J. Anim. Sci. 2006. 84:58-62
© 2006 American Society of Animal Science
Crossbreeding parameter estimation for functional longevity in rabbits using survival analysis methodology1
M. Piles*,2,
J. P. Sánchez
,
J. Orengo*,3,
O. Rafel*,
J. Ramon* and
M. Baselga
* Unitat de Cunicultura, IRTA, Torre Marimón s/n., 08140 Caldes de Montbuí, Barcelona, Spain; and
and
Departamento de Ciencia Animal, Universidad Politécnica de Valencia, Camino de Vera, 14, 46071 Valencia, Spain
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Abstract
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A complete diallel cross involving 3 maternal lines of rabbit was performed to estimate cross-breeding parameters for functional longevity. This trait was defined as the ability to delay involuntary culling. The lines considered, A, V, and Prat, had all been selected by litter size at weaning for a long period. Data were related to a total of 653 does belonging to the 9 genetic types from the diallel cross; does were reared and bred on the same commercial farm. Survival analysis was performed using a Cox proportional hazard model. The model incorporated time-dependent factors, such as year-season, litter size, and the interaction between cycle and physiological status of the female; time-independent factors, such as the genetic type of the doe; and sire and dam random factors. Crossbreeding parameters were estimated from the solutions obtained for the type of doe and its estimated variance-covariance matrix, using a generalized least squares procedure. The estimated parameters were the differences between lines in direct genetic effects and maternal genetic effects and individual heterosis. Relevant differences were observed in direct genetic effects between lines A and Prat but not in any maternal effects. Heterosis was found to be significant and favorable between lines A and Prat, and between the lines V and Prat. The magnitude of this effect was variable but important, especially in the first cross. Results stress the importance of using crosses between specialized lines to produce does for intensive meat rabbit production.
Key Words: crossbreeding parameter • longevity • rabbit • survival analysis
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INTRODUCTION
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Does used on commercial farms in intensive rabbit production usually come from crosses between maternal lines selected for prolificacy (Baselga and Blasco, 1989
). Crossbred does are expected to show better reproductive performance than purebred does because of positive heterosis in reproductive traits, complementarity of lines, and dissipation of accumulated inbreeding within lines (Baselga et al., 2003). Crossbreeding parameters have been estimated for reproductive traits in prolific species (Bidanel et al., 1989; Nofal et al., 1996); however, parameters have not been estimated for longevity, defined as the time from the start of productive life until death or culling. In recent years, this trait in rabbits has received increasing interest because of the problems associated with high doe replacement rates (currently approximately 120%/yr; Rafel et al., 2000), and some investigations have been carried out (Garreau et al., 2001; Sánchez et al., 2004).
A distinctive characteristic of longevity is the presence of censored data, which are encountered when a study finishes before the event, in this case death or culling, occurs. Censored data provide partial information in the sense that we only know that the event had not occurred when the records were obtained (Klein and Moeschberger, 1997). Censored data should be included in the analysis because removing them or treating them as uncensored records could lead to biased estimates (Guo et al., 2001). Survival analysis methodology (Kalbfleisch and Prentice, 1980) allows the treatment of censored data, permits the inclusion of time-dependent covariates into the model, and takes into account the nonnormality of the trait.
The aim of this work was to estimate crossbreeding parameters of functional longevity, defined as the ability to delay involuntary culling (Ducrocq, 1994), in the cross between 3 maternal lines of rabbit.
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MATERIALS AND METHODS
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Animals and Data
Data were related to does that came from a complete diallel cross involving 3 maternal lines of rabbit of different genetic origin, selected for litter size at weaning. The A line was selected since 1980 using a family index (Baselga et al., 1984). Each generation consisted of approximately 120 females and 25 males, and the reproductive management was in nonoverlapping generations. Its average inbreeding coefficient was 14%. The V line was selected since 1982 on the basis of BLUP predictions according to a repeatability animal model (Estany et al., 1989). It had the same size and followed the same reproductive management as the A line. The average inbreeding coefficient in this line was 10%. The Prat line, selected since 1992 using the same procedure of evaluation as the one used for the V line (Gómez et al., 1996), consisted of 152 females and 30 males. In this case, the reproductive management was in overlapping generations and the average inbreeding coefficient was 4%.
Does were produced on the experimental farm of the Institut de Recerca I Tecnologia Agroalimentàries (IRTA), placed in Prat de Llobregat (Barcelona, Spain). At 10 to 12 wk of age, they were transferred to a commercial farm 80 km from the IRTA farm, with controlled lighting and ventilation and a cooling system to prevent excessively high temperatures in summer. They followed a semi-intensive reproductive rhythm, with first mating at approximately 4.5 mo of age and reproductive cycles of 42 d. Does were mated 10 d postpartum, and diagnosis of pregnancy was performed 14 d later by abdominal palpation. Data were collected from April 1997 to September 2002. Table 1 shows the number of does and bucks used to produce the females belonging to the nine genetic groups involved in the experiment. Both were generally used to produce either crossbred or purebred females. During the whole experimental period, the genetic groups were connected through contemporary purebred does, which allows correction for environmental effects.
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Table 1. Type of doe by parental sire and dam lines and information on length of productive life including percentage of censored records (C), number of records, average, minimum (Min), and maximum (Max)
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The trait studied was the length of the doe’s productive life (LPL), defined as the number of days between the date of the first positive diagnosis of pregnancy and the date of culling or death. Does were never culled on account of their production results, so LPL represented functional longevity. There were 653 records relating to the daughters of 69 sires and 150 dams. Records for does culled because of accidents or other technical reasons not related to their health status were treated as censored.
Table 1
shows a general picture of the size of the experiment and of average, minimum, and maximum lengths of productive life by female genetic types relating to both censored and uncensored records. In total, there were 73 right-censored records (11.2%) and 580 uncensored records, with the latter corresponding to does whose complete lifetime had been observed. Average LPL for does with censored records was 590 d (range = 54 to 1,597 d) but was 286 d (range = 20 to 1,315 d) for does with complete records.
Statistical Analyses
The analysis was performed using Survival Kit 3.0 (Ducrocq and Sölkner, 1998). This software implements the survival analysis methodology (Ducrocq and Casella, 1996). The proportional hazard assumption was checked across the 9 genetic types using a graphical test of the Kaplan-Meier estimate of the survival function (Kalbfleisch and Prentice, 1980). Plotting the values for the logarithm of minus the logarithm of the Kaplan-Meier estimate for each genetic type against the logarithm of time should produce parallel lines.
After checking the proportional hazard assumption, a semiparametric Cox proportional (Kalbfleisch and Prentice, 1980) hazard model was fitted, which included the following factors: 1) Genetic type of the doe = time-independent factor with 9 levels, 3 purebred and 6 cross-bred; 2) Year-season = time-dependent factor with 15 classes defined as 90-d intervals from April 1997 to September 2002; 3) Litter size = time-dependent effect with 9 classes defined as follows: nulliparous, 0, 1 to 2, 3 to 4, 5 to 6, 7 to 8, 9 to 10, 11 to 12, and >12 born alive. Changes of level occur at the date of parturition; 4) Interaction between cycle, defined as the period of time from one positive pregnancy test to the next, and physiological status = time-dependent effect of the cycle (first, second, and latter) by physiological status (unproductive, pregnant, and suckling), describing different stages during the reproductive life. Changes of level occurred at different points in the cycle depending on the doe’s fertility (success to conception) in the previous and current cycles. They were therefore calculated for each doe and each cycle; 5) Sire and dam (s and d) = random time-independent factors for the transmitting abilities of doe’s sire and dam, which are assumed to follow a multivariate normal distribution with a mean of zero and variances of I
s2 and Id2, respectively, where s2 and d2 are the variances associated with the sire and dam effects. The same variance was assumed for the sire effect as for the dam effect, and the value was 0.035. This value was obtained from a previous analysis in line V, applying the same model for fixed effects (our unpublished analysis).
Crossbreeding parameters for the lines involved in the experiment were estimated from the solutions obtained for genetic type of the doe and their estimated variance-covariance matrix. These were obtained using a generalized least squares procedure, according to Baselga et al. (2003). The estimated parameters were the differences between the direct genetic effects of the lines, the differences between the maternal genetic effects of the lines, and individual heterosis between the lines.
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RESULTS AND DISCUSSION
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Results of the graphical test to study proportionality across the 9 genetic types are shown in Figure 1. The lines obtained were almost parallel, indicating that the proportional hazard assumption was adequate.
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Figure 1. Graphical test of the proportional hazard assumption across the different genetic types. The SKM,n(t) values on the y-axis are the Kaplan-Meier estimates of the survival curve for the different genetic types, and t = time in days since first positive diagnosis of pregnancy.
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Table 2 shows the estimated values, SE, and relative risk for the different genetic types. As shown, there were relevant differences between the different genetic types. For instance, the maximum relative risk was 2.07, which corresponded to the ratio between the relative risk for the purebred A (1.066) and the corresponding value for the crossbred Prat x A (0.515). This means that a purebred A doe was twice as likely to be replaced as a crossbred Prat x A doe. As a general pattern, the genetic types with the lowest relative risks were those in which the Prat line was involved; these were followed by types involving the V line, and finally by those in which the A line participated. In rabbits, the only previous longevity study to compare different genetic types concerned New Zealand, Californian, and crosses between these two breeds. This work reported the superiority of the New Zealand and crossbred does with respect to the Californian does (Lukefahr and Hamilton, 2000). In other species, differences in survival also have been observed between different breeds, lines, and crossbred animals (in pigs: Hall et al., 2002 and Rodríguez-Zas et al., 2003; in goats: Pérez-Razo et al., 2004; in beef cattle: Núñez-Dominguez et al., 1991; Arthur et al., 1993).
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Table 2. Estimated values and relative risks from survival analysis for genetic type of does relative to A x V does
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Estimable functions between direct genetic effects (dA, dp, dV), maternal genetic effects (mA, mp, mV) and individual heterosis (hAp, hAV, hpV) for the trait LPL are shown in Table 3. Significant differences between direct genetic effects were only found for line Prat with respect to line A. They were favorable for line Prat with relevant magnitude of the differences. When the genotype Prat x Prat was replaced by the genotype A x A, the latter was almost twice as likely (exp(0.607) = 1.8) to be replaced as the former. When the substitution of the genotype was partial, the effect of substitution on relative risk was 1.8 multiplied by the proportion of substitution. The estimated value for the individual heterosis effect depended on the lines involved in the cross. Thus, for the cross between lines A and Prat, the estimated heterosis effect was –0.349, which was significantly different from zero. This means that the average risk associated with the 2 purebreds involved in this cross was 1.42 times greater than that associated with the two reciprocal crosses. For the cross between lines V and Prat, the estimated heterosis effect was –0.244, which was different from 0 at P < 0.10. As before, this meant that the average risk associated with the 2 purebreds involved in this cross was 1.28 times greater than that associated with the 2 reciprocal crosses. Longevity in the V and Prat lines could be determined by several genes, which had different frequencies between one line and the other but that determined the same direct effect. The existence of differences in gene frequencies is sufficient to explain the individual heterosis found between the 2 lines. These differences in gene frequency could be responsible for the fact that the biological mechanisms involved in the 2 lines had different degrees of importance. More research is needed to improve our knowledge of these biological mechanisms. The heterosis effect was not significant for the cross V x A. Nonsignificant differences between maternal genetic effects were found for the lines studied.
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Table 3. Estimable functions between direct genetic effects, maternal genetic effects, and individual heterosis of the trait length of productive life
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To the best of our knowledge, there are no other estimates of crossbreeding parameters of longevity in the literature relating to prolific species. The only previous estimates are for beef cattle and sheep. Vega-Murillo et al. (1999) found a favorable heterosis effect for F1 Angus-Brown Swiss and F1 Hereford-Brown Swiss crosses. In a diallel cross between Hereford, Angus, and Shorthorn breeds, Núñez-Dominguez et al. (1991) reported a heterosis effect of approximately 16% for the age (yr) of the cows at disposal and the same figure for cumulative survival (rate of cows still alive in the 12th yr). On the contrary, in crosses between Dorper and Red Maasai lambs, Nguti et al. (2003) did not find evidence of individual or maternal heterosis for the risk of death during the preweaning and the postweaning periods.
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IMPLICATIONS
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Relevant differences in direct genetic effects for functional longevity, defined as the ability to delay involuntary culling, were found between maternal lines of rabbits highly selected for litter size at weaning. The value of the estimated heterosis effect depended on the lines involved in the cross. Heterosis ranged from relevant to negligible and nonsignificant values, but in 2 of the 3 crosses between different lines that were considered, there was a lower risk of crossbred females being replaced. These results stress the importance of using crosses between specialized lines to produce does for intensive meat rabbit production.
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Footnotes
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1 This research was supported by INIA SC96-024. The authors acknowledge E. A. Gómez for his contribution to the design of the experiment and J. Terrades and the staff at La Balma farm for their contribution to the experimental work. 
3 Current address: Departamento de Producción Animal, Facultad de Veterinaria, Universidad de Murcia, Spain.
2 Corresponding author: miriam.piles{at}irta.es
Received for publication April 25, 2005.
Accepted for publication August 24, 2005.
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LITERATURE CITED
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Abstract
INTRODUCTION
