This paper defines a set of baseline models to test against, when trying to infer the involvement of memory in the emergence of site-fidelity and return rates to previously visited sites in animal movement. While I really like this paper and agree that a discussion of processes that result in site-fidelity other than memory is needed, I have the feeling that the authors in the end try to explain everything very simplistically in the light of the frequency of return rates, disregarding that memory may be beneficial to use space more efficiently. In my opinion there are other metrics that could be used in the context of the suggested baseline models. I will try to explain what I mean by this.

My comments concern mainly the discussion of their findings. The introduction is very well written and not much to add. In general, the paper is very well written, clearly formulated, and easy to follow - although I think in some instances it would be necessary to introduce a concept already earlier than it appears in the text and a few more references would be required (see individual comments below). The methods used to simulate different movement models are clear and the results are presented in a way that is easy to understand.

But during the discussion the authors seem to be focusing solely on the frequency of returns to a given location and suggest using their models to set a baseline frequency of returns that can be expected given a specified model - if the frequency exceeds this baseline frequency this could be attributed to memory, the authors suggest.

I’m not an expert in this topic, but to me this is too simplistic, and I wonder, if processes involving memory could result in return rates below the expected frequency under a memory-free process. E.g., memory may be beneficial to maximise resource acquisition (with respect to distance travelled or energy expenditure) on the search for sites of high rewards while at the same time familiarity may be beneficial for evading predators. Thus, I would expect that some places which are of high quality will be never re-visited (returned to) or much less than expected under one of the suggested baseline models, because the animal moves through space to increase energy efficiency or because memory also brings benefits in terms of predation evasion. So, the frequency need not always be higher but the distribution over space and time will be different when memory is involved.
Or else, the authors show, that animals will return to sites even over large time scales (e.g. 365 days) but how they alternate between e.g. summer and winter range will also show if memory is involved or not – and this can be seen just from visually looking at long time trajectories.
Maybe there are different expectations to test for? With memory involved, wouldn’t you expect that the number of locations revisited will reach a plateau quite quickly, whereas if movement occurs according to one of the baseline models, the number of locations should increase for longer time periods, or something like this (although from e.g. Fig 2 this is also true for some baseline models with extreme parameter settings). This may not be very thought through, but I could imagine that focusing more on the pattern of returns might make more sense or at least deserves some space in the discussion.

Just in general I think the discussion is a bit lengthy and could be shortened at places.

I think this paper is needed and shows nicely, that return to previously visited sites must not be due to memory. But the discussion seems too simplistic to me, and other metrics should be taken into account as well.

Also see individual comments below.

Kind reagrds
Benedikt Gehr

Individual comments

197: This seems quite a lot in my opinion. Also I wonder, if it makes sense to define a return from the step length distribution rather than some area relative to the 95% home range - even though I do realize these two probably correlate quite strongly. In general I think it's a challenge to define what a return really is. Did you do a sensitivity analysis where you for instance would use 50%, 40%, 30% percentile (or to me more sensible, area relative to home range) to see how this changes the results?

209 It wasn’t intuitively clear without explanations (at least for my brain), why you calculated the probability of return per step over all animals - each replicate by definition is independent from all others? I thought it would make more sense to calculate the proportion of revisited steps per animal and average over all animals? This becomes clear in line 207 and following, but it might be helpful to state this clearly already above.

234 Again, I wasn’t sure what we learn from the constrained correlated random walk model before it was explained. I realize now that it can simulate islands and barriers, but maybe this should be elaborated already at the beginning, where the models are introduced, otherwise this is not clear.

315 Is it really just about the baseline frequency? I think the frequency need not always be higher but the distribution over space will be different when memory is involved.

324 I think the reasoning why a constraint was used should be elaborated already at the beginning, otherwise this is not clear, see comment above.

453 I think here you need to provide some example references

458 Again, this univariate approach seems much too simplistic to me

I would like to thank the authors for this very thorough revision of their manuscript. The authors have adressed all my comments and concerns in great detail (as well as from the other two reviewers) and I have nothing else to contribute. I'm very happy to recommend this manuscript for publication as it is and I think it is a very nice and much needed contribution to the field.

Kind regrads
Benedikt Gehr