Problems associated with estimating response to selection by researchers examining 1. unidirectional selection, 2. bidirectional selection, or 3. alternative selection procedures were examined. Theoretical results showed that if genotype by environment interactions exist, and there is an inter-generation environmental trend, then the usual methods of analysis, i. e. ,
 by differences between either the experimental and control or between experimental lines, will result in biased estimates. Covariance analysis, with the control used as a covariate, was examined as a method of removing environmental trends when such interactions exist. The procedure was shown to give relatively unbiased estimates in this situation. Some bias results from errors associated with estimating the control's performance. Procedures to correct for this bias were discussed.
A statistic was also developed that measures the relative proportion of the environmental variance which a control can remove by covariance techniques. This statistic was used to experimentally compare alternative controls from data previously published by Bray rt _al. (1962). The statistic proved to be very useful, and, contrary to popular belief, identifed an inbred as being consistently the best single control for more than one experimental population. The benefits of inbreds as controls were further discussed. From theoretical considerations and practical utility, an inbred or a single cross among inbreds may be the best universal control.

William M Muir

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume XII. Biotechnology, selection experiments, parameter estimation, design of breeding systems, management of genetic resources., , 269–282, 1986
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