| Abstract: | This paper explores stability in a three differential equation model of ungulates, their forage and their predators. Stability most depends on the feeding efficiency of exploiters relative to the growth potential of those exploited. Stable, natural systems probably require relatively inefficient exploitation, refuges for the exploited population or prey switching by generalist exploiters. Increased exploitation of ungulates enhances ungulate-forage stability but, lacking prey refugia, eventually overexploits the ungulates. Multiple, stable equilibria representing sustained ungulate yield and ungulate extinction probably characterize big game. Under traditional management, game populations will approach the zone of attraction of the second of these equilibria. |
