Changes in genetic parameters over generations for a selected commercial population and simulated populations of poultry with different sizes were studied. The traits analyzed from the commercial population were rate of lay, age at first egg, egg weight, deformation, and body weight. In the simulated population, a trait measured on both sexes and a sex-limited trait, measured only on one sex, each with a heritability of 0.1 and 0.5, were analyzed. In the commercial and simulated populations, males and females were selected on the basis of family selection indexes and data was available only after many generations of selection. Parameters for each generation were estimated by fitting an animal model using derivative free maximum likelihood (DFREML) with different data structures. In structure 1, data included the given (base) generation for which the parameters were to be estimated, and all subsequent generations. In structure 2, only data on birds in the given generation and their progeny were in eluded. In both structures, parents of base-generation birds were assumed unrelated and pedigrees traced back to these parents. With commercial data using structure 1, estimates of sigma(a)(2) and h(2) decreased by 14 to 37% across five generations. With structure 2, no trends were observed, though estimates were lower than for structure 1. For simulated data, with a heritability of 0.1, both structures yielded apparently unbiased estimates of the observed additive genetic variances in the (selected) base generation, no matter how many generations of data were utilized, for both sex-limited and normal traits. However, with a heritability of 0.5 the estimated additive genetic variance for both types of trait decreased with a decrease in the number of generations used in the estimation. Estimates based on the first two generations underestimated, while estimates based on five generations of data overestimated, the observed genetic variances in the defined base. The combinations of conditions that lead to varying degrees of bias remain undefined.