= Concave recruitment map
{title2=$N_{t+1}=g(N_t),\quad g''<0$}
For $g(0)=0$ and <strict concavity>, per-capita recruitment $g(N)/N$ strictly decreases because $g(N)=\int_0^Ng'(s)\,ds>Ng'(N)$. Thus a positive <fixed point> is unique if it exists. A slope $g'(0)>1$ makes extinction unstable but does not guarantee a positive intersection: $g(N)=2N+1-e^{-N}$ stays above the identity. A large-population restriction supplies existence; the local fixed-point stability condition remains $|g'(N_*)|<1$.
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