Title: Some Aspects of Selection Indices with Constraints
Abstract: Three aspects of selection indices with constraints were studied. Equations for constructing restricted and optimum indices were modified to handle the general case in which the index and the net merit may consist of an unequal number of traits. A method was developed to estimate the selection intensity required to attain a specific change in one generation of selection when the genetic improvement is optimized for one trait. The required selection intensity may often be very high and make it impractical to achieve the specified genetic gain in one generation. However, estimation of such a selection intensity can be useful for comparative purposes. The effects of restriction of an index on its heritability and on the relationship between the selection efficiency (as measured by gains in net merit) and the heritability of selection index were studied theoretically and with a numerical example. Although generally a loss in efficiency due to restriction of a selection index is expected, the change in heritability of the index is dependent upon the effects of the constraints on variances of the index and the genetic index and is not necessarily in the same direction as the changes in selection efficiency. Therefore, it would be misleading to evaluate the efficiency of an index, conditional or unconditional, on the basis of its heritability.