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Genetic study of longevity in Swedish Landrace sows
Livestock Production Science 63 (2000) 255–264 www.elsevier.com / locate / livprodsci
Genetic study of longevity in Swedish Landrace sows M.H. Yazdi*, L. Rydhmer, E. Ringmar-Cederberg, N. Lundeheim, K. Johansson ¨ , S-755 97 Uppsala, Sweden Department of Animal Breeding and Genetics, Swedish University of Agricultural Sciences, Funbo-Lovsta Received 27 August 1998; received in revised form 8 June 1999; accepted 17 June 1999
Abstract Genetic parameters for length of productive life of Swedish Landrace sows were estimated using a proportional hazards model based on the Weibull distribution. Data were obtained from 7967 sows with at least one farrowing recorded, using the Swedish litter-recording scheme, from 1986 through 1998 from nucleus and multiplier herds. Effects of litter size at first and last farrowing, age at first farrowing, daily gain from birth to performance test ( | 170 days of age), weight, and side-fat thickness at performance test were included in the model as fixed and time-independent explanatory variables. The effect of herd 3 year (of birth) combinations was treated differently in several analyses (random versus fixed and time-independent versus time-dependent). The random effect of sires, incorporating full pedigree information, was taken into account in all analyses as the source of genetic variation (sire model). The length of productive lifetime (longevity) of sows was the dependent variable and was defined as the number of days from first farrowing until culling. The suitability of the Weibull model was assessed by evaluating the log-cumulative hazard versus the log of longevity (in days), which indicated that the Weibull model could be fitted to the data satisfactorily. All explanatory factors except daily gain and side-fat had a significant effect on longevity of sows in all analyses. The effect of herd 3 year had the largest influence among the factors included. Among the various analyses, estimates of heritability for longevity ranged from 0.109 to 0.268 on the original scale. The estimates were similar within each group of models, averaging 0.13 for the time-independent and 0.25 for the time-dependent herd 3 year effect in the model. Correlations between sires’ breeding value estimates were 0.98 between time-independent models and ranged from 0.96 to 0.98 among time-dependent models. It was concluded that there is genetic variation that can be utilised for increasing longevity by selection. 2000 Elsevier Science B.V. All rights reserved. Keywords: Heritability; Life length; Survival analysis; Swine; Weibull distribution
1. Introduction Longevity of sows summarises the effects of functional traits (functional longevity), defined as the ability to delay involuntary culling (Ducrocq and ¨ Solkner, 1998a), and of reproductive performance *Corresponding author. Present address: Institute of Ecology and Resource Management, University of Edinburgh, West Mains Road, Edinburgh EH9 3JG, Scotland, UK.
through the voluntary culling of sows with inferior fertility or a low capacity to produce piglets. Sow longevity is important to farmers owing to the high costs of replacement. Results of several studies have shown that long lifetime production and low culling rates in swine herds have substantial economic benefits (e.g. te Brake, 1986; Jalvingh et al., 1992). Thus, length of productive life (from first farrowing until culling) is a trait that has received increasing attention in swine breeding. This subject has also
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been given more attention in other farm animals, i.e. dairy cattle (e.g. Dekkers et al., 1994; Strandberg and ¨ Solkner, 1996). The effects of environmental factors, such as herd management and housing systems, on longevity of sows in Sweden have been investigated by several authors (Eliasson-Selling and Lundeheim, 1996; Olsson, 1996; Ringmar-Cederberg and Jonsson, 1996; Ringmar-Cederberg et al., 1997). Although there is indirect selection (due to leg weakness, low fertility, etc.) for longevity in all pig breeding programmes, to our knowledge, sow longevity is not included systematically in any such programmes. One method for analysing longevity data is survival analysis which allows inclusion of both censored and uncensored records of animals (Cox, 1972). This approach relies on the concept of hazard, instantaneous or age-specific failure rate (Lawless, 1982; Lee, 1992) or, in the animal breeding context, the animal’s risk of being culled at time t, conditional upon survival to time t (Ducrocq, 1987; Ducrocq et al., 1988a). Proportional hazards models have been extended to incorporate time-dependent covariates (Kalbfleisch and Prentice, 1980). Further, the inclusion of random effects in the proportional hazards models (Smith and Quaas, 1984) and, particularly, the extension of mixed survival models to include relationships between sires (Ducrocq and Casella, 1996) and development of computer programs (Duc¨ rocq and Solkner, 1994, 1998b), have made it possible to estimate the genetic potential of sows for a longer productive life. In this study we analysed longevity data of Landrace sows from Swedish nucleus and multiplier herds with the aim of revealing the most important factors influencing longevity. Since the genetic make-up of sows in the herd is thought to have an important influence on culling rates, the ultimate goal was to estimate the genetic parameters for longevity.
2. Material and methods
2.1. Data The data were obtained from the Swedish litterrecording scheme managed by Quality Genetics. Records of 19 820 Swedish Landrace sows, born
from 1986 through 1997, with at least one farrowing were available in the data bank. The individual record of each animal included herd (the herd that the animal was born in), date of birth, date of first farrowing (f]date), date of culling (c]date), age at first farrowing (age), litter size (born alive) at first farrowing (f]ls), litter size at last farrowing (l]ls), weight of gilt (weight) at field performance test ( | 170 days of age), daily gain (gain) from birth until field performance test, and side-fat thickness (fat) at field performance test. To base conclusions on more precise estimates of the herd 3 year (year of birth) factor, only sows from nucleus and multiplier herds with more than 50 sows that were born, raised and farrowing in the same herd were kept in the data set. In total, sows from 24 herds were included. Animals with extreme values for age at first farrowing ( # 250 and $ 480 days) and records of sires with less than 2 daughters were excluded. After editing, the data set included records of 7967 sows with 5484 (69%) uncensored and 2483 (31%) censored (incomplete records, longevity of animal is equal or longer than known period) records. The l]ls was expressed as a deviation from the average of litter size for all sows in that particular parity. A constant value of 12 was added to each sow’s deviation in order to avoid negative values. Classes of f]ls with 0, 1 and 2 litters were grouped together owing to the very low frequencies of these classes. Also, classes of 16 and higher were added to class 15. The same procedure was used for l]ls for observations in classes outside the range 3 to 19. The end of the recording period was defined as the latest date of farrowing in each herd (for most herds, it was in February 1998). Censoring code and longevity were defined as in Table 1. There were 250 herd 3 year (hy) combinations, and the size of these classes varied from 1 to 151 (average 32 sows). The distribution of sows across hy 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 of 792 sires with an average of 8 daughters each (range 2–141). There were 297 sires lacking censored daughters and 104 sires lacking uncensored daughters. Only 120 sires had more than 8 daughters (average number of daughters per sire) with uncensored records. It was assumed that herd management and culling
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Table 1 Definition of censoring code and longevity in the data set Type of circumstance Animal culled, known culling date Animal alive at the end of recording period Animal with missing culling date Animal sold
Censoring status
Longevity a
No. of observations
uncensored
c date2f date ] ]
5484
censored
latest date2f date ]
1494
censored censored
lf date2f date ] ] date of sale2f date ] a c date5date of culling; f date5date of first farrowing; lf date5date of last farrowing. ] ] ]
policies were changed over time, and hy was changed accordingly in some of the analyses. In these analyses changes in the hy effect were assumed to occur on 1 April (beginning of spring in Sweden) each year or every second year. Hence, hy was a function of calendar time and handled as a timedependent effect. Number of observations, means and standard deviations in the hy and sire classes, as well as ranges and means of other independent and dependent (longevity) variables are presented in Table 2.
2.2. Statistical methods Survival of a sow, measured as length of productive life, was considered as the dependent variable (longevity). The Weibull model, a type of propor-
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tional hazards model well suited for efficient analyses of survival data (Ducrocq et al., 1988a), was used. Survival analysis was performed using The ¨ Survival Kit (Ducrocq and Solkner, 1998b). The hazard function of a sow was modelled according to Ducrocq et al. (1988a): h(t, w(t)) 5 lr ( lt) r 21 exphw(t)9u j where h(t, w(t)) is the hazard function of an individual depending on time t (days from first farrowing), and lr ( lt) r 21 is the baseline hazard function (related to the ageing process) which is assumed to follow a Weibull distribution, where l and r are location and shape parameters of the baseline Weibull hazard function. Vector u 9 5 hb9 u9j is a 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 Variable a
All observations Range
Discrete class sows /hy sows / sire f ls ] l ls b ] Continuous longevity age weight gain fat a
Mean6SD
1–151 2–141 2–15 3–19
31.9622.7 8.3611.9 9.862.1 11.962.5
1–2503 274–480 85–130 333–845 6–22
585.06453.9 364.6634.8 98.768.5 532.5661.3 11.462.1
Censored Mean6SD
Uncensored Mean6SD
12.7616.5 4.766.1 9.962.2 12.262.5
24.2616.8 6.169.4 9.762.1 11.762.5
512.26421.1 365.0635.5 98.269.2 539.3663.9 11.362.1
617.96464.3 364.4634.4 98.968.1 529.4659.8 11.562.1
hy5herd3year 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. ] ]
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corresponding incidence matrix (possibly time-dependent) w(t)9 5 hx(t)9 z(t)9j. Several analyses were carried out with somewhat different models. The effects included in the model for all analyses were: f]ls and l]ls as class, fixed and time-independent covariates; age, weight, gain and fat as continuous, fixed and time-independent covariates; and finally sire as a class, random and time-independent covariate. The additive genetic relationship matrix of sires was incorporated in the analyses. The effect of hy summarizes effects of several factors (e.g. herd management, food supply), and the influence on culling rate might change over time. It is, however, difficult to foresee how often these changes occur and what is the appropriate length of time intervals. Therefore, results from the following models, when hy was treated differently in each model, were compared. FTI RTI FTD1 RTD1 FTD2 RTD2
fixed random fixed random fixed random
time-independent; time-independent; time-dependent time-dependent time-dependent time-dependent
(time (time (time (time
interval interval interval interval
of of of of
1 1 2 2
year); year); years); years).
The exponential part of the above models for effects of explanatory variables, either fixed or random, was as follows: hw(t)9 u j 5 hy j (t) 1 f]ls k 1 l]lsl 1 b 1 (age) 1 b 2 (weight) 1 b 3 (gain) 1 b 4 (fat) 1 s m
(1996) for more details of choosing the log-gamma distribution. The parameter g was either estimated or the hy effect was integrated out in the analysis. The additive genetic effects of sires were assumed to have a multivariate normal distribution, s q |MVN(0, A s 2s ), where subscript q is the number of sires, A is the relationship matrix between sires, and s 2s is the sire variance. The heritability of longevity was calculated from the sire variance component as a proportion of phenotypic variance of the Weibull distribution as described by Ducrocq and Casella (1996) on the logarithmic scale of length of productive life as h 2log 54s 2s /(p 2 / 61 s 2s ), where p 2 / 6 is the variance of the standard extreme value distribution (Lawless, 1982). The variance of hy (s 2hy ), which was estimated from the second moment (trigamma) of the log-gamma distribution (Lawless, 1982), was added to the denominator of the expression used for calculating h 2log when hy was considered as a random effect in the model. The calculation of heritability on the original scale of length of productive life (h 2ori ) was based on the description of Ducrocq (1998, personal communication) as h 2ori 54s 2s /([exph1 /r 3 n j] 2 3(p 2 / 61 s 2s )) where n 5 2Euler’s constant (the mean of the standard extreme value distribution)5 20.5772. The s 2hy was added to the denominator of the expression, as was done for the log scale, when hy was considered as a random effect in the model, and n was then calculated as n 5digamma(g )2log(g )2Euler’s constant, where digamma(g )2log(g ) is the first moment of the loggamma distribution.
where: 3. Results and discussion hy j (t) f lsk ] l lsl ] b 1 (age) b 2 (weight) b 3 (gain) b 4 (fat) sm
is is is is is is is is
the the the the the the the the
j th herd3year effect, th k first-farrowing litter-size effect, th l last-farrowing litter-size effect, partial regression coefficient on age, partial regression coefficient on weight, partial regression coefficient on gain, partial regression coefficient on fat, and th random additive genetic effect of the m sire.
The random effect of hy was assumed to follow a log-gamma distribution with parameter gamma (g ). See Ducrocq et al. (1988b) and Ducrocq and Casella
The average length of productive life was 617 days, which corresponds to an age of 2 years and 8 months at culling (Table 2). This is in accordance with the average life length of sows from French herds reported by Le Cozler et al. (1999). There was a wide range in the number of observations among the different hy classes, as well as the number of daughters per sire. Mean numbers of observations in corresponding classes were 32 and 8 for all observations. The Kaplan and Meier (1958) and baseline survivor curves as well as the baseline hazard curve
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are illustrated in Fig. 1. An increased risk of culling after weaning of the first three litters (around 40, 220 and 400 days on the longevity axis) is reflected in the Kaplan–Meier survivor curve. The parameters of the Weibull distribution, r and l, were very similar in the various analyses. The suitability of the Weibull model was assessed by evaluating the log-cumulative hazard plot (Fig. 2), log (2log S(t)) versus log(t), where S(t) and t are the Kaplan–Meier survivor function and number of days after first farrowing, respectively (Lawless, 1982). Because the relationship is almost a straight line, except for a short period after the first weaning when there was intensive culling, the Weibull model seems to fit the data well. Preliminary survival analyses were carried out to examine the confounding and interaction between fixed effects. No significant interactions were found between fixed effects. Further, age and weight were both regarded to be linearly related to longevity. To test the significance of different effects
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(covariates) a likelihood-ratio test was carried out for all models. Results from RTD1, in which hy was random and time-dependent with a time interval of 1 year, are presented in Table 3. The R 2 of Maddala (measure of proportion of variation explained by the model, see Schemper, 1992) increased significantly when f]ls, l]ls, age and weight were added. The additional changes were very small when adding gain and fat to the model, since the effects of gain and fat were not significant. Among the fixed covariates, l]ls had the most significant influence on risk of culling. Results from likelihood-ratio tests for significance of effects obtained from different models were similar concerning l]ls, weight, gain and fat. For age and f]ls the differences between models were larger, but the probabilities were always below 0.10). The effect of hy was highly significant ( p,0.001) when it was treated as a fixed effect (FTI, FTD1, FTD2). The estimated parameter of the log-gamma distribution of hy (g ), when treated as random,
Fig. 1. Survivor and hazard curves of sow longevity.
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Fig. 2. Graphical test of the Weibull assumption, S(t)5Kaplan–Meier estimate of the survivor function for the sows and t is days from first farrowing.
Table 3 Likelihood ratio test, including shape ( r ) and location ( l) parameters of Weibull distribution, when all covariates a added to model RTD1 b sequentially Covariate
d.f. (total)
x2
sire hy f ls ] l ls ] age weight gain fat
1455 271 284 300 301 302 303 304
1090.1 21.270 60.569 3.1443 5.0541 0.4304 0.7903
d.f.
13 16 1 1 1 1
Prob.
R 2 of Maddala
0.0678 0.0000 0.0762 0.0246 0.5118 0.3740
(RANDOM) (RANDOM) 0.1302 0.1368 0.1371 0.1377 0.1377 0.1378
a
hy5herd3year 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 coefficients for hy effects ranged from 21.737 to 1.141, which corresponds to relative culling rates (exphhyj) from 0.18 to 3.13. These coefficients imply that in the worst case, sows had three times higher risk of culling (probability of being culled) compared with sows in the average hy effect with a relative culling rate of 1. Also, sows in the worst hy class were eighteen times more likely to be culled than sows in the best hy class at any time. Since information on health status (leg weakness, udder
problems, etc.) was not included in this data set, it was impossible to determine exactly how important the health traits were in impairing longevity. However, these effects were implicitly the results of the herd management, which probably explains why hy had such a strong influence on culling in this data set. Le Cozler et al. (1999) also found that the effect of herd strongly affected longevity. The significance of the effect of f]ls was dependent on the model. However, it was significant at p,0.10 in all analyses. The effect of litter size at
M.H. Yazdi et al. / Livestock Production Science 63 (2000) 255 – 264
last farrowing (l]ls) was highly significant ( p,0.01) in all analyses. Estimates of the associated hazard coefficients and the relative culling rates (based on the average litter size of sows with uncensored observations) were very similar for all different models. Representative values for the hazard coefficient and the risk ratio (relative hazard or culling for an individual compared to the baseline hazard) generated by RTD1 are shown in Table 4. Although there was some fluctuations in the risk ratio between litter size classes, owing to a low number of observations at some levels, the risk ratio tended to decrease with increasing litter size for both f]ls and l]ls. The increased risk related to small litters was more pronounced for l]ls. Many farmers are of the opinion that a ‘too large’ first litter increases the risk of early culling; however, this could not be confirmed in the present study. Ringmar-Cederberg and Jonsson (1996) and Eliasson-Selling and Lundeheim (1996) all concluded that reproduction problems of the sow is the most important reason for culling. According to this study, small litters is an important indication
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of these problems. To include only the first and last litter size in the survival analysis is a simplification. Besides, the biological meaning of l]ls of censored sows can be questioned. Inclusion of information on the sow’s all parities as time-dependent covariate would give a better description of the relation between litter size and longevity. The effect of age at first farrowing was significant ( p,0.01) when hy was fixed in the model. Increased age at first farrowing increased the relative culling rate of sows. The hazard regression coefficient for age at first farrowing was 0.00160.0005 per day. A negative relation between age at first farrowing and life length has also been shown by Holder et al. (1995). This may partly be explained by the tendency for sows with a high age at puberty to show delayed oestrus after weaning (Sterning et al., 1998). The hazard regression coefficient for weight at performance test was 0.00460.002 per kg. A high weight at performance test could be a consequence of a high growth rate. Although Gueblez et al. ´ (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 (n unc ) of litter size at first farrowing (f ls) and last farrowing (l ls) from model RTD1 a ] ] Class level b f ls l ls ] ] Hazard coef. Risk ratio n unc Hazard coef. Risk ratio n unc 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
0.22360.244 0.42560.266 0.05560.182 0.23060.153 0.03960.069 0.15360.059 0.09660.050 0.00960.046 0.00060.000 0.02560.047 0.00160.051 0.00160.068 20.12160.098 20.06060.140 20.27760.083 20.47260.116 20.60360.201 20.39760.235
1.250 1.530 1.057 1.259 1.039 1.166 1.100 1.009 1.000 1.026 1.001 1.001 0.886 0.942 0.757 0.624 0.547 0.672
18 15 33 47 276 416 688 932 1092 861 639 290 121 56 180 85 26 19
0.19060.200 0.06560.231 20.19460.157 0.02960.135 20.20260.097 0.03460.073 0.00060.062 0.03360.052 20.06860.049 0.00060.000 20.05860.049 20.14660.053 20.13060.063
1.209 1.067 0.824 1.030 0.817 1.034 1.000 1.034 0.934 1.000 0.943 0.865 0.878
27 20 45 62 126 252 387 656 836 924 849 626 364
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. ] ]
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negative relation between growth rate and longevity, growth rate itself had no significant influence on longevity in this study. Estimates of sire variance, heritability and parameters of the Weibull distribution obtained from different models are presented in Table 5. Estimates of sire variances and heritabilities from FTI and RTI were similar. The sire variances obtained when hy was treated as a time-dependent variable ranged from 0.04 to 0.05, which were higher than those obtained when hy was time-independent (0.02 and 0.03). The increase in sire variances reflects the characteristics of genetic origin that were carried over from year to year since 1986 (the first year in this investigation). In other words, due to the large effect of hy on the longevity of sows and probably invalidity of the proportional hazards throughout the time range, the effects of sire were masked by the hy effect and, consequently, the sire variances became low when hy was time-independent. The resulting heritabilities from models with hy as a time-dependent variable were also higher (on average, 0.25 on original scales) than estimated heritabilities when hy was a timeindependent variable (on average, 0.13 on original scales). Also, the decrease in the sire variances observed when the time-dependent hy was changed from fixed to random indicates that differences in the longevity of sows related to hy had partly genetic origin and modified the variability of longevity due to sire. The length of the time interval (1 versus 2 years) had no significant influence on the sire
variance. It seems that model RTD1 describes data most properly. Heritability on the original scale represents the heritability of length of productive life when all daughters of sires have uncensored records (Ducrocq, 1999). Tholen et al. (1996) estimated the heritability for stayability (the probability of the sow surviving in the herd from parity 1 to parity 4, an all-or-none ´ trait) to be 0.08 and Lopez-Serrano et al. (2000) estimated the heritability for stayability from parity 1 to 3 to be 0.10. Krieter (1995) estimated the heritability of sow longevity, measured as age at culling, to be 0.12. The heritability for the length of productive life in dairy cattle has been estimated to be less than 0.09 on a log scale (Ducrocq et al., 1988b; Vollema and Groen, 1996; Vollema and Groen, 1997). The relative culling rate for daughters of sires ranged from 0.65 to 1.27, using model RTD1. This corresponds to the lowest and highest risk of culling for daughters of the best and worst sires, respectively, compared with daughters of an average sire which have a relative risk of culling equal to 1. Daughters of the worst sires thus had two times higher risk of culling compared with daughters of the best sires. The correlation between breeding value of sires from FTI and that of sires from RTI was 0.98. The corresponding correlation between breeding values from different models when hy was a timedependent variable ranged from 0.96 to 0.99. The correlations between breeding values of sires from
Table 5 Estimates of sire variance (s 2s ), shape ( r ) and location ( l) parameters of the Weibull distribution, and heritability on log (h 2log ) and original (h 2ori ) scales of length of productive life (longevity) Models a,b
s s2
r
lc
2 h log
h 2ori
FTI RTI FTD1 RTD1 FTD2 RTD2
0.02060.011 0.02660.012 0.04560.013 0.03760.012 0.04960.014 0.04760.013
1.40060.016 1.36760.015 1.38860.018 1.36260.016 1.38660.017 1.35960.016
0.237 0.227 0.251 0.227 0.270 0.220
0.048 0.056 0.107 0.075 0.116 0.098
0.109 0.149 0.246 0.212 0.267 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.
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time-dependent models (FTI and RTI) and that of sires from time-dependent models (FTD1, RTD1, FTD2, RTD2) ranged from 0.87 to 0.90. All standard errors of correlations were very similar (0.001). This similarity between the evaluations of sires from different models confirms the similarity of the sire variance components obtained for the different models within time-independent and dependent hy effects. Due to many missing observations concerning the cause of culling and date of mating and weaning it was impossible to directly distinguish between voluntary and involuntary culling of these sows. The aim is, of course, to produce sows that have a long life length due to good health and high production rather than to long farrowing interval or delayed slaughter after last weaning. Therefore, it would be interesting to account for voluntary and involuntary culling when estimating the heritability of longevity, as discussed by Strandberg (1997).
4. Conclusions Among the factors evaluated in the model, hy had the largest influence on the risk of culling of sows. Although litter size at both first and last farrowing had significant effects on risk of culling, the latter had a stronger effect on the risk ratio. The effects of age at first farrowing and weight of gilt at performance test were significant, but not large. The increase in the sire variance and heritability of longevity when hy was time-dependent compared to time-independent indicates that the records of sows were more thoroughly corrected for the effect of hy when it was treated as a time-dependent variable. Obviously, the choice of model is very important when analysing survival data and, consequently, has very strong influence on the results and conclusion. The moderate estimates of heritability (on the original scale when there is no censoring) in these investigations indicate that there is genetic variation among the animals that can be utilised for improving longevity in the Swedish Landrace breed. However, a breeding evaluation of sow longevity demands a high quality data bank that includes censoring records and dates of each mating, farrowing, weaning, exchange between herds and culling. A
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more precise registration of the cause of culling would also increase the possibility to include sow longevity in the breeding evaluation.
Acknowledgements The authors are very grateful to The Swedish Farmers’ Foundation for Agricultural Research for financially supporting this study. Quality Genetics (the Swedish pig-breeding organisation) is acknowledged for providing the data. The authors are in´ ´ debted to V.P. Ducrocq (Station de Genetique Quan´ titative et Appliquee – Institut National de la Recherche Agronomique, France) for kindly placing The Survival Kit at our disposal and answering our questions. The authors gratefully acknowledge E. Strandberg, Department of Animal Breeding and Genetic, SLU, Sweden, for useful comments on the manuscript.
References Cox, D.R., 1972. Regression models and life table (with discussion). J. Royal Stat. Soc., Series B 34, 187–220. Dekkers, J.C.M., Jairath, L.K., Lawrence, B.H., 1994. Relationships between sire genetic evaluations for conformation and functional herd life of daughters. J. Dairy Sci. 77, 844–854. Ducrocq, V.P., 1987. An analysis of length of productive life in dairy cattle, Cornell University, Ithaca, NY, USA, Ph.D. dissertation. Ducrocq, V.P., 1999. Two years of experience with the French genetic evaluation of dairy bulls on production-adjusted longevity of their daughters. In: Proceedings of International Workshop on Genetic Improvement of Functional Traits in Cattle, Jouy-en-Josas, France, May 9–11, 1999. Ducrocq, V.P., Casella, G., 1996. A Bayesian analysis of mixed survival models. Genet. Sel. Evol. 28, 505–529. Ducrocq, V.P., Quaas, R.L., Pollak, E.J., Casella, G., 1988a. Length of productive life of dairy cows. 1. Justification of a Weibull model. J. Dairy Sci. 71, 3061–3070. Ducrocq, V.P., Quaas, R.L., Pollak, E.J., Casella, G., 1988b. Length of productive life of dairy cows. 2. Variance component estimation and sire evaluation. J. Dairy Sci. 71, 3071–3079. ¨ Ducrocq, V.P., Solkner, J., 1994. ‘‘The Survival Kit’’, a FORTRAN package for the analysis of survival data. In: Proceedings of 5th World Congress on Genetics Applied to Livestock Production, Vol. 22, Univ. of Guelph, Ontario, Canada, pp. 51–52. ¨ Ducrocq, V.P., Solkner, J., 1998a. Implementation of a routine breeding value evaluation for longevity of dairy cows using
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survival analysis technique. In: Proceedings of 6th Word Congress on Genetics Applied to Livestock Production, Vol. 23, Univ. of New-England, Armidale, Australia, pp. 359–362. ¨ Ducrocq, V., Solkner, J., 1998b. ‘‘The Survival Kit V3.0’’, a package for large analyses of survival data. In: Proceedings of 6th World Congress on Genetics Applied to Livestock Production, Vol. 27, Univ. of New-England, Armidale, Australia, pp. 447–450. Eliasson-Selling, L., Lundeheim, N., 1996. Longevity of sows in Swedish sow pools. In: Report 111, Proceedings of NJFseminar no. 265. Longevity of sows, Research Centre Foulum, Denmark. ˆ Gueblez, R., Gestin, J.M., Le Henaff, G., 1985. Incidence de l’age ´ ` reproducet de l’epaisseur de lardorsal a` 100 kg sur la carriere ´ de la Recherche Porcine tive de truies Large White. Journees en France 17, 113–120. Holder, R.B., Lamberson, W.R., Bates, R.O., Safranski, T.J., 1995. Lifetime productivity in gilts previously selected for decreased age at puberty. Anim. Sci. 61, 115–121. Jalvingh, A.W., Dijkhuizen, A.A., van Arendonk, J.A.M., Brascamp, E.W., 1992. An economic comparison of management strategies on reproduction and replacement in sow herds using a dynamic probabilistic model. Lives. Prod. Sci. 32, 331–350. Kalbfleisch, J.D., Prentice, R.L., 1980. The Statistical Analysis of Failure Time Data. John Wiley and Sons, New York, NY. Kaplan, E.L., Meier, P., 1958. Nonparametric estimation from incomplete observations. J. Amer. Stat. Ass. 53, 457–481. ¨ ¨ die Nutzungsdauer von Krieter, J., 1995. Zuchtwertschatzung fur ¨ genetisch statistische Methoden in Sauen. 70th Ausschuss fur ¨ Zuchtungskunde, ¨ der Tierzucht, Deutsche Gesellschaft fur Germany. Lawless, J., 1982. Statistical Models and Methods For Lifetime Data. John Wiley and Sons, New York, NY. Le Cozler, Y., Dagorn, J., Lindberg, J.E., Aumaitre, A., Dourmad, J.Y., 1999. Effect of age at first farrowing and herd management on long-term productivity of sows. Livest. Prod. Sci. 53, 135–142. Lee, E.T., 1992. Statistical Methods For Survival Data Analysis, 2nd ed. John Wiley and Sons, New York, NY. ´ Lopez-Serrano, M., Reinsch, N., Looft, H., Kalm, E., 2000. Genetic correlations of growth, backfat thickness and exterior with stayability in Large White and Landrace sows (in press). Olsson, A.C., 1996. Longevity and causes of culling of sow,
Comparative studies in two housing systems for sows in gestation. In: Report 111, Proceedings of NJF-seminar no. 265. Longevity of sows, Research Centre Foulum, Denmark. Ringmar-Cederberg, E., Jonsson, L., 1996. Sow culling in Sweden. In: Report 111, Proceedings of NJF Seminar no. 265. Longevity of sows, Research Centre Foulum, Denmark. Ringmar-Cederberg, E., Johansson, K., Lundeheim, N., Rydhmer, L., 1997. Longevity of Large White and Swedish Landrace Sows. In: 48 th annual meeting of the EAAP, Vienna, Austria, Vol. book no. 3, p. 30. Schemper, M., 1992. Further results on the explained variation in proportional hazards regression. Biometrika 79, 202–204. Smith, S.P., Quaas, R.L., 1984. Productive life span of bull progeny groups: failure time analysis. J. Dairy Sci. 67, 2999– 3007. Sterning, M., Rydhmer, L., Eliasson-Selling, L., 1998. Relationship between age at puberty and interval from weaning to oestrus and between oestrus signs at puberty and after the first weaning in pigs. J. Anim. Sci. 76, 353–359. Strandberg, E., 1997. Breeding strategies to improve longevity. In: 48th Annual Meeting of the EAAP, Vienna, Austria, p. 28. ¨ Strandberg, E., Solkner, J., 1996. Breeding for longevity and survival in dairy cattle. In: Proceedings of International Workshop on Genetic Improvement of Functional Traits in Cattle. Gembloux, Belgium, Interbull Bulletin, Vol. No. 12, pp. 111– 119. te Brake, J.H.A., 1986. Culling of sows and the profitability of piglet production. Netherlands J. Agri. Sci. 34, 427–435. Tholen, E., Bunter, K.L., Hermesch, S., Graser, H.-U., 1996. The genetic foundation of fitness and reproduction traits in Australian pig populations. Relationships between weaning to conception interval, farrowing interval, stayability, and other common reproduction and production traits. Aust. J. Agric. Res. 47, 1275–1290. Vollema, A.R., Groen, A.F., 1996. Genetic parameters of longevity traits of an upgrading population of dairy cattle. J. Dairy Sci. 79, 2261–2267. Vollema, A.R., Groen, A.F., 1997. Longevity on small and large dairy cattle farms: A comparison of phenotypic averages, REML breeding values, and survival analysis breeding values, 48 th annual meeting of the EAAP, Vienna, Austria, Vol. book no. 3, EAAP, 31.
Genetic study of longevity in Swedish Landrace sows M.H. Yazdi*, L. Rydhmer, E. Ringmar-Cederberg, N. Lundeheim, K. Johansson ¨ , S-755 97 Uppsala, Sweden Department of Animal Breeding and Genetics, Swedish University of Agricultural Sciences, Funbo-Lovsta Received 27 August 1998; received in revised form 8 June 1999; accepted 17 June 1999
Abstract Genetic parameters for length of productive life of Swedish Landrace sows were estimated using a proportional hazards model based on the Weibull distribution. Data were obtained from 7967 sows with at least one farrowing recorded, using the Swedish litter-recording scheme, from 1986 through 1998 from nucleus and multiplier herds. Effects of litter size at first and last farrowing, age at first farrowing, daily gain from birth to performance test ( | 170 days of age), weight, and side-fat thickness at performance test were included in the model as fixed and time-independent explanatory variables. The effect of herd 3 year (of birth) combinations was treated differently in several analyses (random versus fixed and time-independent versus time-dependent). The random effect of sires, incorporating full pedigree information, was taken into account in all analyses as the source of genetic variation (sire model). The length of productive lifetime (longevity) of sows was the dependent variable and was defined as the number of days from first farrowing until culling. The suitability of the Weibull model was assessed by evaluating the log-cumulative hazard versus the log of longevity (in days), which indicated that the Weibull model could be fitted to the data satisfactorily. All explanatory factors except daily gain and side-fat had a significant effect on longevity of sows in all analyses. The effect of herd 3 year had the largest influence among the factors included. Among the various analyses, estimates of heritability for longevity ranged from 0.109 to 0.268 on the original scale. The estimates were similar within each group of models, averaging 0.13 for the time-independent and 0.25 for the time-dependent herd 3 year effect in the model. Correlations between sires’ breeding value estimates were 0.98 between time-independent models and ranged from 0.96 to 0.98 among time-dependent models. It was concluded that there is genetic variation that can be utilised for increasing longevity by selection. 2000 Elsevier Science B.V. All rights reserved. Keywords: Heritability; Life length; Survival analysis; Swine; Weibull distribution
1. Introduction Longevity of sows summarises the effects of functional traits (functional longevity), defined as the ability to delay involuntary culling (Ducrocq and ¨ Solkner, 1998a), and of reproductive performance *Corresponding author. Present address: Institute of Ecology and Resource Management, University of Edinburgh, West Mains Road, Edinburgh EH9 3JG, Scotland, UK.
through the voluntary culling of sows with inferior fertility or a low capacity to produce piglets. Sow longevity is important to farmers owing to the high costs of replacement. Results of several studies have shown that long lifetime production and low culling rates in swine herds have substantial economic benefits (e.g. te Brake, 1986; Jalvingh et al., 1992). Thus, length of productive life (from first farrowing until culling) is a trait that has received increasing attention in swine breeding. This subject has also
0301-6226 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0301-6226( 99 )00133-5
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been given more attention in other farm animals, i.e. dairy cattle (e.g. Dekkers et al., 1994; Strandberg and ¨ Solkner, 1996). The effects of environmental factors, such as herd management and housing systems, on longevity of sows in Sweden have been investigated by several authors (Eliasson-Selling and Lundeheim, 1996; Olsson, 1996; Ringmar-Cederberg and Jonsson, 1996; Ringmar-Cederberg et al., 1997). Although there is indirect selection (due to leg weakness, low fertility, etc.) for longevity in all pig breeding programmes, to our knowledge, sow longevity is not included systematically in any such programmes. One method for analysing longevity data is survival analysis which allows inclusion of both censored and uncensored records of animals (Cox, 1972). This approach relies on the concept of hazard, instantaneous or age-specific failure rate (Lawless, 1982; Lee, 1992) or, in the animal breeding context, the animal’s risk of being culled at time t, conditional upon survival to time t (Ducrocq, 1987; Ducrocq et al., 1988a). Proportional hazards models have been extended to incorporate time-dependent covariates (Kalbfleisch and Prentice, 1980). Further, the inclusion of random effects in the proportional hazards models (Smith and Quaas, 1984) and, particularly, the extension of mixed survival models to include relationships between sires (Ducrocq and Casella, 1996) and development of computer programs (Duc¨ rocq and Solkner, 1994, 1998b), have made it possible to estimate the genetic potential of sows for a longer productive life. In this study we analysed longevity data of Landrace sows from Swedish nucleus and multiplier herds with the aim of revealing the most important factors influencing longevity. Since the genetic make-up of sows in the herd is thought to have an important influence on culling rates, the ultimate goal was to estimate the genetic parameters for longevity.
2. Material and methods
2.1. Data The data were obtained from the Swedish litterrecording scheme managed by Quality Genetics. Records of 19 820 Swedish Landrace sows, born
from 1986 through 1997, with at least one farrowing were available in the data bank. The individual record of each animal included herd (the herd that the animal was born in), date of birth, date of first farrowing (f]date), date of culling (c]date), age at first farrowing (age), litter size (born alive) at first farrowing (f]ls), litter size at last farrowing (l]ls), weight of gilt (weight) at field performance test ( | 170 days of age), daily gain (gain) from birth until field performance test, and side-fat thickness (fat) at field performance test. To base conclusions on more precise estimates of the herd 3 year (year of birth) factor, only sows from nucleus and multiplier herds with more than 50 sows that were born, raised and farrowing in the same herd were kept in the data set. In total, sows from 24 herds were included. Animals with extreme values for age at first farrowing ( # 250 and $ 480 days) and records of sires with less than 2 daughters were excluded. After editing, the data set included records of 7967 sows with 5484 (69%) uncensored and 2483 (31%) censored (incomplete records, longevity of animal is equal or longer than known period) records. The l]ls was expressed as a deviation from the average of litter size for all sows in that particular parity. A constant value of 12 was added to each sow’s deviation in order to avoid negative values. Classes of f]ls with 0, 1 and 2 litters were grouped together owing to the very low frequencies of these classes. Also, classes of 16 and higher were added to class 15. The same procedure was used for l]ls for observations in classes outside the range 3 to 19. The end of the recording period was defined as the latest date of farrowing in each herd (for most herds, it was in February 1998). Censoring code and longevity were defined as in Table 1. There were 250 herd 3 year (hy) combinations, and the size of these classes varied from 1 to 151 (average 32 sows). The distribution of sows across hy 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 of 792 sires with an average of 8 daughters each (range 2–141). There were 297 sires lacking censored daughters and 104 sires lacking uncensored daughters. Only 120 sires had more than 8 daughters (average number of daughters per sire) with uncensored records. It was assumed that herd management and culling
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Table 1 Definition of censoring code and longevity in the data set Type of circumstance Animal culled, known culling date Animal alive at the end of recording period Animal with missing culling date Animal sold
Censoring status
Longevity a
No. of observations
uncensored
c date2f date ] ]
5484
censored
latest date2f date ]
1494
censored censored
lf date2f date ] ] date of sale2f date ] a c date5date of culling; f date5date of first farrowing; lf date5date of last farrowing. ] ] ]
policies were changed over time, and hy was changed accordingly in some of the analyses. In these analyses changes in the hy effect were assumed to occur on 1 April (beginning of spring in Sweden) each year or every second year. Hence, hy was a function of calendar time and handled as a timedependent effect. Number of observations, means and standard deviations in the hy and sire classes, as well as ranges and means of other independent and dependent (longevity) variables are presented in Table 2.
2.2. Statistical methods Survival of a sow, measured as length of productive life, was considered as the dependent variable (longevity). The Weibull model, a type of propor-
556 433
tional hazards model well suited for efficient analyses of survival data (Ducrocq et al., 1988a), was used. Survival analysis was performed using The ¨ Survival Kit (Ducrocq and Solkner, 1998b). The hazard function of a sow was modelled according to Ducrocq et al. (1988a): h(t, w(t)) 5 lr ( lt) r 21 exphw(t)9u j where h(t, w(t)) is the hazard function of an individual depending on time t (days from first farrowing), and lr ( lt) r 21 is the baseline hazard function (related to the ageing process) which is assumed to follow a Weibull distribution, where l and r are location and shape parameters of the baseline Weibull hazard function. Vector u 9 5 hb9 u9j is a 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 Variable a
All observations Range
Discrete class sows /hy sows / sire f ls ] l ls b ] Continuous longevity age weight gain fat a
Mean6SD
1–151 2–141 2–15 3–19
31.9622.7 8.3611.9 9.862.1 11.962.5
1–2503 274–480 85–130 333–845 6–22
585.06453.9 364.6634.8 98.768.5 532.5661.3 11.462.1
Censored Mean6SD
Uncensored Mean6SD
12.7616.5 4.766.1 9.962.2 12.262.5
24.2616.8 6.169.4 9.762.1 11.762.5
512.26421.1 365.0635.5 98.269.2 539.3663.9 11.362.1
617.96464.3 364.4634.4 98.968.1 529.4659.8 11.562.1
hy5herd3year 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. ] ]
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258
corresponding incidence matrix (possibly time-dependent) w(t)9 5 hx(t)9 z(t)9j. Several analyses were carried out with somewhat different models. The effects included in the model for all analyses were: f]ls and l]ls as class, fixed and time-independent covariates; age, weight, gain and fat as continuous, fixed and time-independent covariates; and finally sire as a class, random and time-independent covariate. The additive genetic relationship matrix of sires was incorporated in the analyses. The effect of hy summarizes effects of several factors (e.g. herd management, food supply), and the influence on culling rate might change over time. It is, however, difficult to foresee how often these changes occur and what is the appropriate length of time intervals. Therefore, results from the following models, when hy was treated differently in each model, were compared. FTI RTI FTD1 RTD1 FTD2 RTD2
fixed random fixed random fixed random
time-independent; time-independent; time-dependent time-dependent time-dependent time-dependent
(time (time (time (time
interval interval interval interval
of of of of
1 1 2 2
year); year); years); years).
The exponential part of the above models for effects of explanatory variables, either fixed or random, was as follows: hw(t)9 u j 5 hy j (t) 1 f]ls k 1 l]lsl 1 b 1 (age) 1 b 2 (weight) 1 b 3 (gain) 1 b 4 (fat) 1 s m
(1996) for more details of choosing the log-gamma distribution. The parameter g was either estimated or the hy effect was integrated out in the analysis. The additive genetic effects of sires were assumed to have a multivariate normal distribution, s q |MVN(0, A s 2s ), where subscript q is the number of sires, A is the relationship matrix between sires, and s 2s is the sire variance. The heritability of longevity was calculated from the sire variance component as a proportion of phenotypic variance of the Weibull distribution as described by Ducrocq and Casella (1996) on the logarithmic scale of length of productive life as h 2log 54s 2s /(p 2 / 61 s 2s ), where p 2 / 6 is the variance of the standard extreme value distribution (Lawless, 1982). The variance of hy (s 2hy ), which was estimated from the second moment (trigamma) of the log-gamma distribution (Lawless, 1982), was added to the denominator of the expression used for calculating h 2log when hy was considered as a random effect in the model. The calculation of heritability on the original scale of length of productive life (h 2ori ) was based on the description of Ducrocq (1998, personal communication) as h 2ori 54s 2s /([exph1 /r 3 n j] 2 3(p 2 / 61 s 2s )) where n 5 2Euler’s constant (the mean of the standard extreme value distribution)5 20.5772. The s 2hy was added to the denominator of the expression, as was done for the log scale, when hy was considered as a random effect in the model, and n was then calculated as n 5digamma(g )2log(g )2Euler’s constant, where digamma(g )2log(g ) is the first moment of the loggamma distribution.
where: 3. Results and discussion hy j (t) f lsk ] l lsl ] b 1 (age) b 2 (weight) b 3 (gain) b 4 (fat) sm
is is is is is is is is
the the the the the the the the
j th herd3year effect, th k first-farrowing litter-size effect, th l last-farrowing litter-size effect, partial regression coefficient on age, partial regression coefficient on weight, partial regression coefficient on gain, partial regression coefficient on fat, and th random additive genetic effect of the m sire.
The random effect of hy was assumed to follow a log-gamma distribution with parameter gamma (g ). See Ducrocq et al. (1988b) and Ducrocq and Casella
The average length of productive life was 617 days, which corresponds to an age of 2 years and 8 months at culling (Table 2). This is in accordance with the average life length of sows from French herds reported by Le Cozler et al. (1999). There was a wide range in the number of observations among the different hy classes, as well as the number of daughters per sire. Mean numbers of observations in corresponding classes were 32 and 8 for all observations. The Kaplan and Meier (1958) and baseline survivor curves as well as the baseline hazard curve
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are illustrated in Fig. 1. An increased risk of culling after weaning of the first three litters (around 40, 220 and 400 days on the longevity axis) is reflected in the Kaplan–Meier survivor curve. The parameters of the Weibull distribution, r and l, were very similar in the various analyses. The suitability of the Weibull model was assessed by evaluating the log-cumulative hazard plot (Fig. 2), log (2log S(t)) versus log(t), where S(t) and t are the Kaplan–Meier survivor function and number of days after first farrowing, respectively (Lawless, 1982). Because the relationship is almost a straight line, except for a short period after the first weaning when there was intensive culling, the Weibull model seems to fit the data well. Preliminary survival analyses were carried out to examine the confounding and interaction between fixed effects. No significant interactions were found between fixed effects. Further, age and weight were both regarded to be linearly related to longevity. To test the significance of different effects
259
(covariates) a likelihood-ratio test was carried out for all models. Results from RTD1, in which hy was random and time-dependent with a time interval of 1 year, are presented in Table 3. The R 2 of Maddala (measure of proportion of variation explained by the model, see Schemper, 1992) increased significantly when f]ls, l]ls, age and weight were added. The additional changes were very small when adding gain and fat to the model, since the effects of gain and fat were not significant. Among the fixed covariates, l]ls had the most significant influence on risk of culling. Results from likelihood-ratio tests for significance of effects obtained from different models were similar concerning l]ls, weight, gain and fat. For age and f]ls the differences between models were larger, but the probabilities were always below 0.10). The effect of hy was highly significant ( p,0.001) when it was treated as a fixed effect (FTI, FTD1, FTD2). The estimated parameter of the log-gamma distribution of hy (g ), when treated as random,
Fig. 1. Survivor and hazard curves of sow longevity.
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Fig. 2. Graphical test of the Weibull assumption, S(t)5Kaplan–Meier estimate of the survivor function for the sows and t is days from first farrowing.
Table 3 Likelihood ratio test, including shape ( r ) and location ( l) parameters of Weibull distribution, when all covariates a added to model RTD1 b sequentially Covariate
d.f. (total)
x2
sire hy f ls ] l ls ] age weight gain fat
1455 271 284 300 301 302 303 304
1090.1 21.270 60.569 3.1443 5.0541 0.4304 0.7903
d.f.
13 16 1 1 1 1
Prob.
R 2 of Maddala
0.0678 0.0000 0.0762 0.0246 0.5118 0.3740
(RANDOM) (RANDOM) 0.1302 0.1368 0.1371 0.1377 0.1377 0.1378
a
hy5herd3year 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 coefficients for hy effects ranged from 21.737 to 1.141, which corresponds to relative culling rates (exphhyj) from 0.18 to 3.13. These coefficients imply that in the worst case, sows had three times higher risk of culling (probability of being culled) compared with sows in the average hy effect with a relative culling rate of 1. Also, sows in the worst hy class were eighteen times more likely to be culled than sows in the best hy class at any time. Since information on health status (leg weakness, udder
problems, etc.) was not included in this data set, it was impossible to determine exactly how important the health traits were in impairing longevity. However, these effects were implicitly the results of the herd management, which probably explains why hy had such a strong influence on culling in this data set. Le Cozler et al. (1999) also found that the effect of herd strongly affected longevity. The significance of the effect of f]ls was dependent on the model. However, it was significant at p,0.10 in all analyses. The effect of litter size at
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last farrowing (l]ls) was highly significant ( p,0.01) in all analyses. Estimates of the associated hazard coefficients and the relative culling rates (based on the average litter size of sows with uncensored observations) were very similar for all different models. Representative values for the hazard coefficient and the risk ratio (relative hazard or culling for an individual compared to the baseline hazard) generated by RTD1 are shown in Table 4. Although there was some fluctuations in the risk ratio between litter size classes, owing to a low number of observations at some levels, the risk ratio tended to decrease with increasing litter size for both f]ls and l]ls. The increased risk related to small litters was more pronounced for l]ls. Many farmers are of the opinion that a ‘too large’ first litter increases the risk of early culling; however, this could not be confirmed in the present study. Ringmar-Cederberg and Jonsson (1996) and Eliasson-Selling and Lundeheim (1996) all concluded that reproduction problems of the sow is the most important reason for culling. According to this study, small litters is an important indication
261
of these problems. To include only the first and last litter size in the survival analysis is a simplification. Besides, the biological meaning of l]ls of censored sows can be questioned. Inclusion of information on the sow’s all parities as time-dependent covariate would give a better description of the relation between litter size and longevity. The effect of age at first farrowing was significant ( p,0.01) when hy was fixed in the model. Increased age at first farrowing increased the relative culling rate of sows. The hazard regression coefficient for age at first farrowing was 0.00160.0005 per day. A negative relation between age at first farrowing and life length has also been shown by Holder et al. (1995). This may partly be explained by the tendency for sows with a high age at puberty to show delayed oestrus after weaning (Sterning et al., 1998). The hazard regression coefficient for weight at performance test was 0.00460.002 per kg. A high weight at performance test could be a consequence of a high growth rate. Although Gueblez et al. ´ (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 (n unc ) of litter size at first farrowing (f ls) and last farrowing (l ls) from model RTD1 a ] ] Class level b f ls l ls ] ] Hazard coef. Risk ratio n unc Hazard coef. Risk ratio n unc 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
0.22360.244 0.42560.266 0.05560.182 0.23060.153 0.03960.069 0.15360.059 0.09660.050 0.00960.046 0.00060.000 0.02560.047 0.00160.051 0.00160.068 20.12160.098 20.06060.140 20.27760.083 20.47260.116 20.60360.201 20.39760.235
1.250 1.530 1.057 1.259 1.039 1.166 1.100 1.009 1.000 1.026 1.001 1.001 0.886 0.942 0.757 0.624 0.547 0.672
18 15 33 47 276 416 688 932 1092 861 639 290 121 56 180 85 26 19
0.19060.200 0.06560.231 20.19460.157 0.02960.135 20.20260.097 0.03460.073 0.00060.062 0.03360.052 20.06860.049 0.00060.000 20.05860.049 20.14660.053 20.13060.063
1.209 1.067 0.824 1.030 0.817 1.034 1.000 1.034 0.934 1.000 0.943 0.865 0.878
27 20 45 62 126 252 387 656 836 924 849 626 364
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. ] ]
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negative relation between growth rate and longevity, growth rate itself had no significant influence on longevity in this study. Estimates of sire variance, heritability and parameters of the Weibull distribution obtained from different models are presented in Table 5. Estimates of sire variances and heritabilities from FTI and RTI were similar. The sire variances obtained when hy was treated as a time-dependent variable ranged from 0.04 to 0.05, which were higher than those obtained when hy was time-independent (0.02 and 0.03). The increase in sire variances reflects the characteristics of genetic origin that were carried over from year to year since 1986 (the first year in this investigation). In other words, due to the large effect of hy on the longevity of sows and probably invalidity of the proportional hazards throughout the time range, the effects of sire were masked by the hy effect and, consequently, the sire variances became low when hy was time-independent. The resulting heritabilities from models with hy as a time-dependent variable were also higher (on average, 0.25 on original scales) than estimated heritabilities when hy was a timeindependent variable (on average, 0.13 on original scales). Also, the decrease in the sire variances observed when the time-dependent hy was changed from fixed to random indicates that differences in the longevity of sows related to hy had partly genetic origin and modified the variability of longevity due to sire. The length of the time interval (1 versus 2 years) had no significant influence on the sire
variance. It seems that model RTD1 describes data most properly. Heritability on the original scale represents the heritability of length of productive life when all daughters of sires have uncensored records (Ducrocq, 1999). Tholen et al. (1996) estimated the heritability for stayability (the probability of the sow surviving in the herd from parity 1 to parity 4, an all-or-none ´ trait) to be 0.08 and Lopez-Serrano et al. (2000) estimated the heritability for stayability from parity 1 to 3 to be 0.10. Krieter (1995) estimated the heritability of sow longevity, measured as age at culling, to be 0.12. The heritability for the length of productive life in dairy cattle has been estimated to be less than 0.09 on a log scale (Ducrocq et al., 1988b; Vollema and Groen, 1996; Vollema and Groen, 1997). The relative culling rate for daughters of sires ranged from 0.65 to 1.27, using model RTD1. This corresponds to the lowest and highest risk of culling for daughters of the best and worst sires, respectively, compared with daughters of an average sire which have a relative risk of culling equal to 1. Daughters of the worst sires thus had two times higher risk of culling compared with daughters of the best sires. The correlation between breeding value of sires from FTI and that of sires from RTI was 0.98. The corresponding correlation between breeding values from different models when hy was a timedependent variable ranged from 0.96 to 0.99. The correlations between breeding values of sires from
Table 5 Estimates of sire variance (s 2s ), shape ( r ) and location ( l) parameters of the Weibull distribution, and heritability on log (h 2log ) and original (h 2ori ) scales of length of productive life (longevity) Models a,b
s s2
r
lc
2 h log
h 2ori
FTI RTI FTD1 RTD1 FTD2 RTD2
0.02060.011 0.02660.012 0.04560.013 0.03760.012 0.04960.014 0.04760.013
1.40060.016 1.36760.015 1.38860.018 1.36260.016 1.38660.017 1.35960.016
0.237 0.227 0.251 0.227 0.270 0.220
0.048 0.056 0.107 0.075 0.116 0.098
0.109 0.149 0.246 0.212 0.267 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.
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time-dependent models (FTI and RTI) and that of sires from time-dependent models (FTD1, RTD1, FTD2, RTD2) ranged from 0.87 to 0.90. All standard errors of correlations were very similar (0.001). This similarity between the evaluations of sires from different models confirms the similarity of the sire variance components obtained for the different models within time-independent and dependent hy effects. Due to many missing observations concerning the cause of culling and date of mating and weaning it was impossible to directly distinguish between voluntary and involuntary culling of these sows. The aim is, of course, to produce sows that have a long life length due to good health and high production rather than to long farrowing interval or delayed slaughter after last weaning. Therefore, it would be interesting to account for voluntary and involuntary culling when estimating the heritability of longevity, as discussed by Strandberg (1997).
4. Conclusions Among the factors evaluated in the model, hy had the largest influence on the risk of culling of sows. Although litter size at both first and last farrowing had significant effects on risk of culling, the latter had a stronger effect on the risk ratio. The effects of age at first farrowing and weight of gilt at performance test were significant, but not large. The increase in the sire variance and heritability of longevity when hy was time-dependent compared to time-independent indicates that the records of sows were more thoroughly corrected for the effect of hy when it was treated as a time-dependent variable. Obviously, the choice of model is very important when analysing survival data and, consequently, has very strong influence on the results and conclusion. The moderate estimates of heritability (on the original scale when there is no censoring) in these investigations indicate that there is genetic variation among the animals that can be utilised for improving longevity in the Swedish Landrace breed. However, a breeding evaluation of sow longevity demands a high quality data bank that includes censoring records and dates of each mating, farrowing, weaning, exchange between herds and culling. A
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more precise registration of the cause of culling would also increase the possibility to include sow longevity in the breeding evaluation.
Acknowledgements The authors are very grateful to The Swedish Farmers’ Foundation for Agricultural Research for financially supporting this study. Quality Genetics (the Swedish pig-breeding organisation) is acknowledged for providing the data. The authors are in´ ´ debted to V.P. Ducrocq (Station de Genetique Quan´ titative et Appliquee – Institut National de la Recherche Agronomique, France) for kindly placing The Survival Kit at our disposal and answering our questions. The authors gratefully acknowledge E. Strandberg, Department of Animal Breeding and Genetic, SLU, Sweden, for useful comments on the manuscript.
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