Dispersal-induced growth in time-periodic two-patch environments with asymmetric migration

How does the movement of individuals influence the persistence of a single population? A surprising phenomenon known as dispersal-induced growth (DIG) occurs when the population would become extinct if isolated or well mixed, but migration, at an appropriate rate, can induce the persistence of the population. In this paper, we investigate this phenomenon based on a time-periodic two-patch model incorporating asymmetric migration matrices. Through comprehensive analysis of the qualitative properties of the associated principal eigenvalue, including monotonicity, asymptotic behaviors, and the topological structure of the level sets as a function of the migration rate and frequency, we characterize the important factors driving the occurrence of DIG under fixed environmental oscillation frequencies. Our results provide new insights into how the interplay between spatial connectivity and temporal environmental variation enables the population persistence.