Efficiency of indirect selection at selection equilibrium.

Efficiency of indirect selection compared with that of direct selection to increase the mean value of some trait has been usually studied by considering a single generation of indirect and direct responses to selection only. However, under continued selection, genetic variances and covariances, and therefore expected genetic responses, change each generation due to linkage disequilibrium. With directional and truncation selection, genetic parameters asymptote to limiting values after several generations. The efficiency of indirect selection is examined in this limiting situation. The ratio of correlated response to direct response for the trait to improve in the limit is compared with the ratio after the first generation of selection. For all initial parameter values for which indirect selection is more efficient than direct selection, relative efficiency of indirect selection is smaller in the limit than in the first generation. For some parameter values, indirect selection is more efficient than direct selection in the first generation, but less efficient in the limit. Expressions for minimum values of the initial genetic correlation and heritability of the alternative trait required for indirect selection to be preferred in the limit are derived. These values are higher when limiting responses are used instead of single generation responses. The loss in relative efficiency of indirect selection from changes in genetic parameters due to selection should be taken into account when applications of indirect selection are considered.