In this study, we investigated variation in offspring size (OS) of Daphnia magna in relation to multiple maternal traits and environmental variables. Data originated from laboratory experiments conducted at different feeding scenarios. The mother daphnids had different life-history traits and were reared under various feeding and density conditions. OS showed linear relationships with maternal traits, varying positively with maternal body size, age and brood number, and negatively with brood size and with the amount of ingested carbon. OS increased exponentially with crowding. Using stepwise multiple regression analysis, we developed an empirical model for the OS variation with the relevant maternal and environmental variables. Density dependence was considered by multiplying the resulting model by a density-effect function. We found that the ingested carbon and the maternal body size were the strongest determinants of the observed variation in the OS, whereas the brood size had the least impact on OS. Additionally, the brood number had no significant effect in determining the variability in the OS. The validity of the multivariate model was tested against an independent dataset. The model accurately predicted the OS despite several genetic and environmental differences compared with the data used for parameterization.

A selection index for overall economic merit and five subindexes for maternal and lamb traits were constructed. For estimation of breeding values, two computer programs were developed. A multiple-trait animal model was programmed for the ewe traits including number of lambs born ofl-, 2- and 3-years-old ewes and ewe fleece weight of yearlings. In order to reduce the memory requirement, the lamb data (growth rate, carcass weight, carcass grade, fat% and lamb fleece iveight) were analysed by a reduced multiple-trait animal model including genetic maternal effect. Experiences with the computer programs in genetic evaluation of approximately 619 000 animals are presented. It is concluded that the models and computing strategy may be used for genetic evaluation in the national sheep breeding programme in Norway.

Relative economic values for all traits were derived from a profit equation on a 3-year-old ewe basis. The sensitivity towards changed economic values urns found to be low. Further, the genetic change in the ewe traits of the Norwegian breeds has been estimated, and a significant improvement was found, which was two to four times higher in the ram circles than outside. For breeding rams, the genetic change for number of lambs born was estimated to be approximately 0·01 lambs per ewe and year.