The Taylor-Frank method cannot be applied to some biologically important, continuous fitness functions

TL;DR

The paper demonstrates that the Taylor-Frank method is limited to differentiable fitness functions and cannot be applied to certain biologically important cases, requiring a more general approach for kin selection models.

Contribution

It identifies the limitations of the Taylor-Frank method and proposes the need for a more general form of direct fitness in non-differentiable cases.

Findings

Taylor-Frank method fails with non-differentiable fitness functions

Certain microbial and game theory fitness functions are not compatible with Taylor-Frank

A more general direct fitness approach is necessary in these cases

Abstract

The Taylor-Frank method for making kin selection models when fitness is a nonlinear function of a continuous phenotype requires this function to be differentiable. This assumption sometimes fails for biologically important fitness functions, for instance in microbial data and the theory of repeated n-person games, even when fitness functions are smooth and continuous. In these cases, the Taylor-Frank methodology cannot be used, and a more general form of direct fitness must replace the standard one to account for kin selection, even under weak selection.