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捕食者-食饵模型功能反应的结构敏感性

Structural sensitivity in the functional responses of predator-prey models

Sarah K. Wyse, Maria M. Martignoni, May Anne Mata, Eric Foxall, Rebecca C. Tyson

发表信息：
Ecol. Complex. 51 (2022) 101014
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摘要：

在数学建模中，通常可以使用几种不同的函数形式来同样好地拟合数据集，特别是当数据稀疏时。在这种情况下，这些数学上不同但看起来相似的函数形式通常被认为是可互换的。然而，最近的工作表明，类似的功能反应可能会导致显着不同的歧点的Rosenzweig-MacArthur捕食系统。由于分叉行为包括不稳定振荡，预测这种行为的发生显然是重要的。从理论上讲，不同的分叉行为意味着可以从模型中获得不同的预测。这些预测的范围可以从两个物种的稳定共存到灭绝，因此获得更准确的预测对自然资源保护主义者来说显然也很重要。在数学上，给出类似功能响应的分叉结构的这种差异称为结构灵敏度。我们扩展了现有的工作，发现Leslie-Gower-May捕食-被捕食系统在结构上也对功能反应敏感。使用Rosenzweig-MacArthur和Leslie-Gower-May模型，我们的目标是确定是否有某种方法可以获得数据的功能描述，从而使我们的模型在结构上不敏感。我们首先添加随机性的功能性反应，并发现更好的相似性所产生的分歧结构实现。然后，我们使用两种不同的方法来分析功能响应，以确定每个功能的哪一部分对所观察到的分叉行为贡献最大。我们发现，猎物密度周围的共存稳定状态是最重要的功能性反应的定义。最后，我们提出了一个程序，生态学家和数学建模，以提高模型预测的准确性捕食系统。

英文摘要：

In mathematical modeling, several different functional forms can often be used to fit a data set equally well, especially if the data is sparse. In such cases, these mathematically different but similar looking functional forms are typically considered interchangeable. Recent work, however, shows that similar functional responses may nonetheless result in significantly different bifurcation points for the Rosenzweig-MacArthur predator-prey system. Since the bifurcation behaviours include destabilising oscillations, predicting the occurrence of such behaviours is clearly important. Ecologically, different bifurcation behaviours mean that different predictions may be obtained from the models. These predictions can range from stable coexistence to the extinction of both species, so obtaining more accurate predictions is also clearly important for conservationists. Mathematically, this difference in bifurcation structure given similar functional responses is called structural sensitivity. We extend the existing work to find that the Leslie-Gower-May predator-prey system is also structurally sensitive to the functional response. Using the Rosenzweig-MacArthur and Leslie-Gower-May models, we then aim to determine if there is some way to obtain a functional description of data such that our model is not structurally sensitive. We first add stochasticity to the functional responses and find that better similarity of the resulting bifurcation structures is achieved. Then, we analyze the functional responses using two different methods to determine which part of each function contributes most to the observed bifurcation behaviour. We find that prey densities around the coexistence steady state are most important in defining the functional response. Lastly, we propose a procedure for ecologists and mathematical modelers to increase the accuracy of model predictions in predator-prey systems.

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