A mating system to reduce inbreeding in selection programmes: Theoretical basis and modification of compensatory mating

Increased rate of inbreeding in selection programmes may have an important effect on mid- and long-term selection response and reproductive performance through reduction in genetic variance and inbreeding depression. Selection on an inherited trait inflates the rate of inbreeding and reduces the effective population size (R obertson 1961; S antiago and C aballero 1995). This can be particularly important in selection based on index with information from relatives (L ush 1947) or best liner unbiased prediction (BLUP) with an animal model (H enderson 1984). In recent years, various methods have been proposed to reduce the rates of inbreeding in selection programmes while keeping genetic gains at the same level. These methods assume various selection and mating strategies. G rundy et al. (1994) showed that the use of biased heritability estimates for BLUP evaluation is one of the simplest and most efficient methods. A direct reduction in the weight on family mean in index selection (T oro and P erez -E nciso 1990), selection for weighted ancestral Mendelian sampling estimates (W oolliams and T hompson 1994; G rundy et al. 1998) and limited use of selected parents (T oro and N ieto 1984; W ei 1995) have also been shown to be efficient methods. Other methods include nonrandom matings of selected parents, such as factorial mating designs (W oolliams 1989), minimum coancestry mating (T oro et al. 1988) and compensatory mating (S antiago and C aballero 1995). Simultaneous optimization of the selection of candidates and their mating allocations has been also considered through mate selection with linear programming techniques (T oro and P erez -E nciso 1990). Among these methods, compensatory mating is a very simple and efficient method (G rundy et al. 1994; S antiago and C aballero 1995; C aballero et al. 1996). This mating system was derived from the theoretical consideration on effective population size under selection (S antiago and C aballero 1995). Although S antiago and C aballero (1995) considered that implementation of this mating could counteract the cumulative effect of selection on the effective population size, the theoretical basis has been little studied. In this paper, the author gives the theoretical basis of compensatory mating. A modification to enhance the effect of compensatory mating is also proposed and the efficiency is examined by stochastic simulation.