Response.txt

Dear editors,

Thank you for the attention and expertise you used in assessing, for Ecosphere, our paper "Tail associations and their impact on extinction risk" (this was the old title, we will now be changing it in response to a referee request - see below). Thank you also for the generally very positive reviews. We have responded to all referee comments through changes to the manuscript, and below. We find the paper is improved and we hope you now find it ready for formal acceptance to Ecosphere. Our responses to comments are preceded by ">>>" to make them easy to find. Thank you again for an enjoyable and helpful review process.

Yours,
Shyamolina Ghosh, Lawrence Sheppard and Dan Reuman


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Reviewer #1 (Comments to the Author):

Summary of article
This manuscript investigates the effect of asymmetries in tail associations (increased correlation at either extreme low or high values of a population or environmental variable) on extinction risk for populations in stage-structured demographic models and in spatial metapopulations. It extends the little previous ecological work on asymmetric tail associations in spatial metapopulations by including density-dependence and introduces them in stage structured models. The authors find that spatial left-tail associations substantially increase extinction risk in metapopulations, possibly due to lower chance of rescue for populations with low growth rates. They find these asymmetries in vital rate tail associations impact extinction risk very little in stage-structured non-spatial models.

Overarching thoughts
The overall concepts of what asymmetric tail associations are and why they are important ecologically are clearly communicated, with the use of conceptual figures such as Fig 1.

>>>Thank you for the positive feedback!

The inclusion of two kinds of asymmetric tail associations – those between vital rates within a population and spatial tail associations in a metapopulation – illustrate that the type of asymmetric tail association matters to determining their role in extinction risk.

The use of several forms of density dependence in the spatial metapopulation model demonstrates the degree to which effect sizes are not dependent on a specific density dependence formulation, but a broader feature of asymmetric tail associations across metapopulation model structures.

>>>Correct. Thank you for the positive feedback.

I suggest only a few clarifications:

Specific comments
L164-175: Has this particular formulation been analyzed in detail in a classic text? Cite it to guide the reader to more resources on the behavior of this model more generally.

>>>Models of this form (i.e., stochastic matrix models, of which this is an example) are very common in demography, evolutionary ecology, and quantitative conservation biology. As the referee requests, we have added references to the classic books of Caswell and Morris & Doak.

L222-224: Cite introduction or thorough analyses of these models to direct the reader to more resources. Or add those citations to Table 1 and reference it here for brevity.

>>>Thank you for raising this point, as it spurred us to add clarity about where these models come from. These models are all described by Cohen (1995), who also cites the original sources for each model. Details of each model are also given in Appendix S2. These facts are now mentioned at the point in the text to which the referee refers. Thanks again.


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Reviewer #2 (Comments to the Author):

Brief summary: This paper examined the effects of “tail associations” of ecological variables on the extinction risk of metapopulations and stage-structured populations using nonlinear population models. The results show that the effect of tail associations between fecundity and juvenile survival is minor, while that between patches that a metapopulation occupies increases or decreases extinction risk, depending on the domain of different compensatory dynamics. This work is one of the earliest studies that examine how copula structure in ecological variables influence population persistence. The authors investigated this problem using a variety of models, showing the general importance of tail associations of ecological variables on population persistence. Because copula structure in ecological variables should be ubiquitous in nature and ongoing climate change is likely altering correlation structure between variables, the problem investigated in this paper is of interest to the readers of ESA journals.

>>>Thank you for the positive feedback!

General comments
1.      The title seems a bit cryptic to readers who are not a statistician. I would suggest that title be modified to clarify it is about the tails of the distributions of ecological variables.

>>>Thank you for the suggestion. We changed the title as suggested.

2.      A conceptual schematic diagram early in the introduction will greatly help readers understand the main idea quickly and smoothly follow the text. In the current form, it is relatively hard to follow. Figure 1 does help, but a figure showing the idea in a more concrete way using tangible examples would make it much easier for readers to absorb the idea early on in the paper. It also would be helpful to see an example from finance or other fields that are somewhat analogous to ecological situations.

>>>Thank you for this suggestion, which spurred a lot of thought about how to best communicate the main ideas of the manuscript in the initial parts of the manuscript. The referee's suggestion led to two new figures. 

3.      The amount of analyses for metapopulations and age-structured populations seems quite unbalanced. Why is this so? Obviously, the paper would greatly increase its value by including more analyses for stage-structured populations, but then the paper may become too long to fit in the required length for Ecosphere. Would it be more beneficial to focus only on metapopulations in this paper and expand on the stage-structured population part in a separate paper to more deeply examine Tuljapurkar’s approximation?

>>>Thank you for asking these questions. First, this is an initial attempt to understand the impact of asymmetric tail associations on extinction risk, and as such we intentionally used a simple approach for a rapid assessment of whether the basic ideas have merit. Based on our results, we believe this could turn into a broad topic, which many researchers should investigate. Our intention was to provide an initial exploration of the mechanisms rapidly, and in so doing, hopefully to open what could be a practically important topic (for conservation) to consideration by other researchers, as quickly and broadly as possible. With regard to extensive mathematical analyses (e.g. using Tuljapurkar's approaximation) of stochastic matrix models, which the referee suggests, we are journeymen only, not true experts. Mathematical analysis of stochastic matrix models is a deep field. So we believe carving our matrix model results out of the current paper and then undertaking a more systematic exploration ourselves, for possible later publication, does not get these potentially practically important ideas out there as fast and risks the possibility that we will not be able to do the analyses as well as some of our readers. So to us it is important to get these results out there now.
  Second, for stochastic matrix models, our initial explorations suggested that probably the effects of tail association in that context are minor, so we went no further. In contrast, for metapopulation models, our initial explorations (initially our explorations were with the Ricker model only) showed a likely strong effect, so we went further with additional models. So what the referee perceives as imbalance is actually just a rational attempt to explore promising ideas further and to simply identify other ideas as less promising, to help future researchers choose what to work on.  
  Finally, we do not see as much of an imbalance as the referee suggests. To us, the two components are treated with slightly different thoroughness, but not markedly so, and for good reasons (see above). Our matrix modelling results are certainly enough to make the points we wanted to make, i.e., an initial assessment that the influence of tail associations on extinction risk in this context seems likely to be minor.
  
4.      The order of appearance of the metapopulation problem and the age-structured population problem keeps switching throughout the paper. For readability, the order should be consistent.

>>>Thanks for raising this point. We have edited to enforce consistency of this ordering throughout the manuscript.

5.      Whether variables have tail associations can be altered by transformation; e.g., variables may have no tail association in one way but show any of the tail associations discussed in this paper in another. How should researchers who want to use the approached introduced in this paper deal with this? Should they look for a transformation that can give one of such tail associations as long as it is ecologically meaningful in a given system? I suppose so, but this is not mentioned in the paper. 

>>>The referee is mistaken here, transformation does not alter tail associations as we have defined them based on data ranks. This is a standard way of defining tail associations and copula approaches to the study of dependencies, justified by the Ghosh et al paper (which, by the way, has now been formally accepted at Advances in Ecological Research, and is in press) and by Genest & Favre, 2007, J Hydol Eng, "Everything you always wanted to know about copula modelling but were afraid to ask". We have clarified and amended some text, in the Discussion, which helps explain these facts. 

Also, the interpretation that certain variables are “bad” or “good” depends on how it is formulated or transformed. It could be that, if a “bad” variable is associated with a “good” variable in their right tails, for example, their effects cancel each other and leave no overall effect, which would be also an interesting result. This may be related to the discussion about negative associations between Line 411 and 423, but it does not clearly come across. Maybe these are discussed in the Ghosh et al. paper in BioRxiv, but it is not yet published in a peer reviewed journal. These aspects should be worth mentioning in this paper for clarification of the method.

>>>The Ghosh et al paper is now formally accepted. The version on the BioRxiv is essentially the same as the final, accepted version. In spite of thinking for a quite a long time about what the referee may have meant by the above comment, we confess we are not sure, so we do not know quite what to do about this comment. In our model formulations, variables themselves are never "good" or "bad" but are instead assumed to fluctuate, taking values in some years which are "good" for the population (by which we mean they promote increased reproduction or increased survival in that location, in that year), and values in other years which are "bad" (in the opposite sense). Aside from an apparent desire to have us make some additional point (I'm afraid we cannot understand what point), the referee does not appear to be criticizing anything we actually do say. So we suggest proceeding with this part of the manuscript as it is. As we said, the Ghosh et al paper is now accepted, and is already available online on the BioRxiv, and many important  points which seem likely to be related to the referee's point are made there. So readers looking to base some of their own research on the points made in the current manuscript can also use the Ghosh et al paper as an additional background resource before getting started.  

6.      Figure 5 presents cases with d = 0 only and in the appendix different values of d are considered only for global dispersal. Would the results qualitatively hold when different values of d for local dispersal is considered?

>>>If we understand correctly what the referee is saying here, he/she seems to be mistaken. Figs S2-S7 show results for each model for a whole range of d, for local dispersal. These figures are referenced at the end of the second-to-last paragraph of Results, and in the last paragraph of Results. It can be determined through examination of Figs S2-S13 that yes, results will qualitatively hold for nonzero d for the types of dispersal we considered (local and global). A statement to this effect has been added to the last paragraph of Results.

7.      In general, the text in certain parts can be much tightened for readability and clarity.

>>>In the course of doing other edits we went through the entire text again and tightened where possible. Thank you for spurring us to do so.

Minor comment
•       Line 97-105. It is too abstract to follow in the current form until the reader read the last sentence.

>>>We reworded the paragraph.

•       Line 100, insert “same” in between “the” and “variable” for clarity.

>>>Done.

•       As I mentioned above, Q1 and Q2 appear in an opposite order from what I expected from the introduction so far.

>>>We have fixed this ordering issue throughout the manuscript, see our response to point 4 above.

•       Line 299. Because simulation studies can increase the number of replicates relatively easily and usually use a large number of replicates, statistical significance does not mean much in most of cases, including this one.

>>>Thank you, we take the referee's point, here, and have eliminated the statement about significance.

•       Line 357-9. Rewrite the sentence. The paper did not show “how such (climatic) changes modify the asymmetry of tail association of weather variables measured in different places.” It showed only whether the latter part of the sentence happens.

>>>The sentence the referee mentions was the topic sentence of the paragraph. The first part of that sentence was what the argument of the paragraph is about. So yes, we did do this, it was accomplished not in the Results of the paper (which is what the referee seems to have expected), but instead was accomplished at this point in the manuscript, in this very paragraph. We apologize, however, that this was unclear! So we reworded to make it clearer. We also worked on this whole paragraph, and the following one, to make them clearer. 

•       In the second paragraph in Discussion, X’s are used to refer to generic random variables, but it appeared rather abruptly as the letter was not used to denote variables in the paper up to that point in the main text. It would be helpful to give the definition parenthetically in the text. Do i and j refer to different weather variables, to different ecological variable, or also to different patches?

>>>We apologize for this omission! We have now added the definition. We have also clarified the rest of this paragraph.

•       The paragraph starting from Line 372 is very long and winding. This needs to be tightened substantially (to 2/3 to ½ of the current length, which is 1.5 pages).

>>>We split the paragraph into two and shortened, as the referee requests.

•       Line 419-421. This sentence is very confusing. Using “/” and “(respectively)” makes it almost intractable.

>>>We revised, as requested.

•       Line 424-450. I suggest that the sentence starting with “Although” should come after “…with asymmetric tail associations” in Line 445 for a better flow. As a connection, add a sentence like “This result is partly consistent with the prediction from Tuljapurkar’s approximation” before “The long-term stochastic growth rate… (Line 431)”.

>>>In the course of performing other edits, we revised this paragraph so the comment no longer applies.

•       Line 459-460. Please give a brief definition of “the geography of synchrony,” and clarify what “synchrony was found to have a prominent geography…” means here.

>>>Done, and the clarity is improved. Thanks.