Prediction of rates of inbreeding in populations undergoing index selection

For populations undergoing mass selection, previous studies have shown that the rate of inbreeding is directly related to the mean and variance of long-term contributions from ancestors to descendants, and thus prediction of the rate of inbreeding can be achieved via the prediction of long-term contributions. In this paper, it is shown that the same relationship between the rate of inbreeding and long-term contributions is found when selection is based on an index of individual and sib records (index selection) and where sib records may be influenced by a common environment. In these situations, rates of inbreeding may be considerably higher than under mass selection. An expression for the rate of inbreeding is derived for populations undergoing index selection based on variances of (one-generation) family size and incorporating the concept of long-term selective advantage. When the mating structure is hierarchical, and when half-sib records are included in the index, the correlation between parental breeding values and the index values of their offspring is higher for male parents than female parents. This introduces an important asymmetry between the contributions of male and female ancestors to the evolution of inbreeding which is not present when selection is based on individual and/or full-sib records alone. The prediction equation for index selection accounts for this asymmetry. The prediction is compared to rates of inbreeding calculated from simulation. The prediction is good when family size is small relative to the number selected. The reasons for overprediction in other situations are discussed.