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PL2 (11-03)
Methods used to compute multi-trait 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) ~ ~

Published predicted transmitting abilities (PTA's) for productive life (PL) have been computed using approximate multi-trait methods since July 1994. Evaluations of PL are based on direct observations of length of productive life and also correlated traits measured earlier in life. Multi-trait PTA's have higher reliability (REL) than single-trait PTA's, which include only culling observations. New programs were introduced in August 2000 by the Animal Improvement Programs Laboratory (AIPL) to combine direct and indirect information about longevity. Evaluations of milk, fat, and protein yields; somatic cell score (SCS); and udder, feet and legs (F&L), and body size composites were included in the multi-trait predictions.

The traits and correlations included in multi-trait PL were extended to include stillbirths in August 2006 and daughter pregnancy rate (DPR), service sire calving ease (SCE), and daughter calving ease (DCE) in November 2003. The four calving ease and stillbirth traits are combined before use in PL predictions, and DPR is the most important individual trait in predicting PL. Correlation estimates were revised in November 2000, August 2002, and August 2006. In previous revisions, the influence of yield traits in PL predictions was reduced because correlations of yield traits with PL have decreased over time. In November 2000, 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 estimated PL for foreign bulls.


Holsteins. The multi-trait PTA's for PL begin with single-trait evaluations, which have been calculated at AIPL since January 1994 for all breeds. The single-trait PL evaluations for Holstein bulls were combined with information from yield and type PTA's by Holstein Association USA beginning in July 1994 to produce approximate multi-trait PTA's for PL. Advantages of the multi-trait 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 multi-trait methods were described by Weigel (1996, International Bull Evaluation Service Bulletin 12:125) and Weigel et al. (1998, Journal of Dairy Science 81:2040).

New computer programs were introduced to combine single-trait PTA PL into approximate multi-trait PTA PL (VanRaden, 2001, Journal of Dairy Science 84:E47-E55) beginning with August 2000 evaluations. 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 multi-trait evaluations for PL was transferred from Holstein Association USA to AIPL. Major differences from the Holstein Association programs were that PTA SCS was included in PL predictions and that PL predictions begin with PA and only adjust the Mendelian sampling for information from correlated traits. Other differences were 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) were 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 multi-trait PTA's for PL also were implemented in August 2000 for breeds other than Holstein after testing with August 1999 data. The Holstein genetic correlation matrix was used for the other breeds. 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. Composites have slightly different definitions based on breed specific research and because some Holstein traits are not measured by the other breeds. Details regarding the traits included in each composite and their relative values can be found in the Lifetime Net Merit report.


The AIPL PL programs were designed to combine single-trait PTA's into multi-trait 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 multi-trait PL

Genetic merit for PL can be predicted from both direct and indirect measurements of correlated traits (multi-trait analysis). Information on yield (milk, fat, and protein), mastitis resistance (SCS), type (udder, F&L, and body size composites), cow fertility (DPR), and calving ease (SCE and DCE) is now included.

Evaluations for PL from single-trait and approximate multi-trait procedures were compared for bulls in active artificial-insemination (AI) service, elite cows, and all bulls or cows in various birth year groups using August 2000 procedures and correlations:

Multi-trait method Evaluation
Breed Gender Birth year or
animal status
Average PTA PL (mo) Average REL (%)
Single-trait Multi-trait Single-trait Multi-trait
Holstein Association USA
(Weigel et al., 1998)
1994 Holstein Bulls 1989-90 .83 1.19 50 53
(VanRaden, 2001)
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 gains in REL for PTA PL with the AIPL multi-trait methods were higher than with the previous approach. 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.

For Holstein bulls in active AI service and for elite Holstein cows, multi-trait 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 multi-trait methods. Correlations of single-trait PTA PL with multi-trait PTA were .85 for AIPL multi-trait PL and .95 for Holstein Association multi-trait PL. Holstein Assocation multi-trait PTA PL was correlated by only 0.88 to AIPL multi-trait 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 multi-trait PL. Average reliability (REL) increased from 52% for single-trait PL to 58% for multi-trait 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 DPR, SCS, and type traits are missing for some relatives, the AIPL multi-trait programs also were tested for upgrading single-trait PTA's for DPR, SCS, and udder composite to multi-trait 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 that would be required for routine evaluations, but gains were larger for DPR. Therefore, the multi-trait procedure is applied only to PL and to DPR since November 2003.

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. Genetic and phenotypic correlations were based on estimates from scientific studies for Holsteins such as Tsuruta et al. (2005, Journal of Dairy Science 88:1156) and results of additional research. Current genetic correlations among all traits are provided in the Lifetime Net Merit document.

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. Inclusion of DPR as an additional trait in the predictions greatly increased the potential to predict PL, primarily because of the strong genetic correlation of DPR with PL. For August 2006 evaluations, maximum indirect REL's were:

  PTA trait
  Milk Fat Protein PL SCS Udder F&L Size DPR Calving
Indirect REL (%) 67 43 74 61 26 37 16 24 59 28

Maximum REL of indirect predictions of PTA PL was previously only 30% but increased to 75% when cow fertility and the two calving ease traits were added as predictors.


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

Single trait Milk
SCS Udder F&L Size DPR Calving
PTA +1,947 +61 +61 +1.1 3.38 +.90 +.99 +.52 +.1 +29
PA +588 +44 +28 .8 3.31 +.56 +.81 +.73 -.4 +19
REL (%) 81 81 81 55 66 71 67 75 56 65
RELPA (%) 48 48 48 46 47 48 47 48 46 32
Relative weight (%) 1 2 4 32 -10 11 6 -10 15 11

The relative weights assigned to progeny data that are used in multi-trait PTA PL calculation differ for each animal based on how many daughter equivalents are present for each trait. As the REL for single-trait PTA PL approaches 99%, the weight assigned to single-trait PTA PL approaches 1.0 and the weights assigned to the correlated traits decline to 0 . For this bull, the single-trait PTA PL had a REL of only 55% and received a weight of 32% because most daughters were still fairly young. Correlated traits such as PTA DPR received a weight of 15%, PTA's for yield traits received a total weight of 7%, and PTA udder received a weight of 11%. 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, much of the information about PL comes from the highly reliable PL evaluations of the sire and dam.

The example bull's single-trait PTA PL was +1.1 month with a REL of 55%, but his multi-trait PTA PL was +2.0 mo with 62% REL. His multi-trait PTA PL was slightly higher than his single-trait PTA PL because his early evaluations for yield, DPR, and udder traits indicated that he had received a favorable set of genes for PL (as compared with his PA for PL).

As a second example, suppose this bull had no single-trait evaluation for PL because his daughters were not yet 36 months old. His multi-trait PTA would then be +2.1 instead of +2.0 and his multi-trait REL would be only 58% instead of 62% if no direct information from daughter culling was present. The weights on the other traits would be higher, with a sum of 9% for yield traits, -14% for SCS, 23% for DPR, 16% for udder, 12% for feet and leg, and -13% for size composite, and 14% on calving ability index, to make up for the 0% weight on the single-trait PL. When compared to the parent average PL with REL of 46%, the gain in REL from using correlated traits would be 12% for the second example. Advantages are greatest from the middle of first lactation when pregnancy rate data arrives until the beginning of second lactation when actual culling rates become known. The multi-trait approach does not produce large gains in REL but allows information from correlated traits to be used for new bulls and foreign bulls that have little or no daughter culling information available.