Content of review 1, reviewed on March 31, 2022

I found the manuscript and Supplementary Files both well written, and the complex matters that the paper is dealing with are clearly explained. The manuscript got me fascinated by the idea of measuring and ranking sensitivity of species to perturbations over time. With this manuscript, the authors introduce a novel approach that may help us to understand the vulnerability of systems to change and fluctuations. Below, I list three observations that may help the authors to improve the manuscript: 1&2 are two important methodological concerns, and 3 relates to the relevance for ecological research.

  1. The simulations are all based on deterministic models. I'm wondering how the performance of the sensitivity indicators changes when some stochasticity is added to the dynamical system. I would be afraid that the performance would become very low, because the proposed measures are based on a good estimation of the Jacobian matrix. If so, I'm not convinced that these measures will be really useful in practice, since ecosystems are never completely deterministic.

  2. Because sensitivity cannot be calculated for the empirical data, since the underlying model is unknown, the authors use LSTM neural network and assume that forecasting errors per species reflect the sensitivity of that species. I think this is conceptually a great idea, but the authors did not test this assumption. I would suggest to calculate the LSTM ranking in the synthetic timeseries generated with the population dynamic models as well, to validate this assumption.

  3. The results of the empirical time series analysis (Fig. 4) are not very strong, despite the fact that the datasets were carefully chosen. In ecological research, not many of these type of long-term multivariate datasets exist. I think it would be helpful if the authors include a paragraph in the discussion on utilization. For which type of ecosystem and data would this method be useful, and what does the ranking exactly tell us?

Looking forward to see a revised version of this manuscript being published :)

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    © 2022 the Reviewer.