Figure 6.

Time-dependent optimal strategies and radical population dynamics for sects whose initial radical population sizes and defining parameters are the same, with the exception of their sizes N_i (a,c) or their resource availability ω_i (b,d). (a,b) optimal $(p_i^j,k_i^j)$ strategies over several time epochs τ_j; (c,d) resulting $(r_{\mathrm{A}}^j,r_{\mathrm{B}}^j)$ phase plane dynamics. In all panels, Δ_i=μ_B=1, λ_i=3, and $(p_{\mathrm{A}}^0,k_{\mathrm{A}}^0)=(0.25{\omega }_{\mathrm{A}},0.25)$. In (a,c), differential sect sizes are N_A=1000 and N_B=100; available resources are equal and set at ω_i=1 for i=A,B. In (b,d), sect sizes are the same at N_i=1000 for i=A,B and differential resources are set at ω_A=160 and ω_B=32. The notation is the same as in figure 4. The inset magnifies the phase diagram in the later stages of the optimization process, as the system approaches the black square endpoint.