Abstract The extinction and persistence dynamics of quokka (Setonix brachyurus) population at northern jarrah forest of Australia is investigated using mathematical modelling. Predator's management demands a comprehensive understanding of the ecological circumstances associated with predation. Predation by red foxes (Vulpes vulpes) has a significant role in reducing the native animal population. This paper mainly focuses on the extinction dynamics of quokka population and its reduction by red foxes, by qualitative and quantitative analyses of a designed tri-trophic food-chain model composing a prey (quokka), a mesopredator (red fox) and apex predator (dingo). Existence of solution are analysed and shown to be uniformly bounded. We applied the concept of basic reproduction number from epidemiology to the food chain model, to derive a condition for extinction and persistence of predator population. Global stability of the predator-free equilibrium is established by geometric approach. We use Partial Rank Correlation Coefficient (PRCC) for performing global sensitivity analysis to identify most influential model parameter responsible for quokkas prevalence and mortality. Results of numerical simulation for both deterministic and stochastic model confirms the analytical finding and support those of previous studies. The outcome of this work shows that persistence and existence of quokka depend on the demographic impacts of environmental stochasticity on its own population. Based on our results, many conservation strategies are suggested to improve the overall growth of the species. We believe that declination of red fox and the presence of dingoes are important for preserving the uniform occurrence of quokkas.

中文翻译：

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评估三营养食物链模型在设计保护计划中的可行性：Quokka 种群减少的案例

摘要 利用数学模型研究了澳大利亚北部贾拉森林短尾矮袋鼠种群的灭绝和生存动态。捕食者的管理要求全面了解与捕食相关的生态环境。赤狐 (Vulpes vulpes) 的捕食在减少本地动物种群方面具有重要作用。本文主要通过对由猎物 (quokka)、中掠食者 (red fox) 和顶级捕食者 (quokka) 组成的三营养食物链模型进行定性和定量分析，研究短尾矮袋鼠种群的灭绝动态及其被红狐的减少。野狗）。解的存在性被分析并显示为均匀有界的。我们将流行病学中的基本繁殖数概念应用到食物链模型中，得出捕食者种群灭绝和持续存在的条件。无捕食者平衡的全局稳定性是通过几何方法建立的。我们使用偏秩相关系数 (PRCC) 进行全局敏感性分析，以确定对短尾矮袋鼠患病率和死亡率影响最大的模型参数。确定性和随机模型的数值模拟结果证实了分析结果并支持了先前研究的结果。这项工作的结果表明，短尾矮袋鼠的持久性和存在取决于环境随机性对其自身人口的人口影响。根据我们的研究结果，提出了许多保护策略来改善物种的整体增长。