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

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Density-dependent population growth and delayed maturity are key factors in multispecies community dynamics.
• Existing competition models often lack the generality to incorporate these factors across multiple species.
• Understanding species coexistence and stability is crucial for ecological theory and management.

Purpose of the Study:

• To develop a general system of difference equations for multispecies communities incorporating density dependence and maturation delays.
• To establish conditions for the local asymptotic stability of coexistence equilibria in such systems.
• To generalize established competition models (Beverton-Holt, Leslie-Gower) and explore their stability properties.

Main Methods:

• Formulation of a general system of difference equations for multispecies interactions.
• Mathematical proof of a sufficient condition for local asymptotic stability of coexistence equilibria.
• Generalization of the Beverton-Holt and Leslie-Gower models to multispecies contexts with maturation delays.
• Development of a novel estimation approach for interspecific competition coefficients based on stability conjectures.

Main Results:

• A general system accommodates various interspecific interactions (competition, mutualism, predation, etc.) with density dependence and delayed maturity.
• A sufficient condition for local stability of coexistence equilibria is derived, independent of maturation delays.
• This condition requires intraspecific competition to exceed interspecific competition for stable coexistence.
• A novel method for estimating interspecific competition coefficients is proposed, validated against empirical data of Anopheles gambiae.

Conclusions:

• The generalized models exhibit interesting stability properties dependent on relative species abundances at equilibrium.
• The derived stability condition offers a simplified criterion for assessing coexistence potential in complex ecological systems.
• The novel estimation approach provides a data-driven method for quantifying interspecific competition, with implications for ecological modeling and vector control.