Chickens of the Slovenian commercial Prelux-bro line were divergently selected over 34 generations for high and low BW at 8 wk of age. The aim of the study was to estimate responses to selection with a nonlinear model. Estimates of BW for each generation were provided by the mixed model. For fitting generation means against generation or cumulative selection differential, an exponential model was used. Estimates of realized heritability over generations were derived from regression of the response on cumulative selection differential. After 34 generations, the lines differed by approximately 2,220 g for males and 1,860 g for females. Estimates for a selection limit in the high line were 2,598.4 and 2,144.1 g, for males and females, respectively. A selection limit was not reached in the low line. Half of the selection response was obtained after approximately 6 to 8 generations in the high line and 20 to 28 generations in the low line. Estimated realized heritability decreased over generations. Heritability was larger for females than males and reduction of heritability was more rapid in the high line than in the low line. Genetic SD decreased over generations. Phenotypic SD increased over generations in the high line, but was constant in the low line in the initial 22 generations and decreased thereafter. According to the good fit of the nonlinear model and informative parameter estimates, the results confirmed the usefulness of the nonlinear model for analyzing responses to long-term selection.

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Simple reparameterization to improve convergence in linear mixed modelsSlow convergence and mixing are one of the main problems of Markov chain Monte Carlo (McMC) algorithms applied to mixed models in animal breeding. Poor convergence is to a large extent caused by high posterior correlation between variance components and solutions for the levels of associated effects. A simple reparameterization of the conventional model for variance component estimation is presented which improves McMC sampling and provides the same posterior distributions as the conventional model. Reparameterization is based on the rescaling of hierarchical (random) effects in a model, which alleviates posterior correlation. The developed model is compared against the conventional model using several simulated data sets. Results show that presented reparameterization has better behaviour of associated sampling methods and is several times more efficient for the low values of heritability.