Genetic and Environmental Components of Semen Production Traits of Artificial Insemination Holstein Bulls

Genetic and Environmental Components of Semen Production Traits of Artificial Insemination Holstein Bulls J. F. T A Y L O R , B. BEAN, L C. E. M A R S H A L L , : and J. J. S U L L I V A N 3 Department of Animal Science Cornell University Ithaca, NY 14853

ABSTRACT

INTRODUCTION

A multiple trait procedure allowed joint estimation of model effects and variance and covariance components of semen production of Holstein bulls in artificial insemination• Procedural advantages included rapid iteration and positive definite estimates of covariance matrix. Data consisted of 149,339 semen production records for total sperm, volume, and concentration of ejaculate on 2,351 bulls collected in three bull studs from July 1969 through November 1982. Models defined to describe the biology of semen production included effects for ejaculates, age of bull, ambient temperature, week day by bull barn, scheduling, month by year, colorimeter by calibration period, and bulls. Environmental trends but no genetic trends in semen production were detected. Repeatabilities of measures of total sperm, volume, and concentration of all ejaculates were .26, .23, and .37 and for first ejaculates were •31, .23, and .42 over all studs. Heritabilities were .03, .18, and .10 for all ejaculates and .05, .16, and .16 for first ejaculates. Repeatabilities of first ejaculate measures for bulls collected up to 15 mo and again from 60 mo of age were .21, .27, and .19. Genetic correlations between first ejaculate measures on young bulls and milk and milk fat production in daughters ranged from - . 0 6 to .05.

The ability of dairy bulls to produce semen for use in artificial insemination (AI) is dependent upon the collection environment and spermatogenesis. In the past, considerable attention has been paid to evaluating changes of semen production due to variation of age of bull, season of the year, collection frequency, sexual stimuli, bull nutrition, and bull housing (1, 2, 4, 7, 8, 9, 13, 17). However, little appears to be known of the underlying genetic and environmental relationships between semen production traits under commercial collection environments. Seidel and Foote (18) and Hafs et al. (13) estimated variance components of semen characteristics by analysis of variance procedures. Both studies analyzed limited numbers of records (1,536 and 2,864) and numbers of bulls sampled (63 and 68 of five breeds), and no estimates of genetic or environmental covariances were produced. Estimates of genetic and environmental variances and covariances, herein denoted (co)variances, are required for research in the economics of production systems and subsequently in the design of efficient selection programs. Incorporating estimates in mixed model procedures will allow estimation of functions of fixed effects and prediction of realized random variables although without the property of minimum sampling variance (15). Objectives were 1) to illustrate application of a multiple trait restricted maximum likelihood (REML) algorithm for estimation of (co)variance components, 2) to estimate environmental effects and genetic and environmental trends for semen production, 3) to estimate genetic and environmental (co)variance components for semen production in commercial AI studs, and 4) to examine relationships between semen production in young and mature bulls and between semen and milk production traits.

Received March 19, 1984. t Eastern Artificial Insemination Cooperative, Inc., Ithaca, NY 14850. 2 Select Sires, Inc., Plain City, OH 43064. 3American Breeders Service, DeForest, WI 53532. 1985 J Dairy Sei 68:2703-2722

2703

2704

TAYLOR ET AL. MATERIALS AND METHODS

Data consisted of all ejaculates within collection day o f AI Holstein bulls collected by Eastern AI Cooperative Inc., Select Sires Inc., and A m e r i c a n Breeders Service. Studs are n o t identified but are labeled A, B, and C. A total of 149,339 records on 2,351 bulls collected July 1969 t h r o u g h N o v e m b e r 1982 r e m a i n e d after edits. Data on bulls culled f r o m studs for any reason were included. Ejaculates coded lost, contaminated, or electro-ejaculate were r e m o v e d as were those with unidentified ejaculate number. Ejaculates with volumes in excess of 25 ml or concentrations exceeding 4 × 109 s p e r m / m l were further than five standard deviations f r o m the m e a n and r e m o v e d on the advice of bull studs. Records with v o l u m e s or concentrations recorded zero were n o t edited unless the bull was prepuberal or no a t t e m p t at meas u r e m e n t had been made. I n f o r m a t i o n r e c o r d e d on each ejaculate included 1) bull stud, 2) bull code, 3) date of collection, 4) ejaculate n u m b e r within date of collection, 5) original v o l u m e of ejaculate (ml), 6) c o n c e n t r a t i o n of sperm (109/ml), 7) bull location by barn within stud, 8) birth date of bull, and 9) dates of colorim e t e r calibration. S t u d A also recorded colorimeter, c o l o r i m e t e r operator, and daily a m b i e n t t e m p e r a t u r e at m i d m o r n i n g on each day of collection. T o t a l sperm per ejaculate ( 1 0 9 ) w a s calculated as the p r o d u c t of original v o l u m e and concentration. Table 1 contains sample means, standard deviations, and coefficients of variation by bull stud, ejaculate within day of collection, and trait. Sample means and coefficients o f variat i o n by ejaculate for c o n c e n t r a t i o n are similar for all studs; however, large differences exist for v o l u m e and, consequently, total sperm. Stud A averaged 1.6 ml m o r e v o l u m e t h a n stud B and 2.9 ml m o r e than stud C on first ejaculates. These a m o u n t s cannot be used to q u a n t i f y differences b e t w e e n bull studs as t h e y are n o t adjusted for managemental and e n v i r o n m e n t a l differences b e t w e e n studs. For example, stud C does n o t differentiate a m o n g bulls at collection, whereas for studs A and B, bulls were sexually prepared and collected according to semen requirements, resulting in stratified bull groups. Data b e t w e e n studs were c o n n e c t e d only by covariances b e t w e e n related bulls, and consequently, data

Journal of Dairy Science Vol. 68, No. 10, 1985

f r o m each stud were analyzed separately, providing no comparisons o f studs. T h e m i x e d linear m o d e l depicting the biology of total sperm, volume, or concentration o f each ejaculate was: Yijkmnpqrst = gt + E i + Aj + T k + D L m +C n +Op +MYq +DSr + DB s + B t + eijkmnpqrs t where: Yijkmnpqrst = observed total n u m b e r o f sperm, volume, or concentration; = overall mean; E i = fixed effect of i th ejaculate within collection day, where i=1,2,3; A i = fixed effect of the jth age of bull classification, where j = 1, . .., nj, and nj = 27, 23, or 20 for studs A, B, and C. Also j = 1,...,14for10 . . . . . 23 m o old at collection, j = 15 for 24 to 29 m o old at collection, and j = 16 . . . . . nj for 12-mo intervals f r o m 30 m o o f age; T k = fixed effect o f the kth ambient t e m p e r a t u r e class in - 1 2 ° C classes f r o m - 2 4 ° C , wherek= 1,...,10(studA only) ; DL m = fixed effect of day of week of collection by bull location, where m = 1, . . . , n m and nm = 18, 19, or 62 for studs A, B, and C; Cn = fixed effect of period bet w e e n recalibrations of colorim e t e r or c o l o r i m e t e r by calibration period (stud A), where n = 1.... , n n and n n = 45, 4 or 2 for studs A, B, and C; Op = fixed effect of c o l o r i m e t e r operator, where p = 1 . . . . . 10 (stud A only); MYq = fixed effect o f mo-yr of collection; where q = 1, . . . , nq and nq = 8 9 , 1 2 1 , or 157 consecutive mo-yr for studs A, B,

TABLE 1. Sample means (X), standard deviations (SD), and coefficients of variation (CV) for semen production by ejaculate within bull studs.

Bull stud/ no. bulls

A/789

B/858 e"

Ej aculate

No. of observations

Total sperm

Volume

Concentration

(109 )

(ml)

(109/ml)

Z

SD

CV

"X

SD

CV

X

SD

CV

1 2 3 All

33,877 16,216 2,564 52,657

10.9 6.7 4.4 9.3

5.7 2.9 1.7 5.4

53 44 39 58

7.9 7.5 6,8 7.7

3.1 2.3 1.9 2.8

39 30 28 36

1.36 .91 .67 1.19

.54 .34 .26 .53

40 38 39 45

1 2 3 All

22,962 21,475 172 44,609

7.4 3.8 2.9 5.6

5.0 2.7 3.7 4.4

67 72 127 78

6.3 5.6 6,4 5.9

3.0 2.8 3.5 2.9

49 50 55 50

1.17 .67 .47 .93

.56 .36 .42 .54

48 53 89 58

1 2 3 All

26,131 23,888 2,054 52,073

6.9 4.7 3.7 5.8

4.5 2.8 2.2 3.9

65 60 60 68

5.0 4.8 4.9 4.9

2.3 2.1 2.1 2.2

46 44 43 45

1.34 .98 .76 1.15

.56 .40 .33 .52

42 41 44 46

©

Z © ,...]

O C/704

z

¢0 < O Ox 0o Z 9

,g

oo

t,d .,q O

2706

TAYLOR ET AL.

and C; DSr = fixed effect of calendar days from first collection after repletion. A bull is defined as replete having had a minimum of 14 consecutive calendar days with no collection, where r = 1. . . . , 4 1 a n d r = 1for first collection day after repletion, r = 2 . . . . . 40 for 1, .... 39 calendar days from first collection day after repletion, and q = 41 for greater than 39 calendar days from first collection day after repletion; DB s = fixed effect of calendar days between adjacent collections by number of ejaculates on the previous collection day, wheres=l,...,43ands=l for first available collection on a bull s = 2, 3 , 4 for 1 d and 1, 2, or 3 ejaculates previously. Finally s = 41, 42, 43 for />t4 d and 1, 2, or 3 ejaculates previously. No bull stud had all possible day by ejaculate combinations; Bt = random effect of the t th bull, wheret = 1,...,n t andn t = 789, 858, or 704 for studs A, B, and C; and eijkmn pqrst = random residual. Bulls were considered unrelated, errors uncorrelated, and covariances between bulls and residuals nil. The first two conditions were violated by these data. Because of the nature of selection programs for milk and milk fat production, bulls invariably share common ancestors. However, if selection for semen production has not occurred, ignoring covariances between related bulls will inflate sampling variances of estimates but still will allow estimation of (co)variances in the base or unselected population. Residual elements are correlated for repeated collections on a bull both within and between subsequent collection days. To circumvent this problem partially, only first ejaculates on any collection day were reanalyzed by models, omitting the fixed effect of ejaculate. Random bull and residual effects had expecJournal of Dairy Science Vol. 68, No. 10, 1985

tation zero, and all three semen production traits were considered distributed multivariate normal. The multiplicative relationship between traits ensures that total sperm cannot be distributed normally if volume and concentration are jointly normal. However, the largest estimates of skewness and kurtosis were .78 and 4.08 for total sperm of first ejaculate in bull stud B, and distributions for total sperm were approximately normal. Effects of calibration period, co]orimeter, and colorimeter operator were expected to be redundant for volume. Algorithm for Multiple Trait Restricted Maximum Likelihood

The following procedure for multiple trait restricted maximum likelihood (REML) by the expectation-maximization (EM) algorithm (6) is from R. L. Quaas and S. P. Smith (personal communication). The biological model for each trait has exactly the same parameters with only one random effect besides residual. When all animals are recorded for all traits, the multiple trait model for c traits is: y = (Ic*X)/3 + (Ic*Z)u + e

[1]

where: Y = (Y'I, Y2. . . . . Y'c)' and Yi is an N × 1 vector of observations on the ith t r a i t ; i = 1 , . . . , c; t 13= (/31, /3~. . . . . /3'c)' and ~ is a p x 1 vector of fixed effects for the i th trait; (p = rank X); u = ( u ' l , u2,' . . . , U ' c ) ' a n d u i i s a q × l v e c tor of random effects for the ith trait; t t t e = ( e ' l , e 2 , . . . ,ec) a n d e i i s a n N x l v e c tor of random residuals for the ith trait; and * = direct product. Also:

E:l

[E:l E: :1]

with A = G*lq, S = R*IN, and I N the identity matrix of order N. The mixed model equations in terms of the u n k n o w n genetic and environmental (co)vari-

VARIANCES OF SEMEN PRODUCTION ance matrices G and R b e t w e e n traits are:

Where the following terms are all c o m p u t e d at the k TM iterate:

[R-xx R-xz

I..,

A,

A,

A,

A,

Ag~

Uk = ( u l , u g , - . . , u c )

R -1 *Z'Z+G -1 *Iq.

-1 * Z t X

2707

isqx c

~1 Ek = ( e l , e 2 , . . . , e c )

I(S- 1*X')Yl

isNx c

[2] L-1L -T = R k

R -1 * Z ' ) y J L-1D-1L -T =G k Make the t r a n s f o r m a t i o n R - 1 = L'L and G - 1 = L'DL where D = diag(di) is a diagonal matrix of the latent roots of G - 1 R , and L' is a nonu n i q u e matrix with eigenvectors as columns. T h e n the equations in [2] may be solved as c single trait systems:

=

Lz'x z'z + dilq

[31

kz'yfj

The transformed right-hand sides are o b t a i n e d from: t

,

(X Yl . . . . .

t

X'y*) = (X y~ . . . . .

t

C i = (Z'MZ + dilq) -1 A, t ^ ,

e i ej = y*'Myj*-- u^*' i Z ' M y i* -- d~u^ i '^uj Speed of iteration can be increased dramatically b y tridiagonalizing Z'MZ to H ' F H b y preand p o s t m u l t i p l y i n g Z'MZ by a sequence of q - 2 Householder matrices (16). The matrix F is symmetric a b o u t the leading diagonal and is null everywhere except for the leading and adjacent diagonals. The matrix H is orthogonal; hence, H'H = HH' = Iq, and each set of equations in [4] simplifies to:

t

X yc)L,

(F + dilq)H~* = H Z ' M y *

and solutions m a y be back transformed as: /h

A

(/31. . . . .

,~,

A

/3c) = (/31 . . . . .

/3*)L - T -

The L - T is the inverse of the transpose of L. Absorb fixed effects in [3] to obtain: A,

(Z'MZ + d i lq) u i = Z'MY*

[51

Time for the tridiagonalization is equivalent to inversion; however, within each iterate, [5] can be solved in linear time and the trace trC i = t r ( F + dilq) -1 c o m p u t e d during solution (R. L. Quaas, 1982, u n p u b l i s h e d notes). Further,

[4]

A,IA,

A,I

I

~

u i uj = ( u i H ) ( H u j ) ,

for M = I N -- X ( X ' X ) - - X ' . At each iterate, solutions ~* are f o u n d conditioning on d i and updates of G and R obtained to provide d i in the subsequent round• The REML R a n d G are estimated iteratively b y the EM algorithm described b y Dempster et al. (6) as:

~i*' Z'Myj* = (~*' H')(HZ'Myj*)

Gk+ 1 = L -1 Uk+ 1 L - T

due to o r t h o g o n a l i t y of H. Finally, in (R. L. Quass, 1982, u n p u b l i s h e d notes) the log-likelihood of error contrasts up to a c o n s t a n t is:

Rk+ 1 = L -1 Vk+ 1 L - T

L = --(N -- p) in IRI + q ~ In d i - ]~ In IF + dilql

with: q Uk+l N

and:

Vk+ 1 =

--

I

=

~ /A~fA,

A,tA,

~ei e i + d i u i u i ),

[6]

UkU k + diag(trC i)

E~E~ + diag(p + q -

ditrCi)

and the d e t e r m i n a n t IF + dilq[ also can be obtained in solving [5].

Journal of Dairy Science Vol. 68, No. 10, 1985

2708

TAYLOR ET AL. RESULTS AND DISCUSSION

This algorithm has major advantages for (co)variance c o m p o n e n t estimation with m o d e l [1] or variance c o m p o n e n t estimation in single trait models. Perhaps m o s t i m p o r t a n t is the guarantee that estimated G and R will remain positive definite provided priors G O and R o are positive definite. However, convergence to singular R or G has occurred in simulated data with singular population dispersion matrices (T. J. Lawlor, Jr., personal c o m m u n i c a t i o n ) . R e d u c t i o n of the absorbed coefficient m a t r i x Z'MZ to tridiagonal f o r m allows solution of equations [5] and c o m p u t a t i o n of traces trC i to be achieved rapidly. This latter advantage removes previous qualms regarding the rate of convergence of EM t y p e approaches (19), at least for m o d e l [1 ]. Table 2 contains c o m p u t e r (CPU) times required to achieve absorption, tridiagonalization, and iterative steps for bull stud B for an International Business Machines (IBM) 4341 time-sharing system. A f t e r the m o d e l was reparameterized so t h a t t h e coefficient matrix in [3] had full rank, matrices X'X and Z'MZ were half-stored as real *8 as were X ' y i and Z'Myi, whereas X ' Z was stored as integer *2 to m i n i m i z e storage requirements. A f t e r tridiagonalization, the absolute difference ItrZ'MZ - trFI was c o m p u t e d to check that t r Z ' M Z = trF. Each trace s u m m e d the effective n u m b e r of collections per bull over all q bulls, and t r Z ' M Z and the absolute difference b e t w e e n traces are in Table 3 for analyses of all and first ejaculates within bull studs. These results indicate that surprisingly little rounding error was i n t r o d u c e d in tridiagonalizing large coefficient matrices. A l t h o u g h not guaranteed to produce positive definite estimates, priors were estimated by Henderson's M e t h o d 3 as:

R o = (Y'MY -- 0 ' Z ' M Y ) / ( N -- r a n k ( X : Z ) ) G O = (I~'Z'MY -- r a n k ( Z ' M Z )

Ro)/tr(Z'MZ)

for: ~J = ( Z ' M Z ) - - Z ' M Y Y=(Yl .....

Yc)

q x c N X c.

Priors R o and G O were always positive definite. A t each iterate, t h e log-likelihood in [6], which must always increase, was c o m p u t e d to m o n i t o r convergence. T w o stopping criteria were e m p l o y e d , either 30 iterates or: 1 -- L k _ I / L k < 10 -~s where L k is the log-likelihood [6] evaluated at the k th iterate and k /> 1. The second criterion measures the relative change of log-likelihoods in successive iterates and always was satisfied before the f o r m e r criterion with these data. Table 4 contains t h e n u m b e r of iterates needed to satisfy the likelihood stopping criterion and the significant numbers at which elements of R k and G k were changing at convergence. The likelihood stopping criteria allowed iteration to proceed further t h a n necessary. Retrospective e x a m i n a t i o n of estimated (co)variance matrices indicated that 5 to 10 iterates would have been adequate. To check that convergence was to a global m a x i m u m , solutions for R and G at convergence for the all ejaculate model, bull stud A, were inverted and set as priors in a rerun o f the analysis. Solutions again converged to the same results, suggesting the global m a x i m u m . A t convergence, bull evaluations for each trait were s u m m e d to examine their p r o x i m i t y to zero as

TABLE 2. Computer times for absorption, tridiagonalization, and average iterate for bull stud B.

Step

Matrix rank

Time/ average time

Invert X'X Absorb to form Z'MZ Tridiagonalize Z'MZ Average iterate

238 858 858 . ..

1 min 5 s 1 h 16 min 5 s 1 h 20 min 48 s 1 min 16 s

Journal of Dairy Science Vol. 68, No. 10, 1985

VARIANCES OF SEMEN PRODUCTION

2709

TABLE 3. Trace (tr) of Z'MZ, absolute difference between traces of Z'MZ and F, and largest sum of bull evaluations for any trait within bull stud.

Bull stud

Ejaculates modeled

Number of collections

A

All First

B

C

trZ'MZ ~

Absolute difference2

Largest sum of bull evaluations 3

52,657 33,877

49,281 32,011

.1618 .0972

.3886 .0065

All First

44,609 22,962

41,909 21,555

.1994

.1160

.0122 .0111

All First

52,073 26,131

48,190 24,235

.1382 .0684

.0559 .0764

1 Effective number of ejaculates summed over bulls and rounded to the nearest integer. 2Reported as ItrZ'MZ - trFI × 10 s. * Sums × 10 a. Deviations from zero reflect rounding error and lack of convergence.

Ic * l q' ) U^ = 0. T h e sums f a r t h e s t f r o m zero f o r each analysis are in Table 3. T h e s e i n d i c a t e t h a t t h e series o f t r a n s f o r m a t i o n s r e q u i r e d t o perf o r m t h e s e analyses did n o t add a p p r e c i a b l y t o r o u n d i n g error on the IBM 4341. S o l u t i o n s f o r e f f e c t s r e p o r t e d h e r e are f r o m m u l t i p l e trait analyses o f all ejaculate d a t a b y bull s t u d a n d are c o m p a r a b l e only w i t h i n trait and bull stud. F o r each trait, t h e s o l u t i o n f o r o n e class o f each f i x e d e f f e c t was c o n s t r a i n e d t o be z e r o w h e r e necessary, a n d s o l u t i o n s f o r r e m a i n i n g classes are e s t i m a t e s o f d i f f e r e n c e s b e t w e e n t h e s e

classes and t h e c o n s t r a i n e d class. Similarly, e s t i m a t e d s t a n d a r d errors are for d i f f e r e n c e s b e t w e e n levels. F o r e x a m p l e , c o n s t r a i n i n g age o f bull s o l u t i o n o f lO-mo-old bulls, /~1, to be z e r o ]implies t h a t s o l u t i o n s f o r o t h e r age categories, Aj, are e s t i m a t e s o f d i f f e r e n c e s Aj -- A I . A l t h o u g h e s t i m a t e s o f s t a n d a r d errors o f contrasts w e r e calculated, t h e y are n o t r e p o r t e d . Table 5 c o n t a i n s estimates o f ejaculate e f f e c t s within c o l l e c t i o n days a n d age o f bull e f f e c t s f o r s e m e n p r o d u c t i o n traits w i t h i n bull studs. D i f f e r e n c e s b e t w e e n first a n d s e c o n d eja-

TABLE 4. Iterates to convergence and significant figures at whiich elements of covariance matrix estimates Rk 1 and Gk 2 were changing at convergence. Bull stud

Ejaculates modeled

Iterates 3

Change 4 in R k

Changea in G k

A

All First

26 18

12 10

10 7

B

All First

14 23

10 12

7 9

C

All First

13 16

10 10

7 7

1Rk is residual variance covariance matrix at iterate k. Gk is additive genetic variance covariance matrix at iterate k. s First round (k) at which 1 - Lk_I/L k < 10 -Is, where Lk is the log likelihood evalated at iterate k. 4 Changes represent the smallest significant figure at which a change occurred. Journal of Dairy Science Vol. 68, No. 10, 1985

2710

T A Y L O R ET AL.

T A B L E 5. Estimates o f ejaculate within collection day and age o f bull effects on semen production within bull studs. Total sperm Ejaculate

As

B (109)

1 2 3 Age 10 m o 11 m o 12 m o 13 m o 14 m o 15 m o 16 m o 17 m o 18 m o 19 m o 20 m o 21 m o 22 m o 23 m o 24 to 29 mo 3 yr 4 yr 5 yr 6 yr 7 yr 8 yr 9 yr 10 yr 11 yr 12 yr 13 yr 14 yr

Volume C

A

~

B

Concentration C

A

(ml)

6.7 1.7 0

5.2 1.6 0

3.9 1.9 0

1.5 .6 0

0 --4.9 --4.3 --3.1 --2.0 -1.1 -.4 .4 1.7 1.5 1.5 2.3 3.7 3.1 3.1 4.8 5.0 6.5 6.1 6.2 6.0 6.1 5.8 5.7 4.7 4.1 5.7

0 -1.8 --1.4 --.8 --.4 .1 .3 .9 1.1 1.3 2.3 1.8 .4 .6 1.0 5.7 3.8 5.4 5.4 5.4 4.7 3.9 4.3

0 -.2 .3 .8 1,3 1.6 1.8 2.1 2.6 2.5 3.2 3.4 3.4 3.8 4.3 4.7 4.8 5.4 5.3 5.5

0 --.2 --.2 .3 .6 .9 1.2 1.2 1.7 1.2 1.6 1.9 2.5 2.1 2.4 3.3 4.0 4.5 4.8 5.0 5.0 5.1 5.0 4.9 4.8 4.8 4.7

~

.7 .1

.5 .4

B

C

(109/ml)

.70 .18

.73 .24

.64 .29

0

0

0

0

0

0 --.2 -.1 .1 .3 .5 .7 .9 1.1 1.6 2.2 1.6 .9 2.1 1.1 3.5 3.6 4.2 4.6 4.6 4.4 4.8 4.3

0 --.4 -.3 .0 .1 .2 .3 .4 .5 .5 .7 .8 1.1 1.4 1.5 1.8 2.2 2.5 2.6 2.7

0 -.93 --.80 --.66 --.51 --.40 -.34 -.22 -.11 -.00 -.13 -.12 -.07 -.06 -.08 -.08 -.19 --.12 --.20 -.21 -.23 -.21 -.21 -.20 --.25 --.28 --.12

0 --.40 -.29 --.19 -.10 -.02 .01 .10 .12 .06 .14 .05 -.16 --.21 .07 .36 .09 .25 .23 .21 .14 .02 .22

0 --.02 .11 .20 .29 .33 .37 .41 .51 .48 .58 .59 .55 .55 .65 .61 .51 .57 .54 .55

Solutions as deviations from null category for bull studs A, B, and C. Solutions comparable within trait and bull stud.

culates may be obtained from the difference 1 - 2, a n d , h e n c e , t h e d i f f e r e n c e in t o t a l s p e r m production between first and second ejaculates f o r b u l l s t u d A is 6 . 7 - 1.7 = 5 . 0 b i l l i o n s p e r m . F r o m T a b l e 1, l a r g e d i f f e r e n c e s e x i s t in d a t a means between bull studs for ejaculates. After adjustment for fixed effects, Table 5 indicates that differences remain between bull studs for successive ejaculates within collection days. Diff e r e n c e s are, in p a r t , d u e t o d i f f e r e n c e s b e t w e e n b u l l s t u d s in i n t e n s i t i e s o f s e x u a l p r e p a r a t i o n a n d s t i m u l a t i o n p r i o r t o e a c h e j a c u l a t e a n d also d i f f e r e n c e s in i n t e n s i t i e s a p p l i e d t o b u l l s w i t h Journal o f Dairy Science Vol. 68, No. I0, 1985

high demand for semen versus bulls with medium or low demands for semen. T o m i n i m i z e g e n e r a t i o n i n t e r v a l in s e l e c t i o n f o r m i l k , y o u n g b u l l s e n t e r c o l l e c t i o n as s o o n as they are able to produce semen of sufficient quantity and quality to process. Ejaculates are u s u a l l y s a t i s f a c t o r y a t 11 t o 1 2 m o o f age, a n d s e m e n is h a r v e s t e d o n c e o r t w i c e w e e k l y f o r a b o u t 12 w k o r u n t i l a d e q u a t e n u m b e r s o f breeding units have been obtained for progeny testing. Collections on 10-mo-old bulls tend not t o b e p r o c e s s e d as s p e r m n u m b e r s a n d m o r p h o l o g y is u s u a l l y u n s a t i s f a c t o r y . T o a c c o u n t

VARIANCES OF SEMEN PRODUCTION for puberal effects and rate of testes development in young bulls (4), age classification was monthly until 23 mo of age. Each year class is of 12 mo, where an n-yr-old bull (n /> 3) may be in the range 1 2 n - 6 , 12n+5 mo at collection. Final year classes for each bull stud are composites, and the 10-yr class for bull stud B includes all bulls 10 yr or older. Solutions for age effects in Table 5 indicate pronounced age differences for semen production for all bull studs. Within each bull stud and production trait, solutions exhibit constant rate of increase from 11 through 20 or 22 mo of age. The rate of increase is constant over bull studs for semen concentration but differs for total sperm and volume. Differences exist between 10 mo and other age classes apparently in the favor of 10-mo-old bulls for all bull studs. Collection of semen is not a t t e m p t e d routinely prior to 10 mo, and this result is thought to be due to inclusion of older bull(s) with incorrectly recorded birth dates in this category, computed as -<10 too. Ignoring this dass and comparing subsequent age classes to l l - m o - o l d bulls closely aligns all solutions in the 11- to 22-mo range. Total sperm and volume of ejaculate increase until 7 yr of age and remain constant until 9 or 10 yr of age after which decline was gradual for bull stud A. Semen concentration reaches its optimum and remains there once the bull has reached 20 to 22 mo of age. These results agree with (1, 4, 7, 8, 9). Estimates of effects of ambient temperature in 5°C classes on semen production were obtained for bull stud A. These solutions indicate that extreme temperatures have only minor detrimental effects on semen production. The most extreme classes, --24 to --19°C and 27 to 32°C, depressed ejaculate volume by .3 and .2 ml and total sperm b y .3 billion sperm below the o p t i m u m temperature class of 16 to 21°C. No effect of temperature on concentration of ejaculate was identified. These results are expected with a large proportion of bulls being housed and collected within controlled environmental conditions. Where bulls are subjected to extremes of temperature, a greater depression could b e expected, which is consistent with the importance of season of year on production (4, 7, 8, 9). Table 6 contains estimates of effects of day of week of collection on semen production b y

2711

bull barn and stud. Solutions are only for barns with routine collection on Monday through Friday. Solutions for a small proportion of weekend collections are not presented. Motivation for parameterizing as days by barn was to allow for the possibility of an interaction between day of week and location of collection. Everett and Bean (8) illustrated the importance of day of week on semen production, but their model had uniform day effects over all collection :sites. Effect day of week may be interpreted to monitor efficiency of the labor force working with the bulls provided differential treatment of bulls between days is considered in the model. Estimates in Table 6 indicate large differences between barns and days of the week. At the extreme, on Mondays barn C4 exhibited an advantage of 1.4 ml in volume of ejaculate over barn C1 but with 4.6 billion fewer spermatozoa. This paradox is not readily explicable; most solutions reflect the expected relationship of increased total sperm associated with increased ejaculate volumes. Differences between barns are due to differences in bull housing and work crews and are also likely to contain an effect of age of bull. Although age of bull at collecxion was included in the model, this effect partially was confounded with barns; certain barns housed only young bulls and others admitted only progeny tested bulls between 5 and 6 yr of age. Solutions for days within each barn were generally stable, indicating only slight daily variation of semen production. This supports the adequacy of effects of depletion and inten,;ity of collection for adjusting for differential treatment of bulls over days. Trends in semen production Monday through Friday were not uniform between bull studs or even between barns within bull stud. However, over all barns within bull stud, total sperm per ejaculate increased linearly Monday through Friday for bull stud A, peaked Wednesday for bull stud B, and peaked Tuesday and Thursday for bull stud C. Volume of ejaculate was at its greatest midweek for bull studs A and B but lowest at this point for bull stud C. Concentration of ejaculate behaved erratically but was at a maximum on Thursday for all bull studs. Effects of calendar days from first collection after repletion and calendar days between adjacent collections b y number of ejaculates on the Journal of Dairy Science Vol. 68, No. 10, 1985

tJ ,.q

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TABLE 6. Estimates of effects of day of week of collection w i t hi n barn and bull stud on semen production. o CO

Total sperm Barn I

Ms

T

.6

.7 .1 1.2 .9

W

Volume T

F

.9 .8 .5

.8 .5 1.1

.9 .5 1.2

0

.8 1.0

.8 .7

.8 .2

4.1 3.5 3.6 3.0 2.9 3.1 1.9 2.4

2.8 3.6 3.5 2.2 3.0 1.4 2.1 2.0

4.2 3.6 2.5 .9 3.2 4.5 2.1 2.1

4.3 3.5 .8 3.0 3.0 3.3 1.8 1.9

M

T

W

Concentration T

F

M

T

.3 .2 .4

.10 .03 .11

.10 .02 .06

.5

.03 .09

W

T

F

.11 .04

.12 .06 .14

.13 .08 .06

.02

.01 .09

.05 .12

.04 .10

.85 .80 .71 .78 .81 .84 .62 .75

.74 .84 .80 .58 .80 .61 .68 .73

.91 .82 .65 .43 .82 .84 .58 .68

.73 .81 .28 .58 .79 .88 .60 .68

oz (109 ) A1 A2 A3

0 1.1

B1 B2

.8 .4

C1 C2 C3 C4 C5 C6 C7 C8

4.6 3.3 2.5 0 3.1 3.8 1.5 3.0

(ml) .1 0 .2 .5 0 1.4 1.1 1.0 2.8 .9 1.5 .3 .9

(109/ml)

.3 .2 .3

.3 .5 .2

.3 .2

.5 .2

.6 .4

.5 .1

1.6 1.2 0 1.0 .9 .8 .7 .5

1.0 1.3 1.1 1.0 .9 .5 .6 .5

1.3 1.3 .9 .7 1.0 2.1 1.0 .7

0

0 1.9 1.3 1.2 1.7 1.0 .6 .8 .5

.99 .81 .65 0 .83 .83 .60 .78

0

0

Barn w i t h i n bull stud. 2 Solutions for day of week of collection. Monda y through Friday, w i t h i n barn expressed as deviations from null category. Solutions comparable w ith in trait and bull stud.

.t-

VARIANCES OF SEMEN PRODUCTION previous collection day have to be considered in conjunction to describe the process of depletion in regularly ejaculated bulls. Studies (1, 8, 17) discarded collections until bulls had reached equilibrium under conditions of semen harvest. Rather than discard data whenever a bull was laid off, or assume a point of equilibrium, the former effect was included to model the depletion process of replete bulls entering a collection regimen. Bulls having had at least 14 consecutive calendar days without collection were defined as replete. Classes of this effect were daily intervals beginning with 0, the 1st d of collection after repletion, through to I>40 calendar d from first collection. The majority of observations fell in this last class, with observations in earlier classes generated by collections on young bulls and bulls returning to service after progeny testing or after having been laid off for reasons of health or semen requirement. Some of the earliest data from each bull stud were discarded whenever an observation could not be classified in either of the 0 or ~>40-calendar d classes. The latter effect was incorporated in the model to remove differences in collection regimens between bulls. Bulls with high semen demands are collected twice weekly and three times on any collection day at higher sexual preparation and stimulation than bulls with low semen demands ejaculated only once per week. The first class of calendar days between adjacent collections b y previous number of ejaculates included only first available collections on replete bulls. Subsequent classes are in daily intervals up to />14 calendar d between adjacent collections with 1, 2, or 3 collections on the previous collection day. Table 7 contains estimates of effects of calendar days from first collection after repletion on semen production by trait and bull stud. The stability of solutions indicates that after 4 to 5 calendar d, or at most six ejaculates after repletion, bulls are adapted to systems of semen production. Hence, if an effect for stage of depletion of the bull is n o t included in the model as in (1, 8, 17), few initial collections on replete bulls need be discarded. The solution for 1st collection day after repletion relative to subsequent day classes is low for all traits and bull studs, which may be from a lack of familiarity with handling and collection procedures associated with the young and progeny tested

2713

bulls returning to service rather than a lack o f regularity in the biological processes involved in depletion. Table 8 contains estimates of effects of calendar days between adjacent collections by number of ejaculates on the previous collection day. Parameterization of this effect allowed examination of trends in solutions by ejaculates over days or, alternatively, b y ejaculates within days. For solutions for first ejaculates for total sperm in bull stud A, differences between adjacent days gradually decreased until no difference existed from d 10 onward. Differences in solutions between adjacent days for second and third ejaculates behaved similarly but were slightly larger than for first ejaculates until by d 10 no difference in day or ejaculate within day effects existed. Bulls collected in intervals of at least 10 calendar d should exhibit no differences in total sperm produced per ejaculate because of once, twice, or thrice collection on the previous collection day. For collection intervals less than 10 calendar d, comparing solutions within days indicates that as more ejaculates were taken on the previous collection day, fewer sperm were harvested on the following collection day. This effect became more pronounced as collection interval decreased, as measured by the corresponding increases of difference between solutions for first and third ejaculates. These trends of solutions were exhibited by all traits and for all bull studs; however, bull stud A elicited a greater response of semen production than B or C for all traits on increased collection interval. For first ejaculates for total sperm, A achieved an increase of 6.7 - 2.6 = 4.1 billion sperm b y increasing the collection interval from 2 to 9 d whereas for this period B and C increased b y 2.5 and 1.9 billion sperm. With a collection interval of 3 d, A achieved an advantage of 4.9 - 1.8 = 3.1 billion sperm in the subsequent collection if collection was once and not thrice previously; B and C responded by .2 and 1.5 billion sperm. Bull stud A maintained bulls at lower semen reserve than did studs B or C. The greater differences between solutions for ejaculates within collection day for stud A reflects more effective depletion on the previous collection day. Further, the greater response to an increase of collection interval indicates an added advantage of extra days for repletion for bulls Journal of Dairy Science Vol. 68, No. 10, 1985

2714

TAYLOR ET AL.

TABLE 7. Estimates of effects of calendar days from first collection after repletion on semen production by bull stud. Total sperm Days 1

A2

B

Volume C

(109) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 940

-.5 5.1 1.1 .7 .5 .9 .1 .4 .7 .3 .6 .2 ,6 .5 0 .3 0 .7 .4

.7 .7 .4 .8 .6 .5 .6 .5 .3 .5 1.1 .5 .5 .8 1.2 .1 .8 .9 .6 .5 .3 .4

A -

B -

Concentration C

(ml)

.5 4.5 .8 .6 .9 .5 .5 .3 .6 .9 1.0 .7 .3 .3 .5 0 .3 .7

.3 1.7 1.5 .9 .8 .4 .3 .4 .4 ,4 .4 .4 .3 .4 .2 .2 .1 .7

1.5 5.5 .5 .3 .2 .5 .5 .3 .5 .4 .1 .2 .4 .5 .3 .2 .5 .2

.3 1.7 .5 .5 .5 .7 .5 .2 .2 1.0 .6 .2 .0 .5 ,3 0 .3 .4

0

1.0 .6

.4 .3

.1 .3

.4 .4

.9 .6 .7 .1 .9 1.1 .6 .7 .5 0 .6 .5 .6 ,6 .5 .7 .3 .3 1.0 .4 .3

.3 .4 .4 .3 .3 .4 .3 .1 .3 .4 .1 .6 .4 ,5

.3 .4 .3 .4 .3 .1 .3 .3 .4 .4 .5 .6 .4 .5 .6 .4 .2 .3 .1

.4 .3 .2 .4 .3 .4 .2 .5 .3 .1 .2 .3 .4 .3 .2 .3 .2 .1 .4 .1 .2

0 .4 .2 .4 .3 .4 .3

0 .4

B

~(109/ml)

.5 2.5 1.8 1.2 .6 .9 .9 .6 1.2 1.5 .6 1.0 1.1 1.0 .6 .5 .5 .8 1.0 1.1 .8 .6 .6 .8 .5 .4 .7 .8 1.0 .6 1.3 1.1 .7 .9 .7 .7 .5 .8 .6 .7

A

-.03 .55 .03 .04 0 .06 .02 .04 .04 .04 .06 0 .08 .06 .02 .06 .06 .06 .05 .09 .11 .04 .10 .09 .06 .08 .05 .09 .07 .13 .10 .01 .08 .13 .13 .08 .13 .08 .10 ,04 .06

.07 --.30 .23 .15 .08 .04 .06 .05 .12 ,17 .08 .11 .10 .11 .08 .08 .04 .07 .03 .11 .16 .08 .04 .07 .09 .09 .07 .07 .07 .12 0 .09 .12 .10 .08 .07 .07 .03 .12 .15 .07

C ~ .08 .42 .09 .10 .13 .01 .08 .07 .15 ,02 .12 .17 .11 0 .09 .05 .05 .10 .12 .08 .15 .10 .14 .03 .12 .15 .13 .08 ,10 .04 .14 .08 .09 .10 .11 .12 .07 .09 .14 .14 .08

1 Days from repletion. 2 Solutions as deviations from null category for bull studs A, B, and C. Solutions comparable within trait and bull stud.

in s t u d A o v e r s t u d s B a n d C. W i t h i n c o l l e c t i o n d a y s , bull s t u d A m a d e c o l l e c t i o n s o r d e r e d b y bulls within ejaculate; each bull was r e t u r n e d t o its stall f o r at least 30 m i n p r i o r t o e a c h s u c c e s s i v e ejaculate. C o n v e r s e l y , bull s t u d s B

Journal of Dairy Science Vol. 68, No. 10, 1985

and C made collections ordered by ejaculates w i t h i n bull w h e r e o n p r e s e n t a t i o n all r e q u i r e d e j a c u l a t e s w e r e c o l l e c t e d o n a n i n d i v i d u a l bull b e f o r e h e w a s r e t u r n e d t o his stall. T h i s s e c o n d strategy reduced intervals b e t w e e n successive

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2716

TAYLOR ET AL.

ejaculates and also may have caused reduction of sexual stimulation and preparation for each ejaculate. Environmental trends were examined by solutions to month-year effects within bull studs. The month-year parameterization treats months individually over years providing an examination of environmental trends both within and across years. Month-year subclass numbers averaged 592, 369, and 332 first, second, and third ejaculates for bull studs A, B, and C. F o r brevity, Table 9 contains estimates of season-year effects, where seasons were defined as 1 = January through April, 2 = May through August, and 3 = September through December. Solutions for each season were obtained as the average of m o n t h l y solutions in season and were scaled such that the smallest solution for each trait was null. Although this strategy reduces overall variation between solutions, and estimates of differences between season-years are not minimum variance, gross environmental trends of semen production remained unaltered. Existence of seasonal effects was determined b y ranking of seasons within years compared over all years. In Table 9 no bull stud achieved consistently positive environmental trends for semen production during the period for which data were available. Results for bull stud C are unique in that they demonstrate no long or short trends of production for any trait. Solutions for studs A and B indicate important short trends, particularly for concentration, which are reflected in solutions for total sperm. F r o m mid-1972 through mid-1979 concentration oscillated substantially but decreased b y . 39 billion sperm/ml for bull stud B. The oscillation of solutions was emulated by total sperm; however, the expected decline of sperm numbers was offset by increase of volume of 1.0 ml during this period. Bull stud A experienced a precipitous decline of 1.9 billion sperm per ejaculate from mid-1975 through the end of 1977. In the same period, concentration fell b y .26 billion sperm/ ml, and volume per ejaculate decreased by .2 ml per ejaculate. F r o m late 1977 through mid1978 bull stud A recovered 1.5 billion sperm per ejaculate with an increase of .8 ml of volume. After mid-1978 volume and total sperm per ejaculate experienced a slight decline; however, concentration remained essentially constant from mid-1978 on. The decline and Journal of Dairy Science Vol. 68, No. 10, 1985

recovery before and after late 1977 is thought to be due to identification of a decrease of collection pressure after a spate of penis injuries of bulls. Solutions for bull stud A exhibited higher consistency over time than did those for studs B and C. This suggests greater continuity of collection conditions for bulls in stud A. Comparing ranking of seasons within years over all years in Table 9 indicates that season 2 was most favorable for volume, concentration, and total sperm per ejaculate for all bull studs. Season 1 was preferable to season 3 for all semen traits in bull stud B whereas this tendency existed but was not as noticeable for bull studs A and C. The superiority of summer months for sperm production agreed with (4, 7, 8, 9); however, lack o f consistency of rankings of season within all years indicates an important interaction of season and year effects. Genetic trends of semen production may arise from culling of inferior semen producing bulls or as a correlated response to selection for milk production. Generally, no more than 8% of young bulls are culled per year for low semen production. Even if the genetic basis for production of spermatozoa does not change as the bull ages, such low culling rates are unlikely to produce noticeable genetic change. Everett and Keown (10) reported an average annual genetic trend of 31 kg of milk per year for all studs in the Northeast. For high heritabilities for semen production, the genetic correlation between semen and milk production would have to be considerable to detect any response to selection in the one or two generations of bulls in these data. Within each bull stud, bulls were ranked b y ascending stud code, approximating their age and order of entry into each stud. Groups of 10 consecutively ordered bulls were formed and group solutions calculated from raw and weighted averages of semen trait predictions. Weights were reciprocals of approximate standard error of errors of prediction. Plots of both raw and weighted group solutions by group number for each semen production trait exhibited the expected variation between groups; however, no evidence of genetic trends was present. The random bull effect in the model for semen production traits can be partitioned to include additive genetic and nonadditive genetic plus permanent environmental effects.

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2718

TAYLOR ET AL.

C o n s e q u e n t l y , t h e bull c o m p o n e n t s of (co)variance are additive genetic and nonadditive genetic plus p e r m a n e n t e n v i r o n m e n t a l (co)variances with variances yielding estimates of repeatability or u p p e r b o u n d s for heritability. Similarly, genetic correlations also contain nonadditive genetic and p e r m a n e n t environmental c o m p o n e n t s . Estimates o f standard deviations, repeatabilities, genetic and e n v i r o n m e n t a l correlations within and p o o l e d over bull studs for all ejaculates and for first ejaculates are in Tables 10 and 11. Stratification of bulls by stud A into p r o d u c t i o n groups is p r o b a b l y responsible for the large standard deviations associated with bulls for this stud. In p o o l e d estimates, models adjust for m a n a g e m e n t a l differences b e t w e e n studs, and resulting environments are homogeneous. However, as it was n o t possible to isolate effects of differential t r e a t m e n t of bulls and quite possibly o t h e r m a n a g e m e n t a l differences, pooling over all studs m a y be inappropriate. The definition o f the p o p u l a t i o n these statistics describe is nebulous. Estimates of repeatability and standard deviations increased f r o m analysis o f all analyses of first ejaculate as also r e p o r t e d

by Seidel and F o o t e (18). This was e x p e c t e d with the residual c o m p o n e n t after correlated residuals due to r e p e a t e d ejaculates on the same day were removed. However, t h e bull compon e n t reflects increased variation associated with first over second or third ejaculates as in Table 1. Pooled over all bull studs repeatabilities of first versus all ejaculate evaluations were .82, .80, and .87 for total sperm, volume, and concentration. Genetic and e n v i r o n m e n t a l correlations between total sperm and v o l u m e or c o n c e n t r a t i o n were large and similar. Correlations b e t w e e n v o l u m e and c o n c e n t r a t i o n were m o d e r a t e and negative except for stud C with positive environmental correlation. This difference m a y stem f r o m a less p r o n o u n c e d differential treatm e n t of bulls for this stud. Bulls collected under the most intense stimulatory regimens t e n d e d to produce higher volumes and total sperm counts than bulls in low or m e d i u m demand, but these increases were disproportional. Seidel et al. (18) r e p o r t e d c o m p o n e n t s of variance derived by Henderson's M e t h o d 3 leading to repeatabilities of .15, .40, and .44 for total sperm, volume, and concentration.

TABLE 10. Standard deviations, repeatabilities, and genetic and environmental correlations within bull studs and pooled over all studs for all ejaculates. Bull stud A

All 3

Trait

Total sperm

Volume

Co ncentration

Total sperm Volume Concentration

.352 .53 .67

.45 .25 -.12

Total sperm Volume Concentration

.19 .47 .67

Total sperm Volume Concentration Total sperm Volume

Concentration

ab x

oe

.77 - . 12 .50

2.32 1.07 .324

3.17 1.84 .324

.40 .19 --.14

.72 --.23 .31

1.35 .94 .242

2.79 1.91 .360

.18 .66 .68

.54 .25 .05

.62 -.25 .29

1.34 .93 .244

2.87 1.60 .386

.26 .55 .67

.45 .23 -.07

.72 - . 19 .37

1.73 .98 .273

2.96 1.78 .358

10b and o e = Square roots of bull and environmental components of variance. 2 Repeatabilities are underlined. Genetic correlations are above diagonals and environmental correlations are below diagonals. 3 Obtained from pooling estimates of variance. Journal of Dairy Science Vol. 68, No. 10, 1985

VARIANCES OF SEMEN PRODUCTION

2719

TABLE 11. Standard deviations, repeatabilities, and genetic and environmental correlations within bull studs and pooled over all studs for first ejaculates. Bull stud A

AlP

Trait

Total sperm

Volume

Concentration

Obi

ae

Total sperm Volume Concentration

.372 .56 .62

.50 .24 - . 16

.76 -.06 .49

2.55 1.09 .332

3.32 1.94 .338

Total sperm Volume Concentration

.30 .54 .61

.46 .20 - . 17

.74 --. 13 .41

1.97 1.02 .320

2.99 2.02 .383

Total sperm Volume Concentration

.24 .70 .66

.59 .25 .06

.68 --. 11 .35

1.82 .98 .306

3.24 1.68 .418

Total sperm Volume Concentration

.31 .59 .63

.51 .23 -.09

.73 -.10 .42

2.14 1.03 .320

3.21 1.89 .377

10b and o e = Square roots of bull and environmental components of variance. 2 Repeatabilities are underlined. Genetic correlations are above diagonals and environmental correlations are below diagonals. a Obtained from pooling estimates of variance.

Repeatabilities for total sperm and v o l u m e differ f r o m those in Tables 10 and 11; however, this m a y be due to t h e semen collection regimen of four ejaculates per w e e k in (18). Sampling variances estimated in (18) m a y be large with 63 bulls collected and only 174 degrees of f r e e d o m for residual. Both studies indicated t h a t repeatabilities, and hence, heritabilities, o f semen p r o d u c t i o n were low to moderate. Over all studs, 56 bulls w i t h 612 sons were identified with evaluations for all semen production traits. F o r each trait, the additive genetic c o m p o n e n t of variance was estimated as:

^2 = 2Usire ^ ' ~lson/612 Og where: A

Usire is a 612 × 1 v e c t o r o f sire evaluations with o n l y 56 u n i q u e sires, and A Uson is a 612 × 1 v e c t o r o f corresponding son evaluations. A l t h o u g h this e s t i m a t o r is free of p e r m a n e n t e n v i r o n m e n t a l variance, it is biased. T h e bias

arises because of neglected off-diagonal terms of ( Z ' M Z + dilq)-1 relating to each sire-son pair A! A in the e x p e c t a t i o n o f Usire Uson. T h e s e offdiagonals were n o t c o m p u t e d , and, hence, the direction and m a g n i t u d e o f the bias is un o known. A f u r t h e r p r o b l e m arises in that y o u n g bulls culled for low semen p r o d u c t i o n and o t h e r low semen producing bulls are discriminated against and tend n o t to have sons for comparison. For environmental standard deviations pooled over studs f r o m Tables 10 and 11, heritabilities and genetic standard deviations for all and first ejaculates are in Table 12. Heritabilities for v o l u m e in Table 12 are close to corresponding repeatabilities in Tables 10 and 11, and those for t o t a l sperm and c o n c e n t r a t i o n differ considerably. The disparity b e t w e e n repeatabilities and heritabilities for total s p e r m per ejaculate is due, in part, to t h e p r o b l e m of differential semen harvesting of bulls having milk evaluations. These data span at most t w o generations w h e r e sires have been stratified into collection regimens according to total sperm requirements, whereas the m a j o r i t y of sons are collected u n i f o r m l y and await evaluations for milk. The disruption of the sire-son relationJournal of Dairy Science Vol. 68, No. 10, 1985

2720

TAYLOR ET AL.

TABLE 12. Heritabilities and genetic standard deviations over all studs for all and first ejaculates. All ejaculates ~

First ejaculates

Trait

h2

Og

h2

ag

Total sperm, 109 Volume, ml Concentration, 109/ml

.03 .18 .10

.51 .84 .118

.05 .16 .16

.75 .84 .164

h 2 and Og = Heritability and genetic standard deviations.

ship, possibly greater p e r m a n e n t e n v i r o n m e n t a l variation, and the multiplicative relationship a m o n g traits explains the similar disparity for ejaculate concentrations. Within each bull stud, semen p r o d u c t i o n data of first ejaculates were selected according to age of bull at collection to f o r m y o u n g and mature bull data sets. Young bulls were defined to be no greater than 15 m o old and m a t u r e bulls no less than 60 mo old at collection. Table 13 contains numbers of bulls and records describing the six sets o f data and the n u m b e r of bulls represented b o t h at y o u n g and mature ages. Each data set was analyzed by the m o d e l and multiple trait procedure described although certain main effects were lost in partitioning of data. Bulls with evaluations at b o t h ages had evaluations correlated to estimate repeatability of semen p r o d u c t i o n of first ejaculates b e t w e e n y o u n g and m a t u r e ages. Repeatabilities were similar b e t w e e n bull studs and for measures o f total sperm, volume, and c o n c e n t r a t i o n of first ejaculates were .21, .27, and .19 pooled over studs. If the opera-

tional models for semen p r o d u c t i o n traits were true biological models, these estimates should be near unity. Potential factors affecting estimation of these relationships include 1) culling of y o u n g bulls producing low semen, 2) differential semen collection of mature bulls, 3) i m p e r f e c t correlations b e t w e e n p e r m a n e n t environments at the two ages of p e r m a n e n t e n v i r o n m e n t accumulates, and 4) possible interactions of g e n o t y p e × age or g e n o t y p e × perm a n e n t environment. These repeatabilities are low and further indicate that measurements on y o u n g bulls are n o t closely related to mature p r o d u c t i o n (3, 4, 12, 14). Evaluations of semen p r o d u c t i o n for first ejaculates on 336 y o u n g bulls were correlated with their multiple trait A I sire comparisons for first lactations (MTAISC) for milk and milk fat (11). O f the 336 bulls, only 5 were f r o m Select Sires Inc. and 83 were f r o m A m e r i c a n Breeders Service. However, 1,277 of the 1,999 y o u n g bulls evaluated for semen p r o d u c t i o n had United States D e p a r t m e n t o f Agriculture ( U S D A ) h e r d m a t e comparison (HC) evaluations

TABLE 13. Number of bulls and records by age of bull and stud origin. Bull stud

Young ] bulls

Records

Mature 2 bulls

Records

Common 3 bulls

A B C All

587 729 683 1,999

6,950 7,112 6,486 20,548

292 250 334 876

24,062 13,903 14,927 52,892

115 152 324 591

1Young bull data set. Mature bull data set. 3Common to young and mature data sets. Journal of Dairy Science Vol. 68, No. 10, 1985

VARIANCES OF SEMEN PRODUCTION

2721

TABLE 14. Genetic correlations between semen and milk production traits pooled over bull studs.

Evaluation

Trait 1

Total sperm

MTAISC~

Milk Milk fat

-.03 -.06

.O1 .04

--.01 .01

HC 3

Milk Milk fat

,01 .02

.01 .04

.01 .05

Volume

Concerttration

i Semen evaluations are for first ejaculates as young bulls. 2 Mhltiple trait artificial insemination sire comparison. Herdmate comparisons based on at least 20 daughters.

for all lactation milk and milk fat p r o d u c t i o n based on at least 20 daughters. Of these, 203, 396, and 678 bulls were f r o m Eastern AI Cooperative Inc., Select Sires Inc., and A m e r i c a n Breeders Service. To avoid possible incompatabilities b e t w e e n evaluation systems associated with bulls evaluated with few observations, bulls were required to have at least 20 daughters contributing to their HC evaluations. The most recent HC and M T A I S C evaluations incorporating all available daughter i n f o r m a t i o n were used in estimating genetic correlations. Table 14 contains genetic correlations between semen and milk p r o d u c t i o n traits p o o l e d over bull studs f r o m b o t h HC and M T A I S C evaluations. Genetic correlations f r o m b o t h sources o f milk p r o d u c t i o n evaluations are close to zero. These results do n o t substantiate the speculation of negative genetic relationships b e t w e e n semen and milk p r o d u c t i o n by Coulter et al. (5) b u t indicate that selection for milk p r o d u c t i o n has not induced correlated responses in semen p r o d u c t i o n as also f o u n d directly f r o m evidence of t r e n d in bull solutions for semen production. Genetic correlations b e t w e e n semen production of bull and milk p r o d u c t i o n of daughters were near zero, and selection for semen production will not induce correlated responses in milk p r o d u c t i o n . However, heritability o f total sperm p r o d u c t i o n does not appear to justify i m p l e m e n t a t i o n of selection programs based on p e r f o r m a n c e testing of y o u n g bulls, particularly if such programs potentially sacrifice genetic progress for milk. Further, t h e majority o f bulls under c o m m e r c i a l semen harvest p r o d u c e ample semen to fulfill requirements. R a t h e r than

a t t e m p t to alter the p o p u l a t i o n genetic m e a n for semen p r o d u c t i o n , emphasis within bull studs should be placed on optimizing managem e n t for semen harvest and processing for the relatively few high-demand bulls. ACKNOWLEDGMENT

T h e authors t h a n k R. L. Quaas and S. P. Smith for providing their EM algorithm for multiple trait REML. REFERENCES

1 Almquist, J. O. 1982. Effect of long-term ejaculation at high frequency on output of sperm, sexual behavior, and fertility of Holstein bulls; relation of reproductive capacity t o high nutrient allowance. J. Dairy Sci. 65:814. 2 Almquist, J. O., and R. P. Amann. 1976. Reproductive capacity of dairy bulls. XI. Puberal characteristics and postpuberal changes in production of semen and sexual activity of Holstein bulls ejaculated frequently. J. Dairy Sci. 59:986. 3 Almquist, J. O., R. J. Branas, and K. A. Barber. 1976. Postpuberal changes in semen production of Charolais bulls ejaculated at high frequency and the relation between testicular measurements and sperm output. J. Anita. Sci. 42:670. 4 Amann, R. P., and J. O. Almquist. 1976. Bull management to maximize sperm output. Page 1 in Proc. 6th Natl. Assoc. Anim. Breeders Tecb. Conf. 5 Coulter, G. H., R. H. Foote, and T. R. Rounsaville. 1977. Genetic correlations between testicular traits in Holstein bulls and milk and fat production of their daughters. J. Dairy Sci. 60:1304. 6 Dempster, A. P., N. M. Laird, and D. B. Rubin. 1977. Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. B. 39:1. 7 Everett, R. W. 1982. Effect of Dursban 44 on semen output of Holstein bulls. J. Dairy Sci. 65: 1781. 8 Everett, R. W., and B. Bean. t982. Environmental influences on semen output. J. Dairy Sci. 65:1303. Journal of Dairy Science Vol. 68, No. 10, 1985

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9 Everett, R. W., B. Bean, and R. H. Foote. 1978. Sources of variation o f semen output. J. Dairy Sci. 61:90. 10 Everett, R. W., and J. F. Keown. 1983. Mixed model sire evaluation with dairy cattle-experience and genetic gain. Invited paper, 75th Annu. Mtg. Am. Soc. Anim. Sci., Pullman, WA. 11 Everett, R. W., R. L. Quaas, a n d E . J. Pollak. 1983. Multiple trait northeast artificial insemination sire comparison: Implemented new concepts in sire evaluation. Mimeo, Cornell Univ., Ithaca, NY. 12 Foote, R. H., G. E. Seidel, Jr., J. Hahn, W. E. Berndtson, and G. H. Coulter. 1977. Seminal quality, spermatozoal output, and testicutar changes in growing Holstein bulls. J. Dairy Sci. 60:85. 13 Hafs, H. D., R. W, Bratton, C. R. Henderson, and R. H. Foote. 1958. Estimation of some variance components of bovine semen criteria and their use in the design of experiments. J. Dairy Sci. 41:96.

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14 Hahn, J., R. H. Foote, and G. E. Seidel, Jr. 1969. Quality and freezability of semen from growing and aged dairy bulls. J. Dairy Sci. 52:1843. 15 Henderson, C. R. 1975. Best linear unbiased estimation and prediction under a selection model. Biometrics 31:423. 16 Searle, S. R. 1982. Matrix algebra useful for statistics. John Wiley and Sons, New York, NY. 17 Seidel, G. E. Jr., and R. H. Foote. 1969. Influence of semen collection interval and tactile stimuli on semen quality and sperm output in bulls. J. Dairy Sci. 52:1074. 18 Seidel, G. E. Jr., and R. H. Foote. 1973. Variance components of semen criteria from bulls ejaculated frequently and their use in experimental design. J. Dairy Sci. 56:399. 19 Thompson, R. 1977. In Discussion on the paper by Professor Dempster, Professor Laird, and Dr. Rubin. J. R. Star. Soc. B. 39:34.