Table 1.
Parameter definitions and default values.
Fig 1.
Frequency of active behavior at equilibrium in the absence of environmental feedback (Eq (5)), with respect to the payoff differential (β) and social norm threshold ().
(a) Bistability occurs in the black filled area (depending on the initial conditions, the equilibrium is either x* = 0 or x* = 1). (b) The upper equilibrium value (x* = 1) is plotted across the bistability area (reachable for initial frequency x0 > ν). (c) The lower equilibrium value (x* = 0) is plotted across the bistability area (reachable for initial frequency x0 < ν). Environmental sensitivity is ℓ = 0.1 and other parameters are set to their default values (Table 1).
Fig 2.
Frequency of active behavior at equilibrium in the presence of environmental feedback (Eq (16)), with respect to the payoff differential (β) and social norm threshold (), for low to high individual sentivity to the environment (τ) (for (a), (d) and (g) ℓ = 0.1) and environmental reactivity (ℓ).
The place of each panel (a)-(i) gives the values taken for τ and ℓ = 0.25. For example, for (e), ℓ = 0.25 and τ = 1. Bistability occurs in the black filled areas. Stable limit cycles occur in the red filled areas. The environmental impact differential is fixed (lB = 1, lA = 0.7). Other parameters (κ, δB) are set to their default values (Table 1).
Fig 3.
Total switching rate at stationary state.
The total switching rate is equalt to the variance of the asymptotic fluctuations around the equilibrium x* as given by Eq 18. (a) Variance for τ = 0.1. (b) Variance for τ = 1. (c) Variance for τ = 10. The environmental impact differential is fixed (lB = 1, lA = 0.7), environmental sensitivity is ℓ = 0.1 and other parameters are set to their default values (Table 1).
Fig 4.
Influence of the environmental impact differential, lB − lA, on the frequency of active behavior (a, b, c), perceived environmental state (d, e, f), and total switching rate (g, h, i) at equilibrium.
For (a), (d) and (g), the parameters are lB = 1 and lA = 0.1. For (b), (e) and (h), lB = 1 and lA = 0.95. For (c), (f) and (i), lB = 0.15 and lA = 0.1. Individual sensitivity to the environment and environmental reactivity are set to τ = 1 and ℓ = 0.1. Other parameters are set to their default values (Table 1).
Fig 5.
Effect of stochastic fluctuations on behavior-environment dynamics in the bistable case.
(a) Convergence of two trajectories issued from the same initial condition to alternate equilibria. (b) A single trajectory, with color coding for passing time, visits alternate equilibria, from the higher x* (blue tones) to the lower x* (green) to the higher x* (orange) to the lower x* (red). The stochastic simulation algorithm is described in the Methods. Environmental sensitivity ℓ = 0.1 (as in Fig 2A), payoff difference β = −0.25 and social norm threshold ν = 0.3. Other parameters are set to their default values (Table 1).