Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
Relations between morphology, buoyancy and energetics of
requiem sharks
Gil Iosilevskii and Yannis P. Papastamatiou
Article citation details
R. Soc. open sci. 3: 160406.
http://dx.doi.org/10.1098/rsos.160406
Review timeline
Original submission:
Revised submission:
Final acceptance:
16 June 2016
12 September 2016
29 September 2016
Note: Reports are unedited and appear as
submitted by the referee. The review history
appears in chronological order.
Note: This manuscript was transferred from another Royal Society journal without peer review.
Review History
RSOS-160406.R0 (Original submission)
Review form: Reviewer 1
Is the manuscript scientifically sound in its present form?
Yes
Are the interpretations and conclusions justified by the results?
Yes
Is the language acceptable?
Yes
Is it clear how to access all supporting data?
Yes, it is clear.
Yes, it is adequate and clear.
Do you have any ethical concerns with this paper?
No
© 2016 The Authors. Published by the Royal Society under the terms of the Creative Commons
Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use,
provided the original author and source are credited
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
2
Have you any concerns about statistical analyses in this paper?
No
Recommendation?
Major revision is needed (please make suggestions in comments)
Comments to the Author(s)
Please see the attached file. (Appendix A)
Review form: Reviewer 2 (Nicholas Payne)
Is the manuscript scientifically sound in its present form?
Yes
Are the interpretations and conclusions justified by the results?
Yes
Is the language acceptable?
Yes
Is it clear how to access all supporting data?
Yes
Do you have any ethical concerns with this paper?
No
Have you any concerns about statistical analyses in this paper?
No
Recommendation?
Accept with minor revision (please list in comments)
Comments to the Author(s)
This is a beautiful study. I think studies like this that invoke biomechanical principles to explain
the form and function of animals are very important, and here is a great example for shark
morphology and ecology. I imagine there are probably lots of biologists that have wondered
about the drivers of variation in the parameters detailed here, and the authors provide strong
justification for their conclusions about body shape and swimming performance in sharks. I can
see this paper being quite influential.
I have just a few comments and suggestions:
Pg 4, ln 34-37: I agree, but where does this prediction come from? A reference or two to support
this would be useful.
Pg 6 footnotes: I think these points are very important. Several recent studies have – erroneously
in my opinion – underplayed the role of shark’s pectoral fins in generating lift, and this
misconception seems to have been readily taken up in the literature since. The important points
raised in this footnote could even be expanded upon (to form a text box or similar) to briefly
point out how it is inappropriate to extrapolate results from small, benthic sharks operating at
low Reynolds numbers (as per Wilga & Lauder 2000,2001) to suggest that large obligate
swimming sharks generate negligent lift with their pectoral fins.
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
3
Fig 1. I suggest removing gridlines so the parabola can be seen more clearly.
Pg 8, ln 24 – should “normal to the direction of swimming” be “parallel to the direction of
swimming”? Also, please fix “underlying” on ln 21.
Pg 9, Ln 48: small and large compared to what?
Pg 10 ln 43-45: clarify that minimum speed will be limited by stall of the pectoral only for
negatively buoyant fish.
Pg 13 ln 56: suggest defining u (overline) earlier, ie on pg 9
Pg 15 ln 31-36: is there evidence for this prediction?
Pg 15 ln 39: Fig 4?
Pg 20 ln 10-13: it is true that P0 is often considered as such, but there are lots of studies showing
other sources of variation in P0, e.g. Killen et al 2010 Ecol Letts.
Pg 25 ln 47-52: a 10°C increase in temperature typically doubles or triples metabolic rate; this
sentence suggests active metabolic rate will only increase by 40%?
Pg 26 ln 6-15: but surely increasing mass will invariably increase basic MR unless the mass
increase comes solely from increased lipid content? And if lipid content increases, so will
buoyancy, so this assumption, as it is currently written, doesn’t make sense to me.
Ps 30 ln 18-20: this seems an oversimplification to me. Most pelagic species are active predators so
it is perhaps too strong to suggest reduced manoeuvrability imposes no constraints.
Pg 33 ln 3-38: yes, and I also wonder about non-reef associated species that spend a lot of time
swimming near the seafloor and using the ground effect. Perhaps this is also worth considering
and/or briefly mentioning in the context of evolution of increased pec fin span?
Pg 33 ln 25-30: it is not necessary, but you could give more evidence from species like deepwater
sixgills and prickly sharks (Nakamura and Sato 2015, Plos One).
Nick Payne.
Decision letter (RSOS-160406)
28-Aug-2016
Dear Professor Iosilevskii,
The editors assigned to your paper ("EFFECTS OF MORPHOLOGY AND BUOYANCY ON
COST OF TRANSPORT IN SHARKS") has now received comments from reviewers. We would
like you to revise your paper in accordance with the referee and Subject Editor suggestions which
can be found below (not including confidential reports to the Editor). Please note this decision
does not guarantee eventual acceptance.
Please submit a copy of your revised paper within three weeks (i.e. by the 20-Sep-2016). If we do
not hear from you within this time then it will be assumed that the paper has been withdrawn. In
exceptional circumstances, extensions may be possible if agreed with the Editorial Office in
advance.We do not allow multiple rounds of revision so we urge you to make every effort to
fully address all of the comments at this stage. If deemed necessary by the Editors, your
manuscript will be sent back to one or more of the original reviewers for assessment. If the
original reviewers are not available we may invite new reviewers.
To revise your manuscript, log into http://mc.manuscriptcentral.com/rsos and enter your
Author Centre, where you will find your manuscript title listed under "Manuscripts with
Decisions." Under "Actions," click on "Create a Revision." Your manuscript number has been
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
4
appended to denote a revision. Revise your manuscript and upload a new version through your
Author Centre.
When submitting your revised manuscript, you must respond to the comments made by the
referees and upload a file "Response to Referees" in "Section 6 - File Upload". Please use this to
document how you have responded to the comments, and the adjustments you have made. In
order to expedite the processing of the revised manuscript, please be as specific as possible in
your response.
In addition to addressing all of the reviewers' and editor's comments please also ensure that your
revised manuscript contains the following sections as appropriate before the reference list:
• Ethics statement (if applicable)
If your study uses humans or animals please include details of the ethical approval received,
including the name of the committee that granted approval. For human studies please also detail
whether informed consent was obtained. For field studies on animals please include details of all
permissions, licences and/or approvals granted to carry out the fieldwork.
• Data accessibility
It is a condition of publication that all supporting data are made available either as
supplementary information or preferably in a suitable permanent repository. The data
accessibility section should state where the article's supporting data can be accessed. This section
should also include details, where possible of where to access other relevant research materials
such as statistical tools, protocols, software etc can be accessed. If the data has been deposited in
an external repository this section should list the database, accession number and link to the DOI
for all data from the article that has been made publicly available. Data sets that have been
deposited in an external repository and have a DOI should also be appropriately cited in the
manuscript and included in the reference list.
If you wish to submit your supporting data or code to Dryad (http://datadryad.org/), or modify
your current submission to dryad, please use the following link:
http://datadryad.org/submit?journalID=RSOS&manu=RSOS-160406
• Competing interests
Please declare any financial or non-financial competing interests, or state that you have no
competing interests.
• Authors’ contributions
All submissions, other than those with a single author, must include an Authors’ Contributions
section which individually lists the specific contribution of each author. The list of Authors
should meet all of the following criteria; 1) substantial contributions to conception and design, or
acquisition of data, or analysis and interpretation of data; 2) drafting the article or revising it
critically for important intellectual content; and 3) final approval of the version to be published.
All contributors who do not meet all of these criteria should be included in the
acknowledgements.
We suggest the following format:
AB carried out the molecular lab work, participated in data analysis, carried out sequence
alignments, participated in the design of the study and drafted the manuscript; CD carried out
the statistical analyses; EF collected field data; GH conceived of the study, designed the study,
coordinated the study and helped draft the manuscript. All authors gave final approval for
publication.
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
5
• Acknowledgements
Please acknowledge anyone who contributed to the study but did not meet the authorship
criteria.
• Funding statement
Please list the source of funding for each author.
Once again, thank you for submitting your manuscript to Royal Society Open Science and I look
forward to receiving your revision. If you have any questions at all, please do not hesitate to get
in touch.
Yours sincerely,
Andrew Dunn
Senior Publishing Editor, Royal Society Open Science
on behalf of Kevin Padian
Subject Editor, Royal Society Open Science
[email protected]
Comments to Author:
Reviewers' Comments to Author:
Reviewer: 1
Comments to the Author(s)
Please see the attached file.
Reviewer: 2
Comments to the Author(s)
This is a beautiful study. I think studies like this that invoke biomechanical principles to explain
the form and function of animals are very important, and here is a great example for shark
morphology and ecology. I imagine there are probably lots of biologists that have wondered
about the drivers of variation in the parameters detailed here, and the authors provide strong
justification for their conclusions about body shape and swimming performance in sharks. I can
see this paper being quite influential.
I have just a few comments and suggestions:
Pg 4, ln 34-37: I agree, but where does this prediction come from? A reference or two to support
this would be useful.
Pg 6 footnotes: I think these points are very important. Several recent studies have – erroneously
in my opinion – underplayed the role of shark’s pectoral fins in generating lift, and this
misconception seems to have been readily taken up in the literature since. The important points
raised in this footnote could even be expanded upon (to form a text box or similar) to briefly
point out how it is inappropriate to extrapolate results from small, benthic sharks operating at
low Reynolds numbers (as per Wilga & Lauder 2000,2001) to suggest that large obligate
swimming sharks generate negligent lift with their pectoral fins.
Fig 1. I suggest removing gridlines so the parabola can be seen more clearly.
Pg 8, ln 24 – should “normal to the direction of swimming” be “parallel to the direction of
swimming”? Also, please fix “underlying” on ln 21.
Pg 9, Ln 48: small and large compared to what?
Pg 10 ln 43-45: clarify that minimum speed will be limited by stall of the pectoral only for
negatively buoyant fish.
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
6
Pg 13 ln 56: suggest defining u (overline) earlier, ie on pg 9
Pg 15 ln 31-36: is there evidence for this prediction?
Pg 15 ln 39: Fig 4?
Pg 20 ln 10-13: it is true that P0 is often considered as such, but there are lots of studies showing
other sources of variation in P0, e.g. Killen et al 2010 Ecol Letts.
Pg 25 ln 47-52: a 10°C increase in temperature typically doubles or triples metabolic rate; this
sentence suggests active metabolic rate will only increase by 40%?
Pg 26 ln 6-15: but surely increasing mass will invariably increase basic MR unless the mass
increase comes solely from increased lipid content? And if lipid content increases, so will
buoyancy, so this assumption, as it is currently written, doesn’t make sense to me.
Ps 30 ln 18-20: this seems an oversimplification to me. Most pelagic species are active predators so
it is perhaps too strong to suggest reduced manoeuvrability imposes no constraints.
Pg 33 ln 3-38: yes, and I also wonder about non-reef associated species that spend a lot of time
swimming near the seafloor and using the ground effect. Perhaps this is also worth considering
and/or briefly mentioning in the context of evolution of increased pec fin span?
Pg 33 ln 25-30: it is not necessary, but you could give more evidence from species like deepwater
sixgills and prickly sharks (Nakamura and Sato 2015, Plos One).
Nick Payne.
Author's Response to Decision Letter for (RSOS-160406)
See Appendix B.
RSOS-160406.R1 (Revision)
Review form: Reviewer 1
Is the manuscript scientifically sound in its present form?
Yes
Are the interpretations and conclusions justified by the results?
Yes
Is the language acceptable?
Yes
Is it clear how to access all supporting data?
The supporting data are clear and adequate.
Do you have any ethical concerns with this paper?
No
Have you any concerns about statistical analyses in this paper?
No
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
7
Recommendation?
Accept as is
Comments to the Author(s)
The authors have satisfactorily addressed my previous concerns, and I now recommend
publication of this manuscript in Royal Society Open Science without further delay.
Decision letter (RSOS-160406.R1)
29-Sep-2016
Dear Professor Iosilevskii,
I am pleased to inform you that your manuscript entitled "RELATIONS BETWEEN
MORPHOLOGY, BUOYANCY AND ENERGETICS OF REQUIEM SHARKS" is now accepted for
publication in Royal Society Open Science.
You can expect to receive a proof of your article in the near future. Please contact the editorial
office ([email protected] and [email protected]) to let us know if
you are likely to be away from e-mail contact. Due to rapid publication and an extremely tight
schedule, if comments are not received, your paper may experience a delay in publication.
Royal Society Open Science operates under a continuous publication model
(http://bit.ly/cpFAQ). Your article will be published straight into the next open issue and this
will be the final version of the paper. As such, it can be cited immediately by other researchers.
As the issue version of your paper will be the only version to be published I would advise you to
check your proofs thoroughly as changes cannot be made once the paper is published.
In order to raise the profile of your paper once it is published, we can send through a PDF of your
paper to selected colleagues. If you wish to take advantage of this, please reply to this email with
the name and email addresses of up to 10 people who you feel would wish to read your article.
On behalf of the Editors of Royal Society Open Science, we look forward to your continued
contributions to the Journal.
Best wishes,
Alice Power
Editorial Coordinator
Royal Society Open Science
[email protected]
http://rsos.royalsocietypublishing.org/
Reviewer(s)' Comments to Author:
Reviewer: 1
Comments to the Author(s)
The authors have satisfactorily addressed my previous concerns, and I now recommend
publication of this manuscript in Royal Society Open Science without further delay.
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
Appendix
A
This is with regard to the review of the manuscript by G. Iosilevskii and Y. Papastamatiou,
entitled “Effects of Morphology and Buoyancy on Cost of Transport in Sharks”
[Manuscript ID: RSOS-160406].
This paper investigates the hydrodynamic effect of morphology and buoyancy on the cost
of transport in shark swimming using a theoretic model combined with some experimental
measurements. The model seems novel and the paper contains many interesting analyses.
However, there are some points that I feel require clarification before the paper can be
recommended for publication. My major comments are as follows.
1. The motivation of this work is not clear from reading the introduction. It seems that
the three questions in Para. 3 on page 4 are suddenly proposed. In particular, why
is the body temperature important? It has never been mentioned in the first two
paragraphs. The authors may possibly consider reviewing more previous studies
and giving more detailed analyses to bring out the objectives of this paper.
2. In the deduction of the theoretic model, the authors have adopted a lot of
assumptions. But some of them are just simply stated as “we assume that…” or “it
was assumed…”, without any comments on their rationality. For example, on page
5, line 34, the propulsive efficiency is assumed constant 0.75. Can the authors cite
some previous studies to show that this assumption is reasonable? Another big
concern regarding the assumptions is the 𝐶𝐷 − 𝐶𝐿 relation in shark swimming,
which is one of the foundations of the model. According to page 6 and 7 in the
manuscript and the supplementary 2, this relation is estimated by the wind tunnel
measurements on a stationary shark model at a fixed Re (2 × 106 ). The underlying
assumption adopted here is that the lift and drag coefficients in a straight-rigid shark
model are close to those of a swimming shark. This seems very questionable. First,
during forward swimming, the whole shark body is performing an undulatory
motion instead of holding a stretched posture. So the pectoral fins, which generate
most of the lift, inevitably have yawing motion due to the undulation of the anterior
body. As a result, the lift force measured from the stationary fins may differ to the
actual lift during swimming. Second, the undulatory motion will lead to a smaller
drag, so the drag coefficient in this manuscript is overestimated as well. Finally, the
Re in shark swimming is not a constant. The same shark can swim in a wide range
of Re. It is not fair to compare the cost of transport at different swimming speeds
without considering varying the Re.
3. More detailed discussions or explanations are needed when introducing some new
quantities to the readers. For example, u and w are two of the most important nondimensional quantities in this paper. The authors should give more discussions
about their physical meanings, other than just simply stating that they are associated
with the cost of lift generation and parasite drag, respectively.
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
4. The manuscript will be much stronger if the authors could present some direct
evidences to support the major findings. For example, is the preferred swimming
speed of sharks in nature between 𝑣+ and 𝑣∗ as predicted in this paper? Have others
observed that the sharks living in a colder environment really have larger pectoral
fin or higher buoyancy than those living in a warmer environment?
5. A larger shark may always has higher energy consumption even it is swimming at
the same speed as a smaller one. To avoid this size effect, people usually minimize
the energy per unit mass and unit length traveled in a given fluid to find out an
efficient way of swimming (Liu et al., 2012, Phys. Rev. E; Maertens, et al., 2015,
Bioinspir. Biomim.). It means that the COT in equation (21) should be normalized
by the body mass. In this paper, I think it is not fair to compare the swimming
efficiency of sharks at different sizes without normalizing COT by mass. Could the
authors comment on this issue?
6. What is the value of the muscle efficiency 𝜂𝑚 on page 9?
References:
Liu, G, Yu, Y-L, Tong, B-G, Optimal energy-utilization ratio for long-distance cruising of
a model fish, Physical Review E, 86, 016308, 2012.
Maertens, AP, Triantafyllou, MS, Yue, DKP, Efficiency of fish propulsion, Bioinspiration
& biomimetics, 10, 046013, 2015.
Appendix B
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
Reviewer 1
1. The motivation of this work is not clear from reading the introduction. It seems that the
three questions in Para. 3 on page 4 are suddenly proposed. In particular, why is the body
temperature important? It has never been mentioned in the first two paragraphs. The authors
may possibly consider reviewing more previous studies and giving more detailed analyses to
bring out the objectives of this paper.
The Introduction has been modified. We do hope that it is adequate now.
2. In the deduction of the theoretic model, the authors have adopted a lot of assumptions. But
some of them are just simply stated as “we assume that…” or “it was assumed…”, without
any comments on their rationality. For example, on page 5, line 34, the propulsive efficiency
is assumed constant 0.75. Can the authors cite some previous studies to show that this
assumption is reasonable?
We have added clarification footnotes for every tacit assumption (footnotes 1, 3, 4 and
5), and added a few references (12, 19, 21, 22). Being based on the orders of
magnitude, rather than on particular values, the present analysis is insensitive to the
value of the propulsion efficiency. Nonetheless, having found slight inconsistencies in
conversion of pectoral fins span to a fraction of pre-caudal length, we have used the
opportunity to recompile table 2 in Supplementary 1, as well as the figures in the paper,
to a lower value of the propulsion efficiency. The changes are practically imperceptible.
Another big concern regarding the assumptions is the 𝐶𝐶𝐷𝐷 − 𝐶𝐶𝐿𝐿 relation in shark swimming,
which is one of the foundations of the model. According to page 6 and 7 in the manuscript
and the supplementary 2, this relation is estimated by the wind tunnel measurements on a
stationary shark model at a fixed Re (2 × 106). The underlying assumption adopted here is that
the lift and drag coefficients in a straight-rigid shark model are close to those of a swimming
shark. This seems very questionable. First, during forward swimming, the whole shark body
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
is performing an undulatory motion instead of holding a stretched posture. So the pectoral
fins, which generate most of the lift, inevitably have yawing motion due to the undulation of
the anterior body. As a result, the lift force measured from the stationary fins may differ to the
actual lift during swimming.
This is a second order-effect. The ratio between period-averaged lift L in yawing
motion and the steady lift L assumed in the paper is:
( v + rs′ )2 + ( v − rs′ )2
L 1
=
r SCL
L
2
2
(
1
r Sv 2CL
2
)
−1
= 1+
s ′2 r 2
,
v2
where r is the yaw rate, and s′ = ks s is the effective semi-span of a fin. k s depends on
the planform of the fin, but we can safely assume that it is smaller than 0.75, commonly
adopted in rotary wing theories for constant chord blades. Because the motion is
periodic, r = 0 . In turn, r 2 = ψ 02ω 2 2 , where ψ 0 and ω are the yawing amplitude
and the angular frequency. Thus,
2
s 2ω 2ψ 02 k s2
L
2 2 2 s
k
=
1+
=
1
+
2
π
ψ
0 s 2 ,
L
ls
2v 2
where ls = 2π v ω is the stride length, invariably of the order of body length. Any
reasonable combination of numbers that one may plug in in this estimate will yield that
difference between L and L is of the order of ψ 02 , about one hundredth.
Second, the undulatory motion will lead to a smaller drag, so the drag coefficient in this
manuscript is overestimated as well.
Thrust and drag in undulatory motion are actually inseparable. This reality led to a
great confusion in classifying experimental and numerical data as thrust or drag and in
definition of hydrodynamic propulsion efficiency. In this paper, we define drag as the
stretched-body drag at the same speed and the same orientation relative to the
swimming path. Consequently, any variation in friction force between undulating body
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
and the water are accounted for by variation in thrust, and hence by the propulsion
efficiency. When swimming at high Reynolds numbers, these variations cannot be large.
A few clarifying footnotes (footnotes 1, 4 and 5), and a few references (12, 19, 21, 22)
were added.
Finally, the Re in shark swimming is not a constant. The same shark can swim in a wide range
of Re. It is not fair to compare the cost of transport at different swimming speeds without
considering varying the Re.
Drag coefficient has never been assumed independent of the Reynolds number – see
equations (S2)-(S4) in Supplementary 1. We did assume that its variation with the
Reynolds number is slow as compared with variation of drag with velocity. A clarifying
footnote (footnote 3) was added.
3. More detailed discussions or explanations are needed when introducing some new
quantities to the readers. For example, u and w are two of the most important nondimensional
quantities in this paper. The authors should give more discussions about their physical
meanings, other than just simply stating that they are associated with the cost of lift
generation and parasite drag, respectively.
Unfortunately, they have no immediately catchable meaning. They do represent the
optimal swim speeds (they have dimensions of speed) in two opposite extremes – when
metabolic rate is extremely low, and when the shark is neutrally buoyant. We have
reworded the text slightly, and we hope that it is clearer now.
4. The manuscript will be much stronger if the authors could present some direct evidences to
support the major findings. For example, is the preferred swimming speed of sharks in nature
between 𝑣𝑣+ and 𝑣𝑣∗ as predicted in this paper?
There is an indication that voluntary swim speeds of bull, sandbar and blue sharks
match our predictions. We have added Section 3.7 with the comparison.
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
Have others observed that the sharks living in a colder environment really have larger pectoral
fin or higher buoyancy than those living in a warmer environment?
To the best of our knowledge, nobody has tested this hypothesis, certainly not for the
same species.
5. A larger shark may always has higher energy consumption even it is swimming at the same
speed as a smaller one. To avoid this size effect, people usually minimize the energy per unit
mass and unit length traveled in a given fluid to find out an efficient way of swimming (Liu et
al., 2012, Phys. Rev. E; Maertens, et al., 2015, Bioinspir. Biomim.). It means that the COT in
equation (21) should be normalized by the body mass. In this paper, I think it is not fair to
compare the swimming efficiency of sharks at different sizes without normalizing COT by
mass. Could the authors comment on this issue?
There is no ‘right’ way to do it, as in fact, mentioned in Maertes et al (2015). Taking
COT as a ‘plain’ ratio between energy and distance yields a quantity that increases
with mass to the power of 2/3α+2/9, approximately 0.75 – see table 2 (this is third of
the scaling exponent with respect to l). The ratio COT/mass decreases with mass to the
power of 7/9-2/3α, approximately 0.25. The increase of COT with mass manifests the
fact that larger animal has higher energy demands; the decrease of COT/mass with
mass manifests the fact that larger animals will always have lower mass-specific
metabolic demands. In either way, the outcome is intrinsically biased. We have
preferred the direct (‘plain’) definition because it allows direct estimate of the energetic
cost of becoming larger. Of course, optimizing ‘plain’ COT or mass-specific COT yields
the same optimal speed.
6. What is the value of the muscle efficiency 𝜂𝜂𝑚𝑚 on page 9?
24 Joule/mmol ATP. It was specified in the supplementary material, but it is true that it
had to be in the manuscript. It is now specified immediately after equation (13)
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
Reviewer: 2
Pg 4, ln 34-37: I agree, but where does this prediction come from? A reference or two to
support this would be useful.
Introduction has been largely re-written.
Pg 6 footnotes: I think these points are very important. Several recent studies have –
erroneously in my opinion – underplayed the role of shark’s pectoral fins in generating lift,
and this misconception seems to have been readily taken up in the literature since. The
important points raised in this footnote could even be expanded upon (to form a text box or
similar) to briefly point out how it is inappropriate to extrapolate results from small, benthic
sharks operating at low Reynolds numbers (as per Wilga & Lauder 2000,2001) to suggest that
large obligate swimming sharks generate negligent lift with their pectoral fins.
The footnote was rephrased (it is now footnote 2 and a reference to Payne et al (2016)
has been added. Expanding it more would be writing a different paper.
Fig 1. I suggest removing gridlines so the parabola can be seen more clearly.
We changed the color to make it more visible. Removing the grid masks the numerical
information embodied in the graph.
Pg 8, ln 24 – should “normal to the direction of swimming” be “parallel to the direction of
swimming”?
The sentence is correct. Lift is defined as the normal-to-the-swimming path component
of the hydrodynamic force. Footnote 1 has been added to clarify it.
Also, please fix “underlying” on ln 21.
It has been fixed.
Pg 9, Ln 48: small and large compared to what?
The sentence has been rephrased.
Pg 10 ln 43-45: clarify that minimum speed will be limited by stall of the pectoral only for
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
negatively buoyant fish.
It has been clarified.
Pg 13 ln 56: suggest defining u (overline) earlier, ie on pg 9
It is a tough decision. Throughout the paper, we made a conscious attempt not to use
u/w as a single variable in spite of every other parameter being dependent on it.
Working with reduced u would have required reducing all other parameters for
consistency. We felt that it could make the paper unreadable. Re-reading the paper, we
still feel uncomfortable abandoning dimensional quantities. Consequently, in spite of
rationality of this suggestion, we leave it ‘as is’.
Pg 15 ln 31-36: is there evidence for this prediction?
There are countless indications, but no proof - speed measurements found in the
literature lack the necessary complementary morphological data. Speed measurements
for three shark species (bull, sandbar and blue sharks) are now discussed in Section
3.7. Oceanic white tips probably swim at v*, but that will be a subject matter of the
forthcoming paper. The great hammerhead was reported in (Payne et al, 2016) to swim
slightly slower than the predicted v* (0.8 against 0.9 m/s).
Pg 15 ln 39: Fig 4?
Yes of course. It has been corrected.
Pg 20 ln 10-13: it is true that P0 is often considered as such, but there are lots of studies
showing other sources of variation in P0, e.g. Killen et al 2010 Ecol Letts.
This is a good point, but investigating this is beyond the scope of our study and would
be unlikely to change general predictions of our relatively simplistic model. We have
included a sentence acknowledging that this variability does exist (see the paragraph
following (14)).
Pg 25 ln 47-52: a 10°C increase in temperature typically doubles or triples metabolic rate; this
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
sentence suggests active metabolic rate will only increase by 40%?
There is no mistake here. The change of 10°C is too large to be used with linear
approximation of an exponential function. We have changed the text by decreasing the
temperature step and making it negative and not positive. BTW, the commonly accepted
value of 5020 for kT yields Q10 of only 1.8 (at 300°K).
Pg 26 ln 6-15: but surely increasing mass will invariably increase basic MR unless the mass
increase comes solely from increased lipid content? And if lipid content increases, so will
buoyancy, so this assumption, as it is currently written, doesn’t make sense to me.
These primitive partial derivatives manifest the effect of changing a single variable
while keeping the others constant. They are not supposed to represent a realistic
scenario. Any complex (realistic) case can be constructed from the primitive derivatives
as demonstrated in Section 4.7. The wording was altered to reflect this.
Ps 30 ln 18-20: this seems an oversimplification to me. Most pelagic species are active
predators so it is perhaps too strong to suggest reduced manoeuvrability imposes no
constraints.
Maneuverability changes its definition with the context it is used. It was used here to
imply ability to maneuver in confined spaces. The wording was changed to reflect this.
Pg 33 ln 3-38: yes, and I also wonder about non-reef associated species that spend a lot of
time swimming near the seafloor and using the ground effect. Perhaps this is also worth
considering and/or briefly mentioning in the context of evolution of increased pec fin span?
It is correct that by swimming in ground effect a shark can compensate for reduced
span of the pectoral fins. We are not aware of any requiem shark that routinely uses this
strategy.
Pg 33 ln 25-30: it is not necessary, but you could give more evidence from species like
deepwater sixgills and prickly sharks (Nakamura and Sato 2015, Plos One).
Downloaded from http://rsos.royalsocietypublishing.org/ on June 17, 2017
The paper has been promptly cited in the last paragraph of Section 3.6. Careful
analysis of its findings implies that the positive buoyancy was a few hundredth percent –
next to neutral. This remark has been added as footnote 8.