J. Anim. Breed. Genet. 118 (2001), 161±172 Ó 2001 Blackwell Wissenschafts-Verlag, Berlin ISSN 0931±2668

Ms. received: 15.2.2000

Research Institute of Animal Production Prague-UhrÏiÂneÏves, Czech Republic, 2Research Institute of Animal Production Nitra, Slovak Republic and 3Institute of Animal Science and Animal Behaviour Mariensee of the Federal Agricultural Research Centre, Germany

1

Stability of genetic parameter estimates for production traits in pigs By J. WOLF1, D. PESÏKOVICÏOVAÂ2 and E. GROENEVELD3

Summary Changes in variance component estimates in growing sets of performance data in two pig breeds were investigated. Data was used from the ®eld and station test of Czech Landrace (LA: 75 099 observations) and the Slovakian breed, White Meaty swine (WM: 32 203 observations). In LA the traits analysed were estimated lean meat content (LM) and average daily gain (ADGF) on ®eld test and average daily gain (ADGS) and weight of valuable cuts (VCW) on station test. In WM the traits analysed were backfat thickness on ®eld and station test (BFF, BFS, respectively), proportion of valuable cuts (VCP) on station test, ADGF and ADGS. Covariance components were estimated from four- and ®ve-trait animal models using the VCE software. Omitting data from factor levels with a low number of records led to 4.2% of LA records and 21.7% of WM records being deleted. Changes in genetic and residual variance estimates were less than 5% for all traits in LA and less than 12% for all traits except ADGS in WM. The changes in estimated genetic variances caused by 18 months (LA) or 24 months (WM) of new data were 2±25% and the changes in estimated residual variances were less than 5% in LA and less than 20% in WM. In both breeds, changes in heritability estimates did not exceed 0.06 in absolute value. In LA, it is reasonable to use genetic parameter estimates for 3 years before re-estimation. In WM the time interval should be shorter because of changes in the estimates caused by their lower accuracy arising from the smaller size of the data-set and smaller frequency of station testing.

Zusammenfassung StabilitaÈt der SchaÈtzwerte genetischer Parameter fuÈr Produktionsmarkmale beim Schwein È nderungen der VarianzkomponentenschaÈtzwerte in wachsenden FuÈr zwei Schweinerassen wurden A LeistungspruÈfungsdatensaÈtzen untersucht. Die beiden AusgangsdatensaÈtze bestanden aus Feld- und StationspruÈfdaten der Tschechischen Landrasse (LA ± 75 099 Beobachtungen) bzw. der Slowakischen Rasse White Meaty (WM ± 32 203 Beobachtungen). Folgende Merkmale wurden ausgewertet: Mager¯eischanteil (LM) und Lebenstagszunahme (ADGF) aus der FeldpruÈfung sowie PruÈftagszunahme (ADGS) und Gewicht wertvoller TeilstuÈcke (VCW) aus der StationspruÈfung bei der LA; RuÈckenspeckdicke aus der Feld- und StationspruÈfung (BFF bzw. BFS), Anteil wertvoller TeilstuÈcke (VCP) aus der StationspruÈfung sowie ADGF und ADGS bei der Rasse WM. Die Kovarianzkomponenten wurden fuÈr Vier- bzw. FuÈnf-Merkmals-Tiermodelle mit dem Programm VCE berechnet. Das Auslassen von Daten von Klassen mit geringer Besetzung fuÈhrte dazu, daû in der LA 4,2% und in È nderungen in den genetischen und den Rest-Varianzen WM 21,7% der Daten geloÈscht wurden. Die A waren in der LA bei allen Merkmalen kleiner als 5% und in WM bei allen Merkmalen mit Ausnahme von ADGS kleiner als 12%. Durch HinzufuÈgen von Daten aus einem Zeitraum von 18 (LA) bzw. 24 È nderungen in den (WM) Monaten aÈnderten sich die genetischen Varianzen um 2 bis 25%. Die A È nderung der Restvarianzen lagen unter 5% bei der LA und unter 20% bei WM. Die maximale A HeritabilitaÈtskoef®zienten uÈberstieg in beiden Rassen nicht 0,06. Bei der LA sollte ein Zeitintervall von drei Jahren zu einer NeuschaÈtzung der genetischen Parameter ausreichen, bei WM sollte wegen der È nderungen der SchaÈtzwerte, der kleineren Datenmenge und des geringeren Anteils beobachteten A stationsgepruÈfter Tiere das Zeitintervall kuÈrzer sein.

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162

J. Wolf, D. PesÏkovicÏova and E. Groeneveld

Introduction Genetic evaluation of farm animals using multivariate mixed models requires estimates of the variances and covariances among the random effects on different traits. The accuracy 2 of the evaluations is maximized such that best linear unbiased prediction (BLUP) estimates of breeding values are obtained when the variance and covariance component estimates are equal to the true values (HENDERSON 1973). Hence it is desirable to obtain accurate variance and covariance component estimates. The present method of choice for this goal is 3 restricted maximum likelihood (REML) proposed by PATTERSON and THOMPSON (1971). However, REML is very computer-intensive and time-consuming. Consequently, the covariance matrices are often estimated using only two traits at a time, or using a smaller number of traits than the total number. The estimates from these smaller analyses are then combined to obtain the complete estimated variance±covariance matrix. This procedure can lead to inconsistency of the estimates derived from different analyses, such that the complete estimated variance±covariance matrix is not positive de®nite. In addition, smaller REML analyses are often carried out on subsamples of the data, and variance and covariance component estimates derived in this way are in¯uenced by the sampling (JENSEN and MAO 1991). Recent advances in computer hardware and numerical algorithms have enabled the estimation of covariance matrices among large numbers of traits in large data-sets for a reasonable cost. These advances have also enabled the investigation of changes in estimates of variance and covariance components over time as new data is accumulated. The aim of the present article is to investigate these changes as new data is added to a swine performance data-set. A second objective is to determine the effect of omitting data from factor levels with a low number of observations on the estimates of covariance components.

Materials and methods Data Field and station test data was obtained on animals of the Czech Landrace and Slovakian White Meaty breeds. There were 75099 Landrace (LA00) animals born between 1989 (station test) or 1991 (®eld test) and 1997. The following traits were measured: LM, lean meat percentage estimated in the ®eld test using PIGLOG [ultrasonic measurements ± for more details see GROENEVELD et al. (1998)] without any liveweight adjustment; ADGF, average daily gain on ®eld test (in g/day) calculated as weight at end of test divided by age at end of test; ADGS, average daily gain on station test (from 30 to 100 kg live weight) in g/day, with a linear adjustment for weight at the beginning and at the end of test; VCW, weight (kg) of trimmed valuable cuts (neck, shoulder, ham, and loin) in the half-carcass. This is measured at a live weight of around 100 kg, without adjustment for slaughter weight. The weight at end of test ranged from 70 to 110 kg for sows and from 80 to 120 kg for boars. The data-set LA00R was obtained from the data-set LA00 by deleting all records from herds and year±season classes with less than 50 records and all records on animals without littermates tested. The data-sets LA09R and LA18R were derived from LA00R by deleting test data from the most recent 9 months and from the most recent 18 months, respectively. There were 32203 White Meaty (WM00) animals born between 1992 and 1997. The following traits were measured: BFF, backfat thickness on ®eld test (in cm) measured by PIGLOG; VCP, proportion of valuable cuts (neck, shoulder, ham, loin ± all without fat covering) in half-carcass (in percentage) at a live weight of approximately 100 kg; BFS, backfat thickness on station test (in cm), average of three measurements; ADGF, ADGS, the same traits as measured in Landrace and de®ned above.

Stability of genetic parameter estimates for pig production

163

The quantities BFF, VCP, and BFS were not adjusted for liveweight. The data-set WM00R was obtained from data-set WM00 by deleting all records from herd±year±season classes with less than 20 records and all records on animals without littermates tested. Data-sets WM12 and WM24 were obtained from WM00 by deleting records on animals born in 1997 and on animals born in 1996 and 1997, respectively. Summary statistics of the size and structure of the Landrace data-sets LA00, LA00R, LA09R and LA18R and of the White Meaty data-sets WM00, WM00R, WM12 and WM24, are given in Table 1. The LA00R data-set had only 4.2% less records than LA00, whereas WM00R had 21.7% less records than WM00. The data-set LA09R contained 12% less records than LA00R and LA18R contained 25% less records than LA00R. Data-sets WM12 and WM24 contained 13 and 30% less records, respectively, than WM00. All available pedigree information was used in the analyses of all data-sets. The means and standard deviations of the traits in each data-set are given in Table 2. Recording of LM began in 1995, and prior to that time ADGF was the only trait recorded in the ®eld test. Across all of the data, 11% of Landrace and 5% of White Meaty animals were station tested. Trait means and standard deviations were very similar across data-sets within a breed (Table 2).

Table 1. Structure of data-sets for Landrace and White Meaty with measurements of lean meat content (LM), average daily gain (ADGF), and backfat thickness (BFF) on ®eld test as well as average daily gain (ADGS), weight of valuable cuts (VCW), proportion of valuable cuts (VCP), and backfat thickness (BFS) on station Number of observations in data-set

Breed: Landrace Measured traits

LA00

LM, ADGF ADGF ADGS, VCW Total number of Average number Average number Average number

30329 36649 8121 75099 71.3 72.7 10

observations of known ancestors of offspring per sire of offspring per dam

LA00R 29214 35310 7419 71943 71.4 72.7 10.5

LA09R 21130 35298 6767 63195 68.7 70.3 10.4

LA18R 12437 35298 6053 53788 66.3 67.9 10.2

Number of observations in data-set

Breed: White Meaty Measured traits

WM00

BFF, ADGF ADGF ADGS, VCP, BFS Total number of observations Average number of known ancestors Average number of offspring per sire Average number of offspring per dam

29359 1159 1685 32203 35.5 64.4 5.7

WM00R 23020 906 1298 25203 34.8 58.5 5.9

WM12

WM24

25523 1159 1492 28174 32.5 61.9 5.5

20241 1079 1083 22403 28.6 58.9 5.2

Data-sets for Landrace: LA00 basic (largest) data-set; LA00R, herd and year±season classes with less than 50 observations and litter classes with less than two observations were omitted from LA00; LA09R, LA18R, test results from the last 9 or 18 months, respectively, were omitted from LA00R Data-sets for White Meaty: WM00 basic (largest) data-set; WM00R, herd±year±season classes with less than 20 observations and litter classes with less than two observations were omitted from WM00; WM12, WM24, test results from the last 12 or 24 month, respectively, were omitted from WM00

164

J. Wolf, D. PesÏkovicÏova and E. Groeneveld Table 2. Population means and standard deviations for all data-sets Data-set

Breed: Landrace Trait

LA00 Mean

LM (%) ADGF (g/day) ADGS (g/day) VCW (kg)

59.2 539 864 19.6

LA00R SD

2.26 69.7 109 1.43

LA09R

LA18R

Mean

SD

Mean

SD

Mean

59.2 540 865 19.6

2.27 69.8 109 1.41

59.0 535 862 19.5

2.30 68.0 109 1.37

58.6 530 856 19.4

SD 2.37 66.5 105 1.36

Data-set Breed: White Meaty Trait BFF (cm) ADGF (g/day) ADGS (g/day) VCP (%) BFS (cm)

WM00 Mean 1.51 505 826 49.2 2.33

WM00R

SD

Mean

0.306 64.1 110 3.13 0.437

1.51 508 823 49.2 2.32

SD 0.305 62.4 111 3.13 0.437

WM12 Mean 1.50 501 823 48.8 2.37

WM24 SD

Mean

SD

0.303 64.1 110 3.00 0.422

1.48 498 830 48.8 2.44

0.289 64.3 111 2.89 0.415

For abbreviations of traits and data-sets see Table 1

Models For Landrace, a four-trait animal model with different model equations for different traits was used for the estimation of genetic parameters (GROENEVELD et al. 1998). The model equations for animal n were: LMijlmn ˆ YSFi ‡ SEXj ‡ bF WFijlmn ‡ hl ‡ cm ‡ aijlmn ‡ eijlmn ADGFijlmn ˆ YSFi ‡ SEXj ‡ hl ‡ cm ‡ aijlmn ‡ eijlmn ADGSijklmn ˆ YSSi ‡ SEXj ‡ STATk ‡ hl ‡ cm ‡ aijklmn ‡ eijklmn

…1†

VCWijklmn ˆ YSSi ‡ SEXj ‡ STATk ‡ bs WSijklmn ‡ hl ‡ cm ‡ aijklmn ‡ eijklmn where LMijlmn, ADGFijlmn, ADGSijklmn, and VWCijklmn are the measurements of the traits, YSFi and YSSi are the ®xed year-season effects for ®eld and station tests, respectively, SEXj is the ®xed effect of sex, STATk is the ®xed effect of test station, bF and bS are regression coef®cients, WFijlmn and WSijklmn are the live weights at ®eld and station tests, respectively, hl is the random herd or herd of origin effect, cm is the random litter effect, aijlmn or aijklmn is the random additive genetic effect, and eijlmn or eijklmn is the residual effect. The linear model in matrix notation is then: y ˆ Xb ‡ Zh h ‡ Zc c ‡ Zu u ‡ e

…2†

where y is the vector of observations, X is the incidence matrix for ®xed effects, b is the vector of ®xed effects, Zh, Zc, Zu are the incidence matrices for herd, litter and animal effects, respectively, and h, c, u and e are the vectors of herd, litter, animal and residual effects, respectively. The joint distribution of y, e, h, c and u is assumed multivariate normal with expectation:

Stability of genetic parameter estimates for pig production

165

1 0 1 0 Xb y BeC B 0 C C B C B C C B EB BhC ˆ B 0 C @cA @ 0 A 0 u

…3†

and variance: 0 1 0 V y BeC B R B C B 0 C B varB B h C ˆ B Gh Zh0 @ c A @ Gc Z c GA Z 0u u

R Z h Gh R 0 0 Gh 0 0 0 0

Z c Gc 0 0 Gc 0

1 Z u GA 0 C C 0 C C 0 A GA

…4†

where V ˆ R ‡ Zh Gh Z0h ‡ Zc Gc Z0c ‡ Zu Gu Z 0u R ˆ N

GA0 nˆ1 R0n ; Gh ˆ I h Gh0 ; Gc ˆ I c Gco ; GA ˆ A

…5†

Gh0, Gc0, GA0 are the covariance matrices between traits for herd, litter and animal effects, respectively, A is the numerator relationship matrix between animals, Ih and Ic are identity matrices, V is the covariance matrix for y, and R, Gh, Gc, GA are the covariance matrices for e, h, c and u, respectively. No animals were measured both for ®eld test and station test traits, so it was not necessary to ®t a residual covariance between these traits. For the White Meaty breed, a ®ve-trait animal model similar to the one above, was used for the estimation of genetic parameters. The model equations for animal n were (GROENEVELD and PESÏKOVICÏOVA 1999): BFFijmn ˆ hysi ‡ SEXj ‡ bF WFijmn ‡ cm ‡ aijmn ‡ eijmn ADGFijmn ˆ hysi ‡ SEXj ‡ cm ‡ aijmn ‡ eijmn ADGSijmn ˆ stysi ‡ SEXj ‡ cm ‡ aijmn ‡ eijmn VCPijmn ˆ stysi ‡ SEXj ‡ cm ‡ aijmn ‡ eijmn BFSijmn ˆ stysi ‡ SEXj ‡ bS WSijmn ‡ cm ‡ aijmn ‡ eijmn

…6†

where BFFijmn, ADGFijmn, ADGSijmn, VCPijmn, BFSijmn are the values of the appropriate traits, hysi is the random herd±year±season effect, and stysi is the random station±year± season effect, with other notation as de®ned previously. The model in matrix notation is: y ˆ Xb ‡ Zh h ‡ Zs s ‡ Z c c ‡ Zu u ‡ e

…7†

where h and s are the vectors of unknown herd-year-season and station-year-season effects, Zh, Zs are the known incidence matrices for h and s, and other notation is as de®ned previously. The joint distribution of y, e, h, s, c and u has expectation: 0 1 0 1 y Xb BeC B 0 C B C B C BhC B 0 C CˆB C EB …8† BsC B 0 C B C B C @cA @ 0 A u 0

166

J. Wolf, D. PesÏkovicÏova and E. Groeneveld

and variance: 0 1 0 V y BeC B R B C B B h C B Gh Z0h C B varB B s C ˆ B Gs Z0s B C B @ c A @ Gc Z 0 u GA Z 0u u

R R 0 0 0 0

Z h Gh 0 Gh 0 0 0

Z s Gs 0 0 Gs 0 0

Zc Gc 0 0 0 Gc 0

1 Z u GA 0 C C 0 C C 0 C C 0 A GA

…9†

with V ˆ R ‡ Z h Gh Z0h ‡ Z s Gs Z0s ‡ Zc Gc Z 0c ‡ Zu GA Z0u R ˆ N nˆ1 R0n ; Gh ˆ I h Gh0 ; Gs ˆ I s Gso ; Gc ˆ I c Gc0 ; GA ˆ A GA0

…10†

where Gh0 and Gs0 are the covariance matrices of herd-year-season and station-year-season effects, Gh and Gs are the covariance matrices of h and s, respectively, and other notation is as previously. As in the Landrace data, no animals were measured for both ®eld and station test traits, such that no residual covariance was ®tted between these traits, and no covariances were ®tted between herd effects on ®eld-test traits and station effects on station-test traits. The estimation method was REML using a quasi-Newton algorithm with analytical gradients, described by NEUMAIER and GROENEVELD (1998). The software used was VCE 4.0 and later versions (GROENEVELD and GARCIÂA CORTEÂS 1998) running on a LINUX operating system. The number of equations was in the range from 290 000 to 406 000 for Landrace and from 185 000 to 260 000 for White Meaty animals. Breeding value prediction was carried out using PEST software (GROENEVELD et al. 4 1990) using the same models as in the REML analyses. In Landrace, two sets of breeding values were predicted for animals of the data-set LA00. The ®rst set were predicted using variance component estimates from LA00R, and the second set was predicted using variance component estimates from LA18R. Similarly, for White Meaty animals of the WM00 data-set, one set of breeding values was predicted using variance component estimates from WM00 and another set was predicted using variance component estimates from WM24. Spearman rank correlations between the two sets of breeding values were calculated for each breed, using SAS software (SAS INSTITUTE INC. 1990).

Results Effect on parameter estimates of omitting records from small subclasses Estimates of genetic and residual variance components are given in Tables 3 and 4, and estimates of herd, station and litter variance components in Tables 5 and 6. In Landrace there were only minor changes (less than 5%) in estimates of genetic and residual variances between LA00 and LA00R (Table 3). In the White Meaty breed, for BFF, ADGF, VCP and BFS genetic variance component estimates were very similar between WM00R and WM00 (Table 4). However, for ADGS, the estimated genetic variance was 42% higher with WM00R than with WM00 (Table 4). The estimated residual variance was 18% lower with WM00R than with WM00. Differences in genetic variances were usually opposite in direction to differences in residual variances. There was a difference of about 10% between residual variance estimates for backfat traits between data-sets WM00 and WM00R. The differences in estimated heritabilities between LA00 and LA00R were less than 0.02 in absolute value (Table 3). The differences in estimated heritabilities between WM00 and

Stability of genetic parameter estimates for pig production

167

Table 3. Genetic variances and covariances (®rst line), residual variances and covariances (second line) and heritabilities and genetic correlations (third line) for Landrace Trait or pair of traits

Data-set LA00R

LA09R

LA18R

1.654 1.938 0.37

1.643 1.948 0.37

1.820 1.863 0.39

2.052 1.940 0.40

ADGF

788.711 1535.748 0.18

798.857 1530.396 0.18

731.676 1527.880 0.17

687.556 1516.896 0.16

ADGS

3735.197 3584.419 0.37

3673.016 3647.574 0.36

3574.701 3589.876 0.36

3381.117 3411.993 0.36

0.686 0.390 0.53

0.658 0.399 0.55

0.607 0.412 0.51

0.594 0.407 0.51

LM±ADGF

)1.677 )0.478 )0.05

)1.577 )0.592 )0.04

)1.934 )1.696 )0.05

0.402 )3.574 0.01

LM±ADGS

6.173 ± 0.08

8.251 ± 0.11

7.186 ± 0.09

19.648 ± 0.24

LM±VCW

0.565 ± 0.53

0.558 ± 0.54

0.682 ± 0.65

0.717 ± 0.65

811.309 ± 0.47

817.033 ± 0.48

826.334 ± 0.51

846.373 ± 0.56

ADGF±VCW

2.311 ± 0.10

2.106 ± 0.09

0.720 ± 0.03

0.792 ± 0.04

ADGS±VCW

13.425 )11.040 0.27

12.695 )9.882 0.26

13.527 )10.416 0.29

15.428 )11.635 0.34

LM

VCW

ADGF±ADGS

LA00

For abbreviations of traits and data-sets see Table 1

WM00R were less than 0.04 for BFF, ADGF, VCP and BFS, but for ADGS the difference was as high as 0.10 (Table 4). Litter variance as a proportion of total variance was the same for all traits in LA00 and LA00R (Table 5). In WM00 and WM00R of Table 6, there were some differences in the proportion of litter variance. Most notably, for ADGS the proportion of litter variance was reduced from 0.25 in WM00 to 0.20 in WM00R (Table 6). For VCW, the proportion of herd variance was reduced from 0.14 in LA00 to 0.09 in LA00R (Table 5). For BFF, ADGS, VCP and BFS, the estimated proportions of variance for herd±year±season and station±year±season effects were almost the same between WM00 and WM00R (Table 6). For ADGF, the proportion of variance for herd-yearseason was reduced from 0.45 in WM00 to 0.39 in WM00R. Changes in genetic correlations were negligible in Landrace (Table 3), but were somewhat higher in White Meaty, where the largest change was a decrease in the correlation between ADGF and ADGS from 0.55 in WM00 to 0.42 in WM00R (Table 4).

168

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Table 4. Genetic variances and covariances (®rst line), residual variances and covariances (second line) and heritabilities and genetic correlations (third line) for White Meaty Trait or pair of traits BFF

ADGF

ADGS

VCP

BFS

BFF±ADGF

BFF±ADGS

BFF±VCP

BFF±BFS

ADGF±ADGS

ADGF±VCP

ADGF±BFS

ADGS±VCP

ADGS±BFS

VCP±BFS

Data-set WM00

WM00R

WM12

WM24

0.022 0.025 0.30 467.296 1152.989 0.12 3429.674 4159.309 0.28 3.120 3.283 0.38 0.059 0.054 0.39 0.456 1.331 0.14 )0.425 ± )0.05 ±0.181 ± )0.69 0.026 ± 0.73 690.653 ± 0.55 9.425 ± 0.25 )1.092 ± )0.21 22.487 )37.933 0.22 )2.213 4.596 )0.16 )0.313 )0.196 )0.73

0.023 0.022 0.34 444.880 1183.970 0.12 4861.848 3409.025 0.38 3.220 3.218 0.40 0.057 0.059 0.37 0.283 0.482 0.09 )1.240 ± )0.12 )0.199 ± )0.74 0.030 ± 0.84 613.007 ± 0.42 9.485 ± 0.25 )1.380 ± )0.28 26.561 )41.937 0.21 )2.367 4.614 )0.14 )0.330 )0.190 )0.77

0.020 0.025 0.28 459.887 1205.191 0.11 3259.769 4066.267 0.26 2.888 3.391 0.37 0.055 0.056 0.36 0.498 1.498 0.16 )0.441 ± )0.05 )0.165 ± )0.68 0.024 ± 0.72 602.258 ± 0.49 7.398 ± 0.20 )1.183 ± )0.24 17.594 )39.936 0.18 )1.061 4.212 )0.08 )0.280 )0.205 )0.70

0.017 0.025 0.26 460.085 1291.359 0.11 2824.507 4978.022 0.22 2.529 3.734 0.32 0.060 0.058 0.38 0.745 1.711 0.27 )1.025 ± )0.15 )0.140 ± )0.68 0.023 ± 0.72 626.343 ± 0.55 1.228 ± 0.04 )0.857 ± )0.16 14.332 )39.224 0.17 )0.043 5.201 )0.00 )0.216 )0.298 )0.56

For abbreviations of traits and data-sets see Table 1

Effect of accumulation of new data on parameter estimates The genetic variances estimated in Landrace changed by 8 to 10% for the station traits ADGS and VCW, and by 14 to 25% for the ®eld-test traits LM and ADGF (Table 3). The greatest change of 25% was for LM. Changes in residual variances were less than 5% for all

Stability of genetic parameter estimates for pig production

169

Table 5. Proportions of variance for litter and herd effects in Landrace Trait Effect

Data-set

LM

ADGF

ADGS

VCW

Litter

LA00 LA00R LA09R LA18R

0.10 0.10 0.10 0.09

0.19 0.19 0.19 0.20

0.21 0.21 0.22 0.23

0.04 0.04 0.04 0.04

Herd

LA00 LA00R LA09R LA18R

0.10 0.10 0.12 0.13

0.29 0.28 0.30 0.29

0.06 0.06 0.06 0.05

0.14 0.09 0.10 0.10

For abbreviations of traits and data-sets see Table 1

Table 6. Proportions of variance for litter, herd±year±season and station±year±season effects in White Meaty Trait Effect

Data-set

BFF

ADGF

ADGS

VCP

BFS

Litter

WM00 WM00R WM12 WM24

0.12 0.10 0.11 0.11

0.15 0.16 0.15 0.15

0.25 0.20 0.27 0.27

0.02 0.02 0.02 0.01

0.01 0.00 0.00 0.00

Herd±year±season

WM00 WM00R WM12 WM24

0.24 0.23 0.26 0.24

0.45 0.39 0.44 0.42

Station±year±season

WM00 WM00R WM12 WM24

0.14 0.15 0.15 0.11

0.20 0.18 0.19 0.19

0.26 0.25 0.26 0.25

For abbreviations of traits and data-sets see Table 1

traits. Changes in heritability estimates did not exceed 0.04 in absolute value. For ADGS, changes in estimated genetic variance were accompanied by similar changes in residual variance such that the estimated heritability did not change. Similarly, changes in estimated genetic variance for ADGF were accompanied by smaller changes in estimated residual variance. Changes in the proportions of litter variance and herd variance were small, and less than 0.02 and 0.03, respectively (Table 5). In White Meaty, the maximum changes in estimates of genetic variances were small and less than 2% for ADGF and BFS, but substantially larger at around 20% for the remaining three traits BFF, ADGS and VCP (Table 4). The largest changes in estimated residual variances were in ADGS, ADGF and VCP (between 12 and 20%) and the smallest changes, of less than 8%, were for the backfat traits. Changes in estimates of heritabilities and in estimated proportions of litter and herd variances were generally small. Changes in heritabilities ranged up to 0.06, changes in proportions of litter variance ranged up to 0.02, and changes in proportions of herd±year±season variance and station±test±year±season variance ranged up to 0.03 (Tables 4 and 6).

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J. Wolf, D. PesÏkovicÏova and E. Groeneveld

Spearman rank correlations between estimated breeding values obtained using variance components estimated from LA00R and estimated breeding values obtained using variance components estimated from LA18R were 0.994 for LM, 0.998 for ADGF, 0.991 for ADGS and 0.996 for VCW. Spearman rank correlations between estimated breeding values obtained using variance components estimated from WM00R and estimated breeding values obtained using variance components estimated from WM24 were 0.997 for BFF, 0.990 for ADGF, 0.938 for ADGS, 0.983 for VCP and 0.984 for BFS.

Discussion If the usual assumptions of the animal model are satis®ed, REML estimates of variance and covariance components are unbiased estimates of the true components in the base population. Hence if an initial data-set is very large such that the REML estimates are very accurate, the estimates should change very little when subsequent data is added to the 5 initial data-set (SéRENSEN and KENNEDY 1984; VAN DER WERF and DE BOER 1990). The base population consists of all animals in the data-set that have unidenti®ed parents. The assumptions of the animal model include that these animals are unselected on the traits analysed, and that the additive in®nitesimal model of gene effects (e.g. BULMER 1980) holds. The number of records required to obtain accurate variance component estimates depends on the data structure. If all traits are measured on all animals, accurate estimates might be obtained from a relatively small data-set, compared with the situation where different traits are measured on different animals and seldom on the same animals. In farm animals, unselected base populations do not exist. Furthermore, non-linearity between traits will cause changes in the genetic parameters as a result of selection in the population (MEUWISSEN and GODDARD 1997). In a simulation study of milk fat yield and growth performance traits in cattle, JENSEN and MAO (1991) investigated the in¯uence of data structure on estimates of genetic parameters. Scheme 1 comprised all data from a 15-year period and all relationships among animals. Scheme 2 comprised only data from the last 5 years and all relationships among animals. Scheme 3 comprised only data from the last 5 years and only relationships based on the last 5 years of pedigree data. Among others, a two-trait animal model was used. Milk fat yield had a heritability of 0.25, growth rate had a heritability of 0.5, and the genetic correlation between the two traits was 0.2. The estimated heritability of fat yield was 0.25, 0.25 and 0.20 in schemes 1, 2 and 3, respectively. Furthermore, the estimated heritability of growth rate was 0.64, 0.62 and 0.50, and the estimated genetic correlation was 0.26, 0.06 and 0.04 in schemes 1, 2 and 3, respectively. There were only around 2600 animals in scheme 1 and 900 in each of schemes 2 and 3. The small number of animals led to high standard errors of the estimates and de®nitive conclusions were not possible. Nevertheless, the results of JENSEN and MAO (1991) suggest that estimation of genetic correlations requires more data to achieve a given accuracy than estimation of heritabilities. Consistent with JENSEN and MAO (1991), in the present study, from Tables 3 and 4, the absolute changes in heritability estimates between data-sets LA00R, LA09R and LA18R and between data-sets WM00, WM12 and WM24 are about one-third of the absolute changes in genetic correlation estimates. True genetic variance components can change during long-term selection due to factors such as inbreeding, genetic mutation, and migration of animals between populations. In long-term selection experiments in mice (up to 38 generations) BENIWAL et al. (1992a,b) found only small changes in estimates of variance components consistent with expected changes in the true components. However in farm animal populations the factors which change true genetic variance components are much more prevalent than in experimental populations of laboratory animals. Livestock are exchanged between countries and genetic evaluation models usually assume that heritabilities and genetic variances are unaffected.

Stability of genetic parameter estimates for pig production

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Genetic groups are required in the model to account for differences in the additive genetic means for traits. Another problem in farm animal populations is that poor data structure due to lack of balance or missing pedigree information can reduce the accuracy of genetic parameter estimates. APPEL et al. (1996) showed in a simulation study that culling of swine prior to performance testing can cause changes in estimated breeding values. In the present study, the change in variance component estimates caused by the addition of 18 months of new data in Landrace had very little impact on estimated breeding values. For all four traits studied in the Landrace, the rank correlations were greater than 0.99. A rank correlation of 0.98 conservatively ensures that the overwhelming majority of animals are ranked well. Hence it may be appropriate to re-estimate variance components about once every 3 years in the Czech Landrace breed. In the White Meaty the changes in variance component estimates caused by addition of new data were somewhat larger than in the Landrace. Although slightly more new data was added for the White Meaty than for the Landrace (24 versus 18 months), the much larger changes in variance component estimates suggest that the estimates may be less accurate for the White Meaty breed. This may be because there is less data overall and because the White Meaty has a lower proportion of station tested animals than the Czech Landrace. The correlation between estimated breeding values using genetic parameters from WM00 and from WM24 was less than 0.99 for three of the ®ve traits studied in the White Meaty breed. Hence it seems that variance components should be re-estimated more frequently in the White Meaty breed than in the Czech Landrace. The omission of data from subclasses with low numbers of records improves the data structure and can reduce the amount of computing time for variance component estimation. In Landrace there was nearly no effect of omitting this data. However, in the White Meaty breed where over 20% of the records were deleted, there was a considerable change in the variance component estimates for growth at the test station. Hence, omitting this type of data can be recommended for saving computing time, but if it constitutes a large proportion of the data-set, there may be a signi®cant cost in terms of reduced accuracy of the variance component estimates. Acknowledgements The research project was supported by the National Grant Agency of Agricultural Research (Grant No. EP 7123), by the Ministry of Agriculture of the Czech Republic (Research Project MZE-M02±99± 02) and by the Ministry of Agriculture of the Slovak Republic (Project no. 435±50 K). J. W. and D. P. thank the Federal Ministry of Food, Agriculture and Forestry of the Federal Republic of Germany for ®nancial support of several stays at the Institute of Animal Science and Animal Behaviour Mariensee of the Federal Agricultural Research Centre. Furthermore, thanks are due to VEÏRA JELIÂNKOVAÂ from the Association of Pig Breeders in the Czech Republic and to Milan KumiCÏIÂK from the State Breeding Institute of the Slovak Republic for making available the data. The help of Jim Brisbane, Ottawa, in improving the English text is gratefully acknowledged.

References APPEL, L. J.; STRANDBERG, E.; DANELL, B.; LUNDEHEIM, N., 1996: Missing data due to culling of pigs before testing and the effects on the estimation of (co) variance components. Acta Agric. Scand., Sect. A, Anim Sci. 46: 201±209. BENIWAL, B. K.; HASTINGS, I. M.; THOMPSON, R.; HILL, W. G., 1992a: Estimation of changes in genetic parameters in selected lines of mice using REML with an animal model. 1. Lean mass. Heredity 69: 352±360. BENIWAL, B. K.; HASTINGS, I. M.; THOMPSON, R.; HILL, W. G., 1992b: Estimation of changes in genetic parameters in selected lines of mice using REML with an animal model. 2. Body weight, body composition and litter size. Heredity 69: 361±371. BULMER, M. G., 1980: The Mathematical Theory of Quantitative Genetics. Clarendon Press, Oxford, England.

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GROENEVELD, E.; GARCIÂA CORTEÂS, A., 1998: VCE 4.0, a (co) variance component estimation package. In: HAWORTH, L.; LITTLE, M.; SCHMIDT, I. (eds), Proc. Sixth World Congr. Genet. Appl. Livest. 7 Prod., Armidale, Vol. 27. Publisher, Town. pp. 455±456. GROENEVELD, E.; PESÏKOVICÏOVAÂ, D., 1999: Simultaneous estimation of the covariance structure of field and station test traits in Slovakian pig populations. Czech J. Anim. Sci. 44: 145±150. GROENEVELD, E.; KOVAC, M.; WANG, T., 1990: PEST, a general purpose BLUP package for 8 multivariate prediction and estimation. In: HILL, W. G.; THOMPSON, R.; WOOLIAMS, J. A. (eds), 9 Proc. 4th World Congr. Genet. Appl. Livest. Prod., Edinburgh, Vol. 13. Publisher, Town. pp. 488±491. GROENEVELD, E.; WOLF, J.; WOLFOVAÂ, M.; JELIÂNKOVAÂ, V.; VECÏERÏOVAÂ, D., 1998: SchaÈtzung genetischer Parameter fuÈr tschechische Schweinerassen mit einem Mehrmerkmals-Tiermodell. ZuÈchtungskunde 70: 96±107. 10 HENDERSON, C. R., 1973: Sire evaluation and genetic trends. In: (eds), Proc. Animal Breeding and Genetics Symposium in Honor of Dr. Jay L. Lush, American Soc. of Animal Science, Champaign, IL, USA. pp. 10±41. JENSEN, J.; MAO, I. L., 1991: Estimation of genetic parameters using sampled data from populations undergoing selection. J. Dairy Sci. 74: 3544±3551. MEUWISSEN, T. H. E.; GODDARD, M. E., 1997: Selection of farm animals for non-linear traits and profit. Anim. Sci. 65: 1±8. NEUMAIER, A.; GROENEVELD, E., 1998: Restricted maximum likelihood estimation of covariances in sparse linear models. Genet. Sel. Evol. 30: 3±26. PATTERSON, H. D.; THOMPSON, R., 1971: Recovery of inter-block information when block sizes are unequal. Biometrika 58: 545±554. SAS Institute Inc, 1990: The CORR procedure. In: SASÒ Procedures Guide, Version 6, 3rd edn. SAS Institute Inc., Cary, NC, USA. pp. 209±235. SéRENSEN, D. A.; KENNEDY, B. W., 1984: Estimation of genetic variances from selected and unselected populations. J. Anim. Sci. 59: 1213±1223. VAN DER WERF, J. H. J.; de Boer, I. J. M., 1990: Estimation of additive genetic variance when base populations are selected. J. Anim. Sci. 68: 3124±3132. Authors' addresses: J. WOLF (corresponding author), Research Institute of Animal Production  ZÏV), P.O. Box 1, CZ 104 01 Praha 114 ± UhrÏÂõneÏves, Czech Republic, E-mail: (VU  ZÏV), [email protected]; D. PESÏKOVICÏOVAÂ, Research Institute of Animal Production (VU Hlohovska 2, SK 949 92 Nitra, Slovak Republic, E-mail: [email protected]; E. GROENEVELD, Institut fuÈr Tierzucht und Tierverhalten der FAL, HoÈltystr. 10, 11 D 31535 Neustadt, Germany, E-mail: [email protected]