Finding a compromise between tractability and realism has always been at the core of ecological modelling. The introduction of nonlinear functional responses in two-species models has reconciled part of this compromise. However, it remains unclear whether this compromise can be extended to multispecies models. Yet, answering this question is necessary in order to differentiate whether the explanatory power of a model comes from the general form of its polynomial or from a more realistic description of multispecies systems. Here, we study the probability of feasibility (the existence of at least one positive real equilibrium) in complex models by adding higher-order interactions and nonlinear functional responses to the linear Lotka–Volterra model. We characterize complexity by the number of free-equilibrium points generated by a model, which is a function of the polynomial degree and system’s dimension. We show that the probability of generating a feasible system in a model is an increasing function of its complexity, regardless of the specific mechanism invoked. Furthermore, we find that the probability of feasibility in a model will exceed that of the linear Lotka–Volterra model when a minimum level of complexity is reached. Importantly, this minimum level is modulated by parameter restrictions, but can always be exceeded via increasing the polynomial degree or system’s dimension. Our results reveal that conclusions regarding the relevance of mechanisms embedded in complex models must be evaluated in relation to the expected explanatory power of their polynomial forms.

中文翻译：

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生态模型：复杂性更高，可行性更高


在易处理性和现实性之间找到折衷方案一直是生态建模的核心。在两个物种模型中引入非线性函数响应已经部分地协调了这种妥协。然而，目前尚不清楚这种妥协是否可以扩展到多物种模型。然而，为了区分模型的解释力是来自其多项式的一般形式还是来自对多物种系统的更现实的描述，回答这个问题是必要的。在这里，我们通过向线性 Lotka-Volterra 模型添加高阶相互作用和非线性函数响应来研究复杂模型中可行性的概率（至少存在一个正实平衡）。我们通过模型生成的自由平衡点的数量来表征复杂性，该数量是多项式次数和系统维数的函数。我们证明，无论调用何种具体机制，在模型中生成可行系统的概率是其复杂性的递增函数。此外，我们发现，当达到最低复杂度时，模型的可行性概率将超过线性 Lotka-Volterra 模型。重要的是，这个最低水平是通过参数限制来调节的，但总是可以通过增加多项式次数或系统维数来超过。我们的结果表明，关于复杂模型中嵌入机制的相关性的结论必须根据其多项式形式的预期解释力来评估。