Persistent prey species in the Lotka-Volterra apparent competition system with a single shared predator

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Apparent competition occurs when species share a predator, leading to indirect interactions.
• The Lotka-Volterra model is a foundational tool for studying predator-prey dynamics.
• Understanding species persistence and extinction is crucial in ecological modeling.

Purpose of the Study:

• To analyze the Lotka-Volterra n prey-1 predator system with apparent competition.
• To determine conditions for global asymptotic stability and identify persistent prey species.
• To investigate the long-term consequences of apparent competition on prey community structure.

Main Methods:

• Mathematical analysis of the Lotka-Volterra n prey-1 predator model.
• Proof of the existence of a globally asymptotically stable equilibrium.
• Derivation of conditions for asymptotic stability of feasible equilibria.

Main Results:

• The system is proven to have a globally asymptotically stable equilibrium.
• A necessary and sufficient condition is identified to determine which equilibrium is stable.
• The composition of persistent prey species at equilibrium is investigated, revealing potential functional homogenization or predator specialization (monophagy).

Conclusions:

• Apparent competition in this model leads to predictable outcomes regarding species persistence.
• Long-term apparent competition can drive prey communities towards functional homogenization.
• Alternatively, the system may simplify to a specialist predator-prey interaction.