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 thi...

Mathematical models are a very useful tool to understand, describe or predict the population dynamics of species interacting. Ecologists and mathematicians have extensively studied the predator-prey, victim-exploiter, competition and mutualistic relationships. However, mutualism between species has not received the same attention as the other ecological interactions. In this work, we exclude periodic solutions of three types of systems by the construction of Dulac functions. These systems can be used to describe the population dynamics of mutualistic species. The system type I includes a wide variety of mutualistic models in which both the intrinsic rate of increase and the carrying capacity of each species increase by the interaction between species. In particular, the system type I can be applied to exclude periodic solutions of models with conditioned interactions such ...