Behavioural strategy and predator control: a coupled evolutionary predator-prey model for kiwi conservation in New Zealand

Sierra Sharma, Nagaja Sanatkumar 

Conservation management of endangered species can be enhanced by quantitative frameworks that simultaneously model behavioural adaptations alongside population dynamics. This paper presents a Coupled Evolutionary Predator-Prey Model (CEPPM) that integrates replicator dynamics from Evolutionary Game Theory with an extended Lotka-Volterra predator-prey framework, applied to kiwi (Apteryx spp.) under stoat (Mustela erminea) predation in New Zealand, with parameters grounded in published field data.

We identify three analytically derived stoat-removal thresholds (h) that partition management outcomes into four qualitatively distinct regimes: below an effective kiwi recovery threshold h_survival ≈ 0.165, kiwi cannot begin recovery regardless of intervention timing; between h_survival and an analytical stoat suppression threshold h_crit = 0.25, kiwi recover while stoats persist at a low demographic floor; between h_crit and a true stoat eradication threshold h_erad ≈ 0.33, a "kiwi bonus zone" allows stoats to persist (counterintuitively, even as suppression intensifies) because the recovering kiwi population itself subsidises the remaining stoats as prey; and above h_erad, stoats are driven to zero regardless of kiwi abundance. Threshold locations are robust to parameter variation: across literature-derived ranges, h_crit varies 0.14–0.44, h_erad 0.21–0.51, and h_survival 0.07–0.33, with uncertainty driven primarily by stoat demography.

The CEPPM incorporates lowering the risk of open foraging through predator suppression, thereby accelerating kiwi recovery. Open foraging proportions at equilibrium range from ≈44% under unmanaged predation to ≈76% under full stoat suppression, with an analytically derived survival-enabling proportion of ≈41%. This behavioural trajectory is a measurable conservation outcome in its own right, and its omission from population-only models risks over- or under-estimating recovery speed. Interlinking behavioural strategy evolution with population dynamics reveals a non-linear threshold structure and a behavioural dimension of recovery unavailable from either framework alone. Models of this kind can help conservation analyses better represent ecological processes and inform more precisely targeted policy decisions.