Levy Dorian, Harrington Heather A, Van Gorder Robert A
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK.
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK.
J Theor Biol. 2016 May 7;396:163-81. doi: 10.1016/j.jtbi.2016.02.005. Epub 2016 Feb 23.
The role of seasonality on predator-prey interactions in the presence of a resource subsidy is examined using a system of non-autonomous ordinary differential equations (ODEs). The problem is motivated by the Arctic, inhabited by the ecological system of arctic foxes (predator), lemmings (prey), and seal carrion (subsidy). We construct two nonlinear, nonautonomous systems of ODEs named the Primary Model, and the n-Patch Model. The Primary Model considers spatial factors implicitly, and the n-Patch Model considers space explicitly as a "Stepping Stone" system. We establish the boundedness of the dynamics, as well as the necessity of sufficiently nutritional food for the survival of the predator. We investigate the importance of including the resource subsidy explicitly in the model, and the importance of accounting for predator mortality during migration. We find a variety of non-equilibrium dynamics for both systems, obtaining both limit cycles and chaotic oscillations. We were then able to discuss relevant implications for biologically interesting predator-prey systems including subsidy under seasonal effects. Notably, we can observe the extinction or persistence of a species when the corresponding autonomous system might predict the opposite.
利用非自治常微分方程（ODEs）系统，研究了在存在资源补贴的情况下季节性对捕食者 - 猎物相互作用的影响。该问题的灵感来源于北极地区，那里存在北极狐（捕食者）、旅鼠（猎物）和海豹尸体（补贴）构成的生态系统。我们构建了两个非线性、非自治的ODEs系统，分别称为初级模型和n - 斑块模型。初级模型隐含地考虑了空间因素，而n - 斑块模型将空间明确地视为一个“跳板”系统。我们确立了动力学的有界性，以及足够营养的食物对捕食者生存的必要性。我们研究了在模型中明确纳入资源补贴的重要性，以及考虑捕食者在迁徙过程中的死亡率的重要性。我们发现两个系统都存在各种非平衡动力学，包括极限环和混沌振荡。然后我们能够讨论对包括季节性影响下补贴的具有生物学意义的捕食者 - 猎物系统的相关影响。值得注意的是，当相应的自治系统可能做出相反预测时，我们能够观察到一个物种的灭绝或持续存在。
