In response to external changes, ecosystems can undergo catastrophic transitions. Early warning indicators aim to predict such transitions based on the phenomenon of critical slowing down at bifurcation points found under a constant environment. When an explicit rate of environmental change is considered, catastrophic transitions can become distinct phenomena from bifurcations, and result from a delayed response to noncatastrophic bifurcations. We use a trophic metacommunity model where transitions in time series and bifurcations of the system are distinct phenomena. We calculate early warning indicators from the time series of the continually changing system and show that they predict not the bifurcation of the underlying system but the actual catastrophic transition driven by the explicit rate of change. Predictions based on the bifurcation structure could miss catastrophic transitions that can still be captured by early warning signals calculated from time series. Our results expand the repertoire of mechanistic models used to anticipate catastrophic transitions to nonequilibrium ecological systems exposed to a constant rate of environmental change.

中文翻译：

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预警指标捕捉由明确的环境变化率驱动的灾难性转变

为了应对外部变化，生态系统可能会经历灾难性的转变。预警指标旨在根据恒定环境下发现的分叉点严重减速现象来预测这种转变。当考虑环境变化的明确速率时，灾难性转变可能成为与分歧截然不同的现象，并且是由于对非灾难性分歧的延迟响应而导致的。我们使用营养元群落模型，其中时间序列的转变和系统的分叉是不同的现象。我们根据不断变化的系统的时间序列计算预警指标，并表明它们预测的不是底层系统的分叉，而是由显性变化率驱动的实际灾难性转变。基于分叉结构的预测可能会错过灾难性转变，而根据时间序列计算出的预警信号仍然可以捕获这些灾难性转变。我们的结果扩展了用于预测暴露于恒定环境变化率的非平衡生态系统的灾难性转变的机械模型的库。