This is an impressive review of applications of HMMs in ecology. There are some 30 pages of references, a number of which are recent. It could therefore become a valuable review, and attract a large number of citations.

I thought that there were some excellent features to the paper, but also at times there are places where the material is little more than lists of papers. I am a statistician, and I find such lists hard to digest; see eg., pp 4 and 5, and also later in the paper in places where there are multiple references which come thick and fast. What is important for me is that readers understand what can and cannot be done using HMMs, and the paper is lacking in necessary details in places, as I will explain below. There should not be such gaps. Some can be filled in Appendices.

At the start (p5) It is stated that there is a gentle introduction to HMMs., but what is the audience? It is stated that there should be at least some basic understanding of probability concepts, but far more is needed, such as understanding the rules of matrix theory, and the differences between classical and Bayesian inference. See p8, eg., where a diagonal matrix is specified but not defined. The approach of the paper is primarily classical. It is insufficient to simply state on p 10 that standard optimisation routines can be used. Cf p39, where technical challenges are mentioned. Note p10 mentions a posterior distribution. At the very least the authors should check these features and then provide accessible references for readers who will otherwise be unable to appreciate the work of the paper; I fear that otherwise the messages will be lost. It would not be difficult to provide such references, perhaps in no more than 2 pages. In my view, insufficient thought has been given to this.

A serious deficiency at present is the widespread referencing of books without giving appropriate page numbers in those books. That really should be done if you want readers to be able to track down the details that you have in mind. Another oddity is the use of formal Figures, as on p8, and then supplementary figures, as on p10, which are not treated as figures, which I think should be improved. As an aside, I’d appreciate knowing how the figures are drawn within LaTeX! I have myself used TikZ, but is there something simple out there that is specific for HMMs?

I very much like the repeated examples of what the individual terms are for the components of the iconic expression of Equation 1. That really does impress on the reader the simplicity of the HMM modelling, and we see also the wide applicability. This is very good. However, I do not think that anyone will understand the superficial explanation on p9 of how the forward algorithm results in equation 1. In my view this is not at all obvious, and indeed I recall that Zucchini et al say the same. There should be an appropriate reference, as otherwise the entire foundation of the work of the paper will seem like magic. What is so remarkable about the formulation of eqn 1 is how fast it is compared with alternative likelihood formulations. I have first-hand experience of this. I think that this really vital feature is currently lost on p8 (where I would replace would otherwise by might otherwise).

There seems to be a reluctance to explain global state decoding: see eg., Figure 3, and the tantalising mentions on pp 17, 24 and 30. If it’s worth mentioning then it’s benefits should be explained fully.

The computing possibilities in Section 4 are useful. The last 2 sentences in Section 4 are really important, and perhaps could be given prominence earlier: note the paper title?

What about goodness of fit?

Particular comments

Key words are not in alphabetic order

P5: possibly give relevant section references at the end of Section 1.

P9: The definition of the parameter vector should precede its first use.

P10: give a reference for the whale example? Give Latin name?

P12: what kind of covariate function?

P15: apparent survival

P 18: I liked the JS formulation

P23: I thought that the example of Figure 5 needed better explanation and discussion.

P26: I may have got this wrong, but I thought that a novelty of the Glennie et al paper was the use of sparse matrices? If so then that would be worth a mention.

P33: there are terms used here with which I am unfamiliar.

P38: This is hard to read.

Inevitably with so many references there are some omissions. Eg., Certain books are second edition (Zucchini, eg) some authors are missing middle initials; Compagnoni is missing publication details, etc.

8/30: typically these days few would use Newton-Raphson.

8/38: the discussion regarding relative merits of Bayes and ML approaches. In S4 of the Tutorial discussion focuses, I think, on ML. Earlier, in S3 and in the main paper, it is stated that users will use the approach that they are most familiar with; but a problem with MCMC is the relative difficulty of model choice and model selection. So I think that this lacks balance.

11/40: principal

36/38: What does many mean here? This is a crude tool and there are several alternatives, such as using simulated annealing. See eg., Automatic starting point selection for function optimization, 1994, and Optimisation using simulated annealing, 1995, both by Brooks and Morgan. What about using profile likelihood? Do you discuss whether the problem of multiple optima is particularly true for fitting HMMs? (I may have missed this).

67/ 36: O’Neill

81/10: Royle (2004). This is a highly cited paper but the N-mixture model has flaws; see eg., Dennis et al Biometrics; Computational aspects of N-mixture models 2016 and further papers by Haines, Barker, Schofield et al. Infinite estimates of abundance can arise which might be missed in practice due to numerical procedures terminating prematurely. So is it a good reference here?