General Allee effect in two-species population biology

Area of Science:

• Mathematical Biology
• Ecology
• Population Dynamics

Background:

• The Allee effect describes reduced per capita growth rate at low population densities.
• Understanding inter-specific interactions is crucial for ecological dynamics.
• Previous models often simplified Allee effect dynamics.

Purpose of the Study:

• To present a general framework for the strong Allee effect in population models.
• To analyze the strong Allee effect arising from inter-specific interactions.
• To explore the role of equilibria and semistability in these dynamics.

Main Methods:

• Development of a general framework for strong Allee effect.
• Analysis of competition, mutualistic, and predator-prey models.
• Introduction and application of semistability in planar systems.

Main Results:

• The extinction equilibrium is an attractor in strong Allee effect models.
• A 'phase space core' of 3-4 equilibria sufficiently describes dynamics.
• Semistable equilibria increase the number of possible Allee effect cores.

Conclusions:

• The proposed framework unifies the study of strong Allee effects in diverse ecological interactions.
• Semistability is a key concept for understanding complex dynamics driven by the Allee effect.
• The findings provide insights into species persistence and extinction under inter-specific pressures.