Fluctuations-induced coexistence in public goods dynamics

Area of Science:

• Population dynamics
• Evolutionary biology
• Nonlinear dynamical systems

Background:

• Cooperative interactions and their stability are fundamental to population dynamics and evolution.
• Models of producers and non-producers interacting over a common resource are essential for understanding ecological stability.

Purpose of the Study:

• To investigate the impact of noise on the stability of populations with cooperative interactions.
• To analyze the conditions under which coexistence between producers and non-producers is possible.

Main Methods:

• Development of a generic class of nonlinear dynamical systems.
• Analysis using deterministic mean field approximation.
• Characterization of stochastic attractors via phase space arguments and moment closure.
• Validation through spatial Monte Carlo simulations with demographic fluctuations and diffusion.

Main Results:

• Deterministic models predict extinction driven by non-producers.
• Small perturbations destabilize the extinction fixed point, leading to a stochastic attractor.
• Coexistence is stabilized by stochastic nonlinear dynamics, independent of noise amplitude or boundary conditions.
• Additive noise and diffusion-induced noise promote coexistence, while multiplicative or local demographic noise do not.

Conclusions:

• Stochasticity can rescue populations from extinction predicted by deterministic models.
• The type of noise significantly influences population dynamics and stability.
• Understanding noise effects is crucial for predicting the long-term structure and persistence of populations.