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ANIMAL GENETICS |
Departamento de Ciencia Animal, Universidad Politécnica de Valencia, Valencia 46071, Spain
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Abstract |
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 Top Abstract IntroductionMaterials and MethodsResultsDiscussionLiterature Cited |
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Key Words: Bayesian Inference • Genetic Parameters • Litter Size • Monte Carlo Markov Chain • Rabbits • Uterine Capacity
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionLiterature Cited |
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as the maximum number of fetuses a dam can support at birth when the number of ova shed is not a limiting factor. Selection for increased UC has been proposed as an indirect way of improving litter size (Bennett and Leymaster, 1989). Because there is no embryo migration between uterine horns in rabbits, Blasco et al. (1994) proposed that litter size of unilaterally ovariectomized does could be used to estimate UC in rabbits. The remaining ovary duplicates (on average) its ovulation rate (OR), crowding the functional uterine horn; hence, litter size is not expected to be limited by OR. In rabbits, unlike pigs or mice, it is possible to observe the number of corpora lutea and implantation sites by laparoscopy without impairing litter size (Santacreu et al., 1990), which permits recording components of litter size from the same animal. There is little information on genetic parameters of uterine capacity and components of litter size such as ovulation rate, pre-and postimplantation survival, or number of implanted embryos. In rabbits, only preliminary results have been published by Bolet et al. (1994) and Argente et al. (1997). Our objective was to determine response to selection and estimate genetic parameters for a divergent selection experiment for uterine capacity in rabbits. |
Materials and Methods |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionLiterature Cited |
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Rabbits used in this study came from a divergent selection experiment on uterine capacity. Animals were derived from a synthetic population selected for litter size at the experimental farm of the Universidad Politécnica de Valencia. The base population derived from a cross between White New Zealand and Californian breeds. Uterine capacity was assessed as litter size in unilaterally ovariectomized (ULO) does. The left ovary was removed in all does before puberty via midventral incision between 14 and 16 wk of age (Blasco et al., 1994). The females were first mated at 18 wk of age, and 10 d after parturition thereafter. A laparoscopy was performed on all does at d 12 of their second gestation, and corpora lutea and implanted embryos in the functional side of the genital tract were counted. Details of the technique were given by Santacreu et al. (1990). Selection was performed on predicted breeding values for litter size using a BLUP procedure and a repeatability (up to four parities) animal model with year-season and parity as fixed effects; males were selected within sire families to decrease inbreeding. Reproduction was organized into discrete generations. Data from 10 generations of selection were used in the analysis. Number of records was approximately the same for the line selected on high UC and the line selected on low UC. Number of sires, dams, and parities per generation are shown in Table 1. The number of animals in the pedigree was 1,161, of which 85 belonged to the base population. The total number of laparoscopies conducted was 735.
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The following traits were analyzed: OR, assessed as number of corpora lutea; number of implanted embryos (IE), measured as number of implantation sites; UC, total number of rabbits born; prenatal survival (PS), which was calculated as UC/OR; embryo survival (ES), calculated as (IE/OR); and fetal survival (FS), calculated as UC/IE. We use the term embryo to denote fertilized oocytes before and during implantation, whereas fetus refers to the IE. All traits were measured in second parity ULO females with the exception of UC, which was measured over four parities.
Statistical Analyses
The genetic analysis was based on Bayesian methods. A multivariate model was used. Components of UC, measured only in second parity does, were assumed to be distributed as
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where bc contains year-season effect, uc is a vector of additive genetic values, 
2c is the residual variance, Xc and Zc are known incidence matrices, and I is an identity matrix of appropriate order. Uterine capacity, measured up to four parities, was assumed to follow the distribution
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where the vector buc contains year-season and parity effects; uuc is a vector of additive genetic values; puc is a vector of permanent environmental effects; 
2uc is the residual variance; Xuc, Zuc, and Wuc are known incidence matrices; and I is an identity matrix.
The incidence matrices of UC were different from those pertaining to litter size components. To simplify computations, we used data augmentation, a technique that fills the data vector with random imputations, so that incidence matrices were the same for all traits (Sorensen and Gianola, 2002). After data augmentation, the model can be written as
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where y is a vector of augmented data; X, Z, and W are known incidence matrices; and R is the (co)variance residual matrix. Records of different individuals were assumed to be conditionally independent, given the parameters, but correlations between residuals of the same individual were allowed. If the data are sorted by individual, the residual (co)variance matrix can be written as R0 
In, where R0 is the 6 x 6 (co)variance matrix between traits; and In, the identity matrix, has the same order as does the number of individuals.
Bounded uniform priors were used to represent vague previous knowledge about the elements of b. Prior knowledge about additive effects was represented by assuming that these were normally distributed, conditionally on the associated (co)variance components, so that
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where 0 is a vector of zeros, and G is the genetic (co)variance matrix. Sorting the data by individuals, as before, this matrix can be written as G0 A, where G0 is the 6 x 6 genetic (co)variance matrix between the traits, and A is the known additive genetic relationship matrix between members of the genealogy. The distribution of permanent environmental effects was assumed to be a normal process:
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where 0 is a vector of zeros and C is the permanent environmental effects (co)variance matrix. Sorting the data by individuals within traits, this matrix can be written as C0 In, where C0 is the 6 x 6 genetic (co)variance matrix between traits and In is an identity matrix of order n, the number of individuals. Bounded flat priors were used for matrices R0, G0, and C0.
Univariate analysis for UC, and bivariate and trivariate analyses always including UC were performed.
Gibbs Sampling
Marginal posterior distributions of all unknowns were estimated using Gibbs sampling. After some exploratory analyses, we used three chains of 600,000 samples each with a burn-in period of 200,000. This was larger than the minimum burn-in required, which was calculated according to the method of Raftery and Lewis (1992). Because of the large autocorrelation of the chain, only one of each 60 samples was used for inference, and samples from the three chains were pooled to estimate features of posterior distributions. Convergence was tested for each chain separately using the Z criterion of Geweke (1992) based on a comparison of the means of the first and last sections of the chain. For each variable, the distribution of this difference divided by its SE should be approximately N(0,1), so the value of Z is expected to lie in the interval [–1.96, 1.96] (with 95% confidence) if convergence is reached. Monte Carlo estimates of means and variances of posterior distributions obtained from various chains were practically indistinguishable, and minor differences could be ascribed to sampling error. Monte Carlo error of estimates of posterior features was computed using time-series procedures described in Geyer (1992).
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Results |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionLiterature Cited |
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shows raw means and SD for the traits measured in the experiment in the base generation, and Table 3 shows phenotypic correlations between traits. Ovulation rate was much larger than UC in a single uterine horn; hence, the expected overcrowding of the uterine horn necessary to attain maximum UC was accomplished on average. Mean ES and FS were 0.76 and 0.71, respectively, and were weakly correlated (–0.19; Table 3).
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contains Monte Carlo estimates of features of the marginal posterior distributions of heritabilities of all traits. The Z tests did not suggest lack of convergence, and the Monte Carlo SE were small relative to the posterior means and SD. Distributions were seemingly normal.
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shows features of the marginal posterior distributions of genetic correlations between traits. Again, Monte Carlo SE were very low, and Z tests did not suggest lack of convergence. Marginal posterior distributions were often asymmetric; therefore, the highest posterior density (HPD) intervals of 95% probability content were used to describe uncertainty. For example, the genetic correlation between number of IE and OR had a mean estimate of 0.91, and the 95% probability HPD region was [0.71, 0.99]. Table 5 also gives the probability that a positive correlation was >0 and the probability that a negative correlation was <0.
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should be made with caution. Nevertheless, there was evidence of a non-trivial genetic covariance structure. In particular, it seems that genetic correlation between OR and UC (0.56; HPD = 0.24 to 0.84) is positive and moderate. The genetic correlation between OR and number of IE was very large and higher than the phenotypic correlation (0.57; Table 3). The other correlations were similar to the phenotypic correlations, except for those involving ES, probably because of the low heritability of ES.
Figures 1 and 2 show the estimated direct response to selection for UC in the high and low capacity lines and the correlated responses. After 10 generations of selection, the divergence in UC between lines was approximately 1.5 rabbits (Figure 1), which represents a genetic response of 1% per generation. About one-half of this response was obtained in the first two generations of selection. Correlated responses (Figures 1 and 2) showed similar patterns, reflecting positive and moderately large genetic correlations with UC. This result is in agreement with phenotypic differences between lines, although phenotypical trends were much more erratic (Argente et al., 2003).
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionLiterature Cited |
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; however, experimental evidence on the effectiveness of selection is scarce. In addition to early results from this experiment (Argente et al., 1997), only results from two experiments on selection for UC have been published: the French experiment described by Bolet et al. (1994) and Santacreu et al. (1994) in rabbits and the experiment of Kirby and Nielsen (1993) in mice. In the French rabbit experiment, UC was assessed as the number of dead fetuses between implantation and birth. In the mice experiment, UC was assessed as litter size in ULO females, the same criterion as in the present study. Heritability of UC was low in both experiments (0.05 in rabbits and 0.08 in mice). Ovulation rate in ULO females had a higher heritability in both experiments: 0.23 in Bolet et al. (1994) and 0.24 in Nielsen et al. (1996). Heritability of number of IE was greater in this study than in the French rabbit experiment, in which it was null. Survival rates had low heritability in agreement with Bolet et al. (1994) in ULO females and Blasco et al. (1993b) in intact females. Estimates of heritability of survival rate were similar to those found in other species (Blasco et al., 1993a).
A positive correlation between OR and UC and a consequent correlated response in OR was found. Blasco et al. (1994) showed that LS was independent from OR as an average, but some does may have not fully expressed their UC because their OR was not sufficiently high. For example, a doe can have a litter size of 11 having only 11 ova, but their UC might be 
12. As litter size and OR are positively related (Blasco et al., 1993b), when selecting for litter size in ULO does, some correlated response in OR was obtained.
Although selection for UC was successful, it does not seem to be more effective than direct selection for litter size as found in rabbit experiments (Blasco, 1996). In mice, similar results have been obtained; the response in the line selected for high UC was lower than in the line selected for litter size, with 0.09 ± 0.01 and 0.16 ± 0.01 pups per generation, respectively (Kirby and Nielsen, 1993). The French experiment on divergent selection for UC measured as the number of dead fetuses between implantation and birth in rabbits failed to detect a significant response (Santacreu et al., 1994).
In our study, a large difference between lines in UC was found in the first generation, and approximately one-half of the response was obtained in the first two generations of selection. This finding may suggest a gene with large effect segregating in the population. A complex segregation analysis made by Argente et al. (2003) with the same data points in the same direction. Another explanation may be that higher selection pressure was exerted in the first generation of selection because the population was twice as large in the base generation than in subsequent ones. The improvement in UC was associated with an increase in number of IE and in ES. Differences in ES can be due to differences in rate of fertilization; however, fertilization rate seems to be very large in intact females from these lines, and no differences in fertilization rate between high and low UC lines have been found (Santacreu et al., 1996). Differences between both lines also were found in FS. Embryo viability may have a role in ES and FS, but our analysis treated UC as a trait of the dam. Hence, correlated responses could be expected to have a maternal genetic component. In an experiment of crossed embryo transfer between our lines, Mocé et al. (2004) found that FS was affected by the recipient line, suggesting that FS should be regarded as a trait of the dam as done in the present study.
In conclusion, selection for UC produced a response that was similar to that found in experiments in which direct selection for litter size was practiced. An assumption made in this experiment was that UC measured in a single horn is a good measurement of the UC of both horns and that a correlated response in litter size will be found when does have both uterine horns functional. This hypothesis is tested in a companion paper (Santacreu et al., 2005).
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Footnotes |
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3 Current address: Facultad de Zootecnia, Universidad Autónoma de Chihuahua, P.O. Box 4-28, Chihuahua CP 31031, Mexico.
2 Correspondence: P.O. Box 22012 (phone: 34 963877433; fax: 34 963877439; e-mail: ablasco{at}dca.upv.es).
Received for publication January 25, 2005. Accepted for publication July 1, 2005.
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionLiterature Cited |
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