Symmetric underdominant two-cluster equilibrium ($x_{\ast }=(1+\sqrt{1-2\sigma /s})/2,y_{\ast }=1-x_{\ast }$)

With equally many initially pure habitats of each allele, symmetry preserves $y=1-x$. The heterogeneous equilibrium exists for $\sigma <s/2$. Its full-system eigenvalues are $-s+3\sigma$ in the mean-frequency direction and $-s+2\sigma$ in the antisymmetric direction, so it attracts general nearby perturbations only for $\sigma <s/3$. Exact symmetry can preserve both alleles beyond this robust range; at stronger migration it approaches the unstable uniform midpoint.