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The aim of this study was to compare the goodness of fit of the threshold models with homoscedasticity or heteroscedasticity and the grouped data model for the analysis of calving ease in beef cattle by using a parametric bootstrap procedure. Field data included 8,205 records of the Bruna dels Pirineus beef cattle breed in the Pyrenean mountain areas of Catalonia (Spain). The actual distribution was 81.81% of calvings without assistance, 11.02% slightly assisted by the farmer, 5.12% strongly assisted by the farmer, 0.89% assisted by the veterinarian, and 1.16% cesarean, but these percentages were very different in the different herds. This can be explained partially by the different subjective way of scoring of each farmer. Primiparous cows had a greater (P < 0.001) difficulty calving than cows with 5 or more parities (11.74 vs. 4.49% of calvings strongly assisted by the farmer or the veterinarian and 2.8 vs. 0.65% cesarean). Male calves caused greater (P < 0.001) calving difficulty than females (7.71% of male calvings strongly assisted by the farmer or the veterinarian vs. 4.25% of females and 1.83% cesarean in males vs. 0.47% in females). The month and year of calving also had a strong influence on calving ease. These data were analyzed using 3 different models: the threshold models with homoscedasticity or heteroscedasticity and the grouped data model. The bootstrap comparison among models suggested that the threshold models, even allowing for heteroscedasticity, did not fit the herd effects well. In contrast, fitting deficiencies were not observed for the grouped data model in any factor. The variance of direct effect of the calf was estimated using the 3 models, and the heritability estimate ranged from 0.165 for the grouped data model to 0.185 for the hereroscedastic threshold model. This heritability was moderate, but it would justify the inclusion of direct effects of the calf on calving ease in the breeding objective. Overall, results highlighted the flexibility of the grouped data model for the analysis of discrete traits, like calving ease of beef calves. Key words: beef cattle, bootstrap, calving ease, grouped data model, heritability, threshold model doi: 10.2527/jas.2009-2720

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. Key words: animal breeding, genetic variability, litter size, mutation, Ripollesa breed doi: 10.2527/jas.2009-2117

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.sup.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.sup.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. Key words: birth weight, empirical Bayes factor, founder, inbreeding depression, Ripollesa sheep

A performance data set from 376 Ripollesa purebred ewes of the experimental flock of the Universitat Autbnoma 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

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 Autonoma 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].sub.y,x]) as reference parameters. The bivariate model was preferable for both variables, minimizing mean square error and maximizing [[rho].sub.y,x]. 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].sub.a,[??]). The bivariate threshold model was favored, with a [[rho].sub.y,[??]] 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. Key words: days to lambing, goodness-of-fit, litter size, predictive ability, Ripollesa breed

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 Autbnoma 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. Key words: birth weight, conception rate, litter size, prion protein, Ripollesa breed, sheep

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 [less than or equal to] 0.001), the relative position of the delivery within the lambing season (P [less than or equal to] 0.001), and the presence of stillbirths or mummified fetuses within the litter (P [less than or equal to] 0.05). Birth type and parity of the ewe were significant only when birth weight was removed from the model (P [less than or equal to] 0.001 and P [less than or equal to] 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 [less than or equal to] 0.05), as well as for primiparous ewes that lambed in December and January (HR = 5.36; P [less than or equal to] 0.001). Survival probability decreased for lambs born from litters with 1 or more stillbirths or mummified fetuses (HR = 1.61; P [less than or equal to] 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. Key words: lamb survival, proportional hazard, Ripollesa breed, survival analysis

Given that correct assumptions on the baseline survival function are determinant for the validity of further inferences, specific tools to test the fit of a model to real data become essential in proportional hazards models. In this sense, we have proposed a parametric bootstrap to test the fit of survival models. Monte Carlo simulations are used to generate new data sets from the estimates obtained through the assumed models, and then bootstrap intervals can be established for the survival function along the time space studied. Significant fitting deficiencies are revealed when the real survival function is not included within the bootstrap interval. We tested this procedure in a survival data set of Bruna dels Pirineus beef calves, assuming 4 parametric models (exponential, Weibull, exponential time-dependent, Weibull time-dependent) and the Cox's semiparametric model. Fitting deficiencies were not observed for the Cox's model and the exponential time-dependent model, whereas the Weibull time-dependent model suffered from moderate overestimation at different ages. Thus, the exponential time-dependent model appears to be preferable because of its correct fit for survival data of beef calves and its smaller computational and time requirements. Exponential and Weibull models were completely rejected due to the continuous over- and underestimation of the survival probability reported. Results here highlighted the flexibility of parametric models with time-dependent effects, achieving a fit comparable to nonparametric models. Key words: model fitting, parametric bootstrap, proportional hazard, survival analysis

Survival analysis techniques were used to analyze survival up to weaning of beef calves in the Pyrenean mountains areas of Catalonia, Spain. The Kaplan-Meier curve showed that the survival experience was not constant throughout the lactation period, as the mortality rate was more pronounced during the first month of life. The proportional hazards model analysis showed that several factors influenced the instantaneous mortality rate, with the herd-year effect having the strongest influence. Calves born in the first part of the breeding season, from September to February, had the lowest mortality risk (P < 0.001), showing that mortality risk increases as births accumulate. Calves from cows younger than 1,300 d of productive life had a higher risk of mortality (P < 0.05). Unassisted calvings presented the smallest risk of mortality, and mortality risk increased up to five times as birth became more difficult (P < 0.001). This risk also tended to increase slightly when calf birth weight was small (P < 0.10); for bigger calves, no increase of risk was detected, probably because calving difficulty was included in the model. These results suggest the need for improving the environment in the second part of the breeding period and paying more attention to births from younger cows. The survival curve fitted a parametric piecewise exponential function very well, with cut points at 16 and 32 d. The lower risk corresponded to the period of 33 to 180 d, the risk for the periods 17 to 32 d and I to 16 d being multiplied by 7 and 26, respectively. Confirming the robustness of the Cox model, the relative risks estimated for the different factors under this piecewise exponential model or a Weibull time-dependent model were similar to those reported above, as well as to those estimated under a frailty model, including the sire as a random effect. The modal estimates of sire variance under different baseline functions were close to 0.3, although the standard errors were very large. At weaning, the heritability estimate in the binary scale reached a value of only 0.037 because the survival at weaning was very high (96.9%) in this population. Nevertheless, in populations with a higher mortality, the inclusion of survival to weaning in the breeding objective might be justified. Overall, these results show that survival analysis is a powerful tool to analyze the mortality curve until weaning of beef calves. Key Words: Beef Cattle, Heritability, Survival Analysis, Survival to Weaning

The Bayes factor (BF) procedure was applied to examine the additive genetic component of several physiological and vitality variables for newborn pigs. Nine variables were studied: heart rate, arterial oxygen saturation, rectal temperature (all at birth and 60 min later), birth weight, interval between birth and first teats contact, and interval between birth and first colostrum intake. The available numbers of data ranged from 288 (heart rate at 60 min) to 839 records (birth weight) from [F.sub.2] Iberian x Meishan newborn pigs. We compared a model with zero heritability (nonheritable) with the one where the additive genetic background was included. The BF was used to discriminate between both candidate models. Very strong evidence of genetic background was detected for heart rate 60 min after birth (BF = 48.90), and strong evidence was detected for rectal temperature at birth (BF = 13.82). Posterior modes (means) of heritabilities were 0.29 (0.32) and 0.40 (0.39), respectively. In addition, substantial evidence of absence of genetic background was detected for arterial oxygen saturation at birth. Key Words: Bayes Factor, Neonate Metabolism, Survival, Vitality

Iberian x Meishan [F.sub.2] piglet's preweaning survivability was analyzed using categorical data regression procedures within the proportional hazards assumption. A frailty sire model was assumed with the litter effect treated as an additional random source of variation. Moreover, the relative birth weight within litter and the litter effect were considered time-dependent covariates that changed their values in the second day of life due to cross fostering carried out to standardize litters. Six variables had a significant effect on survivability: birth weight (P < 0.01), relative birth weight within litter (P < 0.001), rectal temperature 60 min after birth (P < 0.01), type of presentation at birth (P < 0.05), presence of stillbirths (P < 0.001), and presence of mummified fetuses (P < 0.001). Small piglets ( Key Words: Categorical Survival Analysis, [F.sub.2] Piglets, Preweaning Survival, Proportional Hazards

Eight physiological and vitality variables related to the first minutes of the life of Iberian x Meishan [F.sub.2] piglets were analyzed. Variables included rectal temperature, arterial oxygen saturation, heart rate (all were monitored at birth and 60 min later), time to reach the udder, and time to the first colostrum intake. Litter effect within boar, a random source of variation, influenced all variables, whereas the random boar effect was not significant for heart rate and arterial oxygen saturation at birth and the time to reach the udder. Birth weight influenced rectal temperature at birth (P < 0.01) and 60 min later (P < 0.001), arterial oxygen saturation 1 h after birth (P < 0.05), heart rate 1 h after birth (P < 0.001), time to reach the udder (P < 0.05), and time to the first suckle (P < 0.01), whereas viability score influenced rectal temperatures (at birth and 60 min later; P < 0.001), and time to reach the udder (P < 0.001) and to suckle (P < 0.001). Finally, the order of birth showed significant effects for rectal temperature 1 h after birth (P < 0.001) and time to first colostrum intake (P < 0.001). Correlation coefficients between physiological variables were generally low, with the exception of the ones for rectal temperature 1 h after birth and arterial oxygen saturation 1 h after birth (0.38; P < 0.001), and for rectal temperature at birth and rectal temperature i h after birth (0.34; P < 0.001). Times to reach the udder and to suckle were highly correlated (0.67; P < 0.001) and also were moderately and negatively correlated with rectal temperature 1 h after birth (-0.36 and -0.38 respectively; P < 0.001). Heart rates at birth and i h later, as well as arterial oxygen saturation at birth and 1 h later, were not correlated, showing that the values at birth do not necessarily provide information about the physiological status of the pig 1 h after birth. The recording of physiological variables, birth weight, and viability score may be useful to identify weak piglets quickly and to establish palliative measures. Key Words: Physiological Variables, Piglets, Postnatal Period, Viability

A procedure to take into account the nongenetic relationship between maternal effects in adjacent generations is presented. It considers a correlation between maternal environments provided by a dam and its daughters (lambda). The dispersion structure of the maternal animal model was modified to include a correlation matrix (E) that relates the maternal permanent environmental effects. The structures of the E matrix and its inverse (E(super -1) are described. Both matrices are completely defined by the correlation coefficient (lambda). An algorithm to compute these matrices from pedigree information was also developed. Furthermore, a Bayesian analysis of this model including the (lambda) parameter was developed using Gibbs sampling, with Metropolis steps for the nonstandard conditional distributions. With simulated data, the proposed model reduced the bias in all estimates of dispersion parameters when an antagonism between the maternal effects received by a daughter and its future maternal environment existed. This model also provides an estimate of the environmental relationship between the maternal effects of dams and daughters by the (lambda) parameter. The same Bayesian analysis was also carried out with weaning weight data of the Bruna dels Pirineus breed. The posterior means (standard deviation) of (co)variance ratios were .214 (.081) for direct heritability (h(super 2)(sub d)), .107 (.033) for maternal heritability (h(super 2)(sub m)), .047 (.020) for the proportion of variance due to maternal environmental effects (C(super 2)(sub m)), and -.034 (.043) for the genetic correlation between direct and maternal effects (r(sub dm)). The posterior mean of (lambda) parameter was -.190, and 76% of its marginal posterior distribution took negative values. As occurred with simulated data, considering the maternal environmental correlation in the analysis implied higher h(super 2)(sub m)estimates, lower C(super 2)(sub m) and h(super 2)(sub d) estimates, and less negative values for the marginal posterior distribution of r(sub dm). These results were considered as evidence of the environmental antagonism between maternal effects provided by a dam and its daughters to weaning weight of their progeny in the Bruna dels Pirineus breed. Key Words: Maternal Effects, Bayesian Theory, Gibbs Sampling, Beef Cattle, Weaning Weight

A study was done on the genetic structure of ten Spanish dogs using comparative F statistics analysis. Electrophoretic data showed that 11 out of the 21 loci are polymorphic. Heterozygote deficit was measured to be 17% at the subpopulation, breed and ancenstral trunk levels. It was concluded that F statistics can be used for the analysis of the genetic structure of the Spanish dog populations and the reconstruction of phylogenies.