Fig. 2.

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: $W=0.8$, $d=0.5$, $\mathrm{\Psi }=0.006$, $\mathrm{\Phi }=0.008$. In this case the impact of the background fitness components is very weak. The vector field indicated by the arrows shows that the force of attraction towards the density nullcline increases with population size. However, the dynamics does not converge quickly to the nullcline, and this case is far from timescale separation. Note that, the shape of the density nullcline highly depends on the strategic composition of the population. Thus the impact of the focal game on the population size is strong