J. Anim Sci. 2007. 85:625-631. doi:10.2527/jas.2006-368
© 2007 American Society of Animal Science
Analysis of litter size and days to lambing in the Ripollesa ewe. II. Estimation of variance components and response to phenotypic selection on litter size1
J. Casellas*,2,
G. Caja*,
A. Ferret
,3 and
J. Piedrafita*
* Grup de Recerca en Remugants,
and
Departament de Ciència Animal i dels Aliments, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
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Abstract
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A performance data set from 376 Ripol-lesa purebred ewes of the experimental flock of the Universitat Autònoma of Barcelona was analyzed using a bivariate Bayesian threshold-linear model. The data set contained 1,598 litter size records and 1,699 days-to-lambing records. The model included the additive genetic effect of each animal and 3 nongenetic sources of variation: ewe age, year of lambing, and the permanent environmental effect characterized by the ewe. The flock was phenotypically selected for litter size since 1986, and replacement ewes and rams were selected from the progeny of the more prolific ewes, which had at least 3 deliveries recorded. The phenotypic trend for litter size was positive, whereas days to lambing followed an unclear pattern. Both traits had low heritabilities; 0.13 for litter size and 0.11 for days to lambing. Response to selection was evaluated through (a) the average breeding value of the ewe lambs chosen annually, and (b) the average breeding value of the overall flock. The first measurement suggested a positive trend for litter size, although it showed important oscillations. On the other hand, the average breeding value for the overall flock showed a stable positive tendency after yr 4 of selection, with estimates clearly different from zero after yr 11 of selection. A significant increase in the incidence of multiple births was observed, with a mode of approximately 10%. The correlated response in days to lambing did not show a significant trend. The effect of year of lambing also positively influenced both litter size and days to lambing, although important oscillations were observed between years. Results indicated that litter size in sheep can be effectively improved through phenotypic selection, even in small flocks; moreover, days to lambing could also be genetically improved, given the estimate obtained for its heritability.
Key Words: Bayesian inference • days to lambing • genetic trend • litter size • Ripollesa sheep • threshold models
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INTRODUCTION
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Litter size is one of the most important traits in meat sheep production (Olesen et al., 1994
). It should be included in meat sheep selection programs (Gabiña, 1989), although its inclusion has been limited, probably due to its low heritability (Fogarty, 1995). Phenotypic selection is commonly applied in sheep flocks, in which replacement ewes are empirically selected from the progeny of the most prolific dams. Although this phenotypic selection is a common practice in commercial meat flocks, no literature is available on the expected genetic response in litter size. The Ripollesa flock of the Uni-versitat Autònoma of Barcelona has been phenotypically selected for litter size for the last 19 yr, thus providing adequate material to study the results of phenotypic selection for ewe prolificacy.
Joint analysis of litter size and days to lambing, measured as the interval between the date when the ram is placed with ewes and the subsequent parturition, has shown important improvements in terms of goodness of fit and predictive ability (Casellas et al., 2007). Moreover, genetic trend has traditionally been estimated using frequentist techniques, although it is difficult to obtain a precise estimate of the sampling variance of the estimator of the selection response (Sorensen and Kennedy, 1986). Frequentist properties of breeding value predictors based on estimated variances have not been derived under selection and have often led to approximations that typically ignore this peculiarity of the data (Wang et al., 1994). However, this problem has a conceptually simple solution within the Bayesian framework that yields a full description of the selection response through its marginal posterior distribution.
This study was an attempt to estimate the response in litter size and days to lambing in the Ripollesa breed after a long period (19 yr) of phenotypic selection for litter size.
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MATERIALS AND METHODS
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Animal Care and Use Committee approval was not obtained for this study because the data were obtained from an existing database. The analyzed records were registered in the experimental farm of the Universitat Autónoma of Barcelona (Barcelona, Spain) between years 1986 and 2005.
Data Source
The Ripollesa is a meat-producing breed of Catalonia, Spain, coming from the entrefino Spanish trunk. It is the most abundant native sheep breed in Catalonia, distributed mainly in the provinces of Barcelona and Girona (Milán et al., 2003). Since 1986, the experimental farm of the Universitat Autònoma of Barcelona (Bellaterra, Spain) has had a Ripollesa flock that follows a fall-lambing system (Christmas harvesting), with 80 to 120 reproductive females, and an annual replacement rate of approximately 20% (Casellas et al., 2007).
In general, 3 rams were used each mating season, between April and June, and each ewe was randomly assigned to 1 of the rams. Ewes remained with the rams for 90 d. Artificial insemination was used between 1995 and 1998, and natural service began 10 to 15 d afterwards to avoid multiple paternity compatibilities. Replacement ewe lambs were mated with only 1 ram during the months of July to September. Thus, adult ewes lambed in autumn, whereas ewe lambs lambed in winter. Reproductive records of the Ripollesa flock were collected from 1986 to 2005, with a total of 1,598 parities. Phenotypic selection for prolificacy has been carried out for the last 19 yr. Replacement rams and ewes were selected from the progeny of ewes with the greatest average litter size after at least 3 deliveries were recorded.
Litter size (LS) was defined as a dichotomous trait with 2 levels: single and multiple births. Twin, triplet, and quadruplet deliveries were considered as the same phenotypic expression due to the low incidence of triplets and quadruplets. The data set had 1,598 LS records (single, 864; twins, 705; triplets, 28; and quadruplets, 1). Days to lambing (DL) was defined as the interval between the date when the rams were turned in with the flock and the subsequent parturition of the ewe, as described by Donoghue et al. (2004b). The interval included the time required to be effectively mated and the gestation length. Deliveries resulting from AI were not considered, and neither were pregnancies that did not complete the gestation period. A total of 1,699 DL records were available, with 257 of them (15.1%) censored at 240 d, corresponding to ewes that failed to lamb. See Casellas et al. (2007) for an extensive description of the data set.
Pedigree information included a total of 415 individuals, with 20 rams and 395 ewes. Litter size and DL records corresponded to 376 ewes, implying an average of 4.25 and 4.52 records per ewe, respectively. All female ancestors and most male ancestors (91.9%), were known for animals born in the experimental flock. Rams had an average of 12.5 daughters with phenotypic information within the flock.
Genetic Analysis
A bivariate animal model was used in the analysis of both ewe reproductive traits, with a threshold model (Wright, 1934) for LS and a linear model for DL. Previous analysis of the same data set showed that this threshold-linear model was preferable to univariate models as well as to models with linear approaches for LS (Casellas et al., 2007). Following Van Tassel and Van Vleck (1996) and Van Tassell et al. (1998), we assumed that the vector of LS liabilities (uLS), a set of underlying values sampled from a truncated normal distribution, and the vector of phenotypic DL data (yDL) followed a multivariate normal distribution:
where X, Z1, and Z2 were the incidence matrices of systematic (b' = [bLS ' bDL ' ]), permanent environmental (p' = [pLS ' pDL ' ]), and additive genetic effects (a' = [aLS ' aDL ' ]), and R was the 2 x 2 matrix of residual (co)-variances.
Given that some ewes did not lamb in a given lambing season and the DL trait implied right-censoring, DL censored records were included as a new parameter in the model and augmented following a data augmentation procedure (Tanner and Wong, 1987), according to the methodology described by Guo et al. (2001). The systematic effects considered were ewe age at lambing with 3 levels (<3, 3 to 5, and >5 yr) partially following Altarriba et al. (1998) and Matos el al. (1997), and year of lambing, from 1986 to 2004. Ewe lambs that lambed in January to February were considered to belong to the preceding year.
Multivariate normal priors were assumed for additive genetic and permanent environmental effects:
where A was the numerator relationship matrix, and G and P were the additive genetic and permanent environmental (co)variance matrices, respectively, both with dimensions of 2 x 2. Flat priors were assumed for systematic effects, as well as for G, P, and R, with the exception of the LS residual variance, which was fitted to 1 (Sorensen et al., 1995). In the same way, the threshold for LS liability was arbitrarily fitted to 0, following Sorensen et al. (1995).
Marginal posterior distributions of 
and variance components were obtained using Gibbs sampling (Gelfand and Smith, 1990). An additional step was required, because LS liability was also included as an unknown parameter in the model, and litter size values were sampled through data augmentation (Tanner and Wong, 1987). The Gibbs sampler was run with a single chain of 500,000 points, and the first 50,000 were discarded (Raftery and Lewis, 1992; Casellas et al., 2007).
Response to Selection Measurements
Response to selection was measured as the average breeding value of ewe lambs chosen annually and, following Al-Shorepy and Notter (1997), as the average breeding value of all ewes present in the flock each year from 1986 to 2005. Average breeding values for ewe lambs born before 1990 were grouped in the same category due to the small number of ewe lambs selected in some years (Table 1). To transform the observed genetic trend of threshold traits to probability solutions on the observable scale, we applied the procedure described by Hansen et al. (2004):
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Table 1. Number of ewe lambs chosen for replacement and number of ewes in the flock corresponding to each year from 1986 to 2005
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where Pbase was the overall frequency of the trait (for LS, a 0.4 incidence of multiple births was assumed), Pi was the predicted frequency in the ith year, ABV1986 and ABVi were the modes of the average breeding value in years 1986 and i, and 
( ) was the cumulative distribution function of a standard normal distribution, with the argument as described within parentheses. In the same way, heritability for LS was transformed to the observable scale following Dempster and Lerner (1950).
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RESULTS AND DISCUSSION
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Reproductive traits such as litter size and DL are typical examples of discrete and continuous variables with important economic weights in ovine production systems. Difficulties with the statistical analysis of categorical traits have led to implementation of approximate methods that have yielded a wide range of estimates, negative heritabilities included (Waldron and Thomas, 1992a; Fogarty, 1995), which brings into question the feasibility of improving reproductive traits such as litter size by selection (María, 1995). In addition, data sets for the estimation of variance components of ovine reproductive traits often come from flocks under genetic or phenotypic selection on those traits (Waldron and Thomas, 1992a; Al-Shorepy and Notter, 1997), which was the case with our data set. Frequentist approaches typically ignore this problem, allowing for biased estimates (Wang et al., 1994). From a Bayesian point of view, the marginal posterior distribution of the selection response could be viewed as a weighted average of an infinite number of conditional distributions, where the weighting function is the marginal posterior distribution of variances and other parameters, which are not necessarily of interest (Sorensen et al., 1994). The Bayesian methodology implied important differences with frequentist approaches, where predicted breeding values, and therefore the response to selection, depended on the previously estimated variance components. Indeed, in the Bayesian framework, all of the information on the genetic response is contained in a marginal posterior distribution; therefore, a full Bayesian inference is possible (Wang et al., 1994), although the joint posterior, or any marginal posterior, distribution becomes the same with or without selection (Sorensen et al., 1994). The development of Bayesian threshold and linear mixed models was not completed until the last few decades (Gianola and Foulley, 1983; Van Tassell and Van Vleck, 1996; Van Tassell et al., 1998), and therefore, heritability and genetic trend estimates for reproductive traits in sheep obtained using these approaches are scarce. In fact, our estimates for DL are the first reported using Bayesian models.
The mode of the marginal posterior distribution of heritability for LS in the liability scale was 0.13 (Table 2) and reduced to 0.08 in the observable scale. Historically, LS is probably the most studied reproductive trait, and LS heritabilities have been obtained in many sheep breeds using several statistical approaches. Our heritability estimate in the unobservable scale is larger than the one obtained by Altarriba et al. (1998) in the Rasa Aragonesa breed (0.08) through an animal Bayesian threshold model, and is close to the value reported by Fogarty (1995; 0.10), which was an average of estimates obtained mainly through linear methodologies. On the other hand, implementation of threshold sire models resulted in greater heritability estimates for LS in Swedish Finnsheep (ranging from 0.26 to 0.67; Urioste, 1987), Rambouillet and Finnsheep (0.45 and 0.14, respectively; Matos et al., 1997), and Norwegian sheep breeds (0.26 and 0.39; Olesen et al., 1994). Taking into account the heritability estimate obtained in our study, as well as its highest posterior density region at 95% (HPD95; Table 3), genetic improvement of LS seems feasible as was suggested by previous research (Waldron and Thomas, 1992b; Pérez-Enciso et al., 1995; Al-Shorepy and Notter, 1997). Days to lambing was lowly heritable (0.11), but the value was clearly different from zero (HPD95 = 0.042 to 0.188; Table 2). Comparable results in ovine literature are scarce, probably limited to those reported by Gabiña (1989) with heritabilities ranging between negative estimates and 0.43. Alternatively, heritability of days to calving in beef cattle was 0.07 (Donoghue et al., 2004a). Genetic, permanent environmental, and residual correlations between LS and DL were low and negative, although the null correlation falls within the HPD95 for the genetic correlation (Table 2).
Ripollesa records suggested a positive trend for average LS throughout the study period (Figure 1),whereas the trend was unclear and perhaps negative for DL. Influences due to the environment, characterized by year of lambing, showed irregular behavior, and in several years, were clearly not different from zero (Table 3
). Therefore, a clear tendency cannot be stated for the year of lambing effect, although important influences may be due to the systematic effect of specific years (Table 3). These annual systematic effects could be understood as the sum of multiple sources of variation such as forage availability, weather conditions, incidence of pathologies, etc.
The genetic trend for LS was unclear when we considered the average breeding value of replacement ewes retained annually (Figure 2). Several positive and clearly greater than zero averages, however, have been obtained since 1996, despite the wide dispersion of the marginal posterior densities of the averages of breeding values. These results show that effective selection on LS can be carried out through ewe phenotypic selection. The marginal posterior distribution of breeding value averages for ewe lambs selected annually showed a wide dispersion, likely because: 1) the number of ewe lambs selected annually was small, fewer than 25 individuals (Table 1); 2) animals were selected using the phenotypic information of their mothers, which was influenced by systematic, permanent environmental, and genetic sources of variation; and 3) sire information was not considered. On the other hand, a clear tendency was reported for the average breeding value of the Ripollesa flock over the last 20 yr. Average breeding value increased from estimates close to zero, corresponding to years between 1986 and 1995, to 0.24 in 2005 (Figure 2), the HPD95 clearly being far from zero since 1997. On the observable scale, this implied an increase in incidence of multiple births close to 10% as can be seen in Figure 3. This substantial increase in the average genetic merit for litter size of our Ripollesa flock was directly related to efficient selection of replacement animals over the years. In addition, culling decisions also influenced the flock average breeding value. Mature ewes were culled from the flock when they became unproductive, and then, besides sick ewes and animals with physical problems (e.g., mastitic udders), ewes with a lower average LS were culled. Therefore, ewes with a lower breeding value for LS were culled sooner than the remaining ewes. The genetic trend reported for Ripollesa LS agrees with the values described by Atkins (1980) in Rambouillet sheep, Bhuiyan and Curran (1993) in Romney Marsh, and Pérez-Enciso et al. (1995) in Merino and Lacaune breeds.
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Figure 2. Genetic trend for litter size measured as the average breeding value of ewe lambs (A) and the flock average breeding value (B; error bars show the highest posterior density region at 95%).
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Figure 3. Trend for probability of twins on the observable scale (note that the overall frequency of twins was assumed to be 0.40).
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Study of the correlated genetic response in DL did not reveal a substantial trend based on ewe lambs or on overall flock average breeding values (Figure 4). Despite the magnitude of the maximum (1.831) and minimum (–1.838) estimates for ewe lambs (corresponding to years 1994 and 2002, respectively), the HPD95 always included zero. This result was expected given the moderate genetic correlation observed between LS and DL, as well as its HPD95 (Table 2). However, the heritability reported for this trait suggests that DL can be improved by direct selection.
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Figure 4. Genetic trend for days to lambing measured as average breeding value of ewe lambs (A) and flock average breeding value (B; error bars show the highest posterior density region at 95%).
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In conclusion, present research indicated that phenotypic selection on LS in Ripollesa ewes can lead to genetic improvement of this trait. The Bayesian threshold-linear model allowed for consideration of systematic effects, as well as permanent environmental, genetic, and residual sources of variation. Ours is the first work to analyze the selection response of LS using this methodology. Our results will contribute to the development of breeding schemes for the Ripollesa breed, a representative Mediterranean sheep breed used for meat production.
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IMPLICATIONS
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Our results confirm that it is feasible to improve the reproductive performance of the Ripollesa breed through phenotypic selection. After 19 yr of phenotypic selection, the incidence of multiple births increased by approximately 10%, although correlated response in days to lambing was not observed. The phenotypic improvement was also due to the permanent environmental influences characterized by year of lambing. As a whole, these results highlighted the reproductive potential of the Ripollesa breed, a representative Mediterranean breed of sheep. The Bayesian threshold methodology proved to be useful for the study of discrete and continuous reproductive traits because it avoids the use of analytical approximations that can lead to distorted inferences.
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Footnotes
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1 Research supported by a contract with the Departament d’Agri-cultura, Ramaderia i Pesca de la Generalitat de Catalunya (Spain) and a Universitat Autònoma de Barcelona (Bellaterra, Spain) fellowship granted to J. Casellas. The authors appreciate the assistance of R. Costa and the crew of the S1GCE (Servei de Granges i Camps Experimentals de la UAB, Bellaterra, Spain) for feeding and care of the animals. We thank L. Varona for contributing the software. The English revision of N. Aldam is also acknowledged. 
3 Current address: Grup de Recerca en Nutrició, Maneig i Benestar Animal, Departament de Ciència Animal i dels Aliments, Universitat Autònoma de Barcelona.
2 Corresponding author: joaquim.casellas{at}uab.es
Received for publication June 7, 2006.
Accepted for publication October 17, 2006.
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Abstract
INTRODUCTION
