We study an ecosystem of three keystone species: salmon, bears and vegetation. Bears consume salmon and vegetation for energy and nutrient intake, but the food quality differs significantly due to the nutritional level difference between salmon and vegetation. We propose a stoichiometric predator-prey model that not only tracks the energy flow from one trophic level to another but also nutrient recycling in the system. Analytical results show that bears may coexist with salmon and vegetation at a steady state, but the abundance of salmon may differ under different regimes. Numerical simulations reveal that a smaller vegetation growth rate may drive the vegetation population to extinction, whereas a large vegetation growth rate may drive the salmon population to extinction. Moreover, a large vegetation growth rate may stabilize the system where the bear, salmon and vegetation populations oscillate periodically.

中文翻译：

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关键物种之间的数学模型：熊、鲑鱼和植被。

我们研究了三个关键物种的生态系统：鲑鱼、熊和植被。熊食用鲑鱼和植物来获取能量和营养，但由于鲑鱼和植物之间的营养水平差异，食物质量存在显着差异。我们提出了一种化学计量的捕食者-被捕食者模型，该模型不仅可以跟踪从一个营养级到另一个营养级的能量流，还可以跟踪系统中的养分循环。分析结果表明，熊可能与鲑鱼和植被在稳定状态下共存，但鲑鱼的丰度在不同的情况下可能会有所不同。数值模拟表明，较小的植被生长率可能导致植被种群灭绝，而较大的植被生长率可能导致鲑鱼种群灭绝。此外，较高的植被生长率可以稳定熊、鲑鱼和植被种群周期性波动的系统。