A generalized Price equation for fuzzy set-mappings

The Price equation provides a formal account of selection building on a right-total mapping between two classes of individuals, that is usually interpreted as a parent-offspring relation. This paper presents a new formulation of the Price equation in terms of fuzzy set-mappings to account for structures where the targets of selection may vary in the degree to which they belong to the classes of ‘parents’ and ‘offspring,’ and in the degree to which these two classes of individuals are related. The fuzzy set formulation widens the scope of the Price equation such that it equally applies to natural selection, cultural selection, operant selection, and even selection in physical systems.