On the principal eigenvalue of cooperative elliptic systems with applications to a population model with two reversible states

We prove novel monotonic results of cooperative elliptic eigenvalue problems on a bounded one-dimensional domain under suitable conditions, which are then applied to analyze a population model with state-switching. Our results demonstrate that spatial heterogeneity alone can lead to selection of higher movement rate, which implies that the reduction phenomenon due to [L. Altenberg, Proc. Nat. Acad. Sci. (2012)] fails for general elliptic cooperative systems. This also provides a plausible mechanism for the differing effective growth rates of the high and low movement strains in different spatial placement of nutrients and toxins, as observed in recent biological experiments involving nematode populations.