Dynamic selection procedures for constrained inbreeding and their consequences for pedigree development

A novel selection algorithm for maximizing genetic response while constrain ing the rate of inbreeding is presented. It is shown that the proposed meth od controls the rate of inbreeding by maintaining the sum of squared geneti c contributions at a constant value and represents an improvement on previo us procedures. To maintain a constant rate of inbreeding the contributions from all generations are weighted equally and this is facilitated by modify ing the numerator relationship matrix. By considering the optimization of t he contributions of many generations the initial mating proportions (the ge netic contributions to the next generation) are not equal to their long-ter m values, but are set equal to the expected long-term contributions given t he current information. This is confirmed by the regression of the long-ter m contributions on the assigned mating proportions being close to one. The gain obtained from the selection algorithm is compared with the maximum the oretical genetic gain under constrained inbreeding. It is concluded that th is theoretical upper bound is in general unattainable, but from this a conc ept of genetic efficiency in terms of resources and constraints is derived.