256 M
.H. Yazdi et al. Livestock Production Science 63 2000 255 –264
been given more attention in other farm animals, i.e. from 1986 through 1997, with at least one farrowing
dairy cattle e.g. Dekkers et al., 1994; Strandberg and were available in the data bank. The individual
¨ Solkner, 1996.
record of each animal included herd the herd that The effects of environmental factors, such as herd
the animal was born in, date of birth, date of first management and housing systems, on longevity of
farrowing f date, date of culling c date, age at ]
] sows in Sweden have been investigated by several
first farrowing age, litter size born alive at first authors Eliasson-Selling and Lundeheim, 1996;
farrowing f ls, litter size at last farrowing l ls, ]
] Olsson, 1996; Ringmar-Cederberg and Jonsson,
weight of gilt weight at field performance test 1996; Ringmar-Cederberg et al., 1997. Although
| 170 days of age, daily gain gain from birth until there is indirect selection due to leg weakness, low
field performance test, and side-fat thickness fat at fertility, etc. for longevity in all pig breeding
field performance test. To base conclusions on more programmes, to our knowledge, sow longevity is not
precise estimates of the herd 3 year year of birth included systematically in any such programmes.
factor, only sows from nucleus and multiplier herds One method for analysing longevity data is surviv-
with more than 50 sows that were born, raised and al analysis which allows inclusion of both censored
farrowing in the same herd were kept in the data set. and uncensored records of animals Cox, 1972. This
In total, sows from 24 herds were included. Animals approach relies on the concept of hazard, instanta-
with extreme values for age at first farrowing 250 neous or age-specific failure rate Lawless, 1982;
and 480 days and records of sires with less than 2 Lee, 1992 or, in the animal breeding context, the
daughters were excluded. After editing, the data set animal’s risk of being culled at time t, conditional
included records of 7967 sows with 5484 69 upon survival to time t Ducrocq, 1987; Ducrocq et
uncensored and 2483 31 censored incomplete al., 1988a. Proportional hazards models have been
records, longevity of animal is equal or longer than extended to incorporate time-dependent covariates
known period records. The l ls was expressed as a ]
Kalbfleisch and Prentice, 1980. Further, the inclu- deviation from the average of litter size for all sows
sion of random effects in the proportional hazards in that particular parity. A constant value of 12 was
models Smith and Quaas, 1984 and, particularly, added to each sow’s deviation in order to avoid
the extension of mixed survival models to include negative values. Classes of f ls with 0, 1 and 2 litters
] relationships between sires Ducrocq and Casella,
were grouped together owing to the very low fre- 1996 and development of computer programs Duc-
quencies of these classes. Also, classes of 16 and ¨
rocq and Solkner, 1994, 1998b, have made it higher were added to class 15. The same procedure
possible to estimate the genetic potential of sows for was used for l ls for observations in classes outside
] a longer productive life.
the range 3 to 19. The end of the recording period In this study we analysed longevity data of
was defined as the latest date of farrowing in each Landrace sows from Swedish nucleus and multiplier
herd for most herds, it was in February 1998. herds with the aim of revealing the most important
Censoring code and longevity were defined as in factors influencing longevity. Since the genetic
Table 1. make-up of sows in the herd is thought to have an
There were 250 herd 3 year hy combinations, important influence on culling rates, the ultimate
and the size of these classes varied from 1 to 151 goal was to estimate the genetic parameters for
average 32 sows. The distribution of sows across hy longevity.
was unbalanced: 22 of hy classes had no censored records, 50 had 3 censored, and 9 had no
uncensored animals. The data set comprised a total
2. Material and methods of 792 sires with an average of 8 daughters each
range 2–141. There were 297 sires lacking cen- 2.1. Data
sored daughters and 104 sires lacking uncensored daughters. Only 120 sires had more than 8 daughters
The data were obtained from the Swedish litter- average number of daughters per sire with un-
recording scheme managed by Quality Genetics. censored records.
Records of 19 820 Swedish Landrace sows, born It was assumed that herd management and culling
M .H. Yazdi et al. Livestock Production Science 63 2000 255 –264
257 Table 1
Definition of censoring code and longevity in the data set
a
Type of circumstance Censoring status
Longevity No. of observations
Animal culled, known culling date
uncensored c date2f date
5484 ]
] Animal alive at the end
of recording period censored
latest date2f date 1494
] Animal with missing
culling date censored
lf date2f date 556
] ]
Animal sold censored
date of sale2f date 433
]
a
c date5date of culling; f date5date of first farrowing; lf date5date of last farrowing. ]
] ]
policies were changed over time, and hy was tional hazards model well suited for efficient analy-
changed accordingly in some of the analyses. In ses of survival data Ducrocq et al., 1988a, was
these analyses changes in the hy effect were assumed used. Survival analysis was performed using The
¨ to occur on 1 April beginning of spring in Sweden
Survival Kit Ducrocq and Solkner, 1998b. The each year or every second year. Hence, hy was a
hazard function of a sow was modelled according to function of calendar time and handled as a time-
Ducrocq et al. 1988a: dependent effect. Number of observations, means
r 21
and standard deviations in the hy and sire classes, as ht, wt 5
lrlt exphwt9
u j well as ranges and means of other independent and
dependent longevity variables are presented in where ht, wt is the hazard function of an in-
Table 2. dividual depending on time t days from first farrow-
r 21
ing, and lrlt
is the baseline hazard function 2.2. Statistical methods
related to the ageing process which is assumed to follow a Weibull distribution, where
l and r are Survival of a sow, measured as length of prod-
location and shape parameters of the baseline uctive life, was considered as the dependent variable
Weibull hazard function. Vector u 9 5 hb9 u9j is a
longevity. The Weibull model, a type of propor- vector of fixed b and random u covariates with a
Table 2 Range, means6SD for the number of sows per herd–year class, and per sire, as well as range and mean6SD for other independent discrete
and continuous covariates and dependent longevity variables
a
Variable All observations
Censored Uncensored
Mean6SD Mean6SD
Range Mean6SD
Discrete class sows hy
1–151 31.9622.7
12.7616.5 24.2616.8
sows sire 2–141
8.3611.9 4.766.1
6.169.4 f ls
2–15 9.862.1
9.962.2 9.762.1
]
b
l ls 3–19
11.962.5 12.262.5
11.762.5 ]
Continuous longevity
1–2503 585.06453.9
512.26421.1 617.96464.3
age 274–480
364.6634.8 365.0635.5
364.4634.4 weight
85–130 98.768.5
98.269.2 98.968.1
gain 333–845
532.5661.3 539.3663.9
529.4659.8 fat
6–22 11.462.1
11.362.1 11.562.1
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
Since l ls is a deviation from the parity average, a constant of 12 was added to the mean values of l ls. ]
]
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
