Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA.
J Biol Dyn. 2012;6:891-922. doi: 10.1080/17513758.2012.677485. Epub 2012 Apr 26.
The influence of a resource subsidy on predator-prey interactions is examined using a mathematical model. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). In one version of the model, the predator, prey and subsidy all occur in the same location; in a second version, the predator moves between two patches, one containing only the prey and the other containing only the subsidy. Criteria for feasibility and stability of the different equilibrium states are studied both analytically and numerically. At small subsidy input rates, there is a minimum prey carrying capacity needed to support both predator and prey. At intermediate subsidy input rates, the predator and prey can always coexist. At high subsidy input rates, the prey cannot persist even at high carrying capacities. As predator movement increases, the dynamic stability of the predator-prey-subsidy interactions also increases.
利用数学模型研究了资源补贴对捕食者-猎物相互作用的影响。该模型源于对涉及北极狐（捕食者）、旅鼠（猎物）和海豹尸体（补贴）的生物系统的研究。在模型的一个版本中，捕食者、猎物和补贴都出现在同一个地点；在第二个版本中，捕食者在两个斑块之间移动，一个斑块只包含猎物，另一个斑块只包含补贴。对不同平衡态的可行性和稳定性的标准进行了分析和数值研究。在小的补贴输入率下，存在一个最小的猎物承载能力，以支持捕食者和猎物。在中等的补贴输入率下，捕食者和猎物总是可以共存。在高补贴输入率下，即使在高承载能力下，猎物也无法生存。随着捕食者运动的增加，捕食者-猎物-补贴相互作用的动态稳定性也增加。
