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Nonlinear eco-evolutionary games with global environmental fluctuations and local environmental feedbacks

Fig 4

Local game-environment evolution in a discretely varying global environment.

We use a periodic piecewise function, w₁(t), to describe the global environmental fluctuations. We uniformly select initial points on the x − r_c plane and plot the corresponding dynamical trajectories by numerically solving Eq 9. Trajectories that eventually evolve to (x* = 0), or circulate along an interior closed orbit are distinguished by blue, pink and orange, respectively. The emergence of cyclic evolution of group cooperation and local environment (orange areas), which cannot be observed in static global environments, indicates that the global environmental fluctuations could fundamentally alter the evolutionary outcomes in local feedback-evolving game. In all panels, N = 4, α = 1.5, β = 3.5, θ = 0.5, r_d = 0.6.

doi: https://doi.org/10.1371/journal.pcbi.1011269.g004