This paper addresses an interesting and important challenge in ecology, attempting to provide general statistical scaling laws for stability to facilitate extrapolation and combination of measurements across scales.

The paper is well written, and I see a lot of value in the content. However, I think the authors overstate the generality and applicability of their results.

It is stated several times that the paper’s results will facilitate cross-system comparisons and extrapolation among scales for management. The models used in the paper are based on some pretty strong assumptions. For example, the multi-species model assumes that r and K are constant across patches and that propagules have an equal probability of landing in any patch. Several other assumptions become apparent throughout the paper. The scaling laws, simulations and results in the paper are all based on these assumptions. However, many (most) natural systems in which it would be useful to extrapolate among scales for conservation/management will not fulfil these assumptions. It therefore seems rather dangerous to propose using these scaling laws without testing the potential influence of the assumptions.

The authors do mention these issues briefly in the discussion, but for me those paragraphs (p 18) aren’t enough, given how the rest of the paper is worded. As I see it, there are two main solutions to this. Either sell the paper as an elegant theoretical result that can form a basis for future, more applied, work, or carry out a larger simulation study showing how violation of some of the major assumption influence the applicability of the results.

Other comments:

P 9, L24 – is x here a vector? How is the multi-dimensional aspect of the multi-species system dealt with in the analyses and calculations of stability?

P 6, last paragraph: Can it be assumed that a system with multiple species and multiple sites will act like an additive combination of models 2 and 3?

Eq. 6b and 7b: Parentheses don’t match
P 6, L 31: It would help clarity to write “(e.g. single species…”

Fig. 1: I wonder if it might help to have a separate legend explaining the colors, rather than writing the terms on the figure itself. It took me a while to spot the upper blue line (and thus to understand that invariance-1 was referring to a band around the equilibrium), and also to notice that the other terms were linked to several places on the figure.