Generalize fitness-irrelevance theorems beyond smooth, bounded, time-independent settings

Extend the discrete and continuum fitness-irrelevance theorems for uniformly competitive phenotype-switching systems to rough coefficients, unbounded higher-dimensional phenotype spaces, and switching rates that vary in time, including treatment-dependent switching rates.

Background

The paper proves asymptotic irrelevance of fitness for finite compartmental systems and for continuum phenotype-structured equations under uniform competition. The stated results assume time-independent switching and smooth coefficients; the continuum result is one-dimensional on the main domain considered, with higher-dimensional extensions covered only for bounded phenotype spaces through companion work.

The authors explicitly identify rough coefficients, unbounded higher-dimensional phenotype spaces, and time-dependent switching as settings not covered by the present theorems. These extensions are important for modeling treatment-induced changes in phenotypic transition rates and realistic, potentially unbounded, multidimensional phenotype spaces.