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82

Genetic Analysis of Cow Survival in the Israeli

Dairy Cattle Population

Petek Settar

1

and Joel I. Weller

Institute of Animal Sciences A. R. O., The Volcani Center, Bet Dagan 50250, Israel

Abstract

The linear model method of VanRaden and Klaaskate to analyze herd life was expanded.

Information on conception and protein yield was included in the estimation of predicted herd life of Israeli

Holsteins. Variance components were estimated by a multitrait animal model. Heritability was slightly

higher for herd life than for number of lactations, but genetic correlations were close to unity. Animal model

heritability estimates of herdlife were higher than previous sire model estimates. The expected herd life of

pregnant cows was 420 d greater than open cows. Each kg increase in protein yield increased expected herd

life by 9.5 d. Heritability of expected herd life increased from 0.11 for cows 6 mo after first calving to 0.14

for cows 3 yr from first calving. The genetic correlation of expected and actual herdlife increased from 0.87

for records cut after 6 mo to 0.99 for records cut 3 yr after first calving. Phenotypic correlations increased

from 0.61 to 0.94. Sire genetic evaluations based on expected herd life of live cows were strongly biased if

all records were weighted equally, while evaluations derived by weighting incomplete records to account for

the effects of current herd life on variance components were nearly unbiased.

1

Current adress: Ege University Faculty of Agriculture, • zmir,Turkey

1. Introduction

Longevity, or herd life (HL), is of major

economic importance in dairy cattle (VanRaden and

Wiggans, 1995). Three basic strategies have been

suggested to evaluate longevity for live cows. First,

cow survival to a specific age can be analysed as a

binary trait by either linear or threshold models

(Boettcher, et.al., 1998, Harris,et.al., 1992, Jairath,

et.al., 1998, Vollema and Groen, 1998). Second,

VanRaden and Klaaskate (1993) proposed

estimating life expectancy of live cows and

including these records in a linear model analysis.

Estimates based on incomplete data are regressed

toward the mean, and therefore have lower

heritability and variance than do complete records

(Meijering and Gianola, 1985, VanRaden et.al.,

1991, Weller, 1988). The third method is survival

analysis or consideration of cows still alive as

censored records (Boettcher, et.al., 1998,

Emanuelson et.al., 1998, Vollema and Groen, 1998,

Vukasinovic, et.al., 1997). Although the previous

methods could be applied to either animal or sire

models, survival analysis can only be applied to sire

models, and evaluations will be biased if the number

of daughters per sire with complete records is low

(Vukasinovic, et.al.,1997).

There have been numerous suggestions for

a definition of the longevity trait, based chiefly

either on the number of parities or the actual length

of HL (Vollema and Groen, 1996). Many studies

have proposed analysing functional HL, which is

generally computed as longevity adjusted for milk

yield (Boettcher, et.al., 1998, Dekkers, 1993,

Emanuelson et.al., 1998, Jairath, et.al., 1998,

Strandberg and Hakansson, 1994, Vollema and

Groen, 1996, Vollema and Groen, 1998). This trait

accounts only for culling that is due to causes other

than milk yield. The problem of double counting

of production in a selection index that includes

both milk yield and uncorrected longevity

correlated with yield can also be handled by

computing appropriate economic values for these

traits (VanRaden and Wiggans, 1995). Analysing

HL adjusted for yield is complicated because

selection goals change over time. Until 1980, milk

yield was the primary selection objective of most

breeding programs. Now protein yield is the chief

goal, and many countries put a negative economic

weight on milk yield (Leitch, 1994).

VanRaden and Klaaskate (1993) used

cumulative months in milk, current months in

milk, age at first calving, current months dry for

dry cows, first parity milk yield, and lactation

83

status (dry or milking) to predict the HL of live

cows.

In addition to low yield, the main causes of

cow culling are mastitis and nonconception. In

Israel, all milk recorded cows are checked for

pregnancy 60 d after insemination unless the cow is

reinseminated prior to 60 d (Weller and Ezra, 1997).

Thus, the pregnancy status of all cows is known in

real time, and this information can be used to

increase the accuracy of HL predictions.

Objectives of this study were to measure of

longevity for Israeli Holsteins; to study the effect of

incorporating data on pregnancy, days open (DO),

and protein yields in the computation of expected

HL; to compute adjustment factors for live cows;

and to determine the effects of the adjustment

procedure for incomplete records on genetic

evaluations. Adjustment factors were derived from

variance components for complete and incomplete

HL records estimated by a multitrait animal model

analysis, with records of different lengths considered

as correlated traits.

2. Material and methods

2.1

Estimation of expected HL for live cows and

estimation of variance components

Preliminary data set consisting of 559,035

Israeli Holstein lactation records with first calving

dates from 1984 through 1989, was generated to

predict HL for live cows. Lactation records were

discarded from the analysis if the first parity record

was missing; age at first calving was <570 or >1000

d; any calving intervals were <250 d; mean calving

interval was >500 d; last recorded parity was <7, and

exit day was missing for that parity; cows with >1

parity with valid exit dates; protein yield was <50 or

>600 kg for the last valid parity record; or if days in

milk >500 or if a cow was scored pregnant but days

open = 0. After edits, there were 51,888 valid cow

records in this data set (Table 1).

A linear model was used to estimate HL

from incomplete records. Multiple records were

derived for each cow by cutting the records at 6-mo

intervals beginning 6 mo after first calving until 4 yr

after first calving and then cutting records at yearly

intervals until 6 yr after first calving. At each cut

date, a record was generated only for cows that

survived until that cut date. Thus, up to 10 records

were generated per cow. This data set included

231,458 cow records.

The dependent variable was remaining HL

(RHL), computed as days from the cut date to the

exit date. The independent variables were current

HL (CHL), defined as days from first calving to

cut date; last parity prior to cut (PPC); expected

protein yield of the last parity prior to cut (EPY);

pregnancy status (PS) where 1 = pregnant, and 0 =

not pregnant; DO of the last lactation for cows

pregnant by the cut date, or days in milk for cows

not pregnant at the cut date, days pregnant (DP) at

cut date for pregnant cows; and days dry (DD) at

the cut date if the record was cut during the dry

period. Days pregnant = 0 for cows not pregnant at

the cut date. The EPY was computed as described

previously (Weller, 1988). The HYS were defined

relative to the first parity calving date, and were

absorbed. PPC, PS, and HYS were analyzed as

discrete effects; all other effects were analyzed as

continuous variables.

If predicted RHL <0 then predicted RHL

was set to zero. Estimated HL (EHL) was

computed as HL for cow records that were culled

prior to the cut, and as the sum of predicted RHL

and CHL for records cut after the cut date. Genetic

and environmental variance components among

HL and EHL computed for the 10 cut dates were

estimated by multitrait REML (Misztal, et.al.,

1995) using the animal model for these 11 traits.

2.2. Estimation of Adjustment Factors for Genetic

Evaluations of Incomplete Records

The EHL records as a function of CHL

were first adjusted so that the genetic covariance

between EHL and actual HL records would equal

the genetic variance of the actual records.

Multiplicative adjustment factors were estimated

PROC NLIN of SAS (1988) based on the

following nonlinear function of CHL:

RG

i

= b0 + (b1/CHL

i

) + e

I

[1]

where RG

i

is the ratio of the square root of the

genetic covariance between HL and EHL

i

, EHL at

cut date i, b0 and b1 are regression constants, and

e

i

is the residual. With this formula, as CHL

increases, the term b1/CHL becomes negligible

with respect to b0, and b0 should be approximately

equal to unity. The EHL records were then

multiplied by the predicted values of RG for

Equation [1], PRG, which also increased the mean.

The following nonlinear model was used to adjust

for the increase in the mean as a function of CHL

based on data set 2:

EHLX

j

= b2 + b3/CHL

j

+ e

j

where EHLX

j

= EHL

✕

PRG, for cow j, b2 and b3

= regression constants, and the other terms are as

described previously. Predicted HL (PHL) was

84

then computed as EHLX - b3/CHL; b2 was not

subtracted because, as a constant, it would have the

same effect on all records.

In the animal model analysis, the PHL

records were weighted by the inverse of the ratio of

the residual variances of PHL and HL as a function

of CHL. Weighting factors for the square root of the

residual variances of PHL were computed using the

model of Equation [1]. If this model is appropriate,

then b0 should be approximately equal to the

residual standard deviation of HL.

2.3. Genetic Evaluation for Longevity

Data set 2 was generated for computation of

animal model genetic evaluations for HL and PHL.

The HL was computed for each cow as described

previously, except that if HL >2557 d (7 yr), then

the HL was set equal to 2557 d. The CHL was

computed as days from first calving to January 1,

1990. Cows with CHL <35 d were deleted, leaving

45,300 cow records.

The animal model was used to compute

genetic evaluations for HL, PHL with equal weights

for all records, and PHL weighted as described

previously. Pedigree information from all known

parents and grandparents was included. The pedigree

file included a total of 379 sires. Twenty-five

phantom parent groups were defined by year of birth

and sex of parent (Wiggans, et.al., 1988). Number of

cows, records, sire, and HYS included in data set 2

are also given Table 1. The two methods for

analyzing PHL were compared by correlations of the

sires’ EBV for these methods and the EBV for HL

and by the regression of the HL sire EBV on the

PHL EBV.

Genetic evaluations for HL based on the

method developed were also computed on the

complete Israeli-Holstein dairy cattle population in

September 1998, including 284,541 cows with first

calving dates since January 1, 1985, and at least 35

DIM at the evaluation date. Other edits were the

same as for data set 2. The numbers of cows,

records, bulls, HYS, and genetic groups for this data

set (data set 3) are also given in Table 1. Genetic

trends were computed as the regression of the cows’

EBV on their birth dates, including all cows born

since 1981. Phenotypic trends were computed as the

regression of the cows’ HL on their birth dates, but

including only cows with valid HL records. For live

cows EHL was used instead of HL to calculate the

phenotypic trend. Correlations were computed

between bull EBV for HL and milk and protein

production for bulls with reliability > 0.5 for all

three traits. Bull EBV for milk and protein were

computed by a standard animal model (Weller and

Ezra, 1997).

3. Results and Discussion

The RHL was estimated from data set 1 as

described previously. After removing

nonsignificant effects from the analysis, the final

equation for estimating RHL from the incomplete

records was

RHL = PPC - 908 + 0.131

✕

CHL + (-0.00029)

CHL

2

+ (-0.872) DP + (-5.218) DO +

(0.0169) DO

2

+ (-0.0000313) DO

3

+

(0.00126) CHL

✕

DO + (-0.536) DD +

(9.532) EPY + (-0.011) EPY

2

[3]

All effects included in the final model

were significant at p < 0.0001. The discrete parity

and pregnancy status effects are given in Table 2.

Parity effects show no discernible trend because

this effect is highly confounded with CHL, which

was also included in the model. Pregnancy at the

cut date increased RHL by 420 d, but the effect DP

was negative.

Genetic correlations between HL and EHL

increased from 0.87 for records cut after 6 mo to

0.99 for records cut after 3 yr. The phenotypic

correlation was 0.61 for records cut after 6 mo, and

increased to 0.94 for records cut after 3 yr. The

genetic and phenotypic correlation estimates

between complete and incomplete HL records were

higher than were those reported by VanRaden and

Klaaskate (1993), but they did not include data on

pregnancy status.

Heritability increased from 0.11 for

records cut at 6 mo to 0.14 for records cut after 3

yr and then remained constant. VanRaden and

Klaaskate (1993), using a sire model, reported that

heritability of cut records increased from 0.03 to

0.08.

The genetic covariances between the

complete records and incomplete records were then

used to compute genetic adjustment factors based

on Equation [1]. The coefficients are given in

Table 3. The constant coefficient was equal to 656,

and the square root of the residual variance of HL

was 666. For convenience, the residual weighting

factors were then computed as 656/(656

+45256/CHL). Although both the genetic

covariances and the environmental variances were

monotonic functions of CHL, the ratio of the

residual variances after adjustment to equal genetic

covariances is no longer monotonic. The

85

coefficients of determination for all three nonlinear

models are also given in Table 3. The coefficient of

determination was lowest for the residual variance of

PHL, but all values were >0.9.

The EBV for all animals included in data set

2 were computed for HL and PHL with all records

cut at January 1, 1990. Correlations between sire

EBV for HL and PHL with and without weighting

factors are given in Table 4 for all sires and for sires

with >10 daughters. Because evaluations of young

sires should be most effected by incomplete records,

correlations are also given for sires born after 1981,

1982, 1983, and 1984. Correlations between HL and

PHL computed with and without weighting factors

were 0.94 and 0.93, respectively. Correlations were

lower if only bulls with >10 daughters were

included, and were again marginally higher for PHL

computed with weighting factors. As expected,

correlations decreased with decreases in the bulls’

ages. In all cases differences between correlations

for PHL computed with and without weighting

factors were no more than 1%.

The regressions of sire EBV for HL on PHL

with and without weighting factors are also given in

Table 4. Without weighting factors, slopes for all

bulls were about 1.3 but were nearly equal to unity

for evaluations computed with weighting factors.

Thus, nearly unbiased evaluations are derived with

weighting factors, and evaluations based on equal

weights of all records are biased. For the young

sires, without weighting factors, regressions

increased up to 1.75 for bulls born after 1984 and

were, therefore, highly biased. With weighting

factors, regressions decreased slightly with the bull’s

age but were still 0.85 for bulls born after 1984.

Thus bias was much smaller with weighting factors.

In the analysis of the complete Israeli

Holstein population the phenotypic trend for HL was

–15 d/yr, and the genetic trend was 9 d/yr. The

genetic correlations between the sire EBV for HL

and milk and protein production by birth year of

bulls born since 1986 are given in Table 5. The

correlations for all bulls born since 1986 are also

given. Correlations were lowest in 1988 and 1989,

but no clear trends are evident. In our analysis, HL

was not adjusted for milk production, and EPY was

used to predict HL for live cows. This should tend

to increase the similarity between EBV for

production and HL, especially for young sires whose

daughters are in first lactation. However, the genetic

correlations between protein and HL were nearly

equal for sires born in 1993, as compared to sires

born in 1986.

References

Boettcher, P. J., L. K. Jairath, and J.C.M. Dekkers.

1998. Alternative methods for genetic

evaluation of sires for survival of their

daughters in the first three lactations.

Proc. 6th

World Cong. Genet. Appl. Livest. Prod.,

Armidale, Australia 23:363-366.

Dekkers, J.C.M. 1993. Theoretical basis for

genetic parameters of herd life and effects on

response to selection.

J. Dairy Sci.

76:1433-

1443.

Emanuelson, U., J. Carvalheira, P. A. Oltenacu,

and V. Ducrocq. 1998. Relationships between

adjusted length of productive life and other

traits for Swedish dairy cattle. Proc. 6th World

Cong. Genet. Appl. Livest. Prod., Armidale,

Australia 23:367-370.

Harris, B. L., A. E. Freeman and E. Metzger. 1992.

Analysis of herd life in Guernsey dairy cattle

. J.

Dairy Sci. 75:2008-2016.

Jairath, L., J.C.M. Dekkers, L. R. Schaeffer, Z.

Liu, E. B. Burnside, and B. Kolstad. 1998.

Genetic evaluation for herd life in Canada. J.

Dairy Sci

. 81:550-562.

Leitch, H. W. 1994. Comparison of international

selection indices for dairy cattle breeding. Proc.

Open. Session Interbull Annu. Meet. Ottawa,

Canada, 10: (unnumbered). International Bull

Evaluation Service. Department of Animal

Breeding and Genetics, SLU, Uppsala, Sweden.

Meijering, A., and D. Gianola. 1985. Observations

on sire evaluation with categorical data using

heteroscedatic mixed linear models. J. Dairy

Sci.

68:1226-1232.

Misztal, I., K. Weigel, and T. J. Lawlor. 1995.

Approximation of estimates of (co)variance

components with multiple-trait restricted

maximum likelihood by multiple

diagonalization for more than one random

effect. J. Dairy Sci. 78:1862-1872.

SAS Institute Inc. 1988. SAS/STAT

User’s

Guide, Release 6.03 Edition. SAS Inst. Inc.,

Cary, NC.

Strandberg, E. and L. Hakansson. 1994. Effect of

culling on the estimates of genetic correlation

between milk yield and length of productive life

in dairy cattle.

Proc. 5th World Cong. Genet.

Appl. Livest. Prod

., Guelph, Canada 17:77-80.

VanRaden, P. M., and E.J.H. Klaaskate. 1993.

Genetic evaluation of length of productive life

including predicted longevity of live cows

. J.

Dairy Sci.

76:2758-2764.

VanRaden, P. M., and G. R. Wiggans. 1995.

Productive life evaluations: Calculation,

86

accuracy and economic value. J. Dairy Sci.

78:631-638.

VanRaden, P. M., G. R. Wiggans and C.A. Ernst.

1991. Expansion of projected lactation yield to

stabilize genetic variance. J. Dairy Sci. 74:4344-

4349.

Vollema, A. R., and A. F. Groen. 1996. Genetic

parameters of longevity traits of an upgrading

population of dairy cattle. J. Dairy Sci. 79:2261-

2267.

Vollema, A. R., and A. F. Groen. 1998. A

comparison of breeding value predictors for

longevity using a linear model and survival

analysis. J. Dairy Sci. 81:3315-3320.

Vukasinovic, N, J. Moll, and N. Kunzi. 1997.

Analysis of productive life in Swiss brown

cattle. J. Dairy Sci. 80:2372-2579.

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weighting of records. J. Dairy Sci. 71:1873-

1879.

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somatic cell concentration and female fertility of

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80:586-594.

Table1:. Number of levels of effects included in the three data sets that were analyzed.

Data set

Effects 1 2 3

Cows 85,965 75,825 370,406

Records 51,888 45,300 284,541

Sires 393 379 965

Herd year-season 3319 3074 16,816

Genetic groups 2 25 42

Table 2:. Estimated effects for levels of the class effects on remaining days of herd life.

Effect

Parity Pregnancy status

Level 1 2 3 4 5 6 open pregnant

Effect (d) 62 -56 -108 -123 -51 0 0 420

Table 3: Regression coefficients, coefficients of determination (R

2

), and the

correlations between actual and predicted function of variance components based on

the nonlinear analysis model

Dependent Coefficients

2

R

2

Correlation

variable

1

b0 b1

RG 0.95 293 0.93 0.96

EHLX 1081 224,010 0.98 0.99

Square root of residual

variance of PHL

656 45,256 0.86 0.93

1

The dependent variables are explained in the text.

2

The analysis model was: y = b0 + (b1/CHL

i

) + e

i

where y is the dependent variable, and CHL is

days for first calving to cut date

87

Table 4: Regression coefficients and correlations between estimated sire breeding values of HL and

PHL with and without inclusion of weighting factors.

Weighting Birth year All bulls bulls with >10 daughters

factors of sires No. sires Intercept Slope r No. sires Intercept Slope r

With All 379 12.68 0.98 0.94 212 10.39 0.99 0.87

>1981 157 9.54 0.99 0.86 145 10.09 0.99 0.87

>1982 97 12.31 0.95 0.77 86 13.41 0.94 0.76

>1983 78 14.11 0.95 0.73 68 15.70 0.94 0.72

>1984 39 3.95 0.85 0.61 31 5.50 0.84 0.61

Without All 379 4.85 1.31 0.93 212 3.46 1.30 0.86

>1981 157 0.59 1.30 0.86 145 1.70 1.29 0.86

>1982 97 -5.01 1.47 0.76 86 -3.87 1.46 0.75

>1983 78 -5.22 1.55 0.72 68 -3.94 1.54 0.71

>1984 39 -23.62 1.75 0.63 31 -24.79 1.73 0.62

Table 5: Correlations between EBV for herd life and milk and protein production

based on genetic evaluation of the complete Israeli Holstein population.

Birth Year No. of bulls Correlation with herd life

Milk Protein

1986 40 0.65 0.67

1987 42 0.72 0.65

1988 53 0.43 0.44

1989 33 0.54 0.46

1990 31 0.48 0.64

1991 40 0.59 0.60

1992 42 0.63 0.65

1993 52 0.55 0.68

Total 340 0.53 0.57