Dinosaur diversification rates were not in decline prior to the K-Pg boundary

Determining the tempo and mode of non-avian dinosaur extinction is one of the most contentious issues in palaeobiology. Extensive disagreements remain over whether their extinction was catastrophic and geologically instantaneous or the culmination of long-term evolutionary trends. These conflicts have arisen due to numerous hierarchical sampling biases in the fossil record and differences in analytical methodology, with some studies identifying long-term declines in dinosaur richness prior to the Cretaceous–Palaeogene (K-Pg) boundary and others proposing continued diversification. Here, we use Bayesian phylogenetic generalized linear mixed models to assess the fit of 12 dinosaur phylogenies to three speciation models (null, slowdown to asymptote, downturn). We do not find strong support for the downturn model in our analyses, which suggests that dinosaur speciation rates were not in terminal decline prior to the K-Pg boundary and that the clade was still capable of generating new taxa. Nevertheless, we advocate caution in interpreting the results of such models, as they may not accurately reflect the complexities of the underlying data. Indeed, current phylogenetic methods may not provide the best test for hypotheses of dinosaur extinction; the collection of more dinosaur occurrence data will be essential to test these ideas further.

>These mostly aren't FADs and LADs. Most are the oldest-age and youngest-age bounds on uncertainty associated with taxon ages. So, the same as "Maximum and minimum possible ages" (lines 160-161).
Lines 190-191: "As closely related species are likely to have more similar node count values" >By definition they -must-have similar node counts. If you agree, consider rephrasing 'are more likely to have'.
Line 228: "776 (86%) did not favour any model at all" >I understand entirely why this is written. However, the statement doesn't contain much information. I'd really like to see the densities for the Lloyd et al and Benson et al. results but they aren't shown in Figs 2 or 4. There shouldn't be an issue with space-availability to include these because the panels aren't complex and their sizes could be reduced.
Figures 2 and 4. >It would be useful to write out the name of the dinosaur subgroup on each panel. It's a bit tricky to figure it out as currently-presented. You can make it very easy for readers to see at-a-glance what groups are analysed.
Lines 296-298: "Their conclusions might also have been skewed by reliance on estimated intercepts [11] rather than zero-intercepts, as the latter would, perhaps, be more biologically plausible (as there should be no new nodes at t0)" >I agree that setting the intercept to zero has a big effect on the result -that's clear from the analyses. There are a few things to say on this. Firstly: I'm not sure how many nodes there should be at t = 0, because the count of nodes at t = 0 does not have a straightforward interpretation. In reality, at t > 0, even at infinitesimally small values, at least 1.0 nodes must have occurred because t = 0 is the time of the most basal node in the tree. The fact that infinitessimally small values are essentially equal to zero is important and suggest that when time = 0, the node count should be 1.0. However, zero tips have occurred at time = 0, so in reality we haven't had any data-items that would record time = 0 and nodes = 1. By definition, zero tips occur until time = 1 (because of the algorithm use to scale the trees to time). By time = 1 all we know is that node counts are greater than or equal to 1.0. >These are my recommendations: >(1) Set the intercept to 1.0 instead of or as well as 0. Or constrain the value of the intercept to be between 0 and 1.0 but don't specify it precisely. >(2) Use DIC to evaluate which model is best (i) a model in which the intercept is entirely unconstrained, (ii) a model in which the intercept is between 0 and 1.0, (iii) any other intercept setting that you like.
Lines 297-298: "would, perhaps, be more biologically plausible" >"perhaps" -it's very British to write this way. But it's also quite vague. This isn't a matter of 'biological plausibility'. In fact, it is axiomatic in the analysis. So I think you should include much stronger statements about this.
>The methodological decisions would also be clearer to me if the estimated intercept values were reported in a graph or similar. If the argument is about 'biological plausibility', so this is quite important. Some values of the intercept are presumably more plausible than others (e.g. a value of 1.0 is quite plausible, see above).
Lines 311: "support the idea that dinosaurs were in terminal decline: >Change to "support the hypothesis that dinosaurs were in terminal decline" Lines 334-337: "Our results, and those of many others (e.g. [3,9,10,23,50]), emphasize the fact that the dinosaur fossil record suffers from numerous gaps and biases, and that any apparent decline in diversity could be due to systemic sampling errors" >This may be the view of the authors (and is also my view -I agree with you). However, it is not supported by any of the analyses presented here, which don't contain any test of the effect of sampling rate variation. See also my note on the Introduction (above) -lines 85-137 do not cite sampling rate variation as a potential issue with this type of analysis. However, that does seem to be the view of the current authors.
Lines 351-356: "For example, a recent study found no correlation between rates of dinosaur morphological evolution and extinction, which suggests that analyses based on existing phylogenetic datasets might not be useful for addressing the question of non-avian dinosaur extinction [54]" >It isn't clear why that result would lead to the conclusion stated here unless we assumed a priori that diversification rates must be correlated with phenotypic rates. Even if we did assume that, then the result might imply that the phenotypic rates are inaccurate (likely, given what they are based on).

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? Yes

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
The manuscript of Bensor and colleagues seek to address on the main questions regarding the extinction of non-avian dinosaurs, were evolutionary rates decelerating or very low before their extinction? They main goal is to test the results of a recently published paper that found a downturn of evolutionary rates for most dinosaur clades close to the end of the Cretaceous Period (Sakamoto et al., 2016). I consider that the manuscript is very well written, the figures are very informative, and the conclusions built on well supported results. I haven't found major issues in the manuscript and I have only some moderate comments, but they may imply further analyses or to re-run some analyses (see below). I also made some minor comments and suggestions in an edited version of the manuscript (Appendix A). As a result, I think that the manuscript requires a minor to moderate revision before acceptance.
Comments: -I understand that you haven't used the stochastic dating method 'cal3'. Can you briefly explain why you haven't used it and you prefer a partially stochastic dating but setting a fixed minimum branch length? -You have used a minimum branch length of 1 million years, which it is OK for most datasets. However, if you have large trees, it may result in artificially very old root ages. Can you report the mean and standard deviation of the root ages of each of the eighteen trees (9 new trees and 9 trees from Sakamoto et al. 2016, isn't?). After doing that, please, evaluate if the root ages are compatible with the inferred origin of the clades (e.g. that the origin of Theropoda is not occurring in the Permian). If the latter is the case for any of the trees/clades, I suggest using a shorter minimum branch length or fixing the root of the tree using the inferred minimum divergence time between clades.
-Different minimum branch lengths may have strong impacts in the results. Thus, I would like to see how sensitive are the results to calibrations using at least two other minimum branch lengths, e.g. 0.1 myr and 5 myr. -In the supplementary information you state that you have used a 50% majority rule consensus tree for some analyses (e.g. Arbour et al. 2016). There is no reason to exclude some topologies only because they occur in less than 50% of the most parsimonious trees if you are running a cladistic analysis. So, use a strict consensus tree or a strict reduced consensus tree (with wildcard taxa pruned a posteriori) instead.
-Some of these taxon-character matrices are relatively large (>70 taxa). In some of them you have used the New Technology algorithms of TNT during the tree searches. However, 100 replicates of these algorithms may not generate a good sample of optimal results (e.g. Cau analysis). A more appropriate protocol is to use this combination of algorithms but until an a priori determined number of optimal results is reached. You can do this with the TNT command 'xmult = hits 100;'. I understand that you have followed the search protocols of the original papers, but you should be sure that the tree searches are properly done. It is the same for the consensus trees (see above). I suggest doing searches using the New Technology algorithms if you have more than 70 taxa. -I can't see a good reason to exclude taxa before the time calibrations. Can you explain why you are doing that in a few analyses?
Decision letter (RSOS-201195.R0) We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Mr Bonsor
On behalf of the Editors, we are pleased to inform you that your Manuscript RSOS-201195 "Dinosaur evolutionary rates were not in decline prior to the K-Pg boundary" has been accepted for publication in Royal Society Open Science subject to minor revision in accordance with the referees' reports. Please find the referees' comments along with any feedback from the Editors below my signature.
We invite you to respond to the comments and revise your manuscript. Below the referees' and Editors' comments (where applicable) we provide additional requirements. Final acceptance of your manuscript is dependent on these requirements being met. We provide guidance below to help you prepare your revision.
Note that Reviewer 1 makes a slightly confusing reference to Biology Letters --please assume that the Reviewer in fact means RSOS.
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I wholeheartedly endorse publication in Biology Letters. it is certainly of appropriate significance and I would be disappointed if it was not published.
My key suggestions are as follows: (1) The intercept o the models could be constrained to fall between 0 and 1.0, or set to 1.0 instead of 0. I believe that 1.0 nodes (i.. the root node) should be present at even infintessimally small values of time. Also, DIC could be used to evaluate models with constrained intercepts compared to those with estimated intercepts.
(2) Various minor suggestions about wording. Plus mentioning issues of sampling rate variation and potential solutions (even if not implemented here) in the introduction. They form an important theme of the disucssion after all.
(3) Some relevant literature is not cited -you know, it's literature from my group so you can do eye-rolling if needed. I tried to restrict the amount that I suggested this however.

SPECIFIC COMMENTS
Title: "Evolutionary rates" can mean several different things. It may be more informative instead to write 'diversification rates'.
Lines 53-56: "Determining trends in Mesozoic dinosaur species-richness is a contentious issue and has been the focus of numerous previous studies (e.g. [3,8-10]). Many different hypotheses have been proposed, but there are currently two major schools of thought".
>Change "Determining trends in Mesozoic dinosaur species-richness" to "Determining trends in Mesozoic dinosaur species-richness *leading up the the K-Pg*". That would reflect the focus of this paragraph more accurately and avoid the misleading implication that studies of dinosaur species richness are restricted to opinions about the K-Pg. >Also, I think it would be more instructive to suggest three different viewpoints here, because Sakamoto's study on its own does not reflect a 'major school of thought', whereas an actual 'major school of thought' is missing here. My view of the literature is that two things have been widely suggested: (1) No decline in advance of the boundary.
(2) A decline on the timescale of 100,000s or millions of years related to non-bolide factors such as Deccan flood volcanism (older literature reviewed by Alvarez 1983 PNAS, and also see Dean et al 2020, cited in text, for more recent literature). (3) Sakamoto presented a third view that there was a decline on the timescale of 10s of millions of years without noting that no-one really had suggested this previously.
Lines 75-78: "Reconstruction of past diversity patterns is difficult, as the 'raw' patterns of taxonomic diversity gleaned from the fossil record are subject to many hierarchical biases, ranging from initial fossilization potential, through the availability of fossiliferous rock outcrop, to anthropic collection biases (e.g. >I also think it might be appropriate to cite Benson (2018, Dinosaur macroevolution and macroecology) which contains discussions and plots related to dinosaur diversity dynamics, spatial sampling variation, regional heterogeneity, Sakamoto et al and other topics that are discussed in the current paper. Some of the statements in Section 5 of Benson (2018), on several different topics, are quite similar to those of the current paper.
Lines 78-81: "Different methods have been applied in attempts to correct for these factors, including various subsampling techniques (rarefaction, Shareholder Quorum Subsampling and TRiPs) and comparisons of diversity with collections-related proxies" >Spatial bias is emphasised in earlier text, but none of the methods written into the text here can correct for spatial bias. New approaches to address spatial bias were presented by Close et al (2020), which also report patterns of dinosaur diversity.
>Refs 27-29 are papers evaluating method performance rather than papers about patterns of dinosaur diversity. So they seem to be cited in the wrong place. Arguably, they don't need to be cited at all unless the text includes statements about method performance.
Lines 85-137: These paragraphs list potential problems with the analyses/interpretation of Sakamoto et al. There is another problem that is not mentioned in the text but is potentially very important. Fossil phylogenies are different to phylogenies of living species because times represent sampling events. Sampling events also influence the node counts, because each sampling event adds one tip during the sampled interval and one node during some older interval. Sakamoto et al didn't really do anything that would be appropriate to address this but a lot of progress was made on appropriate models by other groups -primarily Tanja Stadler's group and the fossilise-birth-death (FBD) model. Although it might not be tractable to apply that to this problem right now, I think it would be right to mention this shortcoming and that solutions might be possible in future using models such as the FBD model, even though that is not applied here.
Lines 143-145: "two subtly different versions of the Benson et al.
[30] supertree, which reflect plausible differences in the relationships of several taxa" >The trees reflect difference in hypotheses of sauropod inter-relationships. This could be stated instead of "relationships of several taxa".
Line 146: "first occurrence date (FAD) or last occurrence date (LAD)" >These mostly aren't FADs and LADs. Most are the oldest-age and youngest-age bounds on uncertainty associated with taxon ages. So, the same as "Maximum and minimum possible ages" (lines 160-161).
Lines 190-191: "As closely related species are likely to have more similar node count values" >By definition they -must-have similar node counts. If you agree, consider rephrasing 'are more likely to have'.
Line 228: "776 (86%) did not favour any model at all" >I understand entirely why this is written. However, the statement doesn't contain much information. I'd really like to see the densities for the Lloyd et al and Benson et al. results but they aren't shown in Figs 2 or 4. There shouldn't be an issue with space-availability to include these because the panels aren't complex and their sizes could be reduced. Lines 296-298: "Their conclusions might also have been skewed by reliance on estimated intercepts [11] rather than zero-intercepts, as the latter would, perhaps, be more biologically plausible (as there should be no new nodes at t0)" >I agree that setting the intercept to zero has a big effect on the result -that's clear from the analyses. There are a few things to say on this. Firstly: I'm not sure how many nodes there should be at t = 0, because the count of nodes at t = 0 does not have a straightforward interpretation. In reality, at t > 0, even at infinitesimally small values, at least 1.0 nodes must have occurred because t = 0 is the time of the most basal node in the tree. The fact that infinitessimally small values are essentially equal to zero is important and suggest that when time = 0, the node count should be 1.0. However, zero tips have occurred at time = 0, so in reality we haven't had any data-items that would record time = 0 and nodes = 1. By definition, zero tips occur until time = 1 (because of the algorithm use to scale the trees to time). By time = 1 all we know is that node counts are greater than or equal to 1.0.
>These are my recommendations: >(1) Set the intercept to 1.0 instead of or as well as 0. Or constrain the value of the intercept to be between 0 and 1.0 but don't specify it precisely. >(2) Use DIC to evaluate which model is best (i) a model in which the intercept is entirely unconstrained, (ii) a model in which the intercept is between 0 and 1.0, (iii) any other intercept setting that you like.
Lines 297-298: "would, perhaps, be more biologically plausible" >"perhaps" -it's very British to write this way. But it's also quite vague. This isn't a matter of 'biological plausibility'. In fact, it is axiomatic in the analysis. So I think you should include much stronger statements about this.
>The methodological decisions would also be clearer to me if the estimated intercept values were reported in a graph or similar. If the argument is about 'biological plausibility', so this is quite important. Some values of the intercept are presumably more plausible than others (e.g. a value of 1.0 is quite plausible, see above).
Lines 311: "support the idea that dinosaurs were in terminal decline: >Change to "support the hypothesis that dinosaurs were in terminal decline" Lines 334-337: "Our results, and those of many others (e.g. [3,9,10,23,50]), emphasize the fact that the dinosaur fossil record suffers from numerous gaps and biases, and that any apparent decline in diversity could be due to systemic sampling errors" >This may be the view of the authors (and is also my view -I agree with you). However, it is not supported by any of the analyses presented here, which don't contain any test of the effect of sampling rate variation. See also my note on the Introduction (above) -lines 85-137 do not cite sampling rate variation as a potential issue with this type of analysis. However, that does seem to be the view of the current authors.
Lines 351-356: "For example, a recent study found no correlation between rates of dinosaur morphological evolution and extinction, which suggests that analyses based on existing phylogenetic datasets might not be useful for addressing the question of non-avian dinosaur extinction [54]" >It isn't clear why that result would lead to the conclusion stated here unless we assumed a priori that diversification rates must be correlated with phenotypic rates. Even if we did assume that, then the result might imply that the phenotypic rates are inaccurate (likely, given what they are based on).
The manuscript of Bensor and colleagues seek to address on the main questions regarding the extinction of non-avian dinosaurs, were evolutionary rates decelerating or very low before their extinction? They main goal is to test the results of a recently published paper that found a downturn of evolutionary rates for most dinosaur clades close to the end of the Cretaceous Period (Sakamoto et al., 2016). I consider that the manuscript is very well written, the figures are very informative, and the conclusions built on well supported results. I haven't found major issues in the manuscript and I have only some moderate comments, but they may imply further analyses or to re-run some analyses (see below). I also made some minor comments and suggestions in an edited version of the manuscript. As a result, I think that the manuscript requires a minor to moderate revision before acceptance.
Comments: -I understand that you haven't used the stochastic dating method 'cal3'. Can you briefly explain why you haven't used it and you prefer a partially stochastic dating but setting a fixed minimum branch length? -You have used a minimum branch length of 1 million years, which it is OK for most datasets. However, if you have large trees, it may result in artificially very old root ages. Can you report the mean and standard deviation of the root ages of each of the eighteen trees (9 new trees and 9 trees from Sakamoto et al. 2016, isn't?). After doing that, please, evaluate if the root ages are compatible with the inferred origin of the clades (e.g. that the origin of Theropoda is not occurring in the Permian). If the latter is the case for any of the trees/clades, I suggest using a shorter minimum branch length or fixing the root of the tree using the inferred minimum divergence time between clades.
-Different minimum branch lengths may have strong impacts in the results. Thus, I would like to see how sensitive are the results to calibrations using at least two other minimum branch lengths, e.g. 0.1 myr and 5 myr. -In the supplementary information you state that you have used a 50% majority rule consensus tree for some analyses (e.g. Arbour et al. 2016). There is no reason to exclude some topologies only because they occur in less than 50% of the most parsimonious trees if you are running a cladistic analysis. So, use a strict consensus tree or a strict reduced consensus tree (with wildcard taxa pruned a posteriori) instead.
-Some of these taxon-character matrices are relatively large (>70 taxa). In some of them you have used the New Technology algorithms of TNT during the tree searches. However, 100 replicates of these algorithms may not generate a good sample of optimal results (e.g. Cau analysis). A more appropriate protocol is to use this combination of algorithms but until an a priori determined number of optimal results is reached. You can do this with the TNT command 'xmult = hits 100;'. I understand that you have followed the search protocols of the original papers, but you should be sure that the tree searches are properly done. It is the same for the consensus trees (see above). I suggest doing searches using the New Technology algorithms if you have more than 70 taxa. -I can't see a good reason to exclude taxa before the time calibrations. Can you explain why you are doing that in a few analyses? ===PREPARING YOUR MANUSCRIPT=== Your revised paper should include the changes requested by the referees and Editors of your manuscript. You should provide two versions of this manuscript and both versions must be provided in an editable format:<ul><li>one version identifying all the changes that have been made (for instance, in coloured highlight, in bold text, or tracked changes);</li><li>a 'clean' version of the new manuscript that incorporates the changes made, but does not highlight them. This version will be used for typesetting.</li></ul> Please ensure that any equations included in the paper are editable text and not embedded images.
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Recommendation? Accept as is
Comments to the Author(s) I thank the authors to address each of the comments that I raised in the first version of the manuscript. Although I still think that it is very important to run a proper search of optimal trees, I understand the goal of the authors to obtain the same topologies as the original authors of the phylogenetic anlayses (a good search goes beyond the expertise of the person in a specific taxonomic group). It will be very time consuming to re-run analyses using different search or consensus settings, so I think that the responso of the authors to this criticsm is justified under current circunstances.
Regarding the original comment of line 193, I wanted to know if you used half (above or below the diagonal) of the phylogenetic variance-covariance matrix. I think that it is important to allow replicating the analyses in the future.
I congratulate the authors for their work and I think that the manuscript can be accepted in its current form.

Decision letter (RSOS-201195.R1)
We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Mr Bonsor,
It is a pleasure to accept your manuscript entitled "Dinosaur diversification rates were not in decline prior to the K-Pg boundary" in its current form for publication in Royal Society Open Science. The comments of the reviewer(s) who reviewed your manuscript are included at the foot of this letter.
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Please see the Royal Society Publishing guidance on how you may share your accepted author manuscript at https://royalsociety.org/journals/ethics-policies/media-embargo/. Both reviewers agree to accept this new complete version of the manuscript. Only one comment to be attended by the authors from R2: Regarding the original comment of line 193, I wanted to know if you used half (above or below the diagonal) of the phylogenetic variance-covariance matrix. I think that it is important to allow replicating the analyses in the future.
Reviewer comments to Author: Reviewer: 2 Comments to the Author(s) I thank the authors to address each of the comments that I raised in the first version of the manuscript. Although I still think that it is very important to run a proper search of optimal trees, I understand the goal of the authors to obtain the same topologies as the original authors of the phylogenetic anlayses (a good search goes beyond the expertise of the person in a specific taxonomic group). It will be very time consuming to re-run analyses using different search or consensus settings, so I think that the responso of the authors to this criticsm is justified under current circunstances.
Regarding the original comment of line 193, I wanted to know if you used half (above or below the diagonal) of the phylogenetic variance-covariance matrix. I think that it is important to allow replicating the analyses in the future.

Response to reviewers
We thank the reviewers and editor for their helpful comments. We have pasted these below, with our responses following each in red text.
We fully appreciate the comments below and understand the logic and desire to provide some sensitivity analyses related to how the trees were time calibrated and presented (Reviewer 2). Unfortunately, what appear to be simple changes are not simple in both the context of the paper and our current situation in terms of home-working during the current pandemic. The full set of MCMCglmm models takes almost one month to run if we include the models with intercepts set to 1 (see Reviewer 1). Therefore, each sensitivity analysis suggested below adds (at least) a month of computational time to our revision (and we currently lack access to a cluster due to home connectivity issues, so the analyses are all being run on a laptop that is also being used to work on other things simultaneously). We have therefore done our best to run as many analyses as possible within the revision time frame (originally one week, extended to 2 weeks), and hope these are sufficient to allay the concerns of the reviewers without committing to several months of running non-stop analyses.
Reviewer: 1 I support the publication of this work with minor revision. It presents quite an important set of analyses that probe the findings of Sakamoto et al (2016, PNAS) and add considerably to our ability to interpret those results. This is important because it relates to a long-standing debate about dinosaur decline in advance of the K-Pg extinction event. It also has importance in the development of phylogeny-based approaches to the study of diversification in the fossil recordthis area has longer-term promise to unravel some key questions about macroevolutionary diversification in general. The paper has potential to be a classic in this area as it provides one of the most critical and reflective applications of these methods so far.
I wholeheartedly endorse publication in Biology Letters. it is certainly of appropriate significance and I would be disappointed if it was not published.
We thank the reviewer for these supportive comments.
My key suggestions are as follows: (1) The intercept of the models could be constrained to fall between 0 and 1.0, or set to 1.0 instead of 0. I believe that 1.0 nodes (i.. the root node) should be present at even infinitesimally small values of time. Also, DIC could be used to evaluate models with constrained intercepts compared to those with estimated intercepts.
Constraining the intercepts within the GLMM framework isn't easy to implement, so we have instead repeated the analyses setting the intercepts to 1.0. We expand on this in the comments to specific points below.
(2) Various minor suggestions about wording. Plus mentioning issues of sampling rate variation and potential solutions (even if not implemented here) in the introduction. They form an important theme of the discussion after all.
Agreed. See comments to specific points below. sampling rate variation as a potential issue with this type of analysis. However, that does seem to be the view of the current authors.
References removed and the statement left as our own opinion based on our results. Lines 351-356: "For example, a recent study found no correlation between rates of dinosaur morphological evolution and extinction, which suggests that analyses based on existing phylogenetic datasets might not be useful for addressing the question of non-avian dinosaur extinction [54]" It isn't clear why that result would lead to the conclusion stated here unless we assumed a priori that diversification rates must be correlated with phenotypic rates. Even if we did assume that, then the result might imply that the phenotypic rates are inaccurate (likely, given what they are based on).
Added the text "however, this result may also indicate inaccuracies in the calculation of phenotypic diversification rates" to the section detailed above.

Reviewer: 2
The manuscript of Bensor and colleagues seek to address on the main questions regarding the extinction of non-avian dinosaurs, were evolutionary rates decelerating or very low before their extinction? They main goal is to test the results of a recently published paper that found a downturn of evolutionary rates for most dinosaur clades close to the end of the Cretaceous Period (Sakamoto et al., 2016). I consider that the manuscript is very well written, the figures are very informative, and the conclusions built on well supported results. I haven't found major issues in the manuscript and I have only some moderate comments, but they may imply further analyses or to re-run some analyses (see below). I also made some minor comments and suggestions in an edited version of the manuscript. As a result, I think that the manuscript requires a minor to moderate revision before acceptance.
We thank the reviewer for their positive comments on the MS. I understand that you haven't used the stochastic dating method 'cal3'. Can you briefly explain why you haven't used it and you prefer a partially stochastic dating but setting a fixed minimum branch length?
If we had been starting from scratch, we would have used cal3. However, we were starting with the trees from Sakamoto et al. that were dated using the partially stochastic method outlined in the manuscript. To be consistent with this, as our intention was to replicate and test their conclusions, we chose to use the same method to date our additional trees. We have added a note to the supplemental methods to clarify this, and added the text: "We chose this protocol for consistency with the dated trees in Sakamoto et al [2016]." You have used a minimum branch length of 1 million years, which it is OK for most datasets. However, if you have large trees, it may result in artificially very old root ages. Can you report the mean and standard deviation of the root ages of each of the eighteen trees (9 new trees and 9 trees from Sakamoto et al. 2016, isn't?). After doing that, please, evaluate if the root ages are compatible with the inferred origin of the clades (e.g. that the origin of Theropoda is not occurring in the Permian). If the latter is the case for any of the trees/clades, I suggest using a shorter minimum branch length or fixing the root of the tree using the inferred minimum divergence time between clades.
Note that we did not date the trees used in Sakamoto et al. We use the dated trees from that paper as the aim of the study was to replicate their analyses. We did however have to date the other nine trees, resulting in 900 time calibrated trees (100 for each).
As suggested, we extracted the root age for each of the 900 trees dated in this study. We present the results as Figure S6 and reproduce it below. The dotted black line shows the oldest inferred origin date for the clade, i.e. 201.3 Ma (Early Jurassic) for Ornithischia and Sauropodomorpha, and 231.4 Ma (Carnian) for Theropoda. The red and blue dashed lines show the oldest and youngest ages respectively of taxa in the trees (dates taken from the Paleobiology Database). Note that the majority of the trees have younger (rather than older as feared) root ages, with the exception of the Raven & Maidment (2017) ornithischian tree, and Carballido et al. (2017) sauropod tree. In these cases, the trees contained outgroup taxa that are older than the group, and the dates instead fall within the oldest and youngest ages of the taxa in the trees. This suggests that our dating method is not biasing trees to be too old and thus the minimum branch length of 1 million years is appropriate for the analyses we present here.
We have added a version of this text, along with the figure below, to the supplementary materials. We also refer readers to this material in the text where we describe our time scaling protocols. Different minimum branch lengths may have strong impacts in the results. Thus, I would like to see how sensitive are the results to calibrations using at least two other minimum branch lengths, e.g. 0.1 myr and 5 myr.
Given our findings in response to the comment above, we feel this is not necessary and should not impact the results. We would prefer to avoid running these analyses if possible due to computational limitations associated with working from home, and also feel these will not alter our overall conclusions.
In the supplementary information you state that you have used a 50% majority rule consensus tree for some analyses (e.g. Arbour et al. 2016). There is no reason to exclude some topologies only because they occur in less than 50% of the most parsimonious trees if you are running a cladistic analysis. So, use a strict consensus tree or a strict reduced consensus tree (with wildcard taxa pruned a posteriori) instead.
We made these methodological choices based on the papers the trees were taken from. We wanted to use the trees that the authors of these studies presented as the most strongly supported, following the expert opinions of these authors on their study taxa. We have added a note in the supplemental materials to clarify, and added the following sentence to the main text: "We used the same methods used in these papers to infer the trees, as our aim was to recreate these published trees, not to provide new phylogenetic inferences." Some of these taxon-character matrices are relatively large (>70 taxa). In some of them you have used the New Technology algorithms of TNT during the tree searches. However, 100 replicates of these algorithms may not generate a good sample of optimal results (e.g. Cau analysis). A more appropriate protocol is to use this combination of algorithms but until an a priori determined number of optimal results is reached. You can do this with the TNT command 'xmult = hits 100;'. I understand that you have followed the search protocols of the original papers, but you should be sure that the tree searches are properly done. It is the same for the consensus trees (see above). I suggest doing searches using the New Technology algorithms if you have more than 70 taxa.
We made these methodological choices based on the papers the trees came from. We weren't interested in inferring the best tree for each dataset per se, instead we wanted to recreate the trees presented in the published papers that the authors felt best represented the clades that they are experts on. Perhaps some of these analyses could have been improved if our primary interest was in inferring the trees. But this was not our primary aim. We have added a note in the supplemental materials to clarify, and added the following sentence to the main text: "We used the same methods used in these papers to infer the trees, as our aim was to recreate these published trees, not to provide new phylogenetic inferences." I can't see a good reason to exclude taxa before the time calibrations. Can you explain why you are doing that in a few analyses?
As we were not attempting to provide novel phylogenetic treatments for any of the clades concerned, we followed the methodologies used by the original authors of the published matrices. We matched any a priori or a posteriori pruning of taxa and used the same tree searching methodologies and settings from the papers the trees were originally published in. Our aim was to recreate the trees published by the taxon-experts for each group. We have added a note in the supplemental materials to clarify, and added the following sentence to the main text: "We used the same methods used in these papers to infer the trees, as our aim was to recreate these published trees, not to provide new phylogenetic inferences." Comments from PDF from Reviewer 2: Line 45: "Late" removed and replaced with "late" Line 156 -"Check": Search settings checked and verified Line 172 -"Please, can you explain here that you have 900 new trees and nine from Sakamoto et al.?": This is explained in the last sentence of the paragraph above Line 193 -"one of the triangules below/above the diagonal or the entire matrix?": We weren't sure of the exact meaning of this comment, but we have checked each figure carefully for readability and clarity and corrected where appropriate whilst addressing previous comments from both reviewers.
Line 253 (Figure 2) -"It is not very clear. Can you add a label on the graphic or a silhouette representing the clade?": We have now added clade silhouettes to Figures 2 and 4 (now Figures 2 and S1) to match those in Figures 3 and 5 (now Figures 3 and S2). And also to new Figure S3.