PIP plot: green = mutant y can invade resident x; red = cannot. Singular strategy x* where ∂f/∂y=0. If also ∂²f/∂y²>0 (convergence stable) and locally uninvadable → ESS. If convergence stable but invadable → evolutionary branching point.
When σ < σ_K, the singular point is a branching point: after convergence, a rare mutant can invade and the population splits into two distinct phenotypes — evolutionary speciation.