Selection for an optimum growth curve.

Growth and development can be regarded as a stochastic process in continuous time. Moreover, in some situations of primary production, certain growth patterns may be more economical, or otherwise more desirable, than others. In this paper an attempt is made to develop techniques which could be used to exert some selection pressure for optimal growth curves. A discrete solution to this problem is suggested which should be relatively easy to apply in practice. However, the complete discussion of the situation requires the introduction of certain integral equations to replace the usual matrix equations of the classical theory. The conventional phenotypic and additive genetic covariance matrices give way to continuous kernels and, as expected, it is found that the continuous and the discrete theories are similar. The usual case of unrestricted selection is also developed for the continuous time model and the selection of several characters towards respective optimal curves simultaneously is also treated. Two different numerical procedures for solving the integral equations are proposed.