilities for true and functional herd life from sire transmitting abilities for linear traits in grade Holstein cows. Weights

Functional herd life

Trail

G

P

G

P

Linear trait

True herd life

Functional herd life

Basic form Strength of body Dairyness Stature Body depth Rump, side view Rear legs, side view Foot angie Fore udder attachment Udder depth Rump width Rear legs, rear view Rear udder height Rear udder width Suspensory ligament Fore and rear teat placement Disposition Milkout Functional herd life

-.16 -.11 .00 -.23 -.21 .16 .07 -.16 .47 .38 -.12 -.01

-.03 -.01 .07 .01 .01 .00 -.01 .03 .04 .02 .00

-.08 -.02 -.16 -.21 -.20

-.02 -.01 .03 -.01 -.01 -.01 -.02 .03 .06 .06 -.01 .03 .04 .04 .05

Basic form Strength of body Dairyness Stature Body depth Rump, side view Rear legs, side view Foot angle Fore udder attachment Udder depth Rump width Rear legs, rear view Rear udder height Rear udder width Suspensory ligament Fore and rear teat placement Disposition Milkout

15 2.2 7.8 -7.8 -5.6 7.2 .8 -9.8 11.6 5.9 -4.0 4.2 -55 4.4 5.6 -2.0 25 -.1

-9.9 5.9 -10.2 -5.8 7.3 4.1 3.8 -1.7 7.3 125 -1.5 1.4 -4.5 1.5 5.3 -2.0 5.3 .6

.13 .13 .23 .15 .16 .32 .84

.03 .06 .06 .05

.04 .06 .05 .91

.09 .08 -.12 .46 .47

-.18

-.06 -.01 -.07 .22 .17 .13 .39 1.00

.05 .05

.06 1.00

doheritability" of .09 for both true and milkcorrected herd life in contrast with previous studies in which estimates of heritability for herd life were reduced after correction for absolute milk yield They postulated that correction for relative yield within a herd may more accurately reflect voluntary culling and, thus, allow for expression of sire differences for other disposal reasons. Genetic Co"elations. Genetic correlations between the linear traits and lILT and Ill..F are in Table 2. For most linear traits, phenotypic correlations with lILT and Ill..F were close to zero and smaller than genetic correlations. Two udder traits, attachment and depth, and milkout had the highest positive genetic correlations with lILT and Ill..F. Body traits (stature, body depth, and strength) had negative correlations with both measures of herd life. Correlations of several other linear traits differed for the two herd life measures. Correlations were positive between all udder traits and lILT but slightly negative between Ill..F and rear udder height and rear udder width. Contrary to expectations, dairyness was uncorrelated with lILT but negatively correlated Journal of Dairy Science VoL 75, No.2, 1992

with Ill..F. In addition, foot angle was negatively correlated with both measures of herd life. The genetic correlation between true and functional herd life was .84, which indicates that the two measures are different traits. This value is similar to the estimate of .80 reported by Ducrocq et al. (4), which was calculated as the Spearman rank. correlation between predictions of sire values for lILT and milkcorrected herd life. Weights to Predict Sire Transmitting Abilities for Herd Life from Transmitting Abilities for LInear Traits

Weights to calculate PTA for lILT and HLF from PTA for linear traits (Table 3) were calculated from [4] using the estimated sire (co)variance matrix among herd life measures and linear traits. Because of differences in genetic correlations between linear traits and lILT versus linear traits and Ill..F, many of the weights for a particular linear trait were different in both sign and magnitude for lILT and Ill..F. Furthennore, several of the weights to predict either lILT or Ill..F differed from the corresponding genetic correlation in both sign

561

PREDICTION OF SIRE HERD LIFE FROM LINEAR TYPE

1.00 , - - - - - - - - - - - - - - - and relative magnitude. For example, the ge.90 netic correlation between Ill.F and strength of .eo body is -.02 and between HLP and teat place.70 maxiroom .99 ment is .17, but the corresponding weights are ~ .80 5.9 and -2.0, respectively. Because the appro~ .so priate weights are a function of not only the CD II: .40 sire covariance vector between linear traits and .30 herd life but also the inverse of the sire .20 (co)variance matrix among linear traits (i.e., .10 correlations among linear traits), the weight for a linear trait can be much different from the 100 100 100 Effective progeny Number genetic correlation. Therefore, the biological meaning of the weight for an individual trait Figure 1. Reliability (squared correlation of predicted can be difficult to interpret, and the weights and. true values) of sire transmitting ability for functional should be used as a set of 18. If one or more of herd life in grade Holstein cows for direct prediction, the linear traits were omitted, the appropriate using herd life, and for indirect prediction, using transmitweights to predict HLT and HLP could be ting abilities for linear traits. much different from those presented in Table 3. Although prediction of herd life from a subset of the 18 linear traits might be nearly as reliable as prediction using all traits, use of all because reliability of direct prediction would increase faster with larger heritability. traits currently recorded seems justified in order to obtain maximum reliability. ~

~

~

~

1~

1~

~

CONCLUSIONS

Reliability of Prediction Using LInear Trait Transmitting Abilities

A comparison of reliability of HLP from direct prediction and from indirect predictions using linear traits is shown in Figure 1. Values for HLT are very similar and are not presented. Even though the reliability of direct prediction will eventually approach unity with many effective progeny, the low heritability of HLP results in the need for many effective progeny to attain high reliability values. The trend for reliability of indirect prediction is quite different Even if the true linear trait transmitting abilities were known, the reliability of Ill.F prediction could not be greater than .56. As a result of the moderate heritabilities of linear traits, however, when the effective progeny number is less than 75, indirect prediction from linear traits is more accurate than direct prediction. If the initial progeny test of a sire is based on a limited number of daughters, the reliability of indirect predictions would be low but greater than that resulting from direct prediction. The advantage of indirect prediction could be overstated if the true parameters differ from estimates, especially if the true heritability of herd life is greater than .03. This is so

Weights to predict sire PTA for HLT and for HLP from linear trait PTA were estimated. After the sire (co)variance matrix among linear traits and herd life measure(s) is estimated, the prediction procedure is computationally simple. If all linear traits are measured on each cow, then the same set of weights are used for all sires regardless of the number of progeny records for a particular sire. These weights yield herd life PTA that are equivalent to the values obtained in a multiple-trait model for linear traits augmented for herd life. Use of the weights permits linear trait evaluations to be calculated independently of other traits so that a canonical transformation can be used, and, as a result, computational requirements are greatly reduced in comparison with the augmented MME. The weights are applicable only to type PTA predicted from a multiple-trait model that accounts for the genetic covariances among the traits; ie., they are not applicable to type PTA predicted in single-trait models. This is not a major limitation, however, because type evaluations are usually calculated with multiple-trait models (T. Short, 1991, personal communication). In the future, direct evaluations for herd life might be calculated by the USDA or by anJournal of Dairy Science Vol. 75. No.2, 1992

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other national organization using methods that more accurately model herd life and utilize censored data (4, 16). Until that time or if methodology for censored data is found to produce predictions with low repeatability, indirect prediction of herd life could be conducted in-house by AI organization and breed associations, which routinely calculate multiple-trait sire evaluations for linear traits independent of yield traits. As a result, predictions of herd life would be available at the same time as or even earlier than initial yield evaluations. The primary advantage of estimating herd life from type traits is that PfA would be available early enough to allow selection among sires based on their first sample of daughters. Even though the reliability of these evaluations would be low in comparison with those for type and yield traits, it would be greater than direct selection for herd life based on the same number of daughters because of the low heritability of herd life. The weights presented are specific for the (co)variance matrix estimated from these data. Addition of new or elimination of existing linear traits would change the values of the weights. Because of the difference in the genetic correlations between herd life and linear traits reported for registered versus grade cattle (3, 15) and for Holstein versus other breeds of cattle (14, 15), the weights presented here are not applicable to other dairy cattle populations. An important question concerns the measure of herd life, HLT or HLP, that should be used. Because accurate PfA for yield traits are currently available, predictions of HLP independent of yield would seem to be more useful. Milk-corrected herd life may be a crude approximation of HLP, but it could be a useful component in an index of overall profitability. Yield should continue to be the primary selection trait in grade dairy cattle, whereas herd life should be a secondary trait. ACKNOWLEDGMENTS

Appreciation is extended to K. Meyer, who generously provided her REMLPK programs for variance component estimation, and to E. L. Jensen, who provided Wisconsin DID data. Linear type data and financial support were Journal of Dairy ScieDce VoL 75, No.2, 1992

provided by 21st Century Genetics. Additional financial support was provided by the National Association of Animal Breeders, Columbia, MO. REFERENCES 1 Burnside, E. B. 1987. Impact of somatotropin and other biochemical products on sire summaries and cow indexes. J. Dairy Sci. 70:2444. 2 Burnside, E. B., A. E. McClintock, and K. Hammond. 1984. Type, production and longevity in dairy cattle: a review. Anim. Breed. Abstr. 52:711. 3 Dentine, M. R., B. T. McDaniel, and H. D. Norman. 1987. Evaluation of sires for traits associated with herd life of grade and registered Holstein cattle. J. Dairy Sci. 70:2623. 4 Duaocq, V., R. L. Quaas, E. J. Po11ak, and G. Casella. 1988. Length of productive life of dairy cows. 2. Variance component estimation and sire evaluation. J. Dairy Sci. 71:3071. 5 Everett, R. W., and J. F. Keown. 1984. Mixed model sire evaluation with dairy cattlo-experience and genetic gain. J. Anim. Sci. 59:529. 6 Everett, R. W., J. F. Keown, and E. E. Clapp. 1976. Production and stayability trends in dairy cattle. J. Dairy Sci. 59: 1532. 7Famu1a, T. R. 1981. Exponential stayability model with censoring and covariates. J. Dairy Sci. 64:538. 8 Fosta:, W. W., A. E. Freeman, P. J. Berger, and A. Kuck. 1988. Linear type trait analysis with genetic parameter estimation. J. Dairy Sci. 71:223. 9 Fosta:, W. W., A. E. Freeman, P. J. Berger, and A. Kuck. 1989. Association of type traits scored linearly with production and ha:dlife of Holsteins. J. Dairy Sci. 72:2651. 10 Henderson, C. R. 1977. Best linear unbiased prediction of breeding values not in the model for records. J. Dairy Sci. 60:783. I1Jensen, J., and I. L. Mao. 1988. Transformation algorithms in analysis of single trait and of multitrait models with equal design matrices and one random factor per trait: a review. J. Anim. Sci. 66:2750. 12 Meyer, K. 1986. Restricted maximum likelihood to estimate genetic parameter&-in practice. Proc. 3rd World Congr. Genet AppL Livest Prod., Lincoln, NE XII:454. 13 Norman, H. D., B. G. Cassell, R. E. Pearson, and G. R. Wiggans. 1981. Relation of fust1actation production and conformation to lifetime performance and profitability in Jerseys. J. Dairy Sci. 64:104. 14 Rogers, G. W., G. L. Hargrove, J. B. Cooper, and E. P. Barton. 1991. Relationships among survival and linear type traits in Jerseys. J. Dairy Sci. 74:286. 15 Rogers, G. W., B. T. McDaniel, M. R. Dentine, and L. P. Johnson. 1988. Relationships among survival rates, predicted differa:u:es for yield, and linear type traits. J. Dairy Sci. 71:214. 16 Smith, S. P., and R. L. Quaas. 1984. Productive lifespan of bull progeny groups: failure time analysis. J. Dairy Sci. 67:2999.

PREDICTION OF SIRE HERD LIFE FROM LINEAR TYPE 17 Sullivan, B. P., B. J. Van Doormal, and E. B. Bumside. 1988. An analysis of the linearized type chaIacteristics as predictors of stayability in Canadian Holsteins. J. Daily Sci. 7l{Suppl. 1):267.{Abstr.) 18 Van Arendonk, JAM. 1986. Economic importance and possibilities for improvement of dairy cow herd life. Proc. 3rd World Congr. Genet. Appl. Livest.

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Prod., Lincoln, NE IX:95. 19 VanRaden, P. M. 1986. Computational strategies for estimation of variance components. PhD. Diss., Iowa State Univ., Ames. 20 VanRaden, P. M., E. L. Jensen, T. J. Lawlor, and D. A. Funk. 1990. Prediction of transmittiDg abilities for Holstein type naits. J. Daily Sci. 73:191.

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