258 M
.H. Yazdi et al. Livestock Production Science 63 2000 255 –264
corresponding incidence matrix possibly time-de- 1996 for more details of choosing the log-gamma
pendent wt9 5 hxt9 zt9j. distribution. The parameter
g was either estimated or Several analyses were carried out with somewhat
the hy effect was integrated out in the analysis. The different models. The effects included in the model
additive genetic effects of sires were assumed to for all analyses were: f ls and l ls as class, fixed and
have a multivariate normal distribution, s |MVN0,
q
] ]
2
time-independent covariates; age, weight, gain and A
s , where subscript q is the number of sires, A is
s 2
fat as
continuous, fixed
and time-independent
the relationship matrix between sires, and s is the
s
covariates; and finally sire as a class, random and sire variance.
time-independent covariate. The additive genetic The heritability of longevity was calculated from
relationship matrix of sires was incorporated in the the sire variance component as a proportion of
analyses. phenotypic variance of the Weibull distribution as
The effect of hy summarizes effects of several described by Ducrocq and Casella 1996 on the
factors e.g. herd management, food supply, and the logarithmic scale of length of productive life as
2 2
2 2
2
influence on culling rate might change over time. It h
54 s p 61s , where p 6 is the variance
log s
s
is, however, difficult to foresee how often these of the standard extreme value distribution Lawless,
2
changes occur and what is the appropriate length of 1982. The variance of hy
s , which was esti-
hy
time intervals. Therefore, results from the following mated from the second moment trigamma of the
models, when hy was treated differently in each log-gamma distribution Lawless, 1982, was added
model, were compared. to the denominator of the expression used for
2
calculating h when hy was considered as a random
log
effect in the model. The calculation of heritability on
FTI fixed
time-independent;
2
the original scale of length of productive life h
RTI random
time-independent;
ori
was based on the description of Ducrocq 1998,
FTD1 fixed
time-dependent time interval of 1 year;
2 2
personal communication as h 54
s [exph1 r 3
RTD1 random
time-dependent time interval of 1 year;
ori s
2 2
2
nj] 3p 61s where n 5 2Euler’s constant
FTD2 fixed
time-dependent time interval of 2 years;
s
the mean
of the
standard extreme
value
RTD2 random
time-dependent time interval of 2 years.
2
distribution5 20.5772. The s
was added to the
hy
denominator of the expression, as was done for the The exponential part of the above models for
log scale, when hy was considered as a random effects of explanatory variables, either fixed or
effect in the model, and n was then calculated as
random, was as follows: n 5digammag 2logg 2Euler’s constant, where
hwt9 u j 5 hy t 1 f ls 1 l ls 1 b age
j k
l 1
digamma g 2logg is the first moment of the log-
] ]
gamma distribution. 1 b weight 1 b gain 1 b fat 1 s
2 3
4 m
where:
3. Results and discussion
th
hy t is the j
herd3year effect,
j th
f ls is the k first-farrowing litter-size effect,
The average length of productive life was 617
k
]
th
l ls is the l
last-farrowing litter-size effect,
days, which corresponds to an age of 2 years and 8
l
] b age
is the partial regression coefficient on age,
months at culling Table 2. This is in accordance
1
b weight is the partial regression coefficient on weight,
with the average life length of sows from French
2
b gain is the partial regression coefficient on gain,
herds reported by Le Cozler et al. 1999. There was
3
b fat is the partial regression coefficient on fat, and
a wide range in the number of observations among
4 th
s is the random additive genetic effect of the m sire.
the different hy classes, as well as the number of
m
daughters per sire. Mean numbers of observations in The random effect of hy was assumed to follow a
corresponding classes were 32 and 8 for all observa- log-gamma distribution with parameter gamma
g . tions. The Kaplan and Meier 1958 and baseline
See Ducrocq et al. 1988b and Ducrocq and Casella survivor curves as well as the baseline hazard curve
M .H. Yazdi et al. Livestock Production Science 63 2000 255 –264
259
are illustrated in Fig. 1. An increased risk of culling covariates a likelihood-ratio test was carried out for
after weaning of the first three litters around 40, 220 all models. Results from RTD1, in which hy was
and 400 days on the longevity axis is reflected in the random and time-dependent with a time interval of 1
2
Kaplan–Meier survivor curve. year, are presented in Table 3. The R of Maddala
The parameters of the Weibull distribution, r and
measure of proportion of variation explained by the l, were very similar in the various analyses. The
model, see Schemper, 1992 increased significantly suitability of the Weibull model was assessed by
when f ls, l ls, age and weight were added. The ]
] evaluating the log-cumulative hazard plot Fig. 2,
additional changes were very small when adding log 2log St versus logt, where St and t are the
gain and fat to the model, since the effects of gain Kaplan–Meier survivor function and number of days
and fat were not significant. Among the fixed after first farrowing, respectively Lawless, 1982.
covariates, l ls had the most significant influence on ]
Because the relationship is almost a straight line, risk of culling. Results from likelihood-ratio tests for
except for a short period after the first weaning when significance of effects obtained from different
there was intensive culling, the Weibull model seems models were similar concerning l ls, weight, gain
] to fit the data well.
and fat. For age and f ls the differences between ]
Preliminary survival analyses were carried out to models were larger, but the probabilities were always
examine the confounding and interaction between below 0.10.
fixed effects. No significant interactions were found The effect of hy was highly significant p ,0.001
between fixed effects. Further, age and weight were when it was treated as a fixed effect FTI, FTD1,
both regarded to be linearly related to longevity. FTD2. The estimated parameter of the log-gamma
To test the significance of different effects distribution of hy
g , when treated as random,
Fig. 1. Survivor and hazard curves of sow longevity.
260 M
.H. Yazdi et al. Livestock Production Science 63 2000 255 –264
Fig. 2. Graphical test of the Weibull assumption, St5Kaplan–Meier estimate of the survivor function for the sows and t is days from first farrowing.
Table 3
a b
Likelihood ratio test, including shape r and location l parameters of Weibull distribution, when all covariates added to model RTD1
sequentially
2 2
Covariate d.f. total
x d.f.
Prob. R of Maddala
sire 1455
RANDOM hy
271 1090.1
RANDOM f ls
284 21.270
13 0.0678
0.1302 ]
l ls 300
60.569 16
0.0000 0.1368
] age
301 3.1443
1 0.0762
0.1371 weight
302 5.0541
1 0.0246
0.1377 gain
303 0.4304
1 0.5118
0.1377 fat
304 0.7903
1 0.3740
0.1378
a
hy 5herd3year combinations; f ls5litter size at first farrowing; l ls5litter size at last farrowing; age5age at first farrowing days; ]
] weight5weight of gilt at field performance test kg; gain5daily gain from birth until field performance test g d; fat5side-fat thickness at
field performance test mm.
b
RTD15all covariates except hy were fixed and time-independent. The hy was treated as random and time-dependent with calendar time interval of 1 year.
ranged from 4.90 to 5.76. The estimated hazard problems, etc. was not included in this data set, it
coefficients for hy effects ranged from 21.737 to was impossible to determine exactly how important
1.141, which corresponds to relative culling rates the health traits were in impairing longevity. How-
exphhyj from 0.18 to 3.13. These coefficients imply ever, these effects were implicitly the results of the
that in the worst case, sows had three times higher herd management, which probably explains why hy
risk of culling probability of being culled com- had such a strong influence on culling in this data
pared with sows in the average hy effect with a set. Le Cozler et al. 1999 also found that the effect
relative culling rate of 1. Also, sows in the worst hy of herd strongly affected longevity.
class were eighteen times more likely to be culled The significance of the effect of f ls was depen-
] than sows in the best hy class at any time. Since
dent on the model. However, it was significant at information on health status leg weakness, udder
p ,0.10 in all analyses. The effect of litter size at
M .H. Yazdi et al. Livestock Production Science 63 2000 255 –264
261
last farrowing l ls was highly significant p ,0.01 of these problems. To include only the first and last
] in all analyses. Estimates of the associated hazard
litter size in the survival analysis is a simplification. coefficients and the relative culling rates based on
Besides, the biological meaning of l ls of censored ]
the average litter size of sows with uncensored sows can be questioned. Inclusion of information on
observations were very similar for all different the sow’s all parities as time-dependent covariate
models. Representative values for the hazard coeffi- would give a better description of the relation
cient and the risk ratio relative hazard or culling for between litter size and longevity.
an individual compared to the baseline hazard The effect of age at first farrowing was significant
generated by RTD1 are shown in Table 4. Although p ,0.01 when hy was fixed in the model. Increased
there was some fluctuations in the risk ratio between age at first farrowing increased the relative culling
litter size classes, owing to a low number of observa- rate of sows. The hazard regression coefficient for
tions at some levels, the risk ratio tended to decrease age at first farrowing was 0.00160.0005 per day. A
with increasing litter size for both f ls and l ls. The negative relation between age at first farrowing and
] ]
increased risk related to small litters was more life length has also been shown by Holder et al.
pronounced for l ls. Many farmers are of the opinion 1995. This may partly be explained by the ten-
] that a ‘too large’ first litter increases the risk of early
dency for sows with a high age at puberty to show culling; however, this could not be confirmed in the
delayed oestrus after weaning Sterning et al., 1998. present
study. Ringmar-Cederberg
and Jonsson
The hazard regression coefficient for weight at 1996 and Eliasson-Selling and Lundeheim 1996
performance test was 0.00460.002 per kg. A high all concluded that reproduction problems of the sow
weight at performance test could be a consequence is the most important reason for culling. According
of a high growth rate. Although Gueblez et al. ´
to this study, small litters is an important indication 1985 and Lopez-Serrano et al. 2000 found a
Table 4 Estimates of hazard coefficient, risk ratio based on average of litter size of uncensored observation and number of uncensored observations
a
n of litter size at first farrowing f ls and last farrowing l ls from model RTD1
unc
] ]
b
Class level f ls
l ls ]
] Hazard coef.
Risk ratio n
Hazard coef. Risk ratio
n
unc unc
2 0.22360.244
1.250 18
3 0.42560.266
1.530 15
0.19060.200 1.209
27 4
0.05560.182 1.057
33 0.06560.231
1.067 20
5 0.23060.153
1.259 47
20.19460.157 0.824
45 6
0.03960.069 1.039
276 0.02960.135
1.030 62
7 0.15360.059
1.166 416
20.20260.097 0.817
126 8
0.09660.050 1.100
688 0.03460.073
1.034 252
9 0.00960.046
1.009 932
0.00060.062 1.000
387 10
0.00060.000 1.000
1092 0.03360.052
1.034 656
11 0.02560.047
1.026 861
20.06860.049 0.934
836 12
0.00160.051 1.001
639 0.00060.000
1.000 924
13 0.00160.068
1.001 290
20.05860.049 0.943
849 14
20.12160.098 0.886
121 20.14660.053
0.865 626
15 20.06060.140
0.942 56
20.13060.063 0.878
364 16
20.27760.083 0.757
180 17
20.47260.116 0.624
85 18
20.60360.201 0.547
26 19
20.39760.235 0.672
19
a
RTD15all covariates except herd–year were fixed and time-independent. The herd–year was treated as random and time-dependent with calendar time interval of 1 year.
b
Since l ls is a deviation from the parity average, a constant of 12 was added to the mean values of l ls. ]
]
262 M
.H. Yazdi et al. Livestock Production Science 63 2000 255 –264
negative relation between growth rate and longevity, variance. It seems that model RTD1 describes data
growth rate itself had no significant influence on most properly. Heritability on the original scale
longevity in this study. represents the heritability of length of productive life
Estimates of sire variance, heritability and parame- when all daughters of sires have uncensored records
ters of the Weibull distribution obtained from differ- Ducrocq, 1999.
ent models are presented in Table 5. Estimates of Tholen et al. 1996 estimated the heritability for
sire variances and heritabilities from FTI and RTI stayability the probability of the sow surviving in
were similar. The sire variances obtained when hy the herd from parity 1 to parity 4, an all-or-none
´ was treated as a time-dependent variable ranged from
trait to be 0.08 and Lopez-Serrano et al. 2000 0.04 to 0.05, which were higher than those obtained
estimated the heritability for stayability from parity 1 when hy was time-independent 0.02 and 0.03. The
to 3 to be 0.10. Krieter 1995 estimated the increase in sire variances reflects the characteristics
heritability of sow longevity, measured as age at of genetic origin that were carried over from year to
culling, to be 0.12. The heritability for the length of year since 1986 the first year in this investigation.
productive life in dairy cattle has been estimated to In other words, due to the large effect of hy on the
be less than 0.09 on a log scale Ducrocq et al., longevity of sows and probably invalidity of the
1988b; Vollema and Groen, 1996; Vollema and proportional hazards throughout the time range, the
Groen, 1997. effects of sire were masked by the hy effect and,
The relative culling rate for daughters of sires consequently, the sire variances became low when hy
ranged from 0.65 to 1.27, using model RTD1. This was time-independent. The resulting heritabilities
corresponds to the lowest and highest risk of culling from models with hy as a time-dependent variable
for daughters of the best and worst sires, respective- were also higher on average, 0.25 on original scales
ly, compared with daughters of an average sire than estimated heritabilities when hy was a time-
which have a relative risk of culling equal to 1. independent variable on average, 0.13 on original
Daughters of the worst sires thus had two times scales. Also, the decrease in the sire variances
higher risk of culling compared with daughters of the observed when the time-dependent hy was changed
best sires. The correlation between breeding value of from fixed to random indicates that differences in the
sires from FTI and that of sires from RTI was 0.98. longevity of sows related to hy had partly genetic
The corresponding correlation between breeding origin and modified the variability of longevity due
values from different models when hy was a time- to sire. The length of the time interval 1 versus 2
dependent variable ranged from 0.96 to 0.99. The years had no significant influence on the sire
correlations between breeding values of sires from
Table 5
2 2
Estimates of sire variance s , shape r and location l parameters of the Weibull distribution, and heritability on log h
and original
s log
2
h scales of length of productive life longevity
ori a,b
2 c
2 2
Models s
r l
h h
s log
ori
FTI 0.02060.011
1.40060.016 0.237
0.048 0.109
RTI 0.02660.012
1.36760.015 0.227
0.056 0.149
FTD1 0.04560.013
1.38860.018 0.251
0.107 0.246
RTD1 0.03760.012
1.36260.016 0.227
0.075 0.212
FTD2 0.04960.014
1.38660.017 0.270
0.116 0.267
RTD2 0.04760.013
1.35960.016 0.220
0.098 0.268
a
The effects of f ls litter size at first farrowing, l ls litter size at last farrowing, age age at first farrowing, weight weight of gilt at ]
] field performance test, gain daily gain from birth until field performance test, fat side-fat thickness at field performance test were
included in all models.
b
FTI5hy was fixed and time-independent; RTI5hy was random and time-independent; FTD15hy was fixed and time-dependent time interval of 1 year; RTD15hy was random and time-dependent time interval of 1 year; FTD25hy was fixed and time-dependent time
interval of 2 years; RTD25hy was random and time-dependent time interval of 2 years.
c
The values were multiplied by 100.
M .H. Yazdi et al. Livestock Production Science 63 2000 255 –264
263
time-dependent models FTI and RTI and that of more precise registration of the cause of culling
sires from time-dependent models FTD1, RTD1, would also increase the possibility to include sow
FTD2, RTD2 ranged from 0.87 to 0.90. All standard longevity in the breeding evaluation.
errors of correlations were very similar 0.001. This similarity between the evaluations of sires from
different models confirms the similarity of the sire
Acknowledgements
variance components obtained for the different models within time-independent and dependent hy
The authors are very grateful to The Swedish effects.
Farmers’ Foundation for Agricultural Research for Due to many missing observations concerning the
financially supporting this study. Quality Genetics cause of culling and date of mating and weaning it
the Swedish pig-breeding organisation is acknowl- was impossible to directly distinguish between vol-
edged for providing the data. The authors are in- untary and involuntary culling of these sows. The
´ ´ debted to V.P. Ducrocq Station de Genetique Quan-
aim is, of course, to produce sows that have a long ´
titative et Appliquee – Institut National de la Re- life length due to good health and high production
cherche Agronomique, France for kindly placing rather than to long farrowing interval or delayed
The Survival Kit at our disposal and answering our slaughter after last weaning. Therefore, it would be
questions. The authors gratefully acknowledge E. interesting to account for voluntary and involuntary
Strandberg, Department of Animal Breeding and culling when estimating the heritability of longevity,
Genetic, SLU, Sweden, for useful comments on the as discussed by Strandberg 1997.
manuscript.
4. Conclusions References
