A seasonal commensalism model with a weak Allee effect to describe climate-mediated shifts

Climate change is affecting the life cycle of tight interacting species. Commonly, the seasonal population dynamics of species is analyzed through models with periodic rates; however, assuming periodicity in seasonal phenomena which depend on environmental drivers is very restrictive. In this work, we analyze seasonal commensalism between two species in which the per capita growth rate of each species is affected by a weak Allee effect and the demographic and ecological rates are assumed almost periodic. To do this, we construct and analyze an almost periodic model to describe commensalism using a wide family of functions that describe weak Allee effects and the benefits granted by the interaction. We prove that the model admits a unique almost periodic global attractor for a wide family of functions. Numerical simulations of the solutions of the model shown the result proved in this work. We show that if periodic rates are used when the phenomenon is really almost periodic, underestimation or overestimation of the population size of both species can occur, which can lead to design wrong strategies by the decision makers.