On Predation-Commensalism Processes as Models of Bi-stability and Constructive Role of Systemic Extinctions

Area of Science:

• Mathematical Biology
• Ecology
• Evolutionary Dynamics

Background:

• Traditional predator-prey models often simplify ecological interactions.
• The influence of predator presence on prey sustainability is a complex factor.
• Understanding predator population onset is crucial for ecological and evolutionary studies.

Purpose of the Study:

• To introduce a mathematical model for predator-prey systems incorporating a commensalism effect.
• To investigate the emergence of novel system behaviors, such as bi-stability.
• To analyze the conditions enabling predator establishment, particularly from small initial populations.

Main Methods:

• Development of a novel mathematical model for predator-prey interactions.
• Analysis of system dynamics to identify emergent properties like bi-stability (coexistence of multiple stable states).
• Exploration of initial condition scenarios for predator population establishment.

Main Results:

• The proposed model demonstrates bi-stability, characterized by two distinct attractors with separate basins of attraction.
• The study addresses the challenge of predator establishment from low initial populations.
• Two pathways for predator establishment are identified: historical adaptation and the introduction of biodiversity.

Conclusions:

• The commensalism effect introduces significant complexity and novel dynamics, including bi-stability, into predator-prey systems.
• Predator establishment can be facilitated not only by past environmental conditions but also by the presence of other species (biodiversity).
• The findings offer new insights into the ecological and evolutionary processes governing predator population dynamics.