Intraguild Predation and Competitions of Two Stage-Structured Species in a Seasonal Patchy Model

Some creatures interact with not only the same species but also different species by competing resources and even develop intraguild predation (IGP) to improve their survival. Individuals also react for survival according to spatial heterogeneity and seasonal variation of the environment. However, all these creatures' behaviors may change in their different life stages because of varied physiological structures. Considering these concerns, we propose a two-patch model with environmental seasonality and individuals' two life stages and incorporate intraspecific and interspecific competitions and IGP between two species. We begin by analyzing single-species models to establish threshold dynamics. This analysis shows that a species will eventually go extinct or exhibit oscillatory population dynamics across both patches, attracting all nonnegative solutions. Next, we explore two-species models, without and with IGP, and formulate the invasion indices for both species in each scenario. In both cases, we demonstrate that the population tends to die out if the invasion indices are less than one while remaining persistent if the invasion indices exceed one. Finally, we conduct numerical examples to verify the criterion for threshold dynamics and observe some interesting results, including IGP can reverse the competition outcome, IGP can induce ecological diversity, seasonality can facilitate species survival, and prey species can adapt their maturation time against IGP.