Evaluation of designs for reference families for livestock linkage mapping experiments

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Abstract
The development of dense linkage maps consisting of highly polymorphic loci for livestock species is technically feasible. However, linkage mapping experiments are expensive as they involve many animals and marker typings per animal. To minimize costs of developing linkage maps for livestock species, optimizing designs for mapping studies is necessary. This study provides a general framework for evaluating the efficiency of designs for reference families consisting of two‐ or three‐ generation full‐sib or half‐sib families selected from a segregating population. The influence of number of families, number of offspring per family, family structure (either half‐sib or full‐sib) and marker polymorphism is determined. Evaluation is done for two markers with a recombination rate of .20 and for a marker and a dominant single gene with a recombination rate of .20. Two evaluation criteria are used: expected maximum lod score for detection of linkage and accuracy of an estimated recombination rate defined as probability that the true recombination rate is in an interval around the estimated recombination rate. First, for several designs the contribution of reference families to expected maximum lod score and accuracy is given. Second, the required number of families in a design to obtain a certain value for the evaluation criteria is calculated when number of offspring per family, family structure and marker polymorphism are specified. The required numbers increase when designs are optimized not only for expected maximum lod score but also for accuracy. The required number of animals to map a dominant single gene is very large. Therefore, a set of reference families should be designed for strictly mapping marker loci. Examples illustrate how tabulated results can be generalized to determine the values for a wide range of designs containing two‐ or three‐generation full‐sib or half‐sib families.