Mathematical theory of phenotypical selection

A general concept of phenotypical structure over a genotypical structure is developed. The direct decompositions of multilocus phenotypical structures are considered. Some aspects of phenotypical heredity are described in ter ms of graph theory. The acyclic phenotypical structures are introduced and studied on this base. The evolutionary equations are adjusted to the phenot ypical selection. It is proved that if a phenotypical structure is acyclic then the set of fixed points of the corresponding evolutionary operator is finite except for a proper algebraic subset of the operator space. Some app lications of this theorem are given. (C) 2001 Academic Press.