Fig. 4.

The dynamics of a Hawk–Dove population in our new model with initial conditions $q_h(0)=0.7$ and $n(0)=147$. Model parameters: $W=0.8$, $d=0.5$, $\mathrm{\Psi }=15$, $\mathrm{\Phi }=20$. In this case the impact of the background fitness components is very strong and the system is close to the weak selection limit. The stable restpoint is different to the restpoints from Figs. 2 and 3. Here the density nullcline is nearly flat due to the weak impact of the rare focal game events. The vector field described by the shows a strong attraction of the trajectory towards the density nullcline, then the trajectory traces it until it reaches the restpoint, i.e. we have effective timescale separation