This is a clear, well-written and interesting paper that reviews the applications of hidden Markov models to ecological systems to different questions at a range of organizational levels. I have only one significant comment:

• p. 21: the authors state that the conditional independence assumption means that we can treat the components of a multivariate emissions distribution (e.g. turning angle and move distance) as independent. I agree that this independence is a common assumption, but I don't see why it is necessarily true. (It is consistent with the DAG diagram on ll. 29-35, but that's just a restatement of the assumption that X and Y are conditionally independent.

MAJOR (but not critical) comments:

• The authors could more strongly emphasize the fundamental assumption of HMMs that the underlying latent state is discrete and finite. They state this property both in Table 1 ("A special class of state-space model with a finite number of hidden states ...) and on p. 7 ("Unlike the larger class of state-space models, the state process within an HMM can take on only finitely many possible values"), but it feels like this is a key aspect of the definition that should be clarified earlier. When I am deciding how to model an ecological system with latent variables, I think about (1) whether it would be useful to introduce a latent variable; (2) whether the latent state has serial dependence (i.e., do I need a full state-space model or will a latent mixture model that assumes state occupancy is independent across observations be sufficient [e.g. a finite mixture model or a hierarchical model]?) (3) whether the latent state can be usefully represented as a discrete variable. I don't expect the authors to provide a full taxonomy of models, but an emphasis on finiteness/discreteness (e.g. in the abstract and near the beginning of the Introduction) would help readers understand whether HMMs could usefully be applied to their questions.

• the overall organization as described in Table 1 is really nice. I'm not sure about "stability" as the description of the existential question for the ecosystem level (the descriptions in the boxes seem to be descriptions of states, and "stability" isn't a state); maybe "regime" ? (Similarly, 'abiotic' is not really an "observation" on the same level as counts, presence-absence, etc.)

• The authors should think hard about the intended audience and whether they can do more to increase accessibility (although they may not be able to do much more given the breadth they're covering). They say they expect "some basic understanding of probability theory concepts such as uncertainty, random variables, and probability distributions", but then equation 1 is a "simple matrix product expression" that will not be clear to many ecologists. Maybe 'basic linear algebra, e.g. as in Caswell's book' should be specified?

• population level, existential state (3.2.1): is it worth noting that HMM models of population size require the imposition of a maximum size in order to fulfil the assumptions of a finite set of states?

• Relative to the other sections, I found the ecosystem level treatment (3.4) a little disappointing. A haphazard sample of the references given on p. 36 suggests that most of these are really community-level analyses, not what are usually called 'ecosystem' level (i.e., incorporating stocks and flows of abiotic components -- this agrees with Figure 1, which uses 'abiotic' to define the observation process for the ecosystem level. The authors should be a little more careful here. My own view is that HMMs might be less useful at the ecosystem level precisely because it's harder to imagine discrete/finite sets of underlying latent states, but I'm willing to believe that the limitation also has to do with the awareness and creativity of ecologists. HMMs make sense in the context of communities with multiple stable states, but I would again argue that in many cases these systems are being considered at the community, not the ecosystem level (lake eutrophication systems are a good counterexample).

• It would be nice to comment somewhere on the possibility of making transition probabilities dependent on covariates (this is done in Li and Bolker [2017], I don't know whether there are other good examples)

• Figure 6: it is generally a good idea (although rarely done) to standardize such citation graphs by the total number of papers/citations in the entire field (so a growth in general publication/citation rates in ecology isn't confounded with growing interest in HMMs)

MINOR COMMENTS

• p. 1 l. 44 putting "state" in quotation marks doesn't help define it for readers who don't already know what you mean. Clarify? (Could just delete "described as existing in a 'state'" without loss of generality ...)
• p. 1 l. 52 "tenet" -> "goal" or "aim"?
• p. 2 l. 55 "biodiversity" seems odd here
• p. 4 l. 41 "in our experience" unnecessary?

Michael Li and Benjamin M. Bolker, “Incorporating Periodic Variability in Hidden Markov Models for Animal Movement,” Movement Ecology 5, no. 1 (January 26, 2017): 1, https://doi.org/10.1186/s40462-016-0093-6.

I thought the version of this was worthwhile. I think the revised version is also worthwhile.

I'm still unconvinced by the 'ecosystem' section. Rather than muddling the community and ecosystem levels together (I don't think it's useful to classify any study that includes abiotic factors as covariates in community dynamics as an ecosystem study ...) why not just keep this section very short and say that there is a growth opportunity here?

it still seems to me that most of the examples given in the first paragraph of the "ecosystem" section are just community-level analyses. I don't really see the point in expanding the scope of 'ecosystem' to include a wide range of Markov models of communities (e.g. are Horn 1975 and Wootton 2001 here included because they encompass disturbance, or ???) Similarly, I don't see why occupancy modeling of species distributions driven by climate change (Moritz et al 2008) counts as an ecosystem-level HMM analysis ... I'm similarly unconvinced by a lot of the descriptors at the ecosystem/developmental level in Figure 1. All of the terms in this box (composition, resilience, ...) describe primarily community dynamics!

The authors give lip service to the idea that models should not be more complex than be supported by the data, but there is some tension between "we can build an HMM to incorporate any phenomenon you like!" and "but are we going to be able to fit the model, or even know if we have fitted the model reliably?" The Cole 2019 ref is good; at a more general level Lavine 2009 may also be worth referencing.

Lavine, Michael. “Living Dangerously with Big Fancy Models.” Ecology 91, no. 12 (December 1, 2010): 3487–3487. https://doi.org/10.1890/10-1124.1.

MINOR COMMENTS

all page references are ms pages, not PDF pages

p 1 l 48 "increasing, decreasing" -> "increases, decreases"

p 2-3 give some refs for these examples??

p 3 l. 33 maybe spell out 'environment DNA' for less informed readers?

p. 5 l. 41 "these" -> "these models" ?(avoid 'these' without explicit antecedent; also p. 25 l. 10)

p. 6 l. 36 "a[n?] N x N ..."

l. 55 at first glance this notation is very confusing to me; how can we have a matrix with elements that are function-valued?? I guess I'll see when we get to section 2.2. ... (if the matrix is diagonal anyway, why isn't this just a sequence of functions?) I guess I see how this works, but is this really standard/well-posed mathematical notation? (Thanks to Google books I can see that this is more clearly described in Zucchini et al. p. 36, but it might be worth signposting this more clearly ...)

p. 10 l. 47 delete "potential"?

p. 11 l. 40 "principal"

p. 12 l. 30 "Existential"

p. 14 l. 52 also the probability that an individual was alive at a given time (not just the most likely death time ...) [similar comment applies to p. 21, l. 45; I think the Viterbi algorithm, plus the convenience of specifying a single most likely distribution, makes this 'most likely' state approach slightly overused - it could often mask the fact that many states are nearly equally likely at a given point in time ...]

p. 16 l 31 (and p. 24 l. 43, p. 25 l. 50) "utilised" -> "used" ?

p. 22 l. 49 how much a special case is using HMMs in this case? It was my impression that most geolocation still used continuous state-space models (I did look at Thygesen 2009, so I see it is done ...)

p. 24 l. 39 missing period

p. 29 36 cycles -> stages?

Box 1 l. 44 "as simple as in depicted above" ... ? "as simple as they are depicted" ?

Box 1: It seems a little weird to classify "state space models" as only continuous-state models (I would say that HMMs are a special case of state space models, which include both SSMs sensu stricto (continuous states) and HHMs ...)