= Colonization-competition tradeoff invasion fitness
{title2=$f(y,x)=m[c(y)/c(x)-1]+[B(y)-B(x)][1-m/c(x)]$}
A resident trait $x$ occupies fraction $1-m/c(x)$ when its colonization rate exceeds fire extinction. With net competitive replacement given by ability difference $B(y)-B(x)$, a rare mutant has the displayed per-capita growth. The <selection gradient> is $g(x)=mc'(x)/c(x)+[1-m/c(x)]B'(x)$. A singular trait with negative mutant-fitness curvature is a strict local <evolutionarily stable strategy>. Global strict uninvadability requires that $mc(y)+[c(x)-m]B(y)$ be smaller than its resident value for every other trait. Monotonicity alone does not specify the shape or existence of an optimum.
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