Ecological networks describe the interactions between different species, informing us how they rely on one another for food, pollination, and survival. If a species in an ecosystem is under threat of extinction, it can affect other species in the system and possibly result in their secondary extinction as well. Understanding how (primary) extinctions cause secondary extinctions on ecological networks has been considered previously using computational methods. However, these methods do not provide an explanation for the properties that make ecological networks robust, and they can be computationally expensive. We develop a new analytic model for predicting secondary extinctions that requires no stochastic simulation. Our model can predict secondary extinctions when primary extinctions occur at random or due to some targeting based on the number of links per species or risk of extinction, and can be applied to an ecological network of any number of layers. Using our model, we consider how false negatives and positives in network data affect predictions for network robustness. We have also extended the model to predict scenarios in which secondary extinctions occur once species lose a certain percentage of interaction strength, and to model the loss of interactions as opposed to just species extinction. From our model, it is possible to derive new analytic results such as how ecological networks are most robust when secondary species are of equal degree. Additionally, we show that both specialization and generalization in the distribution of interaction strength can be advantageous for network robustness, depending upon the extinction scenario being considered.

中文翻译：

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预测生态网络灭绝的新分析方法

生态网络描述了不同物种之间的相互作用，告诉我们它们如何相互依赖来获取食物、授粉和生存。如果生态系统中的一个物种面临灭绝的威胁，它可能会影响系统中的其他物种，并可能导致它们的二次灭绝。先前已考虑使用计算方法来了解（初次）灭绝如何导致生态网络上的二次灭绝。然而，这些方法并没有提供对生态网络鲁棒性的解释，而且它们的计算成本可能很高。我们开发了一种新的分析模型来预测二次灭绝，不需要随机模拟。当初次灭绝随机发生或由于基于每个物种的链接数量或灭绝风险的某些目标而发生时，我们的模型可以预测二次灭绝，并且可以应用于任意层数的生态网络。使用我们的模型，我们考虑网络数据中的假阴性和假阳性如何影响网络鲁棒性的预测。我们还扩展了该模型来预测一旦物种失去一定比例的相互作用强度就会发生二次灭绝的情景，并模拟相互作用的丧失而不是仅仅物种灭绝。从我们的模型中，可以得出新的分析结果，例如当次生物种程度相同时，生态网络如何最稳健。此外，我们还表明，交互强度分布的专业化和泛化都有利于网络的鲁棒性，具体取决于所考虑的灭绝场景。