Dear authors,
I read thoroughly and enjoyed your manuscript “Identifying the environmental drivers of corridors and predicting connectivity between seasonal ranges in multiple populations of Alpine ibex (Capra ibex) as tools for conserving migration”. In your work you implemented cutting-edge analyses to study habitat selection and assess connectivity between summer and winter ranges of the Alpine ibex using a nice dataset including GPS locations from 15 different populations. Overall, I think the ms is well written and I found particularly interesting the comparison between the three approaches of data splitting into training and validation datasets. However, I would suggest making an effort to improve the clarity and readability of the Methods section which is sometimes cumbersome. The impressive quantity of analyses sometimes makes hard to grasp the main aim(s) of the entire work. For example, I found the section “Building and validating models of migratory connectivity in ibex” a little redundant with the sub-sections that follow, and even a little confusing. I appreciated the attempt of summarizing the analyses illustrated more in detail later in the ms but, for example, to me it is not always clear which iSSA models were conducted on the whole pooled dataset and which were conducted separately for each population. This is better explained later in the ms, but I would suggest either clarifying this part without omitting any important information on the analyses or merging it completely with the subsections that follow. I believe this might improve the overall readability of this section of the ms. Also, the rationale behind each analytical choice you made it is not always clearly stated and motivated in Methods. For example, I did not fully understand why you included only variables that were significant for 8 out of 15 populations in all your three approaches. In the introduction you stated that you were interested in comparing connectivity assessments when using either population-specific habitat selection criteria or criteria averaged over all populations. I would have expected that to evaluate differences in connectivity assessment based on population-specific criteria, you may also want to account for the different set of variables that may come out as significant in different populations, and then compare results with models where the significance of each variable was assessed at the level of the pooled datasets. Please find below some more specific comments/questions that I hope will be useful to improve the ms.

L116: Can you really aim at determining environmental choices at the individual level without accounting for individual variability (e.g., random effect) in models?

L191: Some authors recommend selecting step lengths from a uniform distribution rather than from the observed distribution, as choosing step lengths too close to observed ones would lead to the risk of overlooking features that induce avoidance (Zeller et al. 2012; Panzacchi et al. 2016)

LL123-126: What are the “population-specific habitat selection criteria” you are referring to here? Since in connectivity models you retained only variables that were significant for “most” populations, and no random effects were included, how did you account for population-specific habitat selection criteria in connectivity assessments?

L205: You did not specify whether you avoided including correlated variables in the same models or not. Please specify that each model was assembled to avoid that. If you included correlated variables in the same model this could be a major issue misleading the interpretation of your regression coefficients.

LL212-213: this sentence is slightly tautological, and I suggest rephrasing it. Also, you state that you were interested in modelling migratory movements at the population scale, but then in all iSSA models you include only variables that are significant for half + 1 populations. The rationale behind this choice needs to be better supported or explained.

L222: what do you mean by "did not converge correctly"? can you summarize what was the issue?

LL227-233: as anticipated above, this is a rather long paragraph that deserves more clarity. In the first lines you refer to “Models based on the 15 populations”. To me, it is not clear at this point which analyses were run on the entire dataset of pooled locations (all populations together), and which were run on each population separately. This is explained better in the following sub-section (“Sampling training and validation datasets”), but I think it should be clearer to the reader already in this paragraph, which seems to be meant to summarize the rationale of the whole analytical approach.

L238: again, I wonder why you included only variables that were significant in 8 out of 15 populations. This criterion may lead to neglect variables that might be relatively important for some populations. Can you explain what is the advantage of your approach over, for example, excluding only variables that were non-significant across all populations? Did you have some data/reference supporting your choice?

LL253-257: in the “leave 10% of population data out” procedure, did you make sure to avoid separating the two tracks of the same individual between the training and validation datasets? As the aim of this part of analysis is to test the robustness of your models in predicting connectivity also for non-tracked individuals, both migratory tracks (i.e., to-and-fro) of each individual i should be included either in the training or in the validation dataset. Otherwise, there is a risk of obtaining over-optimistic estimates. If you did so, please specify.

Appendix7: Table S7.6: Just a curiosity here: how can sex be unknown for collared animals?

References:
Zeller, K.A., McGarigal, K. & Whiteley, A.R. (2012) Estimating landscape resistance to movement: a review. Landscape Ecology, 27, 777–779.

Panzacchi, M., Van Moorter, B., Strand, O., Saerens, M., Kivimäki, I., St. Clair, C. C., Herfindal, I., & Boitani, L. (2016). Predicting the continuum between corridors and barriers to animal movements using Step Selection Functions and Randomized Shortest Paths. Journal of Animal Ecology, 85, 32-42.

Dear authors,
I congratulate with you for your thorough responses to my previous comments. I appreciated your efforts in re-running a good part of the analyses, providing figures that supported well your replies. I also think you did a good job in improving the readability of some challenging parts of the Methods section, which are now clearer. I am satisfied with most of your responses, and there are only few points that I believe still deserve further clarification. I hope you would find the following comments useful to improve the next version of your manuscript.

L214-216: You decided to retain all variables in your models regardless the value of their pairwise correlation, including one pair with correlation as high as r=0.9. I suggest adding a concise explanation of why including highly correlated variables is acceptable in this context, and discussing related limitations when interpreting results (Avgar et al., 2016). Also, it would be beneficial to provide a brief explanation of the rationale behind the inclusion in the models of both step length and log(step length). Is this linked to a specific hypothesis, or just a technical choice? I suggest including a short introduction of the iSSA approach in the ‘Methods’ section, as it may help clarifying the design of your analysis also to readers who are less acquainted with this method. It is common to include movement components such as step length, together with its log-transformation, turning angles, etc., as covariates in the same iSSA model. However, this do make iSSA prone to cross-correlation issues, such as low parameters estimability (Avgar et al., 2016). I think this should be at least discussed in the ms, as discarding correlated variables is a common practice even among authors that use iSSA models (e.g., Biddlecombe et al., 2020; Passoni et al., 2021).

L236-237: You now included a random intercept in the model to account for individual/population variability. However, I see one potential issue. The number of variables in your full model (n=14 plus two interactions) seems relatively high, especially considering that the number of levels for your random effect can be as low as 10 in certain cases (e.g., 'leave 10% of population data out'; L257), which may lead to model overfitting. One alternative approach to account for individual/population variability could involve using a two-stage modeling approach (e.g., through the function Ts.estim() in the R-package “TwoStepCLogit”). This approach would allow fitting models for individual animal/populations, and then subsequently use individual coefficients as data for further inference (see for example Fieberg et al. 2010 and Craiu et al. 2011, 2016, Ladle et al., 2019, Muff et al., 2020).

Minor comments:
L467-470: I wander if this may be linked to some extent to population-specific functional responses to locally available conditions, which you discuss in the following lines.
L902: Fig. 5. Please change “We removed very low connectivity values for design purposes.” to “We removed very low connectivity values for illustrative purposes.”

Cited literature:
Avgar, T., Potts, J. R., Lewis, M. A., & Boyce, M. S. (2016). Integrated step selection analysis: Bridging the gap between resource selection and animal movement. Methods in Ecology and Evolution, 7(5), 619–630. https://doi.org/10.1111/2041-210X.12528

Biddlecombe, B. A., Bayne, E. M., Lunn, N. J., McGeachy, D., & Derocher, A. E. (2020). Comparing sea ice habitat fragmentation metrics using integrated step selection analysis. Ecology and Evolution, 10(11), 4791–4800. https://doi.org/10.1002/ece3.6233

Forester, J. D., Im, H. K., & Rathouz, P. J. (2009). Accounting for animal movement in estimation of resource selection functions: Sampling and data analysis. Ecology, 90(12), 3554–3565. https://doi.org/10.1890/08-0874.1

Ladle, A., Avgar, T., Wheatley, M., Stenhouse, G. B., Nielsen, S. E., & Boyce, M. S. (2019). Grizzly bear response to spatio-temporal variability in human recreational activity. Journal of Applied Ecology, 56(2), 375–386. https://doi.org/10.1111/1365-2664.13277

Muff, S., Signer, J., & Fieberg, J. (2020). Accounting for individual-specific variation in habitat-selection studies: Efficient estimation of mixed-effects models using Bayesian or frequentist computation. Journal of Animal Ecology, 89(1), 80–92. https://doi.org/10.1111/1365-2656.13087

Passoni, G., Coulson, T., Ranc, N., Corradini, A., Hewison, A. J. M., Ciuti, S., Gehr, B.,
Heurich, M., Brieger, F., Sandfort, R., Mysterud, A., Balkenhol, N., & Cagnacci, F. (2021). Roads constrain movement across behavioural processes in a partially migratory ungulate. Movement Ecology, 9(1), 1–12. https://doi.org/10.1186/s40462-021-00292-4

Dear Authors,
I commend you for your comprehensive responses to my previous comments. I am largely satisfied with your explanations. Below, I have provided a few comments and some minor suggestions for your consideration. Specifically, I think the readability of the Method subsection '1. Sampling training and validation datasets' could be further improved. I hope you may find the following comments useful.

L112: Replace: “accounting for the many factors influencing how ibex choose their migration routes.” With “accounting for several factors hypothesised to influence how ibex choose their migration routes”.

L261: Replace “the first procedure seeks to understand…” with “with the first procedure we seeked to understand”. Change accordingly also L266: “Finally, with the third procedure we aimed to evaluate….”. Also, consider being consistent with terminology, when possible: you often use interchangebly the terms ‘procedures’, ‘methods’, ‘approaches’, ‘datasets’ to refer to your three validation/training analyses.

L267: I noticed that you've opted to remove the text you added in the previous round of revision, where you were aiming to clarify the process of constructing your datasets. I agree that this bit of text in particulat was a bit cumbersome, but I still think both this and the next paragraph would benefit from further improving their clarity. This is the very core of your analysis, and it would be a pity if the reader gets confused here! I believe the entire Methods section would significantly benefit from a clearer and more effective explanation. Particularly, readibility in LL281-284 needs to be improved.

I suggest restructuring the paragraph at L277 with something like:
"We created three sets of training/validation datasets for two purposes: developing habitat selection models (training datasets) and assessing connectivity predictions (validation datasets). For the 'leave 10% of whole data out' approach, we built the training dataset by randomly sampling 90% of individuals from the 15 populations, reserving 10% for validation. Similarly, for the 'leave 10% of population data out' appraoch, we randomly sampled 90% of individuals from each population for training, using the remaining 10% for validation. We repeated both sampling 100 times. In the 'leave one population out' approach, data from 14 populations constituted the training dataset, while data from the remaining population served as validation."

286: replace “populations” with “population”