Geometric and topological approaches to shape variation in Ginkgo leaves

Leaf shape is a key plant trait that varies enormously. The range of applications for data on this trait requires frequent methodological development so that researchers have an up-to-date toolkit with which to quantify leaf shape. We generated a dataset of 468 leaves produced by Ginkgo biloba, and 24 fossil leaves produced by evolutionary relatives of extant Ginkgo. We quantified the shape of each leaf by developing a geometric method based on elastic curves and a topological method based on persistent homology. Our geometric method indicates that shape variation in modern leaves is dominated by leaf size, furrow depth and the angle of the two lobes at the leaf base that is also related to leaf width. Our topological method indicates that shape variation in modern leaves is dominated by leaf size and furrow depth. We have applied both methods to modern and fossil material: the methods are complementary, identifying similar primary patterns of variation, but also revealing different aspects of morphological variation. Our topological approach distinguishes long-shoot leaves from short-shoot leaves, both methods indicate that leaf shape influences or is at least related to leaf area, and both could be applied in palaeoclimatic and evolutionary studies of leaf shape.

Line 173: Did this tree naturally grow on the campus or was it introduced from other places? Is there the age information or its DBH and height information? Is it a female tree or a male tree?
Lines 212-212: About the geodesic distance, it is better to show its mathematical expression. Maybe you can refer to Laga et al. (2014).
Line 230: Which were original factors (for obtaining the linearized factors) used for the PCA?
Line 517: I suggest the following references: Lin, S., Niklas, K.J., Wan, Y., Hölscher, D., Hui, C., Ding, Y., Shi, P. 2020. Leaf shape influences the scaling of leaf dry mass vs. area: a test case using bamboos. Annals of Forest Science 77: 11 Shi, P., Ratkowsky, D.A., Li, Y., Zhang, L., Lin, S., Gielis, J. 2018. General leaf-area geometric formula exists for plants -Evidence from the simplified Gielis equation. Forests 9: 714 Decision letter (RSOS-210978.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 Dr Mander
On behalf of the Editors, we are pleased to inform you that your Manuscript RSOS-210978 "Geometric and Topological Approaches to Shape Variation in Ginkgo Leaves" 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.
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Thank you for submitting your manuscript to Royal Society Open Science and we look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. Both reviewers find this manuscript to be well-written, one with experience with an earlier version who cites it as being greatly improved. Both reviewers offer minor edits that the authors should implement for final acceptance. We look forward to your revision, and thanks for submitting.
Reviewer comments to Author: Reviewer: 1 Comments to the Author(s) This paper is a well formulated study that proposes new tools/ methods to evaluate leaf shape, with G. biloba chosen as the target species to explore and test these tools/ methods. The methods and workflow are clearly described and the code for the analyse is publicly available allowing for others to use the methods.
I have a couple of minor requests, the colour choice in fig 3 should be revisited with a view to colour vision deficiency as red and green on the same plots should be avoided.
Line 74-77 leaf shape is linked to a number of different factors with a single reference made to a single review paper. I think it would be better if each factor had a separate citaion rather than linking all of these to the one study.
Reviewer: 2 Comments to the Author(s) The authors used two approaches (a geometric approach and a topological method) to study the variation and the corresponding determining factors for the leaf shape of ginkgo biloba. The fresh leaves and fossil leaves was used as materials. This manuscript was well prepared, and English writing is fluent. The methods appear to be appropriate. For me, using those methods to identify species might be problematic because many closely related species have very similar leaf shapes. However, at a single species level, those methods should be valid in distinguishing different cultivars or varieties. The current work belongs to the latter. Thus, I suggest accepting this manuscript after a minor revision.

Abstract
The current abstract has clearly summarized the background, material, methods and results. However, in the end of this section, the author had better use one or several sentences to further show the meanings or implications of this work in biology or ecology.
Lines 53 and 54: Arrange the key words in alphabet order.
Lines 68-71: The statements are clear and concise, but lack the support of references. I suggest authors to considering citing the following references: Li, Y., Niklas, K.J., Gielis, J., Niinemets, U., Schrader, J., Wang, R.,  Line 517: I suggest the following references: Lin, S., Niklas, K.J., Wan, Y., Hölscher, D., Hui, C., Ding, Y., Shi, P. 2020. Leaf shape influences the scaling of leaf dry mass vs. area: a test case using bamboos. Annals of Forest Science 77: 11 Shi, P., Ratkowsky, D.A., Li, Y., Zhang, L., Lin, S., Gielis, J. 2018. General leaf-area geometric formula exists for plants -Evidence from the simplified Gielis equation. Forests 9: 714 ===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: one version identifying all the changes that have been made (for instance, in coloured highlight, in bold text, or tracked changes); a 'clean' version of the new manuscript that incorporates the changes made, but does not highlight them. This version will be used for typesetting.
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See Appendix A.
Decision letter (RSOS-210978.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 Dr Mander, I am pleased to inform you that your manuscript entitled "Geometric and Topological Approaches to Shape Variation in Ginkgo Leaves" is now accepted for publication in Royal Society Open Science.
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On behalf of the Editors of Royal Society Open Science, thank you for your support of the journal and we look forward to your continued contributions to Royal Society Open Science. Dear Editor, Please find attached a revised manuscript entitled "Geometric and Topological Approaches to Shape Variation in Ginkgo Leaves" (authors: Hang*, Bauer*, Mio and Mander**,) [*denotes equal contribution to this work, **corresponding author]. We thank the reviewers for their comments and detail our responses below. Figure 3. We have updated Figure 3 with an alternative colour palette.