Diffusion dynamics on the coexistence subspace in a stochastic evolutionary game.

Area of Science:

• Evolutionary biology
• Theoretical ecology
• Mathematical modeling

Background:

• Frequency-dependent selection drives species interactions and competition for resources.
• Stochastic evolutionary games incorporate random drift affecting species dynamics.
• Environmental changes introduce complex selection advantages, influencing evolutionary trajectories.

Purpose of the Study:

• To analyze a model of competing species in a random environment.
• To investigate long-term coexistence and subsequent species fixation.
• To develop a simplified method for approximating stochastic evolutionary dynamics.

Main Methods:

• Utilized stability analysis of linear combinations of competing species.
• Approximated stochastic dynamics using diffusion on a one-dimensional coexistence region.
• Applied model reduction techniques for evaluating quasistationary properties.

Main Results:

• The model demonstrates prolonged species coexistence in a random environment.
• The diffusion approximation effectively simplifies the analysis of complex dynamics.
• The method accurately approximates the probability of first extinction and its expected time.

Conclusions:

• A simplified model reduction technique rigorously evaluates quasistationary properties of stochastic evolutionary dynamics.
• This approach facilitates the study of species coexistence and extinction in fluctuating environments.
• The findings offer new insights into the long-term evolutionary dynamics of competing species.