= Selection gradient
{title2=$g(x)=\partial_y f(y,x)|_{y=x}$}
For a differentiable rare-mutant invasion fitness $f(y,x)$ against resident trait $x$, the <selection gradient> gives the first-order growth advantage of a nearby mutant. A zero gradient is a candidate interior evolutionary singularity. Strict local uninvadability follows from negative mutant-fitness curvature; evolutionary approach additionally requires the gradient to point toward the candidate. Boundary traits require one-sided tests. A gradient alone does not prove global evolutionary stability.
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