In any population undergoing selection, the aim is most often to get the highest genetic response. Genetic progress is linked not only to the efficiency of the selection method but also to the genetic variability in the population. Thus to preserve mid- and long-term genetic responses, conservation of genetic variability is an important point. The choice of mating systems which preserve genetic variability or/and optimize genetic gain is well documented (for example Wray and Goddard (1994), Boichard et al. (1997), and Toro et al. (1998), for a review, see de Rochambeau et al. (2000)). However all these methods require the identification of animals (for knowledge of pedigrees or for the identification of groups) or the use of genomic markers. Individual identification of animals is not obvious for all species of economic interest. For example, in fish species it is not possible to tag very young animals. Alternatives are either to keep groups or families in separate tanks or to use genetic markers for a posteriori parentage assignment, but both solutions are very expensive. Moreover, fish breeders are very concerned with this issue because the biological characteristics of fish (high fecundity, maternal effects and social interactions) may lead to a rapid decline in genetic variability.