J. Anim Sci. 2006. 84:2309-2315. doi:10.2527/jas.2005-622
© 2006 American Society of Animal Science
Genetics of litter size in three maternal lines of rabbits: Repeatability versus multiple-trait models
M. Piles*,1,
M. L. García
,
O. Rafel*,
J. Ramon* and
M. Baselga
* Unitat de Cunicultura, IRTA, Torre Marimón s/n., 08140 Caldes de Montbuí, Barcelona, Spain;
and
División de Producción Animal, Departamento de Tecnología Agroalimentaria, Universidad Miguel Hernández, Ctra. Beniel Km. 3.2, Orihuela 03312, Alicante, 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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Variance components were estimated in 3 lines of rabbits selected for litter size at weaning (A, Prat, and V) to test one of the assumptions of the models used for selection: that litter size data at different parities are repeated measurements of the same trait. Multiple-trait analyses were performed for the total number of kits born (TB), the number of kits born alive (BA), and the number of kits weaned (NW) per litter. Estimates were obtained by REML in multivariate analyses, including all of the information of the selection criteria, under a repeatability model or a multiple-trait model, considering litter size at the first, second, and subsequent parities as different traits. Models included the fixed effects of the physiological status of the female and the year-season of mating day, buck and doe random permanent environmental effects, and doe additive genetic effects. Results indicated that prolificacy was determined mainly by doe components and that the service sire had a very small effect. Heritabilities for the first and second parities were greater than the estimates obtained under the repeatability model (0.04 to 0.14 for the repeatability model). In the A and V lines, similar values of heritability were found at the first and second parities, but in the Prat line heritability at the second parity was always greater than at the first and greater parities (values of 0.21, 0.17, and 0.15 for TB, BA, and NW, respectively, in second parities of the Prat line). Genetic correlations between the same traits at different parities were approximately 0.8 for all traits in line A, but much lower in the other 2 lines. On average, the values were 0.64 for TB, 0.48 for BA, and 0.39 for NW between the first and second parities, and 0.65 for TB, 0.56 for BA, and 0.45 for NW between the first and third and greater parities. Genetic correlations between the second and greater parities showed the greatest values (approximately 0.8) in lines A and Prat for all traits, but they were lower in line V (0.63 for BA and 0.37 for NW). The heterogeneity of heritabilities and genetic correlations between parities lower than 0.9 suggests that litter size at different parities could be considered as different traits when genetic evaluations are performed. However, when the accuracies of predicted breeding values under a multiple-trait and a repeatability model were calculated, assuming the first to be the true model, the values obtained were nearly the same for all traits in all lines.
Key Words: genetic parameter • litter size • parity • paternal component • rabbit
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INTRODUCTION
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Litter size at birth or weaning has been the objective of selection in several experiments involving rabbit populations (Baselga et al., 1992
; de Rochambeau et al., 1994, 1998; Gómez et al., 1996). However, response to selection, when estimated, has been low (de Rochambeau et al., 1994; García and Baselga, 2002a,b). One of the arguments proposed to explain this result is that one of the assumptions of the models used for selection—that litter size at different parities are repeated measurements of the same trait—is not correct. In rabbits, Baselga et al. (1992) found evidence of differences in heritabilities and genetic correlations less than 1 for litter size at different parities in 2 populations selected for litter size at weaning. Nevertheless, the estimation of variance components was approached using a statistical method that did not allow all of the available information to be optimally used; therefore, the results obtained could have been biased. In swine, several authors have recommended considering prolificacy at different parities as different characteristics in a multiple-trait analysis for predicting breeding values (Irgang et al., 1994; Roehe and Kennedy, 1995; Noguera et al., 2002). The first aim of this research was to analyze data from 3 selection experiments based on litter size at weaning in rabbits, using REML to check whether the results obtained support the hypothesis of a single trait.
In addition, breeding programs usually include only the doe component of litter size, even though this trait may also be determined by a buck component. A review of genetic parameters of litter size can be found in Blasco (1996) and Garreau et al. (2004), but the magnitude of the buck component associated with these traits is still unknown in rabbits. The second objective of this research was to estimate the variance components related to the male, to find out whether they should be included in the model of selection.
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MATERIALS AND METHODS
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Animals and Data
The research protocol was approved by the animal care and use committee. Three sets of data were analyzed, corresponding to 3 breeding programs for litter size at weaning in rabbits.
The first data set was from animals belonging to line A, which has been selected since 1980 using a family index (Baselga et al., 1984). Each generation consisted of 120 females and 25 males and reproductive management involved nonoverlapping generations. Animals were bred and reared on the farm of the Departamento de Ciencia Animal of the Universidad Politecnica de Valencia (Valencia, Spain) in a building that has an insulated roof and walls, controlled lighting and ventilation, and a cooling system to prevent extreme temperatures in summer. The does followed a semiintensive reproductive rhythm: the first mating was at approximately 4.5 mo of age; with subsequent reproductive cycles of 42 d. Bucks began their reproductive lives at 4.5 mo of age. Data were collected from August 1980 to December 1999. The average number of parities was equal to 3.0 in this line.
The second set of data was from animals belonging to line V, whose selection began in 1982 and was based on BLUP under a repeatability animal model and non-overlapping generations (Estany et al., 1989). The size of the line and rearing conditions were the same as for line A. Data used for the analysis corresponded to the period from June 1982 to September 1999. The average number of parities was equal to 3.6.
Finally, the third data set was from animals belonging to the Prat line, which had been selected since 1992 using the same evaluation procedure as that applied for the V line (Gómez et al., 2002). This line comprised 152 females and 30 males. Animals were housed on the farm of the Institut de Recerca i Tecnologia Agroalimentàries (Barcelona, Spain), which also has environmental control systems. Animals of this line followed the same reproductive rhythm as those from the other 2 lines, but mating between individuals of different generations was allowed. Data corresponded to the period between July 1992 and December 2003. The average number of parities was equal to 4.0.
In all lines, the recorded traits were the total number of kits born (TB), number of kits born alive (BA), and number of kits weaned (NW) per litter at the first, second, and any subsequent parities. Litters with all kits born dead were also included in the analysis, considering that this fact was not uniquely due to environmental factors. The total data recorded by trait and line as well as some descriptive statistics are shown in Table 1.
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Table 1. Values for the total number of kits born (TB), number of kits born alive (BA), and number of kits weaned (NW) at first (1), second (2), and subsequent (>2) parities for A, Prat, and V lines
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Statistical Analyses
To achieve the objectives of this research, several consecutive REML variance component analyses were performed separately on each set of data. First, TB, BA, and NW were analyzed assuming a repeatability animal model:
where y represents the vector of observations for TB, BA, or NW; ß is the vector of fixed effects; u is the vector of doe additive genetic effects; pm and pf are the vectors of buck and doe permanent effects, treated as nongenetic effects, and hereafter referred to as environmental effects; e is the vector of random residuals; and X, Z1, Z2, and Z3 are incidence matrices relating the data to the fixed, genetic, and environmental effects, respectively.
The fixed effects included in the model were: the physiological status of the female and the year-season of the mating day. The physiological status of the female was considered to have 3 levels: 1, for nulliparous does; 2, for multiparous does in lactation at mating; and 3, for multiparous does not in lactation at mating. Year-season was defined as 3-mo intervals between July 1980 and December 1999 in line A, between April 1992 and November 2003 in the Prat line, and between April 1982 and September 2003 in line V. Because litter size at weaning was the selection criterion for the 3 lines, all analyses with the repeatability model were 2-trait analyses, and always included NW. In this way, estimates of the variance components are not biased (Sorensen and Johansson, 1992). Consequently, 2 analyses per line were carried out, including: 1) TB and NW, 2) BA and NW.
In subsequent analyses, litter size at each parity was treated as a different trait. Analyses were also performed including all of the information relating to the selection criteria. In previous analyses, it was found that the genetic correlations between the third and subsequent parities were greater than 0.95 for all traits. Thus, 2 multiple-trait analyses were carried out for each line, including: 1) total number of kits born at the first, second, and subsequent parities and the number of kits weaned at the first, second, and subsequent parities; and 2) number of kits born alive at the first, second, and subsequent parities and the number of kits weaned at the first, second, and subsequent parities. The fixed and random effects were the same as those described in the repeatability model, except for the random permanent male factor, which was not included here. This factor was excluded from these analyses because the results of the first analysis revealed that its importance was almost negligible.
All data sets were analyzed by REML using VCE software by Groeneveld (1996). The consistency of the results was checked by calculating the predicted heritabilities and ratios of environmental variation due to the doe for the repeatability models from the variance component estimates obtained from multiple-trait analyses, considering different parity numbers.
Finally, to evaluate the models and to decide which should be used for the genetic evaluation of selection candidates, the accuracy of predicted breeding values was calculated applying the multiple-trait and repeatability models, assuming that the former was the true model. Thus, correlation between the average breeding values and its estimates was calculated, assuming that the information available for evaluation consisted of individual data corresponding to the first 4 parities of a given doe and the same data from its dam, 3 full sibs and 16 half sibs.
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RESULTS AND DISCUSSION
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Table 1
shows the number of observations, means, and range of variation for the traits analyzed in the 3 lines of selection. In all cases these values were in agreement with previously reported results for the same lines (Gómez et al., 1996; Baselga, 2002a,b). It can be noted that, in general, the prolificacy of these lines was high, comparable to that of competitive commercial breeds, and that the differences between lines in the standard deviation of each trait were very small.
Table 2 shows the ratios of environmental variation due to the buck and the doe in a repeatability analysis for TB, BA, and NW, and the ratios of environmental variation due to the doe in a multiple-trait analysis for the same traits at the first, second, and subsequent parities for the 3 lines.
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Table 2. Ratio (SE) of environmental variation due to the buck and doe (pm, and pf) in a repeatability analysis for the total number of kits born (TB), born alive (BA), and weaned (NW), and ratio (SE) of environmental variation due to the doe in a multiple-trait analysis of the same traits at the first, second, and subsequent parities (pf1, pf2, and pf>2) for A, Prat, and V lines
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The percentage of phenotypic variation due to buck effects in the repeatability model was almost negligible for all traits and lines. The estimates ranged from 1 to 3%, with the smallest values corresponding to NW, as would be expected if it is accepted that survival in lactation is mainly a function of the maternal capabilities of does. In general, the estimates represented between ¹/8 and ¹/2 of total environmental variation attributable to the doe, which ranged from 3 to 10%. This means that TB, BA, and NW are mainly determined by doe components and that the service buck has a very small effect. Consequently, it was decided not to include this factor in the following multiple-trait analyses. In swine, a very small effect has been attributed to the service boar. Thus, See et al. (1993) and Van der Lende et al. (1999) reported estimates of the proportion of total variation for the number of piglets born alive due to the service sire as ranging from 0.01 to 0.03 under a repeatability model for all parities. Hamann et al. (2004) obtained estimates of paternal heritabilities of approximately 5% for the first parity and approximately 3% for parities 2 to 10.
With respect to the environmental effect of the doe in the repeatability model, estimates in the literature for the same traits and same lines are similar to the values reported here: 0.083 ± 0.011 for TB, 0.081 ± 0.012 for BA, and 0.061 ± 0.012 for NW in line A (García and Baselga, 2002a); 0.075 ± 0.025 for NW in the Prat line (Gómez et al., 1996); and 0.121 ± 0.009 for TB, 0.099 ± 0.008 for BA, and 0.081 ± 0.008 for NW in line V (García and Baselga, 2002b). When proportions of phenotypic variance due to environmental female effects were estimated for parities later than the second parity in multiple-trait analyses, the values obtained were greater than those obtained from the repeatability model.
Correlations between environmental effects due to the doe at different parities are shown in Table 3. Estimates ranged from 0.03 to 0.86, but in most cases they were less than 0.3, especially in the case of the Prat line, which showed the lowest values for all traits. Table 4 shows the predicted ratios of doe effects that should have been estimated by a repeatability model if the true model was a multiple-trait model with the variance–covariance components estimated in the corresponding analysis. The level of agreement between the values presented in Table 4 and the estimates of pf (Table 2) is poor, with the predictions being greater than the estimates. This could be because the repeatability model includes the environmental effect of the buck, whereas the multiple-trait model does not. If comparison is made with the sum of pf and pm, the level of agreement improves. This indicates that estimates of environmental doe effects in the multiple-trait model can be upwardly biased, and consequently, that predictions based on them should be greater than the estimates obtained in the repeatability model.
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Table 3. Correlations (SE) between environmental variation due to the doe (rfij) at different parities (i,j) for the total number of kits born (TB), born alive (BA), and weaned (NW) in A, Prat, and V lines
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Table 4. Predicted ratios of environmental variation due to the doe for the repeatability model from the estimates obtained in the multiple-trait analyses, considering a different number of parities, for the total number of kits born (TB), born alive (BA), and weaned (NW) in A, Prat, and V lines
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Table 5 shows the estimated heritabilities in the repeatability and multiple trait models for TB, BA, and NW at the first, second, and greater parities for the 3 lines of selection. For all traits, heritabilities in the repeatability model were much greater (approximately 40% for TB and 80% for BA and NW) in line A than in the other 2 lines, which showed very similar values (approximately 0.11 for TB, 0.07 for BA, and 0.05 for NW). The values obtained here generally agree with previously reported estimates for the same lines by García and Baselga (2002a,b): 0.153 ± 0.017 for TB, 0.130 ± 0.017 for BA, and 0.114 ± 0.016 for NW in line A; 0.102 ± 0.010 for TB, 0.071 ± 0.008 for BA, and 0.047 ± 0.008 for NW in line V and, Gómez et al. (1996): 0.044 ± 0.022 for NW in the Prat line. Similar values were also obtained in other rabbit populations (Garreau et al., 2004). Estimated heritabilities for parities beyond the second parity in multiple-trait analyses were slightly greater than those obtained in the repeatability model for the Prat line, but equal to those for the other lines.
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Table 5. Heritabilities (SE) in a repeatability (h2) and multiple-trait model of first ( ), second ( ), and greater parities (h2>2) for the total number of kits born (TB), born alive (BA), and weaned (NW) in A, Prat, and V lines
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Heritabilities for the first and second parities were greater than estimates for all traits and all lines under the repeatability model, except for NW in the first parity for the Prat line. In lines A and V, similar heritability values were obtained for the first and second parities, but in the Prat line, heritability at the second parity was always greater than in the first and in greater parities. These results do not agree with those reported by Baselga et al. (1992) who, analyzing data for lines A and V, found that the greatest heritability value corresponded to the first parity in both lines and that estimated values decreased from the first to the third parity in line V. In that investigation, analysis of the selection experiments was approached by the pseudo-expectation method (Schaeffer, 1986) applied to single-trait mixed models. This method approximates REML estimates, but is not free of selection bias (Outweltjes et al., 1988). On the other hand, in the single-trait analysis of litter size for parities beyond the first parity, some connections between records could not be accounted for.
Estimates of heritability for NW in the Prat and V lines were lower than those for litter size at birth; this also agrees with the results presented in García and Baselga (2002b).
For all traits in all lines, there was good agreement between the estimated heritabilities in a repeatability model and the predicted values from the estimates obtained in the multiple-trait analyses, considering a different number of parities to approximate the data structure in each population (Table 6).
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Table 6. Predicted heritabilities for the repeatability model from the estimates obtained in the multiple-trait analyses, considering different number of parities, for the total number of kits born (TB), born alive (BA), and weaned (NW) in A, Prat, and V lines
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Genetic correlations between the same traits for different parities are shown in Table 7. Estimates for NW at different parities come from the analysis performed with TB, but estimates were in good agreement with estimates obtained in the analysis with BA. They were high for all traits in line A, with estimates generally being equal to or greater than 0.8. In the other 2 lines the estimated values were much lower, especially between the first and second parities (with averages of 0.64 for TB, 0.48 for BA, and 0.39 for NW) and between the first and third and greater parities (with averages of 0.65 for TB, 0.56 for BA, and 0.45 for NW). The very low value found in the Prat line between the first and second parities agrees with the estimate obtained in the other multiple-trait analysis, which was found to be 0.165 ± 0.158; therefore, this correlation seems to be particularly low in this line. Genetic correlations between the second and greater parities showed the greatest values (approximately 0.8) for lines A and Prat for all traits, but the values were much lower in line V: 0.63 for BA and 0.37 for NW. Residual correlations were in most cases very low or did not differ from zero (Table 8).
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Table 7. Genetic correlations (rgij; SE in parentheses) between different parities (i,j) for the total number of kits born (TB), born alive (BA), and weaned (NW) in A, Prat, and V lines
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Table 8. Residual correlations (reij; SE in parentheses) between different parities (i,j) for the total number of kits born (TB), born alive (BA), and weaned (NW) in A, Prat, and V lines
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Heterogeneity of heritabilities for TB, BA, and NW at different parities, especially in the Prat line, and low genetic correlations between parities suggest that different genes or combinations of genes could be involved in the determination of litter size at the first, second, and subsequent parities. Therefore, different parities may be treated as different traits when genetic evaluations are performed. The heritability estimates obtained under the repeatability model when records for different parities cannot be considered as repeated measures of the same trait are as reduced as the differences in the heritabilities are greater and the genetic correlations lower (Baselga et al., 1992). Thus, as previously mentioned, lower values for heritabilities were obtained with the repeated measure model for the same trait than with the multiple-trait model, especially for the Prat and V lines. Estimates of heritabilities for third and greater parities greater than those obtained under the repeatability model for all parities in the Prat line also suggest smaller differences in the genetic determinism of litter size for subsequent parities in this line. In swine, Haley et al. (1988), Irgang et al. (1994), Roehe and Kennedy (1995), and Noguera et al. (2002) found heterogeneity of heritabilities and correlations lower than 0.9 for the number of piglets born alive at different parities. They consequently suggested the use of multiple-trait models instead of the repeatability model for the genetic evaluation of selection candidates.
However, given the selection differential, response to selection depends on the accuracies of the predicted breeding values. When these were calculated under a multiple-trait and a repeatability model, assuming the first to be the true model, the values obtained were nearly the same for all traits and lines, as can be seen in Table 9. This means that the response to selection would probably be the same if the breeding value estimates of the selection candidates were obtained through a repeatability model or by using an index of selection of litter size at different parities considered as different traits, when information used for genetic evaluation consisted of individual data and data from the dam and full- and half-sibs. Moreover, selection indexes and BLUP are not robust to errors in the estimation of the genetic parameters. Genetic correlations have greater errors than heritabilities and are more difficult to estimate. A multiple-trait model has a greater risk of giving wrong estimates than a repeatability model. Thus, all conclusions about the advantages of multiple-trait models should be evaluated with caution.
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Table 9. Accuracy of predicted breeding values under a multiple-trait and repeatability model, assuming that the first is the true model, for the total number of kits born (TB), born alive (BA), and weaned (NW) in A, Prat, and V lines
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IMPLICATIONS
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Rabbit litter size is mainly determined by the doe component, whereas the buck has a very small effect; therefore, it seems unnecessary to include the buck component in selection models. Heterogeneity of heritabilities and correlations of less than 0.8 between litter size at the first, second, and subsequent order parities found in 3 maternal lines lead us to consider different parities as different traits. However, response to selection would probably be the same if selecting for litter size under a repeatability model or using a selection index for litter size at different parities considered as different traits, because the accuracies of predicted breeding values obtained under the 2 models are nearly equal.
1 Corresponding author: miriam.piles{at}irta.es
Received for publication October 28, 2005.
Accepted for publication April 10, 2006.
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LITERATURE CITED
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Abstract
INTRODUCTION
