The aim of this paper is to offer a new biological interpretation of Fisher’s ‘Fundamental Theorem of Natural Selection’ and from this to consider optimality properties of gene frequency changes. These matters are of continuing interest to biologists and philosophers alike. In particular, the extent to which biological evolution can be calculated from the ‘gene’s-eye’ point of view is also discussed. In this sense, the paper bears indirectly on the concepts of the unit of selection and of the ‘selfish gene’. (...) A new biological significance for the Fundamental Theorem, not previously found in the literature, is offered, together with an optimality principle connected with this theorem. (shrink)