The authors have greatly improved this manuscript. The authors approach the results of this analysis with much more caution and acknowledgement of limitations. As such, the data and interpretations appear appropriate.

Thank you to the uthors for taking my comments and questions into consideration and clarifying issues found in the first draft of this manuscript.

The conceptual basis of this manuscript is indeed very interesting, especially in light of several studies that concluded ossification sequences don't appear to contain phylogenetic signal. It remained possible that ossification sequences could in fact contain such signal, but the taxonomic level of this signal has yet to be fully explored. I'd first like to congratulate the authors on compiling such an exhaustive list of extant ossification sequence data sources. This appendix alone will be a useful tool for many future research projects.

I have several questions and found areas of ambiguity that in their current state render this manuscript unready for publication.

My main concerns are:

. 1)  Clarity of methods


. 2)  Assumptions of the models and tests being deployed (ie., continuous characters, using
branch lengths in a composite reference tree)


. 3)  The strength of conclusions based on largely inference alone


For the first, my recommendation would be to more clearly describe the data and methods. I appreciate the text is concise, but some questions remain and the readership and utilization of the approach would be increased if methods could be explained a little more in depth for non-experts to be able to deploy them in their own work, and to fully understand the present work. Based on the short explanations of the methodologies, I would find myself unable to be able to repeat the work -- the key attribute of reproducible science. However, if these issues can be explained and justified in the text this would make an interesting and useful contribution.

Line 111, I am uncertain what 216 characters this original matrix is derived from. All sequence data? Or are these characters from a previous phylogenetic analysis that includes non-sequence data characters? After the missing data criterion was established, 7 characters remained and these are listed as bone names in the text. What are the actual characters? Their position within the sequence relative to one another? Please clarify what exactly these characters are and amend the text to explain this in the applied order.

Line 136, the absence of lepospondyls (and that only 3 fossil taxa in general are included?) is alarming. The obvious question is, how can a relationship between lissamphibians and lepospondyls be supported by ossification sequence data if no ossification sequence data is available for lepospondyls? More on this below.

Also, why not try using Phlegethontia in a stem tetrapod position? It seems it's position down there is pretty well accepted. Might serve in lieu of a 'fish' basal taxon?

Line 153, Just to be clear, these are the position of ossification events in the series of 7 bones, correct? Could an example using the current data be provided?

Line 157, I feel the philosophy of the reasoning as to why skull length was not used to standardize the data is not sound. Just because results are less clear doesn't mean the method isn't working. What seems most likely is that the vast size differences of the organisms at comparable developmental stages would cause problems. Perhaps exploring this justification would make readers feel less like this was being discarded as an option simply because it didn't give a clear answer.

Line 160, These are the seven characters, correct? Perhaps restate that these are the seven characters that can be found in SM2 (with the definitions there also?). It sounds a bit like these are other data from the seven characters mentioned previously, and I am not sure which interpretation is correct.

Line 172, I wonder if these are truly continuous data. The methodology renders the data continuous-like values, but I feel they aren't actually continuous in the real world (they are discrete events). Does this factor violate the assumptions of the models being fitted to the data? Perhaps a little explanation can clarify this so I don't wonder if the tests are all invalidated by this interpretation.

Also in this section, I wonder about the treatment of branch lengths. Since the reference tree is a composite, the original branch lengths are no longer relevant in the composite tree. An analysis would need to be rerun with all the taxa to get those original branch lengths. So I believe any test involving original branch lengths from separate analysis whose trees were stitched together are invalid. Those characters were not given a chance to participate in the branch lengths of parts of the trees not included in the original analysis (e.g, mammal characters do not get to contribute to branch lengths in the amphibian part of the tree). Please explain if this issue is being taken into account somehow.

Line 254, I like this logic, however, it is not caveat free. That is also ok, but a detailed inspection of what is actually being tested, rather than what is the stated goal leaves me very cautiously accepting the conclusions. I will explore this now, and where my interpretations are incorrect, let this guide the author to clarifying the text to justify the conclusions.

It seems that the actual variable being used to determine the correct topology for lissamphibians is the position of Apateon (and Sclerocephalus in some analyses). This means what is actually being tested is how similar Apateon's ossification sequence is to either salamanders, batrachians, or all lissamphibians with nothing known of variation among fossil taxa (surely there is enough variation among mammals such that sampling only 1 animal could yield drastically different results). In order to test what is described as being tested, a true phylogenetic signal in ossification sequence data needs to be demonstrated and Apateon needs to be demonstrated as representative of a temnospondyl, or at the very least an amphibamid, condition. Basically, when Apateon is better fit on the crown tetrapod stem, I can't help but think this may be due to species specific patterns of ossification or

even neoteny dependent patterns of ossification. Based on the exceedingly limited data from fossils at hand, there is no accommodation of variation. I understand the approach, however, much more caution in the results needs to be expressed in light of the data at hand.

Furthermore, the conclusions of a lepospondyl-lissamphibian link are ultimately entirely based on inference. Simply that if lissamphibians are placed between Apateon and amniotes and the models are best fit to that topology is interpreted as meaning that they share a similar ossification sequence to lepospondyls. However, this is entirely not observable. This, in essence, is not testing the LH, since there are no direct data supporting allying them with that clade at all. The results simply show that lissamphibians do not have a sequence more similar to Apateon than they do to amniotes. That this is consistent with a LH is an inference alone, and the text should reflect that the results are consistent, nothing more.

I'd lastly just like to verify that the argumentation being presented is not circular. It seems that early on we aren't sure if ossification sequence data carries phylogenetic signal. An analysis was performed that searches for a best fit of the sequence data based on phylogenetic congruence. This inherently means an assumption of is applied to the analyses. Finally, it was concluded that this best fit means ossification sequences are phylogenetically informative. However, the best fit model is the one that was attempting to maximize the phylogenetic signal. Just clarify if this isn't the case.

I find for the main goal and all analyses presented, that some discussion should be made about the actual sequence data analyzed and what about it might be phylogenetically significant. From my experience with development, I find ossification sequences can be strongly influenced by function (e.g., the timing of usage of an element). As such, I don't expect there to be much phylogenetic signal, and as a result I am not surprised that Apateon is different from lissamphibians. I do not take that result to mean there is not a close relationship between Apateon and lissamphibians. Much of the discussion is spent on topics not related to the study at hand, and while interesting and useful in a broader context, take away from the main findings of the study.

This paper addresses a fundamental problem of vertebrate phylogeny, one that concerns the relation of a major extant group with extinct ones that were quite diverse and important in the Paleozoic. The authors examine ontogenetic data in the form of ossification sequences of the skull, and integrate information in a large-scope analysis that is sound in the critical examination of the data and of the limits and power of the method. The alternative hypotheses are clearly laid out and the previous attempts to use the kind of data investigated are properly revised. The study benefits from published data on exceptional fossils and makes the best out of those data - yet sampling is limited to relative few species – that is the nature of the data. The authors took steps to account for biases that could be introduced by stratigraphic (time) provenance of fossils (e.g., lines 261-263). At the end it is tree lengths and few fossils what provide the tests, but given the importance of the subject and the critical and thorough approach used, I find much merit in this paper and its conclusions to advance discussion of temnospondyls / lepospondyls / lissamphibia relationships. I suggest the authors revise a couple of potentially relevant references that contain much data (see below) and clarify some points below. One issue that is left largely ignored is that of intraspecific variation, which can be significant in extant amphibians. The data used is in many cases a studied optimization or rather consensus of that variation, but this needs to be mentioned at least, and its potential effect on the study discussed. The paper concerns skull data, but valuable insights on published, postcranial data on ossification sequences are presented. Abstract, line 17, ‚perhaps because the diversity of methods used hampers comparisons‘. I would rephrase this, as this paper conducts specific analyses and points into a direction that does not make this clause here fitting – I would write ‘integration of data’ as opposed to ‘comparison’. As formulated, there is a contradiction in the Introduction in terms of the use of molecular data – please rephrase. Line 105 – for mammals, the most comprehensive dataset of cranial ossification is that of Koyabu et al. 2014 Nature Communications (not Weisbecker 2011) Weisbecker and Mitgutsch 2010 presented a comprehensive summary and analysis of anuran cranial ossification patterns. Besides citing it for obvious reasons, please make sure you have considered all the data mentioned there. Weisbecker V, Mitgutsch C (2010) A large-scale survey of heterochrony in anuran cranial ossification patterns. J Zool Syst Evol Res 48, 332-347. Lines 245-246 – there is a statement on the disagreement of the authors with Irisarri et al. 2017 calibration dates, but no justification or discussion of why. Some explanation/argument, would be fitting here. This paper is otherwise cited in line 582 – I guess there for the topology but not for the divergence times, correct? Figure big phylogeny: given that the divergence dates of the placental clades is far from being universally accepted, based on empirical work of alternative groups, it would be good to add some statement to this effect.

Overview: Major revisions necessary (or a more explicit re-focus regarding what is actually being tested)

This paper is an important review and analysis of the growing number of data sets about skeletal development in early tetrapods and their potential descendants. Although such individual data sets often are published today, comparing them to one another in a comprehensive fashion, and within a phylogenetic framework is cumbersome and rarely done with any breadth. The authors of this paper attempt to do just that while also answering lingering questions in vertebrate paleontology.

In general, the many data sets are brought together with care and thought -- something difficult to do given all the different ways that ossification sequences can be put together and interpreted, and the different morphologies across tetrapods. The authors also make a neat statistical assessment of comparisons across taxa, although by using just a single method. That approach is fine, but the paper would be much strengthened by including other methods as well (PGi, other methods of ranking to standardize, etc.), and comparing results across different analyses. Not only would this provide another measure of "confidence" regarding the results, but it would allow the authors' work to be more easily compared to the work of others, who may have used different methods to assess the evolution of skeletal development (hardly anyone seems to use the same methods these days). It may also help future workers select particular methods, if the authors could provide some review and comparisons regarding the strengths and weaknesses of each, and whether results are repeatable across different methods. The authors, in fact, bring up the issue of all these different methods in their abstract, but then make the same mistake they lament, by using just one. An even larger issue, however, is taxon sampling, discussed in detail below.

Major issues:

The authors compared ossification sequences for cranial elements only. To my knowledge, in most lepospondyls for which we have ossification sequence data, the skulls are already ossified in all preserved material. Occasionally data exists for one or two elements, but not for all seven scored by the authors. Perhaps this type of work would be better focused on postcranial ossification material, so that more lepospondyl taxa may be included? In fact, the lepospondyl taxon for which the most cranial development information exists, is an Aistopod, and that group in the last few years has been supported as a stem tetrapod rather than a lepospondyl (see work by Pardo, Anderson, etc.). That is a major concern for a study that turns up a result of lepospondyl ossification sequences best aligning with those of modern amphibians. Lepospondyl taxa must be included, and to do this, postcranial elements will need to be included. Indeed, it seems very inappropriate to test a topology without including the key taxa upon which it is based. What is really being compared is a situation in which amphibians and amniotes are widely separated from one another by any extinct tetrapods, rather than whether amphibians specifically share a relationship with lepospondyls, to the exclusion of amniotes (ie what is implied in the LH topology). As discussed below, actually including Lepospondyl taxa with data changes the whole pattern of character tracing, which affects ancestral reconstruction, number of evolutionary steps/events, etc. The answer may be completely different, and a different topology supported. Another more minor issue may be the proportion of extant vs. extinct taxa, wherein the "pull of the recent" may be dictating early tetrapod evolution in terms of pattern of character evolution. Why are we still using living taxa to explain the evolution of their ancestors? It should be the other way around.

Specifics, by line number:

55 -- More recent work suggests that salamanders (and maybe caecilians) have lost a tympanic ear that would have been present ancestrally (Anderson et al. 2016). That renders the point here mostly irrelevant, and somewhat more supportive of temnospondyl origins.

84 -- Substitute "among" for "between" because this refers to more than two hypotheses being compared.

108-109 -- authors need to be more forth coming in the methods about the sources of data and taxa included. Most readers won't access the sup data, and given my reservations above, they need to be honest about which extinct taxa were used (especially among lepospondyls), and the proportion of early tetrapods and outgroups to extant tetrapods. Not including enough extinct taxa will cause a bias of the "pull of the recent", in which the simply more common conditions of the living groups will outweigh, or even mask, the ancestral conditions present in extinct taxa. That would mean very little could actually be said about the evolution of skeletal development, and invalidate the authors' results here.

111- It seems a little unreasonable to choose a method that cannot handle missing data, given that this study focuses on comparisons between fossils and living animals. Most fossil data are incomplete in some way, and this is particularly true for lepospondyls vs. temnospondyls (the latter have a much better fossil record, and more complete ossification sequences).

122- yes another big point in trying to do these comparisons is that some taxa are simply very different. Temnospondyls as a whole, but especially Apateon show early ossification of postcranial material and late ossification of cranial. That is extremely hard to compare with lepospondyls, which generally have a completely ossified skull before the postcranial ossifications. By leaving out either postcranial or cranial elements from the analysis (or, just many other cranial elements, as in this case), the results will be very biased; some taxa that are otherwise wholly different in their total ossification sequence, make look more similar when only a subset is analyzed. This should be done with much more caution, and much more warning to the readers. A lot of information in the methods is left out.

133- this is incorrect. Firstly, Schoch 2006 used the actinopt Amia with fairly few homology problems. Secondly, some part of the development of Eusthenopteran were published (Cote, 2002; Schultze 1984), though admittedly little about cranial development. It would provide some data about postcranial though.

138 -- The authors themselves bring up one the major concerns noted above, and honestly state that no lepospondyls were used. How can their results be valid? With no actual lepospondyls, and no non- tetrapod outgroups, it seems fairly impossible to test their hypothesis directly, let alone confidently place living amphibians with a taxon not even present in the study.

157 -- size already was shown to not correlate well with developmental stage nor ossification sequence, although my own work suggested that because fossil data are missing so much, using size as an approximation for fossil cases, only, doesn't really change our results too much, given that they are so poorly resolved anyway.

169 -- statistical tests are not my strong skill, so an additional reviewer may be helpful to assess the appropriateness of CoMET and AIC for this application. However, I would add that other authors have compared sequence data in a phylogenetic framework (PGi for example, by Harrison and Larsson), so why aren't those methods also used and compared to CoMET's output? It isn't even discussed why more recent methods are not used.

186- perhaps the paper was a bit rushed? Why not wait for the corresponding consultant to reply, before abandoning some of the models? The paper would be strengthened by just waiting a little to see if these can be done, and if they cannot, explaining why more thoroughly.

192- true, but this is primarily character mapping with a more refined and modelled approach. That is different from phylogenetic analysis. In the former case, the authors are mapping characters onto existing hypotheses for check for best fit (more in line with objectives anyway, given that the goal was to test those specific topologies). Doing a phylogenetic analysis would have a different goal: see if the signal from development data agrees or disagrees with topologies based on adult phenotypes. That is a different type of analysis with a different type of goal. It doesn't need to be included here if the explicit focus is testing existing hypotheses of relationships. However, the two approaches should not be conflated in the methods. They are not alternative approaches because they do not accomplish the same thing, as misconstrued earlier in the methods and repeated again here, though implied rather than stated outright.

203 -- use a different phrase because "consensual relationship" in English means something of a romantic or sexual nature.

206 -- this is a bit puzzling, because molecular divergence estimates often include fossil calibrations anyway. Those gaps cannot be completely avoided. Also what is the purpose of the time tree? It is not explained in the methods. If developmental sequences are being mapped onto existing typologies already, why introduce yet another tree, and do stratigraphic data really add anything to the analysis? This is unclear as presented currently. It seems a time tree is unnecessary, given that so few extinct taxa are included, and as the authors note, there is so much disagreement regarding molecular divergence times anyway. With ossification sequence being so limited, the time tree feels a little redundant/unable to be fully utilized.

238 -- no mention is made regarding the horrid state of squamate relationships. Which topology is used, the one based on morphology or the one based on molecular data? Certainly most of the citations favor the molecular tree, but that is not stated, and the disagreement/issues are not mentioned. The disparity would probably affect divergence estimates for squamates.

245 -- no reasons are provided for "disagreeing" with Irisarri's dates. Please elaborate so that the reader is informed and the choice may be assessed.

254-255 -- this is not really true. Software will test any hypotheses given to it, with any data set of scored characters. However, the lack of lepospondyl taxa in the analysis means that the program is filling in missing data for the taxon, or if the taxon is just left off completely, the character evolution may not be correct, even if the remaining topology can computationally be assessed. In other words, adding in those missing taxa could change which pattern of character evolution is the best match, and thus which topology best explains the data.

263- it is unclear why branch lengths would all be made equal in the end, after all the methodology regarding the different evolutionary models that the authors implemented earlier in the methods section. Were those other models used and tested? Perhaps this just needs to be explained better.

277 -- the LH topology minus the actual lepospondyls might be best supported when lepospondyls also are not included in the other topologies, but what happens where their ossification data are included?? As noted above, that changes the whole pattern of character tracing, ancestral reconstruction, number of evolutionary steps/events, etc. The answer may be completely different. It seems very inappropriate to test a topology without including the key taxa upon which it is based. What is really being compared is a situation in which amphibians and amniotes are widely separated from one another by any extinct tetrapods, rather than whether amphibians specifically share a relationship with lepospondyls, to the exclusion of amniotes (ie what is implied in the LH topology).

314- the data are unpublished, but I did do this in my dissertation (Olori, 2011), which might be a good starting point, at least in terms of source material. I never published those results because of all of the concerns and problems regarding ossification sequences well discussed by the authors here.

352 -- clever subtitle, but first we need to revisit whether lepospondyls are monophyletic (unfortunately this problem seems to keep recurring every few years). The following discussion is weird, given that no data actually exist for lepospondyl cranial development, other than the fact that it is very early relative to temnospondyls. 

I am happy to review future versions if the authors plan to continue work on the study. I think with the major issues addressed the paper would be a nice contribution to the literature and a great jumping off point for future use of sequence data in phylogenetic studies, as the authors suggest. I definitely agree with their assessment of the potential for these types of data.