Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Population survival and extinction are central questions in population biology.
• Reaction-diffusion equations with linear diffusion terms are commonly used to model population dynamics, but have limitations in predicting population fronts.
• Nonlinear diffusivity functions offer a potential improvement over linear diffusion models.

Purpose of the Study:

• To investigate how nonlinear diffusivity functions affect population survival and extinction.
• To compare the predictive power of nonlinear diffusion models with classical linear diffusion models.
• To provide clear insights into population extinction dynamics using an interpretable discrete simulation model.

Main Methods:

• Developed a discrete simulation model to study population dynamics.
• Incorporated nonlinear diffusivity functions dependent on population density.
• Compared simulation results with predictions from classical linear diffusion models.

Main Results:

• The choice of nonlinear diffusivity function significantly impacts population survival or extinction.
• Discrete models provide clearer insights into the effects of nonlinear diffusivity compared to continuum frameworks.
• Specific nonlinear diffusivity functions were found to either encourage or suppress population extinction.

Conclusions:

• Nonlinear diffusion models offer a more nuanced understanding of population dynamics and extinction.
• Discrete simulation approaches are valuable for interpreting complex ecological models.
• Findings contribute to predicting population persistence and managing extinction risks.