The use of Mendelian indices to reduce the rate of inbreeding in selection programmes

Genetic response and inbreeding can be balanced by altering the emphasis placed on ancestral information in genetic evaluation. The breeding value of an individual can be expressed as a weighted sum of Mendelian deviations of itself and all its ancestors. With standard BLUP selection the weights given to Mendelian terms are c(T), where T is the number of generations separating ancestor and individual and c is equal to 0.5. Selection indices with altered weights are investigated using a stochastic simulation and compared for genetic response and inbreeding after 25 years of selection for discrete and overlapping generation models. The trait analysed is measured in both sexes and has a heritability of 0.35. Two selection indices are studied: the Geometric Mendelian Index (GM) which used values of c between 0 and 0.5, and the Truncated Mendelian Index (TM) which uses Mendelian terms from a limited number of generations (for example when T=2 the selection criterion includes individual, parental and grand-parental Mendelian terms). A consequence of reducing ancestral information is that accrued progress is disregarded. This is critical for overlapping generations as sources of information vary between individuals. This is corrected by adding a weighted average of ancestral information of the Individuals generation to the index. With discrete generations, TM with only parental information included reduced inbreeding by 24% and increased cumulative response by 6% compared to standard BLUP by generation 25. As T increases the method tends towards BLUP. With GM, maximum benefits over standard BLUP were obtained at c equal to 0.3 with 23% less inbreeding and 8% and more cumulative response by generation 25. The Mendelian Indices were less effective for overlapping generations. Both types of indices were efficient methods for increasing long-term response. Moreover, comparison with other recent selection schemes highlights common methodologies.