= Fixed-quota harvesting of Lotka-Volterra populations
{title2=$\det DH=X^-/(X^--h)>1$}
In logarithmic prey/predator coordinates, the <Lotka-Volterra predator-prey model> has divergence zero. Removing a fixed prey quota $h$ changes $\log X$ to $\log(X-h)$ and expands logarithmic area by $X/(X-h)$. Thus a periodic annually harvested orbit has an expanding <return map> <determinant> and cannot be asymptotically stable. A continuous-quota approximation gives a coexistence <equilibrium> with positive <Jacobian matrix> <trace> $h/X_*$, unlike proportional harvesting, which only changes the prey growth parameter in this idealized model.
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