This manuscript quantifies the proportion of linear and non-linear trends across 6 437 vertebrate population time series, and also estimates the temporal variability of such trends; for both aspects it evaluates whether there are systematic patterns of temporal change across habitats, regions, taxa and IUCN extinction risk categories. The main findings were that ~45% of the trends were better described by non-linear trends; linear trends tended to be more variable over time; non-linearity and temporal variability varied between regions, taxa and extinction risk categories, with marine populations having lower prevalence of non-linearity and being more variable over time. The study provides a much-needed evaluation of the variation and variability of population trends using high quality data, and thus has the potential to be an important contribution for conservation and biodiversity assessments. I think the manuscript is of good quality, with adequate rationale and methods, and overall the discussion points are well supported by the results. However, I have a few comments and suggestions which I hope can be addressed to strengthen it.

My main comment is that while the study is well balanced in the discussion of the results, at several points it felt like there was an “implicit support” for non-linear patters and a “focus on declines”. That is (and the Authors also make this clear in their conclusions), while evaluating the prevalence of non-linear patterns is needed and a nuanced interpretation of “average no net change” is fundamental (I couldn’t agree more!), the manuscript refers to “linear models misclassifying declines” e.g. My interpretation of the results is that an overall balance also emerged here, and there was large agreement between linear and non-linear classifications in broad terms (looking at Fig. 3); and please note this is not to negate the importance of revealing/detecting non-linear trends. Broadly, the results show that almost half of the trends are non-linear (meaning that over half are linear). Of the linear trends, ~30% are declines vs increases vs no trend each; of the non-linear ones, almost half were convex/concave with the rest being similarly classified as decreases or increases; and across all populations, ~30% were either declining or increasing, with ~40% being stable. Thus, I would argue that this also supports the notion of a “mixed balance of linear vs non-linear trends, as well as between declining-increasing-stable trends”. All these results are clearly mentioned, and I thought this was a point worth making – which does not contradict the Authors' conclusions and would in my opinion further emphasize the points being made regarding the importance of reporting and interpreting the underlying variability in biodiversity change patterns.

Regarding the interpretation of the results, another general point relates to the different life-history strategies among vertebrates, namely how could different life-history traits affect the temporal patterns or our ability to detect them. The Authors briefly mention this under hypothesis 2) and focus on amphibians vs the other groups. I wondered whether life span and reproductive strategies could also be relevant traits to discuss at least. For instance, higher temporal variability and non-linearity may be less likely to occur or to be detected for long-lived compared to short-lived species, and similarly for low vs high reproductive output (e.g. elephant vs frogs).

The methods seem adequate, but I think a few points need more explanation and/or discussion to make the results as clear and robust as possible. First, for the temporal variability metrics that rely on model fitting, it was not clear to me how they are calculated when the second order polynomial term in not-significant. Also, more details are needed to explain the values and range of these metrics to aid interpretation, and some more technical aspects (like the parameter k to account for zeros in D) need to be better explained too. Second, I wondered if there is some statistical expectation or artifact in linear trends being more variable overall compared to non-linear models. This is not my area of expertise and I am not a statistician, but I thought to mention this in case there is some theoretical background supporting this expectation. Third, it was not clear why the Authors did not use GLM for the non-linear proportion exploration, similarly to the temporal variability analysis. Finally, I wondered about the uneven number of populations falling into the different categories being tested and whether this could affect the power to detect the patterns being tested (e.g. much fewer time series in tropical regions or for Critically Endangered species or for amphibians).

A few smaller points: many sentences/statements seemed to lack supporting references or more adequate ones could be used, and references were also missing for some R packages; across the Results section there was a lack of referring to the corresponding figures and information in the supplement. Also, I wondered if using the term “conservation biogeography” rather than “conservation” was too restrictive(?), or whether using “conservation and biodiversity assessments” could be more suitable.

I hope my comments are useful to the Authors to improve the manuscript.

Specific comments:
1. Consider adding “vertebrates” to the title, and please add it to the Abstract, to clarify what taxa are being analysed (this is never mentioned in the ms).
2. The keywords could be improved, as several are also in the title.
3. Line 13: “add value” is vague.
4. Line 34: Consider if “misclassifying” is the most accurate term (see main comment); perhaps “unable to quantify”?
5. Lines 34-36: Suggest re-wording the result for marine populations (e.g. “Marine populations exhibited higher temporal variability”) and perhaps this is missing another key finding – the lower proportion of non-linear trends. Also, could add “regions” to the different factors.
6. Line 42: “populations”.
7. Line 43: “assessments”.
8. Line 56: This paper by Daskalova et al. used LPI data as well. Perhaps these references could be useful:
using BioTIME:
Daskalova et al. 2020, Landscape-scale forest loss as a catalyst of population and biodiversity change. Science 368, 1341–1347.
Antão et al. 2020, Temperature-related biodiversity change across temperate marine and terrestrial systems. Nature Ecology & Evolution 4, 927–933.

Using other data sources:
Pilotto et al. 2020, Meta-analysis of multidecadal biodiversity trends in Europe. Nature Communications 11, 3486.
Haase et al. 2023, The recovery of European freshwater biodiversity has come to a halt. Nature 620, 582–588.
Crossley et al. 2020, No net insect abundance and diversity declines across US Long Term Ecological Research sites. Nat Ecol Evol 4, 1368–1376.

I would also suggest making a clear distinction between community- and species/population level changes in these sentences. E.g. Dornelas et al. 2019 used BioTIME to analyse population trends, as did Williams et al. 2021 using both BioTIME and LPI data.

Williams et al. 2022, Vertebrate population trends are influenced by interactions between land use, climatic position, habitat loss and climate change. Glob Change Biol, 28, 797–815.

1. Line 58: Suggest adding here several relevant references, namely Blowes et al. 2019, Dornelas et al. 2019, Pilotto et al. 2020, Crossley et al. 2020, Crossley et al. 2021, Inger et al. 2015, and/or others that are relevant.

Crossley et al. 2021, Recent climate change is creating hotspots of butterfly increase and decline across North America. Glob Change Biol, 27: 2702-2714.
Inger et al. 2015, Common European birds are declining rapidly while less abundant species’ numbers are rising. Ecology Letters 18, 28–36.

1. Line 66: Not clear what “assimilated models” means.
2. Lines 64-69: I wondered if there are more studies that have used the LPI data that should be referenced in these two initial sections, as well as studies using e.g. TRIM method to estimate population trends (to avoid such a heavy bias towards BioTIME?).
3. Line 75: Missing reference(s).
4. Lines 87, 89 and throughout: Suggest always using “temporal variability”.
5. Line 90: “it is not captured”.
6. Line 92: “strong variations” in what?

7. Lines 104-108: Missing reference(s), e.g. some studies highlighting IUCN classification caveats? Some suggestions could be:
   Brito et al. 2010, How similar are national red lists and the IUCN Red List? Biol. Conserv. 143, 1154–1158.
   Rondinini et al. 2014, Update or outdate: Long-term viability of the IUCN Red List. Conserv. Lett. 7, 126–130.
   Bachman et al. 2019, Progress, challenges and opportunities for Red Listing. Biol. Conserv. 234, 45–55.
   Rueda-Cediel et al. 2018, Effects of uncertainty and variability on population declines and IUCN Red List classifications. Conserv. Biol. 32, 916–925.
   Fraixedas et al. 2022, Nationally reported metrics can’t adequately guide transformative change in biodiversity policy. Proceedings of the National Academy of Sciences 119, e2117299119.

8. Line 110: Suggest adding “vertebrate population data …”.

9. Line 114: Not clear what “realms” are, and results for this are never presented in the main text.
10. Lines 115-117: Perhaps more adequate references for the spatial clustering of drivers would be e.g.:
    Bowler et al. 2020, Mapping human pressures on biodiversity across the planet uncovers anthropogenic threat complexes. People and Nature 2, 380–394.
    Halpern et al. 2015, Spatial and temporal changes in cumulative human impacts on the world’s ocean. Nature Communications 6, 7615.
    Jaureguiberry et al. 2022, The direct drivers of recent global anthropogenic biodiversity loss. Science Advances 8, eabm9982.

I also wondered if there could be more specific expectations for #1 since there is no analysis of drivers, i.e. which regions or realms would be expected to show higher prevalence of which dynamics. This point would also be relevant for the discussion, as highlighted by the fewer tropical populations included.

1. Line 117: Perhaps adding e.g. Williams et al. 2022 to have a population level study would be useful. Also, suggest splitting into two sentences after the references.
2. Line 125: Missing reference(s).
3. Line 128: Not clear what “a higher diversity in its form” means.
4. Line 152: “classifications” of what?
5. Line 166: “through time”?
6. Lines 197-199: This needs to be better explained and is missing some references too (?). It was not clear to me why the second order polynomial is considered the trend, or how this would be done when that parameter is not significant.
7. Lines 203-228: Missing reference(s) for using CV in population stability studies and any for the use of MSE. As per my main comment, more details are needed to understand how the second order polynomial is used for MSE (e.g. when not significant), as well as for the effect of the parameter k for D. E.g. why not use the actual number of zeros in each time series? And it’s not clear what the “time series mean” in line 224 is. Please also add some indication of the range of values for the less common metrics.
8. Line 225: Should it be “for each time step”?
9. Lines 274-275: These details belong to the methods.
10. Results: Please indicate the figures and tables when describing all the different results, including the ones in the appendix.
11. Line 286-289: How much did this affect the overall prevalence of non-linearity? Would it make sense to also have the analysis selecting only time series >30 or 40 years?
12. Line 311: “increases” rather than “decreases”.
13. Lines 301-314: Suggest deleting “only” and rather indicating a close percentage e.g.; for line 312 it’s more than 2/3 (see main comment).
14. Lines 335-337: “non-anectodic” is vague, suggest rephrasing this sentence, or perhaps it is not needed.
15. Lines 391-393: Suggest explaining this clearly, do you refer to the larger std. errors?
16. Line 398: “consistent”.
17. Line 433: A small note to say that there are also many examples of highly variable and cyclical population patterns that would not necessarily require conservation attention.
18. Lines 440-443: These seem to be contradictory/confusing statements. Missing reference(s) for the increasing population trend with high risk of extinction; do you mean this could happen in colonisation of new areas?
19. Line 451: Missing references.
20. Lines 452-454: Marine populations also showed a higher prevalence stable trends right? Again other references on the higher variability of marine environments and of marine species responses should be added here.
21. Line 461: Why the focus on “dramatic declines”?
22. Line 465: Suggest saying “there is extensive variation”.
23. Lines 467-474: Missing references; see also suggested ones above.
24. Line 486: Delete “as the relative proportion”?
25. Line 501: More recent references are also Blowes et al. 2019 and Pilotto et al. 2020 e.g.
26. Line 502: “We urge to consider” is missing something.
27. Line 510-511: Where is this perception discussed or proposed?
28. Figure 2: It’s not clear why the y axes have different names.
29. Figure 3: Suggest adding the totals to each linear category box.

I appreciate how the Authors have thoroughly addressed my comments and all the suggestions on the previous version of the ms. The results are robust and are better showcased, and the Discussion is really nice and balanced. I believe the study will be a relevant contribution to conservation and to improve efforts to quantify biodiversity change.

I have only rather minor comments for this version, which I hope can still be useful.
1. It felt like the results were quite well summarised in the response letter, but less so in the Abstract, so this could be improved still; e.g. in lines 32-34 adding that mammals showed higher prevalence of non-linearity, and that there were no differences between IUCN categories; this also seems to miss differences between habitat types.
2. Lines 90, 92, and throughout: Suggest always using “temporal variability”.
3. Line 91: Do you mean as a signal or indication of loss of stability?
4. Line 119: It remains confusing to mention “realms” in the main text, which seems to be what is meant by “habitat types”? Realm is only shown in SM, so I suggest to amend this.
5. Line 136: This is missing something.
6. Line 180: Is the estimation of linear trends not part of the main analysis too?
7. Lines 184-185: This is also the case for the linear models, right?
8. Lines 195-200, SM2: It could be worth mentioning somewhere in the ms that the difference between methods to estimate trends was more relevant for rare species, which are overall hard to monitor and evaluate.
9. Line 237: Missing reference for CV in ecology.
10. Line 250: Do you mean “IUCN category” rather than “species s”?
11. Lines 251-261: The description of the models could be improved. E.g. “beta1 * points” is confusing, as it could suggest an interaction term; why not use the same notation for the time series duration (e.g. beta1_duration)? Then, you could simplify the sentences to explain the terms beta1-beta5 together. For the random effect, suggest spelling out “species” rather than having “s” in the formula and in line 258. These suggestions would apply to the other models as well, both for temporal variability and in the SM.
12. Lines 260-261: Do you rather mean something like “duration varies among time series and among the other factors being explored, while it also affects estimates of change on temporal data”? This statement is missing a reference and/or could refer to SM.
13. Line 267: As for above, do you mean IUCN categories here?
14. Line 269: See comment 11.
15. Line 277: “redundancy”.
16. Line 342-343: This is slightly not significant. I suggest you could have the two factors that showed no effect in a "combined" sentence.
17. Line 353: Would probability or prevalence of non-linearity be more adequate?
18. Line 357: Are these "non-linear no trend" trajectories?
19. Lines 376-377: “fishes proved to be significantly more variable than all other vertebrate groups except amphibians (Fig. 5C).” Is this correct? I did not understand what the difference for amphibians was here.
20. Lines 379-380: Need to specify which metrics and figures these results refer to.
21. Lines 381-382: This sentence is confusing.
22. Lines 402-403: Perhaps "with similar proportions" would be clearer (and deleting similarly).
23. Line 424: Missing reference(s).
24. Line 465: Suggest adding “the prevalence in non-linearity”.
25. Line 484: But there were differences among groups for both non-linearity and temporal variability, right?
26. Figure 1: Missing labels for the axes.
27. Figure S1.3: Perhaps panel F could be shown in the main text? This would illustrate the spatial distribution of the data analysed and also show the "mix" of linear and non-linear trends; you could have different symbols for showing Marine/Terrestrial/Freshwater time series.
28. SM3, Line 116: “starting”.
29. SM4, Methods: See comment 11.
30. Figure S4.1: Suggest indicating the metrics names in the figure and avoid repeating the factors per panel.
31. Figure S5.2: Suggest splitting the results of each factor into two different figures.