An almost periodic model to describe phenology mismatches in mutualistic interactions

We study seasonal mutualistic interactions between two species. The model takes into account the climate-mediated shifts that can change the phenologies of mutualistic species. We show conditions on the parameters of the model that guarantee global stability. Numerical simulations are performed for different scenarios associated with seasonal changes. They show that if periodic time-dependence is used to approximate an almost periodic one, then not only the densities of the mutualistic populations but also the overlapping intervals describing the interval of co-occurrence can be either underestimated or overestimated. Therefore, using an almost periodic model can be more adequate to design conservation strategies for asynchronous phenology.