Non-spatial Dynamics and Spatiotemporal Patterns Formation in a Predator-Prey Model with Double Allee and Dome-shaped...

Area of Science:

• Theoretical Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Species extinction is a significant threat to biodiversity, with Allee effects increasing extinction vulnerability.
• Allee effects, arising from multiple processes, can act concurrently on a single species, especially at low population densities.
• Cooperative behaviors, like group defense against predation, are influenced by Allee effects.

Purpose of the Study:

• To investigate the dynamics of a predator-prey system incorporating a double Allee effect in prey growth.
• To analyze the role of prey group defense, modeled by a dome-shaped response function, in spatio-temporal dynamics.
• To understand the combined impact of Allee effects and group defense on population stability and pattern formation.

Main Methods:

• Mathematical modeling of a predator-prey system with a double Allee effect and a simplified Monod-Haldane functional response.
• Analysis of spatio-temporal dynamics, including stability analysis and investigation of Turing instability.
• Examination of phase space to identify bi-stability and tri-stability phenomena.

Main Results:

• Prey group defense generally enhances stability, but excessive defense can lead to predator extinction.
• The double Allee effect creates multi-stability (bi- or tri-stability) in the phase space, making dynamics sensitive to initial conditions.
• Combined Allee effects and group defense lead to periods of stability interspersed with oscillations; double Allee effects increase instability regions, while group defense decreases them in spatial systems.

Conclusions:

• The interplay between Allee effects and group defense critically influences predator-prey system stability and ecological outcomes.
• Spatial patterns like spots and stripes emerge in heterogeneous environments, with Allee effects promoting instability and group defense promoting stability.
• The system exhibits complex dynamics, including oscillations and chaos, in specific parameter regions, highlighting the sensitivity to initial population sizes and environmental factors.