On the Thermodynamics of Self-Organization in Dissipative Systems: Reflections on the Unification of Physics and Biology

Round 1

Reviewer 1 Report

The paper presents a coherent collection of experimental scenarios where fluids participate in diverse types of dissipative self-organization. Together, they hint at an overarching principle of nonequilibrium thermodynamics. As a consequence, the authors put forth discussions on the emergence of lifelike behaviors in matter, thereby contributing to bridge physics and biology. The paper encourages diverse communities in their search for a complete and universal physical theory of life, departing from nonequilibrium thermodynamic concepts.

I recommend publication, after some issues are clarified.

1) In section “1.1 Dissipative Structures and Organisms”, the authors argue that “biological organisms are a subset of dissipative structures”. Also, that “To make this point clear, it would help to contrast dissipative structures/organisms with machines.” I do not dispute this point. I agree that there are differences and that discussing them is relevant to the paper.

However, I don’t understand why dissipative structures and machines should be regarded as such well-defined opposites (“are organisms … machines OR are they a different class … such as dissipative structures”). Why using “or”, as if there was no ambiguity whatsoever between these notions? Why should there be such a strong dichotomy between them, as argued in the paper? Additionally, is this really a necessary condition for the argument of the authors to hold (namely, that they regard organisms more as dissipative structures than as complex machines)?

In what follows, I explain in detail my concerns to each “bullet” in pages 3 and 4:

- bullet 1: it seems to me that the word “machine” can be used to denote a function attributed by humans to a certain object, be it engineered by humans or by non-human processes; for instance, the bone of a dead animal or the naturally fallen trunk of a tree could both be used as hammers, or as levers (i.e., as “machines”). This reminds me of philosopher Carol Cleland’s viewpoint, in her book “The Quest for a Universal Theory of Life” (Cambridge Univ. Press, 2019), and I quote:

“… an important distinction in philosophy of language between terms designating categories (e.g., water and star) that would exist had there been no human beings and categories (e.g., bachelor and garbage) that are carved out by human interests and concerns; philosophers dub the former ‘natural kinds’ and the latter ‘non-natural [human] kinds’.”

I understand that, for instance, Rayleigh-Bénard cells are distinctive of balloons, let’s say, for balloons have their sizes and shapes precisely set out by humans, and each particle constituting the balloon should remain at a fixed neighborhood with respect to the others. But comparing the cells with the functionality of the balloons (which can be categorized as transport machines, for instance) would sound unfair to me. In other words, I think that the first bullet risks of mixing natural kinds (dissipative structures) with human kinds (machines), and that this does not contribute to the clarity of the paper.

- bullet 2: Bones of animals are structures created from - but not maintained by - dissipative, entropy generating processes. Can’t we see them as examples of dissipative structures? Flipping things around, couldn’t we say that the irreversible assemblage of machines implies entropy being produced during the assembling process? For instance, “clicks” between two assembling parts generates entropy (as irreversibility guarantees that the assembled object does not fall apart), just as nuts and bolts produce heat during the screwing process.

- bullet 3: Can’t we regard mechanics as the limit of zero-temperature, non-thermalizable kinetics and dynamics, whereas equilibrium thermodynamics as the limit of a truly Boltzmann distribution for the dynamical degrees of freedom, after all frictions have made the system thermalize? Again, I am unable to see a rough cut separating mechanics from thermodynamics. The paper itself shows that, in many cases, both mechanical (dynamical) and thermodynamical (entropy-production) pictures provide good explanation to the same phenomena.

- bullet 4: Is the lack of self-healing a matter of impossibility by principle? I suspect it to be rather a matter of technological development. In principle, we could have self-healing machines in the future, couldn’t we?

- bullet 5: A phone can also be used as a paper weight, right? Objects employed as machines allow some degree of licenciousness (or adaptability to new functions), don’t they?  Thinking about the work by Frances H Arnold (Nobel Prize in Chemistry 2018), for instance, where the notions of machines and functionality are employed in the context of directed enzyme evolution, it makes me look at machines and dissipative structures as parts of a continuum. A recent paper by Grzybowski and Huck, namely, “The nanotechnology of life-inspired systems” (Nat. Nanotech. 11, 585, 2016), also seems to me as an indication of the smooth connection between the notions of machines and of dissipative self-organization.

To summarize, I recommend that the authors either clarify their arguments, or reframe their claims. (Comment: I have mentioned some references so as to make my arguments as clear as possible; I am not recommending citations.)

2) Throughout the paper, there are several typos and other minor issues that need revision. I list some below:

- lines 8 and 9 of page 2: the word ‘question(s)’ appears three times in a sequence;

- “a perception-action based models”;

- “this article is to first is to”;

- “focuses some very interesting …”;

- “design of a machines is based”;

- “[13, ?, 29, 30, 31, 32]” ;

- “this study are therefore are to identify” ;

- Reynolds number: mathematical expression with undefined terms;

- Eq.(6): T is not defined;

- Fig.7: missing color scales;

- Eq.(10): \mu as in index? inconsistent units? ^2 not well defined? d\Omega = dv, dx, or something else?

- “is equal to zero is the center” ;

- “enttropy” ;

- “shown that the both the flocking” ;

- “We discuss a two of these behaviors”;

- “was a infused” ;

- “past deacades” ;

- “anthromorphize” ;

- “cosndierable” ;

- “theromodynamic” ;

- “undelying” ;

After appropriate revision, the paper may be suitable for publication.

Author Response

Response to Review 1

1) In section “1.1 Dissipative Structures and Organisms”, the authors argue that “biological organisms are a subset of dissipative structures”. Also, that “To make this point clear, it would help to contrast dissipative structures/organisms with machines.” I do not dispute this point. I agree that there are differences and that discussing them is relevant to the paper.

However, I don’t understand why dissipative structures and machines should be regarded as such well-defined opposites (“are organisms … machines OR are they a different class … such as dissipative structures”). Why using “or”, as if there was no ambiguity whatsoever between these notions? Why should there be such a strong dichotomy between them, as argued in the paper? Additionally, is this really a necessary condition for the argument of the authors to hold (namely, that they regard organisms more as dissipative structures than as complex machines)?

 Response: As stated, our intention is to contrast and note some fundamental differences between two kinds of organized structures, one set we call machines and the other are dissipative structures. A machine is a designed and assembled structure.  It is an assembly of parts, each with a distinct function. Machines are not self-organized; their structure does not require continuous dissipation of free energy and the resulting generation of entropy.  In contrast, dissipative structures exist only when entropy generating irreversible processes that created it are operating; the structure ceases to exist when the processes cease operating; the system then relaxes to an equilibrium state. We do not think there is any ambiguity between the two systems: either the existence of a structure requires production of entropy or it does not. Dissipative structures require production of entropy, machines do not. We would like to note that when a machine is operating, it produces entropy, but that entropy generation is not needed of its structure.  Generally, entropy generation during the operation of a machine is undesirable, it makes the machine less efficient. Our view is that machines and dissipative structures offer very distinct paradigms for understanding biological organisms and that organisms are not complex machines, they are dissipative structures.  We understand that the reviewer may hold a different opinion.  

If we find practical use for dissipative structures -- which we hope we will -- that still does not justify calling them "machines".  We think they need to be called dissipative structures to distinguish them from machines which are of a different class, as explained above.

In response to the reviewer's comments, we have added additional comments to our article making these points and our view clearer.

In what follows, I explain in detail my concerns to each “bullet” in pages 3 and 4:

- bullet 1: it seems to me that the word “machine” can be used to denote a function attributed by humans to a certain object, be it engineered by humans or by non-human processes; for instance, the bone of a dead animal or the naturally fallen trunk of a tree could both be used as hammers, or as levers (i.e., as “machines”). This reminds me of philosopher Carol Cleland’s viewpoint, in her book “The Quest for a Universal Theory of Life” (Cambridge Univ. Press, 2019), and I quote:

“… an important distinction in philosophy of language between terms designating categories (e.g., water and star) that would exist had there been no human beings and categories (e.g., bachelor and garbage) that are carved out by human interests and concerns; philosophers dub the former ‘natural kinds’ and the latter ‘non-natural [human] kinds’.”

I understand that, for instance, Rayleigh-Bénard cells are distinctive of balloons, let’s say, for balloons have their sizes and shapes precisely set out by humans, and each particle constituting the balloon should remain at a fixed neighborhood with respect to the others. But comparing the cells with the functionality of the balloons (which can be categorized as transport machines, for instance) would sound unfair to me. In other words, I think that the first bullet risks of mixing natural kinds (dissipative structures) with human kinds (machines), and that this does not contribute to the clarity of the paper.

 Response:  Again, the distinction being made in this article is between dissipative structures, whose structure is maintained by entropy generating processes, and machines, whose structure does not need entropy generation.  We agree that the distinction made by Carol Cleveland, "natural kind" and "non-natural [human] kind" is important. The mixing of the "natural kind" and "human kind" started with Descartes, who claimed that organisms are complex machines and thus a machine has become a paradigm for understanding an organism as an assembly of parts. While this paradigm is not a universally accepted paradigm, a clear alternative paradigm is important to identify.  In our view, dissipative structures provide a distinctly different paradigm. We now have examples of bio-analog behavior emerging in dissipative structures.

  A dead tree or a bone of a dead animal is not a dissipative structure. When an organism dies, its biochemical state reaches thermodynamic equilibrium with no generation of entropy.   (There is bumper sticker that reads: Chemists don’t die, they reach equilibrium!) Machines, such as carts and windmills can be made of natural materials that were once living organisms. There is no ambiguity between such machines and dissipative structures.

For clarification, these points are reiterated in paragraphs below the bullet points.

- bullet 2: Bones of animals are structures created from - but not maintained by - dissipative, entropy generating processes. Can’t we see them as examples of dissipative structures? Flipping things around, couldn’t we say that the irreversible assemblage of machines implies entropy being produced during the assembling process? For instance, “clicks” between two assembling parts generates entropy (as irreversibility guarantees that the assembled object does not fall apart), just as nuts and bolts produce heat during the screwing process.

Response: First, we would like to point out that a bone in a living organism is a dissipative structure and it has a metabolism which generates entropy; it is continuously replaced by new bone tissue. In humans, it is estimated that a bone is completely regenerated in about 7-10 years. Also, a broken bone can heal.  A bone of a dead animal is not a dissipative structure, it does not regenerate or heal.

  It is obvious that the assemblage and functioning of a machine generates entropy – as every process does, except an idealized "infinitely slow" process. But a machine's structure still exists when there is no entropy generation; the structure of a machine does not fall apart if there is no energy and/or matter flow through it.  In contrast, when entropy generation stops, a dissipative structure falls apart (no heat flow, no Benard convection rolls).

- bullet 3: Can’t we regard mechanics as the limit of zero-temperature, non-thermalizable kinetics and dynamics, whereas equilibrium thermodynamics as the limit of a truly Boltzmann distribution for the dynamical degrees of freedom, after all frictions have made the system thermalize? Again, I am unable to see a rough cut separating mechanics from thermodynamics. The paper itself shows that, in many cases, both mechanical (dynamical) and thermodynamical (entropy-production) pictures provide good explanation to the same phenomena.

  Response: As explained in the article, the distinction being made is between mechanics with reversible laws and thermodynamics with irreversible laws.  That irreversible laws could be somehow derived from reversible laws (with the use of "probability") is not relevant to this article. We are simply noting that reversible laws of mechanics are used to describe machines and entropy production is an undesirable factor whose reduction only improves the function of a machine. To describe dissipative structures, irreversible laws of thermodynamics are used. Even if one uses Newtonian, or Lagrangian or Hamiltonian mechanics to "derive" the needed irreversible laws, still irreversibility is needed, and that is the point.  In the case of machines, irreversibility is not needed to describe the machine's structure or function; entropy generation generally reduces the efficiency of a machine.

- bullet 4: Is the lack of self-healing a matter of impossibility by principle? I suspect it to be rather a matter of technological development. In principle, we could have self-healing machines in the future, couldn’t we?

Response: The reviewer raises an interesting point. The self-healing property of a dissipative structure is an inherent property; it is a consequence of the stability of a dissipative structure, and it has its limits.  Equilibrium systems are also stable; when the structure is perturbed, it is restored. There are metal wires with "memory" which can be bent and twisted but, upon heating, return to their original shape. As the reviewer notes, in the future it might be possible to constructing machines that are self-repairing to some extent.  But, unlike dissipative structures, that property is not inherent in general to all machines; it is an additional designed property.

We have added a paragraph to discuss and clarify this aspect of our discussion.

- bullet 5: A phone can also be used as a paper weight, right? Objects employed as machines allow some degree of licenciousness (or adaptability to new functions), don’t they?  Thinking about the work by Frances H Arnold (Nobel Prize in Chemistry 2018), for instance, where the notions of machines and functionality are employed in the context of directed enzyme evolution, it makes me look at machines and dissipative structures as parts of a continuum. A recent paper by Grzybowski and Huck, namely, “The nanotechnology of life-inspired systems” (Nat. Nanotech. 11, 585, 2016), also seems to me as an indication of the smooth connection between the notions of machines and of dissipative self-organization.

Response:

In our view, there is no smooth transition from machines to dissipative structures, they belong to different classes. A smooth transition from machines to dissipative structures is another way of saying a dissipative structure or an organism is a complex machine. What smooth transition takes a mechanical clock to a chemical clock? Biomimicry i.e. design inspired by the biological world, is well known and has its presence in nano-technology. Indeed, it is possible to have dissipative structures at a nano scale. But the difference between a dissipative structure and a machine exists at a nano scale as well.  We understand that the referee may have a different view on this topic.  

   Practical use of a dissipative structure does not make it a machine: we use a dog for its ability to smell, and a horse to pull a cart.  But that does not make a dog or a horse a machine.  Indeed, we hope our understanding and study of dissipative structures will lead to the discovery and creation of dissipative structures that are of practical use.  It is our opinion, however, that they should be distinguished from the traditional machines.

To summarize, I recommend that the authors either clarify their arguments, or reframe their claims. (Comment: I have mentioned some references so as to make my arguments as clear as possible; I am not recommending citations.)

2) Throughout the paper, there are several typos and other minor issues that need revision. I list some below:

- lines 8 and 9 of page 2: the word ‘question(s)’ appears three times in a sequence;

- “a perception-action based models”;

- “this article is to first is to”;

- “focuses some very interesting …”;

- “design of a machines is based”;

- “[13, ?, 29, 30, 31, 32]” ;

- “this study are therefore are to identify” ;

- Reynolds number: mathematical expression with undefined terms;

- Eq.(6): T is not defined;

- Fig.7: missing color scales;

- Eq.(10): \mu as in index? inconsistent units? ^2 not well defined? d\Omega = dv, dx, or something else?

- “is equal to zero is the center” ;

- “enttropy” ;

- “shown that the both the flocking” ;

- “We discuss a two of these behaviors”;

- “was a infused” ;

- “past deacades” ;

- “anthromorphize” ;

- “cosndierable” ;

- “theromodynamic” ;

- “undelying” ;

Response: We are extremely thankful to the reviewer for such a thorough and patient reading and for pointing out these corrections. I apologize for the poor proof reading of the manuscript and have attempted to make the recommended changes and also carefully proof-read the document again to identify and correct any other errors.

Reviewer 2 Report

This paper is an ambitious study that integrates thermodynamic methods used in the natural sciences with epistemology to discuss dissipative structures in nonliving systems and self-organizing phenomena in living systems in a unified manner. Entropy that emerges as a side-effect of energy being dispersed or transformed controls the state of the system and the behavior of the system is purpose-oriented to maximize entropy production and optimized to preserve the stability of the system. The attempt the authors intend to make is very suggestive and creative. However, the lack of discussion on the relevance of the dissipative structures presented here to biological phenomena has not allowed us to substantiate their attempts. This lack of relevance needs to be carefully supplemented for each and every experimental example. In addition, wind-dispersal seed is a natural phenomenon rather than a biological phenomenon. It is necessary to relate dissipative structures to phenomena that are more specific to biological activities.

1. The authors would give their views on life and dissipative structures in terms of heat (or uncompensated heat) in section 1.1. One of the similarities between life and dissipative structures is whether they are equipped with the ability to retain heat and convert it into other forms of energy.
2. Throughout sections 1.2 and 1.3, the relationship between optimality and entropy production is discussed, but there is some ambiguity in the relationship. Is it optimality to maximize entropy production or to maintain the system stable?
3. The relationship between Benard convection and the Hamiltonian path is unclear. An increase in the externally imposed temperature gradient leads to a transition from conduction heat to thermal convection, but how does this relate to the change in paths in Figure 3?
4. For the self-organized phenomenon of benzoquinone particles using a magnetic field, the relationship between the population of particles being linked to the movement of the pacemaker and the maximization of entropy generation is unclear.
5. How does the occurrence of spirals relate to the stability of the system? Rather, does the system evolve in such a way that it is oriented toward homogenization of the system state variables (that is, maximization of entropy)?

Mainor points

1. It is unclear what the color change of the path in Figure 3 represents.
2. The arrow of the path from 2 to 3 in Figure 3e is wrong.
3. It is unclear what the color change in Figure 4 represents.
4. Figure 5 is of poor quality, and needs annotations in the figure as to what it represents.
5. Not sure what equation 7 was used for.
6. What do the different colors in Figure 7 represent?
7. The first term on the right side of equation 10 is wrong.
8. Does Figure 8 represent the REP of the entire flow region at each position when the object is displaced from the center?
9. Isn't the notation for cold probe and hot probe in Figure 10 opposite?

Author Response

Response to Reviewer 2

This paper is an ambitious study that integrates thermodynamic methods used in the natural sciences with epistemology to discuss dissipative structures in nonliving systems and self-organizing phenomena in living systems in a unified manner. Entropy that emerges as a side-effect of energy being dispersed or transformed controls the state of the system and the behavior of the system is purpose-oriented to maximize entropy production and optimized to preserve the stability of the system. The attempt the authors intend to make is very suggestive and creative. However, the lack of discussion on the relevance of the dissipative structures presented here to biological phenomena has not allowed us to substantiate their attempts. This lack of relevance needs to be carefully supplemented for each and every experimental example. In addition, wind-dispersal seed is a natural phenomenon rather than a biological phenomenon. It is necessary to relate dissipative structures to phenomena that are more specific to biological activities.

 Response: We understand the reviewer’s apprehension in accepting this proposal. We agree with the comment that perhaps one could provide more in terms of biological evidence. Already there are plenty of examples of dissipative structures in biological systems, and bio-analog dissipative structures. Some of these can be (due to Prigogine and co-workers) can be found in refs. 10, 11 and 12 of and we have added two more references as well.

• Goldbetter A. (2017) Dissipative structures and biological rhythms. Chaos 27, 104612 (2017); doi: 10.1063/1.4990783
• Goldbeter, A. (1996) Biochemical Oscillations and Cellular Rhythms. The Molecular Bases of Periodic and Chaotic Behaviour. (Cambridge University Press, Cambridge, UK)

   However, we would point out that this paper does not aim to ‘prove’ without a shadow of doubt that thermodynamic principles unify physics and biology for this would be impossible at this stage and no amount of supporting data from either side would establish it. As the reviewer points out, we are suggesting this link in this review paper, based on the large number of experiments and theoretical studies we have conducted. This paper is also an invitation to the scientific community to contribute to this important question and we hope to be able to add more to both sides of the argument to inch closer towards a more reliable answer to this question in the coming years.

The reviewer’s comment about wind dispersal being natural, rather than biological, appears to evoke a sense of dualism and it is possible that we differ on philosophical grounds. Firstly the statement seems to suggest that ‘biology’ is not ‘natural’ and secondly, it may be reflective at some level of a belief that trees are at best unsophisticated systems which more likely fall in the category of non-living beings. We contest the underlying philosophy behind such a belief. While it is somewhat outside the purview of this paper, it needs to be pointed out that recent studies have borne out the fact that trees and forests are quite intelligent systems which are capable of:  ‘consciousness’ at various levels including the ability to respond to external stimuli, their environment; cooperative behavior; self-replication etc. all traits commonly associated with complex biological, living systems. The argument we are making is that trees are part of a Darwinian evolutionary process which is the cornerstone of biology and the evolution of the various variety of seed shapes is nature’s selection process to find shapes which maximize the potential to survive through invocation of thermodynamic principle such as the maximum rate of entropy production.           

1. The authors would give their views on life and dissipative structures in terms of heat (or uncompensated heat) in section 1.1. One of the similarities between life and dissipative structures is whether they are equipped with the ability to retain heat and convert it into other forms of energy.

Response: We are in agreement about this statement.

2. Throughout sections 1.2 and 1.3, the relationship between optimality and entropy production is discussed, but there is some ambiguity in the relationship. Is it optimality to maximize entropy production or to maintain the system stable?

Response: This is a significant and fundamental point and we appreciate the reviewer for asking it. It is our error for not having clearly addressed the point. In invoking the Maximum REP, we are in fact making an argument about stability; of the various configurations or self-organized states that a system allows for, the stable one is seen to the one which maximizes the rate of entropy production. We have shown this explicitly for the examples of a particle orienting itself in a fluid; the Segre-Silberberg and for some of the other examples discussed in Table 2. This point has now been made clear in section 1.3 and also highlighted in the conclusion of the paper.

3. The relationship between Benard convection and the Hamiltonian path is unclear. An increase in the externally imposed temperature gradient leads to a transition from conduction heat to thermal convection, but how does this relate to the change in paths in Figure 3?

Response: We do not determine the transition behavior from conduction to convection here. That is well established in the literature as referred to in this paper. What this example tries to do is present a heuristic argument for the convective process and an energy dispersal (or entropy) based framework for possible states the system could adopt in response to being heated at a point. The imposition of physical rules upon the different combinatorial possibilities allows us to argue for the persistence of the most stable or frequently observed mechanisms of energy distribution, namely waves and spirals. A more rigorous argument to this end, invoking entropic principles, have been made earlier by Anila and co-workers. The presentation here restates these results from a geometric perspective.

4. For the self-organized phenomenon of benzoquinone particles using a magnetic field, the relationship between the population of particles being linked to the movement of the pacemaker and the maximization of entropy generation is unclear.

Response: The flocking of benzoquinone particles is perhaps the most complex problem referenced in the paper and we have not yet been able to measure or directly compute entropy generation for this problem. We have however, been able to find an alternative argument based on the free energy of the system which appears to be an equally powerful indicator of stability [Communications in Nonlinear Science and Numerical Simulation, 2022]; a computation of the Gibbs free energy for the system (including regular and irregularly shaped BQ particles) correctly shows that the minimum (i.e. most negative) Gibbs free energy corresponds to the experimental observed flocks. Since the free energy can be argued to be the compliment of the REP, indirectly, this is indicative of a maximization of REP. Section 3.4 now contains some updates and greater explanation based on the arguments presented here.

5. How does the occurrence of spirals relate to the stability of the system? Rather, does the system evolve in such a way that it is oriented toward homogenization of the system state variables (that is, maximization of entropy)?

Response: The emergence of spiral patterns in both the examples presented in 3.1 and 3.2 are indeed indicative of homogenization of the system, through flow and energy dispersal. In both these cases, we point out that the maximization of entropy is also accompanied by a second selection principle, namely the maximization of the rate of entropy production which is a property of the most stable state of the system. Since this is a review article, we did not see it necessary to reproduce entire detailed arguments laid out in previous work (for instance see the reference 16 published in the European Physical Journal B, 2014). We do however elaborate some of these points in the paper in section 3.2.

Minor points

1. It is unclear what the color change of the path in Figure 3 represents.
2. The arrow of the path from 2 to 3 in Figure 3e is wrong.
3. It is unclear what the color change in Figure 4 represents.
4. Figure 5 is of poor quality, and needs annotations in the figure as to what it represents.

Points 1-4 have been addressed in the text. The color scheme has been discussed in the caption but we just want to point out that in figure 3 particularly, the color itself is of no consequence since the image is merely a schematic of the problem being discussed. However the elaborate caption should make things clearer now, we hope.

5. Not sure what equation 7 was used for.

This is a crucial equation which introduces rotation of the cylinder and helps capture the fact that REP is a maximum closer to the wall.

6. What do the different colors in Figure 7 represent?
7. The first term on the right side of equation 10 is wrong.

Points 6 and 7 have been addressed and corrected in the text.

8. Does Figure 8 represent the REP of the entire flow region at each position when the object is displaced from the center?

Yes, this is correct.

9. Isn't the notation for cold probe and hot probe in Figure 10 opposite?

No, it is correct as presented.

Round 2

Reviewer 2 Report

My focus on wind dispersal is the role of wind. Subject supplying energy and generating entropy is wind. When wind is generated, objects, whether living or non-living, are simply carried by wind currents. The uptake of water by tree, for example, is a completely biological activity, because tree itself are the main source of energy for the uptake. In this context, the reviewer stated that wind dispersal is a natural phenomenon. However, the description of 'consciousness' at various levels added by the authors could be a sufficient reason to consider wind dispersal as a biological activity. Since the description of Figure 13 is not included in the text, we recommend acceptance of this manuscript if that is corrected.

Author Response

Thank you very much for your careful reading and recommendations to improve the article. The reference to the figure 13 has now been added to the section 4 of the manuscript.  

Round 3

Reviewer 2 Report

The reviewer recommends acceptance of this manuscript because the authors have responded sincerely and appropriately to the reviewers' criticisms.