= Symmetric underdominant two-cluster equilibrium
{title2=$x_*=(1+\sqrt{1-2\sigma/s})/2,\quad y_*=1-x_*$}
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.
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