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J. Anim. Sci. 2005. 83:340-343
© 2005 American Society of Animal Science

ANIMAL GENETICS

Genetic parameters of fertility in two lines of rabbits with different reproductive potential

M. Piles*,1, O. Rafel*, J. Ramon* and L. Varona{dagger}

* Unitat de Cunicultura, IRTA, 08140 Caldes de Montbuí, Barcelona, Spain; and and {dagger} Area de Producció Animal, Centre UdL–IRTA, 25198 Lleida, Spain


   Abstract
Top
 Abstract
Introduction
 Material and Methods
 Results and Discussion
 Implications
 Literature Cited
 
A Bayesian analysis with a threshold model was performed for fertility defined as a binary trait (1 = successful mating, 0 = unsuccessful mating) in two populations of rabbits of different reproductive potential and different genetic origin: Line P selected for litter size and Line C selected for growth rate. There were 20,793 records of natural mating (86.2% successful) in Line C between 1983 and 2003, and 17,548 records (80.5% successful) in Line P, between 1992 and 2003. Data related to 5,388 and 3,848 females and 1,021 and 685 males in Lines C and P, respectively. The pedigree included 6,409 and 4,533 individuals in Lines C and P, respectively. The binary response was modeled under a probit approach. The model for the latent variable included male and female additive genetic effects, male and female permanent environmental effects, and the year-season and physiological status of the female (nulliparous, multiparous lactating, or multiparous nonlactating) as systematic effects. Means (standard deviation in parentheses) of the estimated marginal posterior distribution (EMPD) of male heritability were 0.013 (0.006) and 0.010 (0.008) in Lines C and P, respectively, and those of EMPD of female heritability were 0.056 (0.013) and 0.062 (0.018) in Lines C and P, respectively. Means of the EMPD of the proportion of the phenotypic variance due to environmental male and female effects were, respectively, 0.031 (0.007) and 0.128 (0.018) in Line C and 0.053 (0.010) and 0.231 (0.024) in Line P. Means (standard deviations in parentheses) of the EMPD of genetic correlation between male and female fertility were 0.733 (0.197) in Line C and 0.434 (0.381) in Line P. The posterior distribution of genetic correlations presents a huge dispersion, and the estimates should be taken with caution because of the almost negligible estimate of the male genetic component. Results indicate that little genetic variation exists for female fertility, and practically none for male fertility. It would, therefore, be possible to improve reproductive performance by including female fertility in a breeding program, but response to selection would be very small.

Key Words: Bayesian Theory • Fertility • Genetic Parameters • Rabbit • Threshold Model


   Introduction
Top
 Abstract
 Introduction
Material and Methods
 Results and Discussion
 Implications
 Literature Cited
 
In rabbit meat production, the efficiency of production and the profitability of farms greatly depend on reproductive success, which in turn is conditioned by fertility and litter size. Fertility can be considered a trait of the female, male, or both sexes. Several authors have shown that there is genetic variation in mating or conception rate in cattle (Weller and Ron, 1992Go; Boichard and Manfredi, 1994Go; Weigel and Rekaya, 2000Go) and in pigs (Varona and Noguera, 2001Go), but in rabbits, information in the literature is scarce, with just three studies concerning repeatability (Blasco et al., 1979Go) and heritability (Khalil and Soliman, 1989Go; Moura et al., 2001Go) of female fertility measured as the number of presentations to the male per parturition, and no estimates of variance components relating to male fertility. Selection efforts have been focused on litter size, and only a low-intensity selection has been practiced by culling sterile individuals.

Male fertility may be of economic interest because a male can influence the success of conception for a large number of females, especially when AI is practiced. This could be improved by direct or indirect selection through its components, such as the measurements defining semen quality.

Success to mating or to conception shows a binary expression. The threshold model postulates that the observed response is related to an underlying normal variable and to a fixed threshold that divides the continuous scale into two intervals that delimit the two response categories (Wright, 1934Go). Procedures developed by Sorensen et al. (1995)Go and Moreno et al. (1997)Go based on Markov Chain Monte Carlo methods allow for the analysis of categorical traits using this model.

The aim of this work was to estimate variance components of male and female fertility defined as success or failure to mating, and their genetic relationship in two populations of rabbits with different genetic origin and reproductive potential.


   Material and Methods
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 Abstract
 Introduction
 Material and Methods
Results and Discussion
 Implications
 Literature Cited
 
Animals and Data
Animals belonged to two synthetic lines of rabbits of different genetic origin: Line C, selected for growth rate during the fattening period, and Line P, selected for litter size at weaning (Gómez et al., 2002aGo,bGo). They were housed separately on two farms belonging to the Institut de Recerca i Tecnologia Agroalimenta ‘ries (IRTA), both of which applied the same management system. Does follow a semi-intensive reproductive schedule: first mating when they are approximately 4.5 mo old, with subsequent 42-d reproductive cycles. Males started their reproductive life at 6 mo. Diagnosis of pregnancy was made by palpation, 14 d after mating. The assigned fertility score was 1 when the female was diagnosed as pregnant and 0 when it was not. These data were confirmed with the information about the day of parturition. Therefore, errors in diagnosis of gestation were only possible in the case of females that died before the date of parturition, which represent less than 1% of the data. There were 20,793 records (16,740 successful, 86.2%) of natural mating in Line C between 1983 and 2003 and 17,548 records (15,134 successful, 80.5%) in Line P, between 1992 and 2003. Data included 5,388 and 3,848 females and 1,021 and 685 males in Lines C and P, respectively, and data were separately analyzed for each line. The pedigree included 6,409 and 4,533 individuals in Lines C and P, respectively.

Model and Statistical Analyses
The statistical analysis was performed for each line separately. The model assumed for the underlying variable (l), was:


where ß is the vector of systematic effects; um and uf are the vectors of male and female additive genetic effects, respectively; pm and pf are the vectors of male and female permanent environmental effects; e is the vector of random residuals; and X, Z1, Z2, Z3, and Z4 are incidence matrices relating to the underlying variable with systematic, genetic, and permanent environmental effects. The systematic effects included in the model were the physiological status of the female and the year-season at mating day. The physiological status of the female was considered to have three 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 6-mo intervals (from April to September and October to March) between November 1983 and June 2003 in Line C and, between July 1992 and November 2003 in Line P.

Given ß, um, uf, pm and pf, the elements of the vector l are conditionally independent and distributed as:


with {sigma}2e the residual variance (set to 1).

The observed data (success or failure to mating) are conditionally independent, given ß, um, uf, pm, and pf. Therefore, the conditional distribution of the data given the parameters can be written, following Sorensen et al. (1995)Go, as follows:


where y = {yi} (i = 1, 2, ..., n) denotes the vector of observed data and I(yi = j) is an indicator function that assumes the value 1 if the response falls into category j and 0 otherwise.

A Bayesian framework was adopted for inference. The joint posterior distribution of all parameters was as follows:


with the following prior densities: p(ß) ~ U(–5, 5), p(um, uf) | G) ~N(0, A {otimes} G), p(pm, | {sigma}2m) ~ N(0, I {sigma}2m) p (pf|{sigma}2f) ~ m N(0, I {sigma}2f) where A is the numerator relationship matrix, G is the matrix of (co)variance components, and {sigma}2m and {sigma}2f are the permanent environmental variances of male and female, respectively. Prior densities for G, {sigma}2m and {sigma}2f were vague proper distributions to convey the lack of information relating to these parameters: p(G) ~ IW(Sg, 5), P({sigma}2m) ~ {chi}–2 (sm, 5), p({sigma}2f) ~ {chi}–2 (sf, 5) with sm = 0.1, sp = 0.1, and

Statistical inferences were derived from the samples of the marginal posterior distributions obtained using the Gibbs sampler algorithm (Gelfand and Smith, 1990Go). The Gibbs sampler is an updating sampling scheme that requires random draws from all the full conditional distributions. These distributions were derived for the models used by Sorensen et al. (1995)Go. Implementation of the Gibbs sampler was undertaken using two chains of 2,000,000 iterations. The first 250,000 iterations of each chain were discarded, and samples of the parameters of interest were saved from every fifth iteration. The sampling variance of the chains was obtained by computing Monte Carlo standard errors (Geyer, 1992Go). The effective sample size was estimated using the Geyer algorithm (Geyer, 1992Go). Gelman and Rubin’s (1992)Go diagnostic test was used to assess convergence. Statistics of marginal posterior distributions were directly calculated from the samples.


   Results and Discussion
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 Abstract
 Introduction
 Material and Methods
 Results and Discussion
Implications
 Literature Cited
 
Trace plots (not shown) of different chains completely overlapped for all unknowns, suggesting convergence. Table 1Go shows summary statistics of marginal posterior distributions of male and female heritabilities, percentages of environmental variation due to male and female, and the genetic correlation between male and female fertility. The Gelman and Rubin test (1992)Go indicated convergence for all parameters because values for the calculated "shrink" factors were all close to 1. As expected, the highest value of the correlation between samples and the lowest value of effective sample size corresponded to the genetic correlation between male and female fertility and heritability of male fertility in both lines indicating poor mixing, but the Monte Carlo standard errors were small (always less than 2% of the posterior mean). Thus, estimates could be considered sufficiently accurate.


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  		Table 1. Summary statistics of marginal posterior distributions of male and female heritabilities (h2m, (h2f ), genetic correlation (rg) between male and female fertility, percentage of environmental variation due to male and female (pm, pf), and phenotypic variance ({sigma}2)
 
Heritability of male fertility and the percentage of environmental variation due to the male were practically null in both lines, with the repeatability for these traits being 4.4% in Line C and 6.3% in Line P. This result indicates that most of the phenotypic variance of this trait can be explained by sources of variation unrelated with the male. Female heritabilities were low in both lines (approximately 5%), and the percentages of environmental variation due to the female were 13 and 23%, respectively, with the repeatability of female fertility being 18.4 and 29.3% in Lines C and P, respectively. These results indicate that genetic variation exists for female fertility and that it could therefore be possible to improve reproductive performance by including this trait in a breeding program. The phenotypic CV in the underlying scale was high: 1.56 and 1.18 in Lines C and P, respectively; however, due to the low value of heritability, direct response to selection could be small. The posterior mean of genetic correlation between male and female fertility was high and positive in Line C (0.73 with the probability of a positive value equal to 0.999 from the marginal posterior density), indicating that genetic control of fertility could be partly the same for males and females. In Line P, the posterior standard deviation was higher possibly due to fewer mates, the probability of a positive value being 0.87. However, the posterior distribution of genetic correlations presents a huge dispersion, and the estimates should be taken with caution because the estimate of the male genetic component was almost negligible. Estimates of heritabilities agree with the values reported by Varona and Noguera (2001)Go in pigs for fertility also defined as success to mating (h2m = 0.028 and (h2f = 0.038), or Weller and Ron (1992)Go, Boichard and Manfredi (1994)Go, and Weigel and Rekaya (2000)Go in dairy cattle, whose estimates of female heritability for nonreturn rate at 56 d after AI ranged from 2.2 to 3.5%. However, reported estimates of genetic correlation between male and female fertility in pigs and dairy cattle were small or moderate and negative. In rabbits, Blasco et al. (1979)Go estimated the repeatability of the trait number of presentations to the buck to achieve a fertile mating and obtained a null value. Khalil and Soliman (1989)Go and Moura et al. (2001)Go estimated the heritability of the interval between parturitions and number of services per parturition and also obtained values that were close to zero.

Table 2Go shows summary statistics of the EMPD of differences between levels of physiological status of the female effect in the underlying scale. In Line C, fertility was higher for multiparous does that were not in lactation at mating than those in lactation, and higher for nullipaurous does than for multiparous does in lactation at mating. Our results suggest that lactation has a negative effect on fertility, thereby confirming findings previously reported by Fortun-Lamothe and Bolet (1995). In Line P, no differences were found between levels of the physiological status of the female effect.


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  		Table 2. Summary statistics of estimated marginal posterior distributions of differences between levels of physiological status of the female effect
 

   Implications
Top
 Abstract
 Introduction
 Material and Methods
 Results and Discussion
 Implications
Literature Cited
 
This study demonstrates the existence of genetic and environmental variation for female rabbit (but negligible for male) fertility, defined as success or failure to natural mating. The genetic correlation between both traits was high and positive, suggesting that their genetic control could be partly the same, but this result should be confirmed. Reproductive performance could therefore be improved by including female fertility in a breeding program, but because of the low values of heritability, the efficacy of selection could be very limited. An alternative may be indirect selection for other related traits, such as semen quality traits, but further research is needed to determine their genetic correlations with fertility and thereby evaluate possible selection strategies.

1 Correspondence: Torre Marimón s/n. (phone: +34 93 865 1011; fax: +34 93 865 3777; e-mail: miriam.piles{at}irta.es).

Received for publication August 3, 2004. Accepted for publication November 2, 2004.


   Literature Cited
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 Abstract
 Introduction
 Material and Methods
 Results and Discussion
 Implications
 Literature Cited
 


Blasco, A., F. García, and M. Baselga. 1979. Estudio de la repetibilidad de caracteres productivos en el conejo de carne. Pages 97–110 in Proc. 4th Symp. Nacional de Cunicultura, León, Spain.

Boichard, D., and E. Manfredi. 1994. Genetic analysis of conception rate in French Holstein cattle. Acta Agric. Scan. (Sect. A) 44:138–145.

Fortun-Lamothe, L., and G. Bolet. Les effets de la lactation sur les performances de reproduction chez la lapine. INRA Prod. Anim. 8:49–53.

Gelfand, A., and A. F. M. Smith. 1990. Sampling-based approaches to calculating marginal densities. J. Am. Stat. Assoc. 85:398–409.

Gelman, A., and D. B. Rubin. 1992. Inference from iterative simulation using multiple sequences. Stat. Sci. 7:457–472.

Geyer, C. J. 1992. Practical Markov Chain Monte Carlo. Stat. Sci. 7: 473–511.

Gómez, E. A., O. Rafel, and J. Ramon. 2002a. The Caldes strain. Rabbit genetic resources in Mediterranean countries. Pages 189–198 in Options méditerranéennes, serie B: Etudes et recherches.

Gómez, E. A., O. Rafel, and J. Ramon. 2002b. The Prat strain. Rabbit genetic resources in Mediterranean countries. Pages 199–208 in Options méditerranéennes, serie B: Etudes et recherches.

Khalil, M. H., and A. M. Soliman. 1989. Genetic analysis of some reproductive traits in female rabbits. J. Appl. Rabbit Res. 12:205–208.

Moreno, C., D. Sorensen, L. A. García-Cortés, L. Varona, and J. Altarriba. 1997. On biased inference about variance components in the binary threshold model. Genet. Sel. Evol. 29:145–160.

Moura, A. S. A. M. T., A. R. C. Costa, and R. Polastre. 2001. Variance components and response to selection for reproductive litter and growth traits through a multi-purpose index. World Rabbit Sci. 9:77–86.

Sorensen, D. S., S. Andersen, D. Gianola, and I. Korsgaard. 1995. Bayesian inference in threshold models using Gibbs sampling. Genet. Sel. Evol. 27:229–249.

Varona, L., and J. L. Noguera. 2001. Variance components of fertility in Spanish Landrace pigs. Livest. Prod. Sci. 67:217–221.

Weigel, K. A., and R. Rekaya. 2000. Genetic parameters for reproductive traits of Holstein cattle in California and Minnesota. J. Dairy Sci. 83:1072–1080.[Abstract]

Weller, J., and M. Ron. 1992. Genetic analysis of fertility traits in Israeli Holsteins by linear and threshold models. J. Dairy Sci. 75:2541–2548.[Abstract]

Wright, S. 1934. An analysis of variability in number of digits in an inbred strain of guinea pigs. Genetics 19:506–536.[Free Full Text]


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