1. Individual‐level traits mediate interaction outcomes and community structure. It is important, therefore, to identify the minimum number of traits that characterise ecological networks, that is, their ‘minimum dimensionality’. Existing methods for estimating minimum dimensionality often lack three features associated with increased trait numbers: alternative interaction modes (e.g. feeding strategies such as active vs. sit‐and‐wait feeding), trait‐mediated ‘forbidden links’ and a mechanistic description of interactions. Omitting these features can underestimate the trait numbers involved, and therefore, minimum dimensionality. We develop a ‘minimum mechanistic dimensionality’ measure, accounting for these three features.
2. The only input our method requires is the network of interaction outcomes. We assume how traits are mechanistically involved in alternative interaction modes. These unidentified traits are contrasted using pairwise performance inequalities between interacting species. For example, if a predator feeds upon a prey species via a typical predation mode, in each step of the predation sequence, the predator's performance must be greater than the prey's. We construct a system of inequalities from all observed outcomes, which we attempt to solve with mixed integer linear programming. The number of traits required for a feasible system of inequalities provides our minimum dimensionality estimate.
3. We applied our method to 658 published empirical ecological networks including primary consumption, predator–prey, parasitism, pollination, seed dispersal and animal dominance networks, to compare with minimum dimensionality estimates when the three focal features are missing. Minimum dimensionality was typically higher when including alternative interaction modes (54% of empirical networks), ‘forbidden interactions’ as trait‐mediated interaction outcomes (92%) or a mechanistic perspective (81%), compared to estimates missing these features. Additionally, we tested minimum dimensionality estimates on simulated networks with known dimensionality. Our method typically estimated a higher minimum dimensionality, closer to the actual dimensionality, while avoiding the overestimation associated with a previous method.
4. Our method can reduce the risk of omitting traits involved in different interaction modes, in failure outcomes or mechanistically. More accurate estimates will allow us to parameterise models of theoretical networks with more realistic structure at the interaction outcome level. Thus, we hope our method can improve predictions of community structure and structure‐dependent dynamics.

中文翻译：

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结合替代的交互模式，禁止的链接和基于特征的机制增加了生态网络的最小特征维数

1. 个人层面的特质介导互动结果和社区结构。因此，重要的是要确定构成生态网络特征的最少数量的特征，即它们的“最小维数”。现有的估计最小尺寸的方法通常缺乏与特征数量增加相关的三个特征：替代的交互模式（例如主动或静坐等主动进食的进食策略），特征介导的“禁止链接”和对相互作用的机械描述。忽略这些特征可能会低估所涉及的特征数量，因此会最小化维度。考虑到这三个特征，我们制定了“最小机械尺寸”度量。
2. 我们的方法唯一需要的输入就是交互结果的网络。我们假设特质是如何机械地参与其他交互模式的。使用相互作用物种之间的成对性能不平等来对比这些不确定的性状。例如，如果捕食者通过典型的捕食模式捕食猎物，则在捕食序列的每个步骤中，捕食者的性能必须大于猎物的性能。我们从所有观察到的结果构建了一个不等式系统，我们试图用混合整数线性规划来解决。可行的不等式系统所需的特征数量提供了我们的最小维数估计。
3. 我们将我们的方法应用于658个已发布的经验生态网络，包括主要消费，捕食者-被捕食，寄生，授粉，种子传播和动物优势网络，以便在缺少三个焦点特征时与最小维数估计进行比较。与缺少这些特征的估计相比，当包含替代交互模式（占经验网络的54％），作为特征介导的交互结果的“禁止交互”（92％）或机械观点（81％）时，最小维度通常更高。此外，我们在已知维数的模拟网络上测试了最小维数估计。我们的方法通常会估算较高的最小尺寸，更接近实际尺寸，同时避免与先前方法相关的过高估计。
4. 我们的方法可以减少在不同的交互模式，失败结果或机制上遗漏涉及不同特征的风险。更准确的估计值将使我们能够在交互结果级别上对具有更实际结构的理论网络模型进行参数化。因此，我们希望我们的方法可以改善对社区结构和结构依赖性动力学的预测。