Methods for predicting rates of inbreeding in selected populations

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Abstract
In selected populations, families superior for the selected trait are likely to contribute more offspring to the next generation than inferior families and, as a consequence, the rate of inbreeding is likely to be higher in selected populations than in randomly mated populations of the same structure. Methods to predict rates of inbreeding in selected populations are discussed. The method of Burrows based on probabilities of coselection is reappraised in conjunction with the transition matrix method of Woolliams. The method of Latter based on variances and covariances of family size is also examined. These methods are one-generation approaches in the sense that they only account for selective advantage over a single generation, from parents to offspring. Two-generation methods are developed that account for selective advantage over two generations, from grandparent to grandoffspring as well as from parent to offspring. Predictions are compared to results from simulation. The best one-generation method was found to underpredict rates of inbreeding by 10–25%, and the two-generation methods were found to underpredict rates of inbreeding by 9–18%.