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ANIMAL GENETICS |
,4
* IRTA—Unitat de Cunicultura, Torre Marimón s/n., Barcelona, Spain and
and
Departamento de Ciencia Animal, Universidad Politécnica de Valencia, Valencia 46071, Spain
Abstract
Two elliptical selection experiments were performed in two contemporary sire lines of rabbits (C and R) in order to optimize the experimental design for estimating the genetic parameters of the growth rate (GR) and feed conversion ratio (FCR). Twelve males and 19 females from line C, and 13 males and 23 females from line R, were selected from an ellipse defined by a quadratic index based on these traits. Data from 160 rabbits of each of the parental generations of lines C and R and their offspring (275 and 266 animals, respectively) were used for the analysis. A Bayesian framework was adopted for inference. Marginal posterior distributions of the genetic parameters were obtained by Gibbs sampling. An animal model including batch, parity order, litter size, and common environmental litter effects was assumed. Posterior means (posterior standard deviations) for heritabilities of GR and FCR were estimated to be 0.31 (0.10) and 0.31 (0.10), respectively, in line C and 0.21 (0.08) and 0.25 (0.12) in line R. Posterior means of the proportion of the variance due to common litter environmental effects were 0.14 (0.06) and 0.21 (0.06) for GR and FCR, respectively, in line C and 0.17 (0.06) and 0.22 (0.06) in line R. Posterior means of genetic correlation between both traits were -0.49 (0.25) in line C and -0.47 (0.32) in line R, indicating that selection for GR was expected to result in a similar correlated response in FCR in both lines.
Key Words: Bayesian Theory • Elliptical Selection • Feed Conversion Ratio • Genetic Parameters • Growth Rate • Rabbit
Introduction
Feed conversion ratio (FCR, feed intake/weight gain), is the most important trait in meat rabbit production (Armero and Blasco, 1992
). Despite its importance, current programs do not select terminal sires for FCR but instead they select for growth rate (GR, weight gain/time). However, only four estimates of the genetic correlation between FCR and GR have been published: two of them out of the parametric space (Lampo and Van der Broeck, 1975; Randi and Scossiroli, 1980) and the other two, which are given without standard errors, differ widely (Vrillon et al., 1979; Moura et al., 1997).
Measuring FCR is expensive; thus, sample size should be minimized when estimating the genetic parameters of these traits. Cameron and Thompson (1986) proposed elliptical selection as an optimal experimental design for the estimation of variance components in multitrait situations. They showed that this design can be up to 40% more efficient when compared with other designs. Despite being the most efficient design, only one elliptical selection experiment can be found in the literature (Blasco et al., 1993). Consequently, the objective of this study was to estimate the genetic parameters of the feed conversion ratio and growth rate in rabbits by means of such an elliptical selection experiment. A Bayesian framework was used for the statistical analysis because experimental size is necessarily limited when collecting data that is expensive, as is the case for FCR. In these cases, the Bayesian approach gives a more useful description of the uncertainty of the estimates (Blasco, 2001).
Materials and Methods
Experimental Design
Two elliptical selection experiments of GR and FCR were designed for two rabbit lines C and R, respectively. Cameron and Thompson (1986) proposed elliptical selection as an optimum experimental design. The elliptical selection design is a generalization of the univariate design, which is based on selecting parents with extreme values and estimating the heritability by offspring-parent regression. It is represented by a bivariate normal distribution, with the shape of an elliptical bell (Figure 1). The extreme individuals are the animals that lie outside of an ellipse defined by a quadratic index, 
xi, where xi is the GR and FCR data vector of individual i, and P0 is the phenotypic (co)variance matrix of these traits. Optimal selection pressure p is calculated iteratively assuming prior information about the genetic parameters. The selection threshold for the index is calculated as cE = -2 log p (Cameron and Thompson, 1986). Matrix P0 is calculated with the data of the parental generation.
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Animals
Line C originated by crossing animals from five New Zealand White lines and a California x New Zealand synthetic line. Line R originated by crossing a California line with a synthetic line created by mating rabbits from commercial male lines. Animals were allocated to individual cages in the experimental farm of IRTA (Institut de Recerca i Tecnologia Agroalimentàries) and were fed ad libitum with a commercial diet (16.4% crude protein, 15.2% crude fiber, 4% fat). Body weight and feed intake during the fattening period (from weaning at 4wk of age, to 9 wk of age) were recorded.
The parental generations were formed by randomly choosing 60 males and 100 females per line after weaning. According to the optimal selection pressure, 15 males and 25 females were selected in each parental generation, but some of them had to be eliminated for health reasons. The number of animals actually measured and the intensity of selection from weighted selection differentials are given in Table 1. The offspring generation consisted of 275 rabbits for line C and 266 for line R. Figure 2 shows the ellipse thresholds of both lines and the phenotypic values of GR and FCR for the selected rabbits outside them.
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where y is the trait (GR or FCR); G is the group effect (lines R or C); B is the batch effect (10 levels); L is the effect of litter size in which the animal was born, with eight levels (<6, 6, 7, 8, 9, 10, 11, >11); P is the parity order effect with three levels (first, second, third, and higher); c is a common litter environmental effect; a is an individual additive genetic value; and e is the residual. A Bayesian approach was used for the analysis, as described by Sorensen et al. (1994). Flat priors with boundaries were used for G, B, L, and P, and also for variance components. The prior distributions for random effects and residuals were 
, 
, 
, where A is the relationship matrix between individuals, with the information of the experimental animals and their parents only (i.e., with sib and parental relationships).
Genetic analysis was also based on Bayesian methods. All individuals had records for GR and FCR. These traits were assumed to be conditionally normally distributed as follows:
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where bGR and bFCR are random vectors including the effects of batch, litter size in which the animal was born, and parity order for GR and FCR, respectively; cGR and cFCR are vectors of common litter environmental effects; aGR and aFCR are vectors of individual additive genetic values for GR and FCR, respectively; X, Z, and W are known incidence matrices; and R is the residual (co)variance matrix. Pairs of records from different individuals are assumed to be conditionally independent given the parameters, but a correlation between residuals of the same individual is allowed. Hence, sorting the data by individual, the residual (co)variance matrix can be written as R0 
In with R0 being the 2 x 2 residual (co)variance matrix between GR and FCR and In an identity matrix of the same order as the number of individuals.
Bounded uniform priors were used to represent vague previous knowledge of bGR and bFCR. Prior knowledge concerning permanent and additive effects was represented by assuming that they were normally distributed, conditionally on the associated variance components. Thus, for the additive genetic effects,
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where 0 is a vector of zeroes and G is the genetic variance covariance matrix. Sorting the data by individual as before, this matrix can be written as G0 A, where G0 is the 2 x 2 genetic (co)variance matrix between GR and FCR and A is the known additive genetic relationship matrix between elements of the additive genetic effects vector.
The distribution of permanent environmental effects was assumed to be normal and of the form
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where 0 is a vector of zeroes and C is the common litter effects matrix. Sorting the data by individual, this matrix can be written as C0 In, with C0 being the 2 x 2 common litter effects (co)variance matrix between GR and FCR. Bounded flat priors were used for matrixes R0, G0, and C0. Marginal posterior distributions of all unknowns were estimated using a Gibbs sampling procedure. Details about this technique can be found in Sorensen and Gianola (2002). Implementation of the Gibbs sampler was made using two coupled chains of 300,000 iterations, as described in García-Cortés et al. (1998). The first 20,000 iterations of each chain were discarded, and samples of the parameters of interest were saved for each of 10 iterations. Gibbs samples were used to estimate features of the marginal posterior distribution (i.e., mean, standard deviation, and posterior credibility regions of size 95%). Convergence was tested for each chain using the criteria of Geweke (1992) and Johnson (1996). Autocorrelation between samples and Monte Carlo error of features of marginal distributions (Geyer, 1992) were also calculated.
Results and Discussion
Elliptic selection is proposed as a method to optimize experimental resources when analyzing genetic parameters of two or more traits. Although the method is optimal when the unknown genetic matrix G0 is used in the index instead of the phenotypic matrix P0, Cameron and Thompson (1986) show that the design is robust to changes in the P0 matrix. In our case, the same individuals in both lines would have been selected if we had used the respective G0 matrixes that were estimated. To calculate the optimal selection pressure, we had only two reliable prior estimates of the genetic correlation available from the literature, and both were very different, -0.19 (Vrillon et al., 1979) and -0.82 (Moura et al., 1997). However, we gave more credibility to the Moura et al. (1997) estimation because our criteria were also based on estimates of the same parameters in pigs and mice, and we used a prior genetic correlation of -0.7, which gave an optimal selection pressure of 25%. The selection pressures actually applied were not the optimum ones (13 and 17% for males and 11 and 16% for females of lines C and R, respectively), but Cameron and Thompson (1986) found similar efficiencies when selection pressure was close to 20%.
Tables 2, 3, and 4 show the results of the Gibbs sampling processes for the estimation of line effects, heritabilities, and genetic correlations, respectively. As there is no formal proof of convergence, it is convenient to apply several tests and to inspect the chains. None of the tests detected lack of convergence, and the burn-in applied was much higher than that proposed by the Johnson procedure. The autocorrelations between samples were not very high, indicating good mixing, and the Monte Carlo standard errors were very small (always lower than 2% of the posterior mean). Thus, estimates of features of marginal posterior distributions could be considered accurate enough.
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. Similar values were reported by Torres et al. (1992), Feki et al. (1996), and Ramon et al. (1996) in other lines of rabbits. Line R showed higher GR and higher FCR than line C, but these differences disappeared when both lines were compared after correcting for differences in live weight. The posterior means (posterior standard deviation) of the differences were, after correction, -0.55 (0.65) for GR and -0.029 (0.026) for FCR. The marginal posterior means of the levels of the different environmental effects were estimated. The parity effect was low, with the higher average difference between GR levels being of 3.3 g/d (6% of the mean) and the higher range of 5 g/d (9% of the mean), in line C. For FCR, the higher average difference between levels was 0.09 (3% of the mean) in line R and the range between effects was never higher than 5% of the mean. Litter size effect was also small. The higher average difference between GR levels was 3.9 g/d (7% of the mean) and the higher range was 8.5 g/d (16% of the mean), in line C. For FCR, the higher average difference between levels was 0.15 (5%) and the maximum range was 0.35 (12%), also in line C.
Table 3 shows the results of the analyses for the heritabilities and proportions of the phenotypic variance due to common litter effects. Figure 3 shows the estimated marginal posterior distributions. All of them are nearly symmetrical, and they approximate a normal distribution shape; therefore, the standard deviations give a good indication of the accuracy of the estimates. The marginal posterior means of the heritabilities of GR and FCR were moderately high in both lines. One advantage of the Bayesian approach through MCMC procedures is the possibility of easy construction of all types of credibility intervals. Table 3 gives the limit k in the interval from k to infinity that represents 95% of the probability area of the marginal posterior distributions for all parameters. With these intervals, we know that the probability of the parameter’s being lower than k is only 5%. For example, for k equal to 0.16, the interval from 0.16 to +
for the growth rate heritability of line C contains 95% of the area of the marginal posterior distributions for GR; therefore, the probability of the heritability’s being lower than 0.16 is less than 5%.
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; Rochambeau et al., 1989; Estany et al., 1992; Ferraz and Eler, 1994; Lukefahr et al., 1996; McNitt and Lukefahr, 1996; Moura et al., 1997; Su et al., 1999; Piles, 2000). The estimate of heritability for GR in line R is in agreement with the values previously reported by Estany et al. (1992) and Piles (2000) in the same line and they are moderate. Four estimates of FCR heritability are reported in the literature, two of them are null or almost null (Lampo and Van der Broeck, 1975; Randi and Scossiroli, 1980), one of them has a rather high value (0.71, Vrillon et al., 1979) and the other one is moderate (0.29, Moura et al., 1997), although both the latter values are without standard errors. Our estimates are also moderate and mean we can conclude that selection for FCR is feasible.
In rabbits, a nonnegligible part of phenotypic variation in growth and feed efficiency traits is due to environmental effects related to the mother or the litter. The importance of these effects during the fattening period is due to the short interval of time between weaning and slaughter age compared with other species, such as pigs, in which this interval is proportionally much longer and, consequently, maternal and common litter effects are not important. In rabbits, the influence of these effects is exerted prior to slaughter age and is higher for body weight, at slaughter or at weaning age, than for growth rate (Camacho, 1989; Estany et al., 1992; Lukefahr et al., 1996; McNitt and Lukefahr, 1996). Three of the four analyses of FCR found in the literature (Lampo and Van der Broeck, 1975; Vrillon et al., 1979; Randi and Scossiroli, 1980) did not include the common litter effect; thus, the results may be biased.
Correlations between GR and FCR in lines C and R are shown in Table 4. Both phenotypic and genetic correlations were negative, but genetic correlations were higher in all cases. Estimated marginal posterior distributions of genetic correlation can be found in Figure 4. As these distributions are not symmetric, Table 4 contains the high posterior density interval (i.e., the shortest interval with a 95% probability). Phenotypic correlations were low, and were different from reported values of -0.65 (Lampo and Van der Broeck, 1975), -0.61 (Randi and Scossiroli, 1980), and -0.68 (Moura et al., 1997). Only four estimates of the genetic correlation between the growth rate and feed conversion ratio have been published. Two of the estimates (Lampo and Van der Broeck, 1975; Randi and Scossiroli, 1980) are out of the parametric space (they are higher than -1 due to a very low heritability of FCR), whereas the other two are very different and are given without standard errors (-0.19 for Vrillon et al. [1979] and -0.82 for Moura et al. [1997]). Table 4 gives the marginal posterior means for the genetic correlations, which were moderate. Posterior means give lower estimates than modes when the posterior distributions are asymmetric. Restricted maximum likelihood estimates can be considered as joint posterior modes; thus, they are expected to give higher absolute values for the correlations, which may partially explain the high value of the correlation given by Moura et al. (1997) compared with our estimates. Moura et al. (1997) conducted two divergent selection experiments for GR and FCR in a composite rabbit population. After three generations of selection, they found that GR was more effective for improving FCR than direct selection of FCR. This was due to their high estimate of the correlation between traits (-0.82) and the difference between heritabilities (0.48 for GR and 0.29 for FCR). In our case, selection for GR would not be as efficient for improving FCR as the inclusion of FCR in an index. Based on our estimates, FCR would improve by more than 77% if an index were used compared to indirect selection using GR.
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Heritabilities of growth rate and feed conversion ratio are moderate in rabbits, which predicts successful selection of these traits; however, the genetic correlation between both traits is not very high. Therefore, both traits should be used in an index in order to improve the response to selection in feed conversion ratio, which is the most important trait in rabbit production. It is important to obtain the genetic parameter estimates for growth rate and feed conversion ratio in the population to be selected because there is very little information in the literature about them. These estimates can differ dramatically between populations. Elliptical selection is an effective procedure to minimize the uncertainty of these genetic parameter estimates.
Footnotes
1 This research was supported by INIA SC00-011. The authors acknowledge the staff of the farm at IRTA (N. Picornell, O. Perucho, N. Aloy, and C. Requena) for their contribution to the experimental work and L. Varona for allowing the use of his computing program. 
3 Present address: Departamento de Ganadería, CITA-IVIA, Ctra Náquera-Moncada, 46113 Valencia, Spain.
2 Correspondence: IRTA-08140 Caldes de Montbuí (phone: +34 93 865 1011; fax: +34 93 865 3777; e-mail: miriam.piles{at}irta.es).
Received for publication June 30, 2003. Accepted for publication October 30, 2003.
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2) for growth rate (GR) and feed conversion ratio (FCR) in lines C and R
p) and genetic correlation (
