Segregation analysis of a sex ratio distortion locus in congenic mice

The congenic HG.CAST-(D17Mit196-D17Mit190) (HQ17(hg/hg)) mouse strain showed a significant departure on the expected 50%/50% offspring sex ratio in more than 2400 progeny (55.7% females). The entire pedigree file included data from 13 nonoverlapping purebred generations and an F(2) cross with the C57BL/6J inbred strain. Offspring sex ratio data were analyzed on the basis of 40 purebred HQ17(hg)(/hg) sires and 29 F(1) HQ17(hg)(/hg) x B6 sires under a Bayesian Binomial segregation model accounting for 4 different autosomal inheritance models of gene action (i.e., additive, dominance, recessive, and overdominance) and X-linked and Y-linked loci. For each model, the segregation effect was evaluated as a single regression coefficient for all sires or assuming 2 independent regression coefficients accounting for offspring sex ratio departures in purebred and F(1) sires, respectively. The deviance information criterion clearly favored the autosomal dominance model with different regression coefficients for the 2 groups of sires. Under this model, the dominance effect increased the percentage of female offspring by 4.3% (HQ17(hg)(/hg) purebred sires) and 8.2% (F(1) sires) with the highest posterior density regions ranging from 0.5% to 10.6% and from 1.3% to 14.4%, respectively. This article provides significant evidence of genetic determinism for sex ratio distortion in the HQ17(hg)(/hg) strain and develops new analytical tools to perform segregation studies on dichotomous traits.

Accounting for additive genetic mutations on litter size in Ripollesa sheep

Little is known about mutational variability in livestock, among which only a few mutations with relatively large effects have been reported. In this manuscript, mutational variability was analyzed in 1,765 litter size records from 404 Ripollesa ewes to characterize the magnitude of this genetic source of variation and check the suitability of including mutational effects in genetic evaluations of this breed. Threshold animal models accounting for additive genetic mutations were preferred to models without mutational contributions, with an average difference in the deviance information criterion of more than 5 units. Moreover, the statistical relevance of the additive genetic mutation term was checked through a Bayes factor approach, which showed that the models with mutational variability were 8.5 to 22.7 times more probable than the others. The mutational heritability (percentage of the phenotypic variance accounted for by mutational variance) was 0.6 or 0.9%, depending on whether genetic dominance effects were accounted for by the analytical model. The inclusion of mutational effects in the genetic model for evaluating litter size in Ripollesa ewes called for some minor modifications in the genetic merit order of the individuals evaluated, which suggested that the continuous uploading of new additive mutations could be taken into account to optimize the selection scheme. This study is the first attempt to estimate mutational variances in a livestock species and thereby contribute to better characterization of the genetic background of productive traits of interest.

Evidence of maternal QTL affecting growth and obesity in adult mice

Most quantitative trait loci (QTL) studies fail to account for the effect that the maternal genotype may have on an individual's phenotypes, even though maternal effect QTL have been shown to account for considerable variation in growth and obesity traits in mouse models. Moreover, the fetal programming theory suggests that maternal effects influence an offspring's adult fitness, although the genetic nature of fetal programming remains unclear. Within this context, our study focused on mapping genomic regions associated with maternal effect QTL by analyzing the phenotypes of chromosomes 2 and 7 subcongenic mice from genetically distinct dams. We analyzed 12 chromosome 2 subcongenic strains that spanned from 70 to 180 Mb with CAST/EiJ donor regions on the background of C57BL/6 J, and 14 chromosome 7 subcongenic strains that spanned from 81 to 111 Mb with BALB/cByJ donor regions on C57BL/6ByJ background. Maternal QTL analyses were performed on the basis of overlapping donor regions between subcongenic strains. We identified several highly significant (P < 5 x 10(-4)) maternal QTL influencing total body weight, organ weight, and fat pad weights in both sets of subcongenics. These QTL accounted for 1.9-11.7% of the phenotypic variance for growth and obesity and greatly narrowed the genomic regions associated with the maternal genetic effects. These maternal effect QTL controlled phenotypic traits in adult mice, suggesting that maternal influences at early stages of development may permanently affect offspring performance. Identification of maternal effects in our survey of two sets of subcongenic strains, representing approximately 5% of the mouse genome, supports the hypothesis that maternal effects represent significant sources of genetic variation that are largely ignored in genetic studies.

Genetic background and phenotypic characterization over two farrowings of leg conformation defects in Landrace and Large White sows

A Bayesian threshold animal model was applied to evaluate the prevalence over 2 farrowings and genetic background of overall leg conformation score and the presence or absence of 6 specific leg defects (abnormal hoof growth, splay footed, plantigradism, straight pasterns, sickle-hocked legs, and the presence of swelling or injuries) in purebred Landrace and Large White sows. Data sets contained phenotypic records from 2,477 and 1,550 Landrace and Large White females, respectively, at the end of the growing period. Leg conformation data from first and second farrowings were available for 223 and 191 Landrace sows and 213 and 193 Large White sows, respectively. Overall leg conformation deteriorated with age, with statistically relevant differences between females at the end of the growing period, first farrowing (FF), and second farrowing (SF). In a similar way, the prevalence of the 6 specific leg defects increased between the end of the growing period and FF (with the exception of straight pasterns in the Landrace population). Differences between FF and second farrowing were statistically relevant for hoof growth (highest posterior density regions at 95% did not overlap), plantigradism, sickle-hocked legs, and overall leg conformation score in Landrace and for sickle-hocked leg and overall leg conformation score in Large White. The statistical relevance of the genetic background was tested through the Bayes factor (BF) between the model with the additive genetic component and the model with 0 heritability (nonheritable). Heritability (h(2)) was discarded (BF < 1) for sickle-hocked leg in both breeds, whereas decisive evidence (BF > 100) of genetic background was obtained for overall leg conformation score in Landrace and Large White sows (h(2) = 0.27 and 0.38, respectively), hoof growth in both breeds (h(2) = 0.22 and 0.26, respectively), and plantigradism (h(2) = 0.34) and the presence of swelling or injuries in Landrace (h(2) = 0.27). Note that a BF > 100 implies that the model with infinitesimal genetic effects was more than 100 times more suitable than the model without genetic effects, a conclusive estimate within the Bayesian framework. The remaining traits (splay footed and straight pasterns) registered BF values ranging from 11.6 to 35.1 and h(2) values ranging from 0.09 to 0.19. These results indicated a moderate genetic determinism for leg conformation in Landrace and Large White sows.

Fine mapping and association analysis of a quantitative trait locus for milk production traits on Bos taurus autosome 4

To fine map a quantitative trait locus (QTL) affecting milk production traits previously associated with microsatellite RM188, we implemented an interval mapping analysis by using microsatellite markers in a large Israeli Holstein half-sib sire family, and linkage disequilibrium (LD) mapping in a large set of US Holstein bulls. Interval mapping located the target QTL to the near vicinity of RM188. For the LD mapping, we identified 42 single nucleotide polymorphisms (SNP) in 15 genes in a 12-Mb region on bovine chromosome 4. A total of 24 tag SNP were genotyped in 882 bulls belonging to the University of California Davis archival collection of Holstein bull DNA samples with predicted transmitted ability phenotypes. Marker-to-marker LD analysis revealed 2 LD blocks, with intrablock r(2) values of 0.10 and 0.46, respectively; outside the blocks, r(2) values ranged from 0.002 to 0.23. A standard additive/dominance model using the generalized linear model procedure of SAS and the regression module of HelixTree software were used to test marker-trait associations. Single nucleotide polymorphism 9 on ARL4A, SNP10 on XR_027435.1, SNP12 on ETV1, SNP21 on SNX13, and SNP24 were significantly associated with milk production traits. We propose the interval encompassing ARL4A and SNX13 genes as a candidate region in bovine chromosome 4 for a concordant QTL related to milk protein traits in dairy cattle. Functional studies are needed to confirm this result.

Lack of Socs2 expression reduces lifespan in high-growth mice

The high-growth (HG) phenotype in mice is characterized by a 30-50% postweaning overgrowth with a substantial increase in plasma insulin-like growth factor I (IGF1) levels, which is directly related to a deletion (hg) on chromosome 10 that includes the suppressor of cytokine signaling 2 (Socs2) gene. Reduced plasma IGF1 levels have been associated with extended lifespan in mice, although the aging-related effects of abnormally high IGF1 levels without elevated growth hormone levels have never been assessed in mammals. Within this context, the hg deletion was introgressed into C57BL/6J (B6) and FVB backgrounds, and a survival analysis was performed on the longevity records of 200 B6 (91 wild-type and 109 homozygous hg mutants) and 69 FVB (32 wild-type and 37 hg mutants) mice. Longevity was examined using a piecewise Weibull proportional hazards model solved through a Bayesian perspective and Markov chain Monte Carlo sampling. Lifespan was significantly reduced in both strains in homozygous hg mice, with a death risk between 3.689 (B6) and 4.347 (FVB) times higher than in wild-type mice (non-overlapped highest posterior density regions at 95%). These results highlight the effects of the Socs2 gene on aging regulation, likely related with variations described in plasma IGF1 levels. This result is consistent with previous research in dwarf mutant mice and other species, and characterizes the HG mutant mice as a unique and interesting animal model for accelerated aging research.

Analysis of founder-specific inbreeding depression on birth weight in Ripollesa lambs

Although inbreeding (F) is a topic of major concern in animal breeding, estimates of inbreeding depression are usually obtained by modeling the overall F coefficient of each individual, without considering that the recessive (deleterious) genetic load of a given population may be unevenly distributed among the founder genomes. The founder-specific partial F coefficient is calculated as the identity-by-descent probability at any given autosomal locus related to a particular founder and allows a more detailed analysis of inbreeding depression on productive traits. Within this context, birth BW data from 2,459 Ripollesa lambs were analyzed under a hierarchical animal model without F-related covariates (model 0), with inbreeding depression modeled by the overall F coefficient (model F1), or by the partial F coefficient of 9 founders that made a relevant contribution to the population inbreeding (model F2). A straightforward empirical Bayes factor (BF) was developed for testing statistical relevance of each F-related covariate, in which greater-than-1 values favored the model including the covariate. The deviance information criterion (DIC) clearly supported model F1 (5,767.8) rather than model 0 (5,771.2), suggesting that inbreeding depression had a relevant influence on birth BW data. The linear effect of inbreeding depression was statistically relevant in model F1 (BF = 2.52 x 10(35)), with lamb birth BW declining by -13.6 g with each 1% F increase. The quadratic effect of inbreeding depression was almost null in model F1 (BF = 0.02), as suggested by the reduction in DIC (5,766.9) when this effect was removed from model F1. On the other hand, model F2 provided a similar DIC (5,767.9) value, with this parameter decreasing to 5,764.7 when nonrelevant founder-specific inbreeding depression effects were removed. Substantial heterogeneity in founder-specific inbreeding depression was reported by model F2, in which estimates for 4 of the 9 founders did not differ from zero (BF between 0.05 and 0.42), whereas 5 founders originated moderate (-8.2 g for each 1% F increase; BF = 1.42) to large inbreeding depression (-96.2 g for each 1% F increase; BF = 8.80 x 10(19)). The substantial variability between founder estimates suggested that inbreeding depression effects may mainly be due to a few alleles with major deleterious effects. These results contribute valuable information that should help to achieve more accurate management of inbreeding in the Ripollesa breed.

Bayesian threshold analysis of direct and maternal genetic parameters for piglet mortality at farrowing in Large White, Landrace, and Pietrain populations

A Bayesian threshold model was fitted to analyze the genetic parameters for farrowing mortality at the piglet level in Large White, Landrace, and Pietrain populations. Field data were collected between 1999 and 2006. They were provided by 3 pig selection nucleus farms of a commercial breeding company registered in the Spanish Pig Data Bank (BDporc). Analyses were performed on 3 data sets of Large White (60,535 piglets born from 4,551 litters), Landrace (57,987 piglets from 5,008 litters), and Pietrain (42,707 piglets from 4,328 litters) populations. In the analysis, farrowing mortality was considered as a binary trait at the piglet level and scored as 1 (alive piglet) or 0 (dead piglet) at farrowing or within the first 12 h of life. Each breed was analyzed separately, and operational models included systematic effects (year-season, sex, litter size, and order of parity), direct and maternal additive genetic effects, and common litter effects. Analyses were performed by Bayesian methods using Gibbs sampling. The posterior means of direct heritability were 0.02, 0.06, and 0.10, and the posterior means of maternal heritability were 0.05, 0.13, and 0.06 for Large White, Landrace, and Pietrain populations, respectively. The posterior means of genetic correlation between the direct and maternal genetic effects for Landrace and Pietrain populations were -0.56 and -0.53, and the highest posterior intervals at 95% did not include zero. In contrast, the posterior mean of the genetic correlation between direct and maternal effects was 0.15 in the Large White population, with the null correlation included in the highest posterior interval at 95%. These results suggest that the genetic model of evaluation for the Landrace and Pietrain populations should include direct and maternal genetic effects, whereas farrowing mortality could be considered as a sow trait in the Large White population.

Bayes factor between Student t and Gaussian mixed models within an animal breeding context

The implementation of Student t mixed models in animal breeding has been suggested as a useful statistical tool to effectively mute the impact of preferential treatment or other sources of outliers in field data. Nevertheless, these additional sources of variation are undeclared and we do not know whether a Student t mixed model is required or if a standard, and less parameterized, Gaussian mixed model would be sufficient to serve the intended purpose. Within this context, our aim was to develop the Bayes factor between two nested models that only differed in a bounded variable in order to easily compare a Student t and a Gaussian mixed model. It is important to highlight that the Student t density converges to a Gaussian process when degrees of freedom tend to infinity. The twomodels can then be viewed as nested models that differ in terms of degrees of freedom. The Bayes factor can be easily calculated from the output of a Markov chain Monte Carlo sampling of the complex model (Student t mixed model). The performance of this Bayes factor was tested under simulation and on a real dataset, using the deviation information criterion (DIC) as the standard reference criterion. The two statistical tools showed similar trends along the parameter space, although the Bayes factor appeared to be the more conservative. There was considerable evidence favoring the Student t mixed model for data sets simulated under Student t processes with limited degrees of freedom, and moderate advantages associated with using the Gaussian mixed model when working with datasets simulated with 50 or more degrees of freedom. For the analysis of real data (weight of Pietrain pigs at six months), both the Bayes factor and DIC slightly favored the Student t mixed model, with there being a reduced incidence of outlier individuals in this population.

Between-groups within-gene heterogeneity of residual variances in microarray gene expression data

Background

The analysis of microarray gene expression data typically tries to identify differential gene expression patterns in terms of differences of the mathematical expectation between groups of arrays (e.g. treatments or biological conditions). Nevertheless, the differential expression pattern could also be characterized by group-specific dispersion patterns, although little is known about this phenomenon in microarray data. Commonly, a homogeneous gene-specific residual variance is assumed in hierarchical mixed models for gene expression data, although it could result in substantial biases if this assumption is not true.

Results

In this manuscript, a hierarchical mixed model with within-gene heterogeneous residual variances is proposed to analyze gene expression data from non-competitive hybridized microarrays. Moreover, a straightforward Bayes factor is adapted to easily check within-gene (between groups) heterogeneity of residual variances when samples are grouped in two different treatments. This Bayes factor only requires the analysis of the complex model (hierarchical mixed model with between-groups heterogeneous residual variances for all analyzed genes) and gene-specific Bayes factors are provided from the output of a simple Markov chain Monte Carlo sampling.

Conclusion

This statistical development opens new research possibilities within the gene expression framework, where heterogeneity in residual variability could be viewed as an alternative and plausible characterization of differential expression patterns.

Effect of leg conformation on survivability of Duroc, Landrace, and Large White sows

Sow longevity influences farm economy and can be considered an important indicator of animal welfare. Body features such as leg conformation can play a key role in sow longevity, although little is known about its effect on culling decisions. Within this context, longevity data from 587 Duroc, 239 Landrace, and 217 Large White sows were analyzed with special emphasis on the effect of leg conformation. Sow longevity was analyzed twice for each breed, testing the effect of a subjective overall score for leg conformation, or the presence or absence of 6 specific leg conformation defects. Each preliminary model also included a teat conformation score with 3 levels, farm or origin, backfat thickness at 6 mo of age, and 2 continuous sources of variation, namely the age at the first farrowing and the number of piglets born alive at each farrowing. Overall leg conformation score influenced (P < 0.01) sow longevity in Duroc, Landrace, and Large White sows, with a greater hazard ratio (HR) for poorly conformed sows (1.56, 2.16, and 1.79, respectively) than for well-conformed sows (0.32, 0.66, and 0.68, respectively). Abnormal hoof growth reduced survivability in Duroc (HR = 2.78; P < 0.001) and Landrace sows (HR = 1.88; P < 0.01); the presence of splayed feet (P < 0.05) or bumps and injuries (P < 0.001) increased the risk of culling in Duroc sows (HR = 2.08 and 3.57, respectively), whereas the incidence of straight pastern increased the HR in Large White sows (HR = 2.49; P < 0.01). In all 3 breeds, longevity decreased for plantigrade sows, with a greater HR in Duroc (HR = 3.38; P < 0.001) than in Landrace (HR = 1.53; P < 0.10) and Large White sows (HR = 1.73; P < 0.05). Teat conformation did not influence sow longevity (P > 0.10). Estimates of heritability for longevity in Duroc sows ranged from 0.05 to 0.07 depending on the algorithm applied. Leg conformation had a substantial effect on sow longevity, where an accurate removal of poorly leg-conformed candidate gilts before first mating could improve sow survival and reduce culling costs. These moderate estimates of heritability indicated that survivability of Duroc sows could be genetically improved by direct selection for leg conformation.

Bayesian inference in a piecewise Weibull proportional hazards model with unknown change points

The main difference between parametric and non-parametric survival analyses relies on model flexibility. Parametric models have been suggested as preferable because of their lower programming needs although they generally suffer from a reduced flexibility to fit field data. In this sense, parametric survival functions can be redefined as piecewise survival functions whose slopes change at given points. It substantially increases the flexibility of the parametric survival model. Unfortunately, we lack accurate methods to establish a required number of change points and their position within the time space. In this study, a Weibull survival model with a piecewise baseline hazard function was developed, with change points included as unknown parameters in the model. Concretely, a Weibull log-normal animal frailty model was assumed, and it was solved with a Bayesian approach. The required fully conditional posterior distributions were derived. During the sampling process, all the parameters in the model were updated using a Metropolis-Hastings step, with the exception of the genetic variance that was updated with a standard Gibbs sampler. This methodology was tested with simulated data sets, each one analysed through several models with different number of change points. The models were compared with the Deviance Information Criterion, with appealing results. Simulation results showed that the estimated marginal posterior distributions covered well and placed high density to the true parameter values used in the simulation data. Moreover, results showed that the piecewise baseline hazard function could appropriately fit survival data, as well as other smooth distributions, with a reduced number of change points.

Survival quantitative trait locus fine mapping by measuring and testing for Hardy-Weinberg and linkage disequilibrium

I show that fine-scale localization of a survival-related locus can be accomplished on the basis of deviations from Hardy-Weinberg equilibrium and linkage disequilibrium at closely linked marker loci. The method is based on chi(2)-tests and they can be performed for age-specific samples of alive (or dead) individuals, as for combined samples of alive and dead individuals.

Analysis of litter size and days to lambing in the Ripollesa ewe. I. Comparison of models with linear and threshold approaches1

The analysis focused on model fitting of 2 ewe reproductive traits, litter size, and days to lambing (interval between the introduction of the ram into the flock and the subsequent parturition of the ewes). The experimental data set of the Universitat Autònoma of Barcelona flock was used, including 1,598 records of litter size and 1,699 records of days to lambing from 376 Ripollesa ewes between 1986 and 2005. Univariate and bivariate models were considered as beginning points with linear or threshold approximation for litter size. Model fitting was evaluated in terms of goodness-of-fit and predictive ability, using the mean square error and the correlation between phenotypic and predicted records (rho(y,ŷ)) as reference parameters. The bivariate model was preferable for both variables, minimizing mean square error and maximizing rho(y,ŷ). A threshold approximation for litter size was preferable over a linear approximation. Models were also compared with a simulation study, comparing the correlation coefficient between simulated and predicted breeding values (rho(a,â)). The bivariate threshold model was favored, with a rho(y,ŷ) of 0.677 and 0.834 for litter size and days to lambing, respectively. Correlation coefficients between simulated and predicted breeding values in the bivariate linear model were reduced slightly to 0.651 and 0.831, respectively, and they were lowest with linear univariate models (0.642 and 0.802). Although the bivariate models for ewe litter size and days to lambing were more accurate than the univariate models, the threshold approaches showed a greater advantage under the bivariate model. For the purpose of genetic evaluation of litter size in sheep, use of the threshold-linear model seems justified. In the Ripollesa breed, the evaluation of litter size can benefit from recording birth weight.

Association analyses between the prion protein locus and reproductive and lamb weight traits in Ripollesa sheep1

The objective of this study was to analyze the association between the haplotypes of the prion protein (PrP) locus and several reproductive and lamb weight traits in Ripollesa sheep. Prion protein genotypes were available for a total of 310 sheep (7 rams, 114 ewes, and 189 lambs), all of them belonging to the purebred Ripollesa flock of the Universitat Autònoma of Barcelona, for which all sheep had a known pedigree. In addition, the genotype of 24 historical descendants of the previously genotyped adult individuals was reconstructed, provided that both parents were homozygous for PrP haplotypes. Only 3 haplotypes (ARR, ARQ, and ARH) were observed in the PrP locus of the sheep sampled. Reproductive traits included conception rate and litter size, whereas birth BW and 90-d BW were the lamb weight traits studied. The additive effect of PrP haplotypes was analyzed through Bayesian animal threshold and linear models, for reproduction and weight traits, respectively. Ewe reproductive data belonged to 89 ewes that gave 492 conception rate records and 440 litter size records. Analyses of BW at birth and at 90 d of age were made on 323 and 164 lamb records, respectively. No associations between PrP haplotypes and conception rate and BW traits were observed. For litter size, the effect of the ARH haplotype was greater than that of the ARQ haplotype. Differences between ARH and ARR haplotypes also suggested an advantage for the ARH. As a whole, our results indicated that the selection favorable to increase litter size in Ripollesa ewes may also increase the ARH haplotype frequency, which contradicts the recommendations of the current European Union legislation aiming to increase the genetic resistance to scrapie. As a consequence, scrapie genotyping needs to be included as a new selection criterion in the breed.

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

A performance data set from 376 Ripollesa 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.

Survival analysis from birth to slaughter of Ripollesa lambs under semi-intensive management1

The survivability from birth to slaughter of 1,487 Ripollesa lambs with a preslaughter overall mortality of 9.6% was studied under the proportional hazards framework, assuming a Weibull distribution for the baseline hazards function. A sire frailty model was fitted, with the common environment received by the lamb as an additional random source of variation. Common environment was considered time-dependent and was characterized by the dam and the contemporary lamb group during the preweaning and fattening periods, respectively. Only 3 fixed effects were statistically significant: the linear and quadratic effects of birth weight (P < 0.001), the relative position of the delivery within the lambing season (P < 0.001), and the presence of stillbirths or mummified fetuses within the litter (P < 0.05). Birth type and parity of the ewe were significant only when birth weight was removed from the model (P < 0.001 and P < 0.05, respectively). Nevertheless, the model including birth weight became preferable according to the Akaike's information criterion. Survivability dramatically decreased with extreme birth weights, although it reached a survival probability greater than 93.5% within the 3.3 to 5.4 kg range, indicating an optimum birth weight range of Ripollesa lambs for survival purposes. The hazard ratio (HR) increased for births occurring within the last third of the lambing period (HR = 1.70; P < 0.05), as well as for primiparous ewes that lambed in December and January (HR = 5.36; P < 0.001). Survival probability decreased for lambs born from litters with 1 or more stillbirths or mummified fetuses (HR = 1.61; P < 0.05). The variance component estimated for sire variance (0.07) was clearly lower than that of the common environment (1.87), with a heritability estimate of 0.027.

Bayes factor for testing between different structures of random genetic groups: a case study using weaning weight in Bruna dels Pirineus beef cattle

The implementation of genetic groups in BLUP evaluations accounts for different expectations of breeding values in base animals. Notwithstanding, many feasible structures of genetic groups exist and there are no analytical tools described to compare them easily. In this sense, the recent development of a simple and stable procedure to calculate the Bayes factor between nested competing models allowed us to develop a new approach of that method focused on compared models with different structures of random genetic groups. The procedure is based on a reparameterization of the model in terms of intraclass correlation of genetic groups. The Bayes factor can be easily calculated from the output of a Markov chain Monte Carlo sampling by averaging conditional densities at the null intraclass correlation. It compares two nested models, a model with a given structure of genetic groups against a model without genetic groups. The calculation of the Bayes factor between different structures of genetic groups can be quickly and easily obtained from the Bayes factor between the nested models. We applied this approach to a weaning weight data set of the Bruna dels Pirineus beef cattle, comparing several structures of genetic groups, and the final results showed that the preferable structure was an only group for unknown dams and different groups for unknown sires for each year of calving.