An almost periodic $\theta$-logistic model to describe climate-mediated shifts in mutualistic species with $K$ strategies

Abstract

Mutualism relationships have a great impact in biodiversity. From an ecological perspective, modeling the dynamics of large long-lived mutualistic species when their phenology changes can be useful. In this work, we propose an almost periodic $\theta$-logistic model to describe changes in the phenology of species that have concave (linear) decreasing per capita growth rates (species with a $K$ strategy). We prove that a single global almost periodic attractor exists when some conditions over the parameters of the model are satisfied. Numerical solutions show sustained oscillations on the population which tend to a unique globally stable almost periodic orbit. Modeling seasonal drivers through periodic functions can lead to underestimate or to overestimate population densities with respect to almost periodic functions (synchronous mismatch).This misleading estimation can lead to the design of erroneous conservation strategies, which could have a great impact on biodiversity management.