Global stability of coexistence equilibria for n-species models of facultative mutualism

Abstract

We further pursue an investigation on an abstract model characterizing the dynamics of a general class of $n$-species facultative mutualisms that was initiated in Georgescu et al. (2017), establishing biologically relevant sufficient conditions for the global asymptotic stability of the coexistence equilibria. These conditions are given in terms of per-species limits of growth-to-loss ratios computed at higher population densities, complemented by either monotonicity or sublinearity inequalities, and are observed to hold for $n$-species versions of mutualistic models in current use. The specific modeling details that require either of these conditions being satisfied are outlined and discussed. As mutualisms can enhance species diversification and facilitate stable coexistence via a plethora of mechanisms, it is then important to understand the stability of speciose mutualisms, our results being of potential interest to theoretical ecologists studying the coexistence of many interacting species and to conservationists aiming for rare species preservation.