Characterize convergence under non-uniform competition

Determine which forms of non-uniform competition preserve convergence of phenotype distributions in switching population models, and quantify how close the asymptotic composition remains to the stationary distribution of the switching dynamics when competition is nearly uniform.

Background

The main theorems require uniform competition, meaning that all phenotypes experience the same density-dependent growth modulation. The paper gives a weighted-competition counterexample in which the population approaches a stable periodic orbit rather than a stationary equilibrium, demonstrating that convergence can fail when the common-brake structure is lost.

The authors leave unresolved the broader classification of non-uniform competition laws that still guarantee convergence and the stability or quantitative deviation from the switching stationary distribution under small departures from uniform competition.