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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.
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76:1433-
1443.
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68:1226-1232.
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diagonalization for more than one random
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User’s
Guide, Release 6.03 Edition. SAS Inst. Inc.,
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in dairy cattle.
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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.
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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
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2267.
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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
