Intra- and Inter-Specific Competitions of Two Stage-Structured Species in a Patchy Environment

With metamorphosis or not, creatures have varying ability in their different life stages to compete for resource, space or mating. Interaction of species with environment and competition between species are key factors in the evolution of ecological population. Taking these concerns into account, we study a model with two life stages, immature and mature, and incorporate both intra- and inter-specific competitions between two species in a two-patch environment. The structure of monotone dynamics in such a model leads us to explore its local and global dynamics. The investigation starts with the single-species model on which we establish the threshold dynamics that either the species eventually goes extinction or exists on both patches, which is determined by the parameters. Then we study the two-species model and formulate the threshold competition strength which monotonously but oppositely depends on the maturation times of two species, and indicates how the competitor invade an environment. Moreover, we demonstrate two mechanisms which give rise to dominance dynamics, under competition-dependent and -independent criteria respectively. Finally, we conduct numerical simulations to show that the proposed model admits multiple positive equilibria due to the consideration of two life stages.