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Repeated records on fertility, litter size, and ovulation rate of Rambouillet ewes and on fertility and litter size of Finnsheep ewes were used to estimate heritabilities and repeatabilities with linear and nonlinear sire and animal models. Linear sire (LSM) and animal models were used with all traits. Nonlinear models were the threshold, Poisson, and negative binomial. Threshold sire (TSM) and animal models were used with all traits. Litter size and ovulation rate were analyzed also with Poisson sire and animal models and with negative binomial sire and animal models. Variance components for linear models were estimated using REML; in the threshold, Poisson, and negative binomial, they were estimated using approximate marginal maximum likelihood. Poisson and negative binomial analyses yielded results difficult to interpret due to problems in variance component estimation. Animal models resulted in slightly greater estimates of heritability for fertility than did sire models, but ovulation rate heritability estimates from sire models were much greater than estimates form animal models. Differences between sire and animal models for heritability estimates for litter size were not consistent. Threshold models resulted in higher heritability estimates for all traits in both breeds and with both sire and animal models. In general, repeatabilities were consistent across models. For example, LSM (TSM) repeatabilities were .10 (.14) for fertility, .20 (.25) for litter size, and .25 (.29) for ovulation rate in the Rambouillet, and .17 (.17) for fertility and .11 (.13 for litter size in the Finnsheep.

The performance of linear and nonlinear sire and animal models in the analyses of reproductive traits (fertility, litter size, and ovulation rate) in two sheep populations (Rambouillet and Finnsheep) was compared in terms of goodness of fit and predictive ability. Linear sire (LSM) and animal (LAM) models were used with all traits. Nonlinear models were the threshold, Poisson, and negative binomial. Threshold sire (TSM) and animal (TAM) models were also used with all traits. Litter size and ovulation rate were analyzed also with Poisson and negative binomial sire (PSM and NBSM, respectively) and animal (PAM and NBAM, respectively) models. Variance components were those reported in the companion article. For PAM a new set of variance components derived from estimates found with the linear animal model also was used (PAM-L). Mean squares error (MSE) and correlations between fitted and observed values were used to assess goodness of fit. Predictive ability was assessed by partitioning the data sets for the different traits into two subsets with the restriction that all levels of fixed effects were represented in each subset. Parameters from one subset were employed to predict observations in the other, and then MSE and correlations between observed and predicted values were used as criteria for model comparison. Within estimation procedure, breed, and trait, goodness of fit of sire and animal models was similar. Linear and threshold models resulted in similar fit, and both outperformed Poisson and negative binomial models. In terms of predictive ability, linear and threshold models performed only slightly better than Poisson and negative binomial models. Goodness of fit and predictive ability generally were better when models included permanent environmental effects.

Approximate and exact Bayesian analyses of survival from birth to weaning measured as an "all or none" trait were conducted on 2,554 Rambouillet lambs using an asymptotic normal approximation and Monte Carlo numerical integration with importance sampling, respectively. A linear logistic model was used to assess the effects of year, age of dam, sex of lamb, and type of birth on the survival probability. A least squares analysis of the data, ignoring their discrete nature, was also performed. The Bayesian analyses were compared by plotting the marginal posterior distributions and by constructing 95% highest-posterior-density regions for some parameters of interest. The analyses were repeated for a reduced data set consisting of 300 observations selected at random from the original file. For all practical purposes, the Bayesian and non-Bayesian analyses yielded identical results despite their different interpretations. Also, the asymptotic normal approximations to the true posterior distributions were excellent. Undoubtedly, this is because the likelihood functions contained a large amount of information about the parameters. Four-year-old ewes produced lambs with greater survival rates than either younger or older ewes. Female and male lambs had similar rates, and single-born lambs had a 10% higher survival rate than multiple-born lambs.

The objectives of this study were to identify nongenetic factors influencing scrotal circumference size and growth and to estimate heritabilities of scrotal circumference size at different ages and scrotal circumference growth between ages. Data on scrotal circumference, live weight, and age were recorded over 6 yr (1982 to 1987) on 541 spring-born Rambouillet ram lambs (109 sires, 307 dams) at the Dixon Springs Agricultural Center. Scrotal circumference and live weight were predicted at four ages (90, 120, 150, and 180 d) for each lamb. The two models used to evaluate factors affecting scrotal circumference size at fixed ages were the same except for the addition of live weight and live weight squared to one of the models. Likewise, the two models used for scrotal circumference growth between ages were the same except for the addition of live weight change and live weight change squared to one of the models. Year and type of birth were significant sources of variation for both traits under both models. Regression coefficients for live weight and live weight squared on scrotal circumference size and for live weight change and live weight change squared on scrotal circumference growth and for day of birth within year for both traits were generally different from zero (P less than .05). Heritability estimates for scrotal circumference size at fixed ages ranged from .19 to .41. Adjustments for live weight led to an average 41.5% increase in heritability estimates. For scrotal circumference growth, heritabilities ranged from .17 to .60 and adjustments for live weight change resulted in an average 13% decrease in estimates.(ABSTRACT TRUNCATED AT 250 WORDS)