Tracking primary hyperplane competitors during genetic search

Holland's fundamental theorem of genetic algorithms (the schema theorem) provides a lower bound on the sampling rate of a single hyperplane during genetic search. However, the theorem tracks the change in representation for a single hyperplaneas if its representation is independent of other hyperplanes. Hyperplane samples are clearly interdependent and interactions in the hyperplane samples means that Holland's notion of implicit parallelism does not universally hold when conflicting hyperplanes interact. A set of equations are defined which allows one to model the interaction of strings, or of schemata representing hyperplanes at order-N and hyperplanes less than order-N. These equations do not account for the effects of higher order hyperplanes or co-lateral competitions. Nevertheless, these equations can serve to better describe the interaction of primary hyperplane competitors.