In mathematical modelling, 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 destabilizing 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 so that different functional responses yield the same bifurcation structure, i.e., we aim to describe 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 analyse 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 modellers to increase the accuracy of model predictions in predator–prey systems.

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，尤其是在数据稀疏的情况下。在这种情况下，这些数学上不同但外观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仍然会导致 Rosenzweig-MacArthur 捕食者 - 猎物系统的分叉点显着不同。由于分岔行为包括不稳定的振荡，因此预测此类行为的发生显然很重要。在生态学上，不同的分岔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稳定共存到两个物种的灭绝，. 在数学上，给定类似功能响应的分叉结构的这种差异称为结构敏感性。我们扩展了现有的工作，发现 Leslie-Gower-May 捕食者-猎物系统在结构上对功能反应也很敏感。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，以便不同的功能响应产生相同的分叉结构，即，我们的目标是描述数据，使得我们的模型在结构上不敏感。我们首先将随机性添加到功能响应中，并发现得到的分叉结构具有更好的相似性。然后，我们使用两种不同的方法分析功能响应，以确定每个功能的哪个部分对观察到的分叉行为贡献最大。我们发现，共存稳态周围的猎物密度对于定义功能响应是最重要的。最后，我们提出一个程序生态学家和数学建模师，以提高捕食者 - 猎物系统中模型预测的准确性。