Presented is a technical report concerning the use of a mathematical model describing certain aspects of the duplication and selection processes in natural genetic adaptation. This reproductive plan/model occurs in artificial genetics (the use of ideas from genetics to develop general problem solving techniques for computers). The reproductive plan is a sequential stochastic process involving n-tuples (corresponding to chromosomes in genetics) which may be simple numeric constants or complex structures such as computer algorithms. The plan also involves a sequence of probability distributions defined over n-tuples. The report consists of five chapters: introduction; reproductive plans; deterministic problem bases; a chapter divided into sections on the search for an arena, the linear additive model, the linear models and pure problem bases; and conclusions. An appendix illustrating the theorem involved and a list of references conclude the report. (PEB)