Comparability of specialist models with different phenotypic switching functions

Determine a rigorous normalization or comparison framework for the heterogeneous specialist cell population model with state variables u1(x,t), u2(x,t), and m(x,t) and phenotypic switching functions γ12(u1,u2,m) and γ21(u1,u2,m), so that ECM-dependent, space-dependent, and cell-dependent switching functions can be fairly compared despite the switching rate parameter s being multiplied by a time-varying factor bounded in [0,1]. The goal is to enable meaningful cross-model comparisons of invasion speeds and phenotype distributions when the effective switching rate differs dynamically between switching mechanisms.

Background

The paper introduces a heterogeneous specialist population model in which two phenotypes (ECM-degrading motile cells and proliferative non-motile cells) switch between states according to functions γ12 and γ21. Several switching mechanisms are considered: constant, ECM-dependent, space-dependent, and cell-dependent (Table 1).

For ECM-, space-, and cell-dependent switching, the switching rate s is multiplied by a term in [0,1] that varies over space and time, making direct comparison across mechanisms nontrivial. The authors explicitly note that it is unclear how to compare these models because the effective switching rate differs dynamically, complicating assessments of invasion speed and phenotypic structure. A principled framework is needed to normalize or otherwise account for the time-varying modulation when comparing outcomes across switching types.