On the Relatedness Between R. A. Fisher’s FTNS and J. S. Metcalfe’s Construction

Abstract

There is a deep-rooted misunderstanding in R. A. Fisher’s well-known fundamental theorem of natural selection (FTNS). The results from the theorem belong to two methodologies: the dynamical system and statistical inference. FTNS first emerged in the realm of biological genetics. As universal Darwinism had its influence, however, the concept of evolution was gradually formalised, as was FTNS. Motoo Kimura became a pioneer in the trial by his 1958 paper. The suggestion encouraged J. S. Metcalfe to construct his FTNS-type model and apply it to economics. Metcalfe’s object is the evolution of the characteristics of a population (firms, households, etc.) in the market. His construction is original, and he focuses on how moments of the characteristics evolve. The analysis takes FTNS as part of a dynamical system. In contrast, S. A. Frank constructs the mathematics of the FTNS more faithfully to the original in light of G. Price’s study. It clarifies that there is statistical parameter space (manifold) behind FTNS. Here, we encounter the difficulty of (1) the relationship or interconnectedness of these two spaces and (2) the application of the relatedness to the actual phenomenon. In this chapter, we amplify an aspect of this task: if we can truly understand the potential of FTNS as Fisher himself did, that is, the structure of evolution in the background of two methodological spaces, then we must have new types of optimality besides existing efficiency. This chapter provides a preliminary report of this analysis.