Past exam of the short options course of the University of Oxford / 2023 / 9 / c / ii / Solution

Since $\gamma =1-\delta /r_2$, increasing hunting effort moves leftward on these diagrams. The first stability threshold corresponds toAbove this removal rate, a sufficiently small grey population can be eliminated while reds recover. Until the second threshold, however, the system is bistable: an initially large grey population can still win, so the history and initial abundances matter. The second threshold isAbove it, any positive red population recovers and the grey population tends to zero, regardless of its initial abundance in this deterministic model. This threshold is smaller than $r_2$, so competition from surviving reds can make eradication possible with less removal than would be necessary to suppress grey growth without competitors. If $\delta >r_2$, part (a)(iii) supplies the simpler competitor-independent extinction bound. These are model predictions about long-term dynamics; neither finite-time extinction nor uncertainty in ecological parameters is encoded in the equations.