Stability of Difference Equations with Interspecific Density Dependence, Competition, and Maturation Delays.

Abstract

A general system of difference equations is presented for multispecies communities with density dependent population growth and delayed maturity. Interspecific competition, mutualism, predation, commensalism, and amensalism are accommodated. A sufficient condition for the local asymptotic stability of a coexistence equilibrium in this system is then proven. Using this system, the generalisation of the Beverton-Holt and Leslie-Gower models of competition to multispecies systems with possible maturation delays is presented and shown to yield interesting stability properties. The stability of coexistence depends on the relative abundances of the species at the unique interior equilibrium. A sufficient condition for local stability is derived that only requires intraspecific competition to outweigh interspecific competition. The condition does not depend on maturation delays. The derived stability properties are used to develop a novel estimation approach for the coefficients of interspecific competition. This approach finds an optimal configuration given two conjectures. First, coexisting species strive to outcompete competitors. Second, persisting species are more likely in stable systems with strong dampening of perturbations and high ecological resilience. The optimal solution is compared to estimates of niche overlap using an empirical example of malaria mosquito vectors with delayed maturity in the Anopheles gambiae sensu lato species complex.