In this report only a brief survey of the restricted selection index theory will be given. The different methods, procedures and computation algorithms are described from Niebel and Van Vleck (1982 a, b, c) in detail. In chronological order the main steps in the development of the restricted selection index theory can be obtained from table 1. The idea of imposing restrictions on the genetic change of some characters was first introduced by Kempthorne and Nordskog (1959). They suggested forcing the linear function representing the covariance between genotypes involved and the selection index to be zero to prevent any genetic change in those traits while maximizing selection response in other traits. TALLIS (1962) derived an index to produce changes in means of genotypic values of traits that are proportional to desired changes in a specified direction and thus introduced the idea of proportional restrictions. With this approach, James (1968) showed how restrictions for a fixed change in certain traits could be imposed simultaneously with proportional change in other traits. Harville and Reeves (1972) proved that there exist indexes whose use could move the proportionally restricted traits further in the desired direction than with Tallis's index. The results of these procedures is that genetic changes in the restricted traits are equal to constraints (equal restriction). Rao (1962) considered the problem where the changes in the fixed restricted traits are in a specified direction (fixed unequal restriction).

E. Niebel, L. D van Vleck

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume 7. Symposia (1), , 272–276, 1982
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