Social behavior-induced multistability in minimal competitive ecosystems

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Understanding population interactions is crucial in ecology.
• Minimal models simplify complex ecological systems for analysis.
• Previous models often assume exclusive outcomes for competing species.

Purpose of the Study:

• To introduce and analyze minimal models of coordinated population behavior.
• To investigate population dynamics under mutualism, predation, and competition.
• To explore the conditions for population coexistence and extinction.

Main Methods:

• Development of minimal mathematical models for population interactions.
• Analysis of system equilibria to determine population outcomes.
• Investigation of stability properties, including asymptotic stability and Hopf bifurcations.

Main Results:

• Symbiotic populations achieve global asymptotic stability.
• Predator-prey systems exhibit Hopf bifurcations.
• Competition models demonstrate tristability, where populations can coexist, one can dominate, or both can disappear, challenging the competitive exclusion principle.

Conclusions:

• Minimal models effectively capture key dynamics of population interactions.
• The principle of competitive exclusion is not universally applicable, particularly in competition scenarios.
• Tristability in competition offers new insights into ecological dynamics and species coexistence.