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PL1 (01-01)
Revised methods to compute multitrait productive life

P.M. VanRaden and G.R. Wiggans
Animal Improvement Programs Laboratory, ARS-USDA, Beltsville, MD 20705-2350
301-504-8334 (voice) ~ 301-504-8092 (fax) ~ ~

Methods to compute multitrait predicted transmitting abilities (PTA's) for productive life (PL) were updated in August 2000. New programs were developed at the Animal Improvement Programs Laboratory (AIPL) to combine direct and indirect information about longevity. Information on milk, fat, and protein yields; somatic cell score (SCS); and udder, feet and legs (F&L), and body size composites is included in the analysis to increase the accuracy of PTA's for PL.

For November 2000 evaluations, a revised correlation matrix was used for PL calculations. The new matrix generally reduced the influence of information from yield, type, and health traits on PL. In addition, foreign bulls received credit for correlated yield and type traits instead of just parent average (PA) or breed average for PL. In May 2001, Interbull somatic cell score evaluations became available and were used as another correlated trait to increase the reliability of PL for foreign bulls.

Across all breeds, 17 hours were required with the AIPL genetic evaluation system to obtain PA's for the eight traits, to estimate Mendelian sampling for PL from Mendelian sampling of correlated traits, to adjust progeny PTA PL for multitrait PTA PL of parents, and to compute net merit indexes for all bulls and cows. Evaluations for all eight traits were loaded into memory at the start of the multitrait programs because disk access to parent evaluations was too slow (nearly 3 days). Although all steps were completed in one pass of data, which were ordered by animal age, the methods also could be applied to upgrade single-trait PTA to multitrait for each animal separately.


Holsteins. The multitrait PTA's for PL begin with single-trait evaluations, which have been calculated at AIPL since January 1994 for all breeds. However, since July 1994, the single-trait PL evaluations for Holstein bulls were combined with information from yield and type PTA's by Holstein Association USA to produce approximate multitrait PTA's for PL. Advantages of the multitrait analysis are greatest when daughters are in first lactation because yield and type data arrive before culling information. The single-trait methods were described by VanRaden and Klaaskate (1993, Journal of Dairy Science 76:2758) and VanRaden and Wiggans (1995, Journal of Dairy Science 78:631). The Holstein Association multitrait methods were described by Weigel (1996, International Bull Evaluation Service Bulletin 12:125) and Weigel et al. (1998, Journal of Dairy Science 81:2040).

For August 2000 evaluations, the Holstein Udder, Feet and Legs, and Body Size Composites (Holstein Association USA, 2000, Holstein Type-Production Sire Summaries, August, p. 12-13) were provided to AIPL before evaluation release day for use in the calculation of economic indexes for lifetime net merit. Because of the earlier availability of type information, calculation of multitrait evaluations for PL could be transferred from Holstein Association USA to AIPL. New computer programs based on the methods of Weigel et al. (1998) were developed at AIPL to combine single-trait PTA PL into approximate multitrait PTA PL (VanRaden, 2000, Journal of Dairy Science 83:Suppl. 1:5). Major differences from the Holstein Association programs are that PTA SCS is included in PL predictions and that PL predictions begin with PA and only adjust the Mendelian sampling for information from correlated traits. Other differences are that the udder, F&L, and body size composites are used in PL prediction rather than all 17 individual linear type traits. Also, all three yield traits (milk, fat, and protein) are used in PL prediction instead of just two (milk and fat). Earlier studies excluded SCS and protein because data for those traits were not widely available in earlier years.

Other breeds. The AIPL programs to compute multitrait PTA's for PL also were implemented in August 2000 for breeds other than Holstein after testing with August 1999 data. Holstein genetic correlations of PL with type, yield, and SCS are used. Udder and body size composites are the same as defined for Holsteins. Foot angle is used in place of the Holstein F&L composite because two traits in that composite [rear legs (rear-view) and feet-leg score] are not measured for other breeds.


The AIPL PL programs were designed to combine single-trait PTA's into multitrait predictions of PL for cows as well as for bulls. Expected correlations among the differences between PTA and PA for each trait for cows are determined from the daughter equivalents from the cow's own records and progeny instead of only from progeny as for bulls. The methods were tested with May 2000 data and implemented in August 2000.

Single-trait versus multitrait PL

Genetic merit for PL can be predicted from both direct and indirect measurements of correlated traits (multitrait analysis). Information on yield (milk, fat, and protein), mastitis resistance (SCS), and type (udder, F&L, and body size composites) is included.

For Holsteins, PTA udder, PTA F&L, and PTA size are the Udder, Feet and Legs, and Body Size Composite Indexes, respectively that are calculated by Holstein Association USA (2000, Holstein Type-Production Sire Summaries, August, p. 12). For other breeds, the PTA's for the individual linear type traits are converted to standardized transmitting abilities (STA's) by dividing by the standard deviation (SD) of the true transmitting ability before combining the traits into the composites.The traits included in each composite and their relative values are:

PTA composite Type trait Relative value (%) SD
Holstein Other breeds Holstein Other breeds
Udder Fore udder 16 16 1.00 1.03
Rear udder height 16 16 1.00 1.45
Rear udder width 12 12 1.00 1.51
Udder cleft 10 10 1.00 .86
Udder depth 30 30 1.00 1.24
Teat placement 16 16 1.00 1.07
Udder composite 100 100 .78 .71
F&L Rear legs (side view) -8 . . . 1.00 . . .
Rear legs (rear view) 18 . . . 1.00 . . .
Foot angle 24 100 1.00 .63
Feet and legs score 50 . . . 1.00 . . .
F&L composite 100 100 .88 1.00
Size Stature 50 50 1.00 1.28
Strength 25 25 1.00 .86
Body depth 15 15 1.00 .90
Rump width 10 10 1.00 .77
Size composite 100 100 .94 .92

Evaluations for PL from single-trait and approximate multitrait procedures were compared for bulls in active artificial-insemination (AI) service, elite cows, and all bulls or cows in various birth year groups:

Multitrait method Evaluation
Breed Gender Birth year or
animal status
Average PTA PL (mo) Average REL (%)
Single-trait Multitrait Single-trait Multitrait
Holstein Association USA
(Weigel et al., 1998)
1994 Holstein Bulls 1989-90 .83 1.19 50 53
(VanRaden, 2000)
1999 Jersey Bulls 1990-95 .66 .62 52 58
Active AI 1.69 2.12 53 63
2000 Holstein Bulls 1990-95 .60 .50 58 65
Active AI .85 1.10 56 66
Cows 1995-97 .61 .66 28 31
Elite 1.36 1.58 33 39

The gain in REL for PTA PL with the AIPL multitrait method was higher than with the Holstein Association method. The Holstein Association programs for PL used regression on PTA without removing parent contribution. The REL from that approach was lower because indirect rather than direct evaluations of parents were used whenever indirect traits of daughters were included. That use of indirect PL for parents limited the gain in bull REL because most sires had a direct REL of 99%, whereas their indirect REL was only about 60%. The USDA programs subtract PA from PTA and then apply regressions to the estimates of Mendelian sampling. The PTA and REL in the comparison table are based on genetic correlations from August rather than November 2000.

For Holstein bulls in active AI service and for elite Holstein cows, multitrait PTA's for PL were higher than single-trait PTA's as expected. However, for all Holstein bulls and cows that were born during recent years, little difference was found for average PTA PL between AIPL single-trait and multitrait methods. Correlations of single-trait PTA PL with multitrait PTA were .85 for AIPL multitrait PL and .95 for Holstein Association multitrait PL. Holstein Assocation multitrait PTA PL was correlated by only 0.88 to AIPL multitrait PTA PL. Those correlations are consistent with the larger gains in REL from the new procedures.

For recent Jersey bulls with August 1999 PTA's, average PTA PL was .66 months with a standard deviation (SD) of 1.14 months for single-trait PL and .62 months with an SD of 1.24 months for multitrait PL. Average reliability (REL) increased from 52% for single-trait PL to 58% for multitrait PL, and the two predictions were correlated by .88. For other non-Holstein breeds, increases in REL were 5%, which was somewhat larger than the 3% increase reported for Holsteins by Weigel et al. (1998) because SCS was included and because bulls that had no daughters measured for PL (all daughters less than 3 years old) were included for the non-Holstein breeds.

Because SCS and type traits are missing for some relatives, the AIPL multitrait programs also were tested for upgrading single-trait PTA's for SCS and udder composite to multitrait PTA's that use correlated information from other traits. For Holstein bulls, the average REL increased only from 68.6 to 68.9% for SCS and from 77.9 to 78.1% for udder composite. For Holstein cows, REL increased from 32.8 to 33.2% for SCS and from 30.0 to 31.6% for udder composite. The small gains in evaluation accuracy for those traits did not justify the added computing complexity and disk storage that would be required for routine evaluations. Therefore, the multitrait procedure is applied only for PL.

PL parameters

Heritabilities were obtained from official evaluation procedures except that Jersey heritabilities for type were used for all non-Holstein breeds instead of the official values, which vary by breed. For August 2000 evaluations, genetic and phenotypic correlations were based on estimates from previous scientific studies for Holsteins (Short and Lawlor, 1992, Journal of Dairy Science 75:1987; Schutz, 1993, Journal of Dairy Science 76:658; VanRaden and Klaaskate, 1993, Journal of Dairy Science 76:2758; D. Weigel, 1993, Ph.D. thesis; Misztal et al., 1994, Journal of Dairy Science 75:544); those correlations were updated in November 2000 based on results of additional research For some trait pairs, no phenotypic correlations were available, and the phenotypic correlations were assumed to equal genetic correlations. For November 2000 evaluations, genetic correlations (above diagonal), phenotypic correlations (below diagonal), and heritabilities (on diagonal) were:

PTA trait PTA trait
Milk Fat Protein PL SCS Size Udder F&L
Milk .30* .65 .90 .29 .20 .01 -.20 -.02
Fat .77 .30 .76 .26 .20 .01 -.20 -.02
Protein .93 .82 .30 .30 .20 .01 -.20 -.02
PL .34 .29 .34 .085 -.40 -.04 .30 .19
SCS -.10 -.10 -.10 -.30 .10 -.11 -.33 -.02
Size .06 .06 .06 .03 -.11 .40 .26 .22
Udder -.10 -.10 -.10 .08 -.33 .26 .27 .10
F&L .01 .01 .01 .19 -.02 .22 .10 .15
*Holstein heritabilities in blue on diagonal; heritabilities for other breeds are the same except for yield traits (.35), size (.35), and udder (.20).

Correlations among PTA's for yield and PL tended to be lower for bulls born in recent years than for those born in earlier years. Genetic merit for PL was more highly correlated with genetic merit for milk yield than with protein yield for earlier bulls but is more highly correlated with protein yield for recent bulls.

Maximum indirect REL's indicate how well the genetic merit for a trait can be estimated based on data only from other traits. Such REL's were computed for each trait from the genetic correlations with all other traits using multiple regression. For November 2000 evaluations, maximum indirect REL's were:

PTA trait
Milk Fat Protein PL SCS Size Udder F&L
Indirect REL (%) 82 60 86 45 32 17 28 12

For August 2000 evaluations, maximum REL of indirect predictions of PTA PL was 63%. The lower maximum indirect REL of 45% for November 2000 PTA PL resulted from the lower correlations between PTA traits that were implemented. Consequently, direct REL's for PTA PL also decreased.

The changes in PL parameters between August and November 2000 evaluations caused November multitrait PTA PL to become more similar to single-trait PTA PL that were reported before August. Reliability of multitrait PTA PL was 69% in August for bulls born during 1990 through 1995 but decreased to 65% in November with the lower genetic correlations. Mean REL for single-trait PTA PL was 62%. The standard deviation of single-trait PTA PL for bulls born during 1990 through 1995 was 1.08 months versus 1.18 months for August multitrait PTA PL. With the lower genetic correlations, standard deviation of multitrait PTA PL decreased slightly to 1.13 months in November.

To determine how the changes in PL parameters affected evaluations of individual bulls, evaluations of active AI bulls in August 2000 were compared with evaluations based on the same data but using November 2000 correlations [comparison table no longer available]. This comparison can aid in distinguishing whether variation between the August and November 2000 PL evaluations of a bull was caused by the change in the genetic correlations or simply by the addition of 3 months of new data.


Data for an example bull and the relative weights assigned to progeny data for each trait can help in understanding the new multitrait method:

Single trait Milk
SCS Size Udder F&L
PTA +1,947 +61 +61 +1.1 +3.38 +.52 +.90 +.99
PA +588 +44 +28 -.4 +3.31 +.73 +.56 +.81
REL (%) 81 81 81 61 66 75 71 67
RELPA (%) 48 48 48 46 47 48 48 47
Relative weight (%) 3 4 5 54 -5 -8 16 4

The relative weights assigned to progeny data that are used in multitrait PTA PL calculation differ for each animal based on how many daughter equivalents are present for each trait. The weights assigned to the correlated traits decline to 0 as the REL for single-trait PTA PL approaches 99%. For this bull, single-trait PTA PL received a weight of 54%, PTA's for yield traits received a total weight of 12%, and PTA udder received a weight of 16%. Traits that are more highly correlated with PL and that have higher heritabilities receive more weight than traits with lower correlations and heritabilities. For this bull and many others, the majority of information about PL comes from the highly reliable PL evaluations of the sire and dam.

This bull's single-trait PTA PL was +1.1 month with a REL of 61%, but his multitrait PTA PL was +1.4 mo with 63% REL. His multitrait PTA PL was higher than his single-trait PTA PL because his early evaluations for yield and udder traits indicated that he had received a favorable set of genes for PL (as compared with his PA's).