Stability is a key attribute of complex food webs that has been for a long time in the focus of studies. It remained an intriguing question how large and complex food webs are persisting if smaller and simple ones tend to be more stable at least from a mathematic perspective. Presuming that with the increasing size of food webs their stability also grows, we analyzed the relationship between number of nodes in food webs and their stability based on 450 food webs ranging from a few to 200 nodes. Our results show that stability increases non-linearly with food web size based both on return times after disturbance and on robustness calculated from secondary extinction rates of higher trophic levels. As a methodologic novelty we accounted for food web generation time in the return time calculation process. Our results contribute to the explanation of large and complex food web persistence: in spite of the fact that with increasing species number the stability of food webs decreases at small node numbers, there is a constant stability increase over a large interval of increasing food web size. Therefore, in food web stability studies, we stress the use of food web generation times.

中文翻译：

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提高大型食物网的网络稳定性

稳定性是长期以来一直是研究重点的复杂食物网的关键属性。如果较小和简单的食物网至少在数学上趋于稳定，那么仍然存在着一个巨大而复杂的食物网，这将是一个有趣的问题。假设随着食物网尺寸的增加，其稳定性也在增长，我们基于450个食物网（从几到200个节点）分析了食物网中节点数与其稳定性之间的关系。我们的结果表明，基于扰动后的返回时间以及根据较高营养级次灭绝率计算出的鲁棒性，稳定性随着食物网尺寸的增加而非线性增加。作为一种方法上的新颖性，我们在返回时间计算过程中考虑了食物网生成时间。我们的结果有助于解释大型复杂的食物网的持久性：尽管随着物种数量的增加，食物网的稳定性在小节点数时降低，但在增加食物网尺寸的较大间隔内，稳定性不断提高。因此，在食物网稳定性研究中，我们强调使用食物网生成时间。