Review I:

I recommend that this paper be accepted for publication, substantially
in its present form. It stakes out the ground for believing that the
classical (Prigogine) non-equilibrium thermodynamic theory provides a
superior approach to the stability and dynamics of large ecosystems
than the more ad hoc approach of traditional evolutionary theory of
the May type, wherein the stable state is regarded as the state
defined by zero growth in all species populations.  It is pointed out
that the conditions for this state in conventional theory make it a
state unlikely to be attained, in contradiction to the observation
that large ecosystems seem to achieve this state readily.

        It is shown that irreversible thermodynamics provides a
natural approach to the stability of such systems. The parameters of
the theory are more physical and thus testable, in principle, than
those of the community matrix appearing in standard evolutionary
analysis. It is argued that the thermodynamic approach is in general a
more satisfactory approach to the stability properties of large
ecosystems, since it predicts the evolution of these systems to stable
states, using accepted standard principles.

    The thermodynamic approach is not free from pifalls and
assumptions which are to some degree contentious (e.g. the linearity
assumptions in the Prigogine analysis). Nonetheless these are
generally recognized and pointed out by the authour. He makes it clear
that further study is required. A particular area not studied by the
authour is the possibility of phase changes occurring in regimes far
from equilibrium.

    The manuscript as it stands needs some minor editing. The
continual use of horizontal bars where equal signs are intended is a
small but annoying point of this kind.

Review II:

The author of the paper addresses to a very interesting problem.  He
is looking for a thermodynamic explanation of the stability of
ecosystems. This question arises from the fact that ecosystems are
complex systems that invole a large number of
intereactions. Therefore, the stability of such systems is not well
undestood from the theoretical point of view.

In order to deal with this problem, the author used the framework of
irreversible thermodynamics; however, from the thermodynamic point of
view he has several misinterpretations of the non-equilibrium
thermodynamic theory.

The main misinterpretation occurs when the stationary state is
described as a state where entropy production is zero. The Prigogine's
theorem states that in this stationary states the entropy production
is a minimum. Of course this minimum may be zero, but this is a
particular case that has to be proved under specific conditions.  In
the paper the zero entropy production as a feature of the steady state
in ecosystems is not proved.

It seems to me that the author is taking an ecosystem without
considering spatial variations in the thermodynamic variables, this is
an assumption that has to be established from the beginning. This
assumption leads to a very restricted model for ecosystems.

In thermodynamics an appropiate definition of the system including the
independent state variables is required. The use of populations as the
only independent thermodynamic variable is restricting, since in
ecosystems the main interaction between populations is through the
available resources, which could play the role of energy. The energy
and work from the enviroment are not taken into account in the
proposed thermodynamic framework. These exclusions requires a
convicing justification.

The author needs to explain why it is not appearing a second time
derivative in equation (33)

Some other questions are:

How the ecosystem does receive negative entropy from sunlight through
photosynthesis?  Is photosyntesis an internal process in the
ecosystem?

Can author explain why \Gamma^{e}_{\gamma} is not equal to 1/T
dq_{\gamma}/dt?

Author must define all the symbols used, for example in eq. (2)
b_{\gamma} c_{\gamma \gamma '} are undefined.

In Classical Linear Irreversible thermodynamics there are not
relaxation times associated with the thermodynamic variables. The
author needs to define the "natural relaxation times" in this
framework.

Moreover the author has not referred previous relevant works where
part of the goal claimed in this paper has addressed, for instance:

Chakrabarti, C.G. Ghosh, S. Bhadra, S. Non-equilibrium thermodynamics
of Lotka-Volterra ecosystems: Stability and evolution, J. Biol. Phys.
21, 273 (1995).

Nielsen, S.N. Thermodynamics of an ecosystem interpreted as a
hierarchy of embedded systems. Ecol. Model. 135, 279 (2000).

Dilao R, Domingos T Periodic and quasi-periodic behavior in
resource-dependent age structured population models, B Math. Biol. 63,
207 MAR 2001

Dilao R, Domingos T, A general approach to the modelling of trophic
chains Ecol. Model. 132, 191 (2000)

Volkov, I. Banavar, J.R., Maritan, A. Organization of ecosystems in
the vicinity of a novel phase transition, Phys. Rev. Lett. 92, 218703
(2004).

For these reasons I cannot recomend the publication of the paper.

Review III:

I agree that the manuscript (JTBI852) can be published, but the
following corrections should be made:

1. To shorten the introduction leaving clear the objective of the
   work.

2. When it refers to stability, it should be clear if it is local or
global and I believe that both terms are mixed.

3. Section 3 of the work, On the applicability..., it should be clear
what is established in the literature and what the contribution would
be otherwise to reduce it if all is already said in the literature.

4. Section 4, the proposed..., it should be written clearly its
formalism as an alternative for the ecosystems, on the other hand it
should revise the equation 20 since the rate of entropy production is
the one that should be in function of generalized flows and forces
respectively.

5. It should avoid the expression "Universal evolution criterion" that
is used on several occasions in the manuscript (abstract, pages 3,
18). That has been strongly criticized in the literature.

6. It should have a topic dedicated to explain the ecological model in
particular, how the simulation was performed, how the different
magnitudes were calculated and what is the source of the parameters
used and do not leave this for the appendix that are not clear.

7. On the other hand, as far as I am concerned, of Lotka-Volterra
model doesn't exhibit limit cycle and much less chaos, locally it is a
centre and it is conservative. For that reason I understand the
necessity of an independent topic where this problem is approached.

Review V:

The author develops a model in the framework of classical irreversible
thermodynamics theory which treats organisms in an n-species ecosystem
as units involved in entropy exchange. The motivation for the model
appears to be the apparent "paradox" of how stable complex ecosystems
seem to exist quite commonly when theory suggests that the conditions
for stability in a complex system are rather restrictive. The major
result appears to be that the model yields a stationary state which
has paralleles in formulations such as the Lotka-Volterra equations
and their extensions.

I do not claim to be competent to critically examine the math
involved, and I assume it is unflawed.

I do not understand, however, how this work adds anything to our
insight into issues pertaining to ecosystem stability in the real
world. The purpose, as I see it, of a mathematical model is primarily
to enable us to deduce the consequences of our assumptions (which are
hopefully inspired by some familiarity with the systems under study),
and secondarily to help us refine our insight into how the system
functions. As a population ecologist, this paper doesn't help me
understand ecosystem dynamics beyond what I already know.

The "paradox" which seems to be the motivation for this paper is
itself more apparent than real: the citations to this are the classic
writings of Robert May in the 1970s, no reference is made to the huge
body of theoretical literature in ecology on non-equilibrium systems
in the 1980s and beyond. Indeed, there are rather few references to
theoretical ecology papers. I do not think that most ecologists would
agree that an ecological steady-state is the typical outcome of
ecosystem evolution.

The paper is not very clearly written, and will be difficult reading
for most ecologists. I do not think this paper is suitable for the
Journal of Theoretical Biology. It is better suited to a journal in
Physics, or perhaps something like the Journal of Mathematical
Biology. JTB has always been, to me, a journal publishing theory
strongly rooted in empirical realities and nuances. This paper may be
satisfying to physicists who seek grand unified theories, but I do not
think it furthers our understanding of ecology in any meaningful way.

Review VI:

This paper contains some important ideas that it seems to me could
make it an important paper if published.  My general recommendation
would be to publish BUT there are some important changes that I
believe must be made first that will take the author some work. I
believe the central points of the paper though warrant both the work
on the part of the author and also the patience and perseverance of
the journal in going through revision. What I'm talking about fall
roughly into three categories. The first although substantive can be
thought of as a matter of presentation. More particularly, it concerns
what the paper is claiming to do and how this is presented to the
reader. The impression the reader gets at first is that the paper is
far more general in its application than it is. To be entirely fair,
the author does present most of the appropriate caveats but rather
than being up front they are buried in the paper. The second area is
in the area of attribution. This is really a pretty easy one, but
important. There are some very key people who should be mentioned as
predecessors of some of the ideas in this paper. I'll say who I think
they should be. The third area of concern is errors of statement or
fact. It is not clear whether these are misunderstandings of the
author or misstatements, although given his apparent depth of
knowledge it seems likely to be the latter. I'll cover these areas in
more detail below:

1) The author's most general conclusion "that the evolution of
   community stability through natural selection is a manifestation of
   nonequilibrium thermodynamic directives" is entirely correct. In
   addition, the notion that that latter phase of development or
   evolution toward the mature or stationary state the rate of change
   of the specific entropy production takes a negative sign or zero in
   the case of the stationary state (which as is pointed out below is
   only stationary for some finite period before all such systems we
   know of fully senesce and collapse or "die". But what is not
   pointed out at the beginning is not only the fact that this is only
   a part of such a system's "life" but what the author offers as a
   formalism only applies to a very constrained and idealized
   context. This does not mean that it is not valid or that it is not
   useful, only that it is only a part of the picture. Author should
   state this more clearly up front.

For example, the author states on page 3 that "For ecosystems....which
have been significantly perturbed such that the generalized flows are
no longer linearly proportional to the generalized forces...some
results from linear CIT theory cannot be used." Totally correct, but
this includes a very good part of the origin or 'birth' of an
ecosystem its development and growth and this should be stated earlier
in the paper.

On page 20 (almost near the end of the paper) the author says "One
question we have not addressed here....is why ecosystems have a
tendency to grow and increase in complexity....then he correctly cites
Swenson's principle as a way to account for it and says (also
correctly) that what he has focussed on does not contradict this
principle but can be seen to work with it. All this is fine, but the
growth and development or ecosystems are a crucial part of the
discussion of their stability. The author should really warn or tell
the reader up at the very front of the paper that he does not intend
to address this (and that he will make some general remarks about it
at the end as he's done). The implication otherwise I believe misleads
the reader.

see some further discussion on over claiming at the end of part 3
 
2) On the question of mostly what I think are missing citations, the
    author in his overview says on page 2 "Kay (1991) and Schneider
    and Kay (1994) have argued in a convincing way..for the
    description of ecosystem characteristics and evolution in terms of
    thermodynamic theory. First, my suggestion although not imperative
    would be to leave these authors out. What they argue where valid
    is often from other authors who are either not credited or
    credited inadequately. And there are no new ideas in this
    work. What is important and crucial though is to include some
    references here to pioneers who really did do the groundwork or at
    least point to it in this regard. I'm thinking of Lotka, the Odums
    (Howard on energy flows and Eugene and Howard on succession),
    Margalef (who had a lot of it right, although some of it very
    wrong!), and certainly Zotin should be mentioned here (author
    cites Zotin elsewhere but he should be cited here). These authors
    I really believe should all be mentioned.

On page 6 the author refers to the "problem of the population of one"
and cites Swenson, 1989. This is an extremely important idea and it is
right to attribute it to Swenson, but the paper he cites, to the best
of my knowledge does not contain this idea. I've included a number of
references below from Swenson that do and the author should use one or
more of these to make this point rather than the one he uses (several
are online and I've put the URLs).

3) In the abstract author says ecosystems evolve towards a stable
   stationary state. Ecosystems and living systems in general do
   evolve (or "develop") to roughly speaking a stationary state (a
   mature state), but in fact they also typically senesce and
   "die". Abiotic systems, and perhaps only those in the laboratory
   like for example the classic Benard cell experiment or the thermal
   diffusion tube experiment (which is a typically used example of the
   central principle on which this author is seeking to lean [see
   discussion below]) develop to stationary states and can be held
   there as long as the conditions are maintained by the
   experimenter. Ecosystems and living systems in general are, as the
   author claims special cases of the more general thermodynamic
   nonliving 'self-organizing," spontaneously ordered systems (or
   "autocatakinetic systems" to use Swenson's term), but it is
   important to keep the language precise. Living systems or
   "replicative systems" (systems with replicating components) all
   tend to age, use up their degrees of freedom and discontinuously
   crash or "die".  The author is entirely right though that they all
   develop in a general direction towards a particular end state with
   particular thermodynamic properties and in general they are what
   the author describes but there is a little too much extrapolation
   from the idea nonliving laboratory case to the replicative one
   without drawing the distinction.

Author uses the term "universal evolution criterion" after
Prigogine. This term is somewhat misleading. First, with due respect
to Prigogine it was always an exaggerated and therefore somewhat
confusing term even in its best days. Since, as does the author's work
it refers to a very limited range of real world dynamics the word
'universal' is somewhat misleading although it's true that it is
'universal' within that very narrow range. What it is not is a
"universal evolution criterion" per se. In fact Prigogine actually
thought that this might be true in his early work, but clearly
rejected it later on. There was a brief period, roughly 20 years ago
where a number of authors made this mistake, that is of over
generalizing it despite the logical and empirical evidence to the
contrary.

There is also as far as I can tell a confusion or conflation between
gross entropy production and (e.g., mass) specific entropy
production. If the author is erroneously conflating these it is
important that he not. Many have done this before him including
Prigogine himself in one particular paper but clarified in later
work. In living things in general as they grow and develop the
specific entropy production decreases (think of it as generalized
specific metabolism), but the gross entropy production (viz., the
total amount of food or energy gradient required to maintain it in its
growth) increases as required by the balance equation of the second
law. Swenson has a good discussion of this although I cannot find the
citation showing that even if there were no other factors operating to
cause it this is the expected (and necessary) result simply for
example as the result of allometric surface/volume relations. That is
since transport of matter/energy into a thing is some function of the
surface while what must be internally 'fed' is some function of the
volume then allometric relations predict that the efficiency of
transport ceteris parabus will decrease (why things divide etc. or why
there are many things rather than one, or why lungs etc. see the
generalized discussion on the extension of space-time 'diffusive'
surfaces in Swenson's paper the author cites and also in broader terms
in the "Development of Space-Time..." paper in the Annals New York
Academy of Sciences below ). In any case, the specific entropy
production goes down while the gross entropy production goes up.

In the classic textbook cases that demonstrate what the author calls
the 'universal evolution criterion' (sometimes also misleadingly
called the 'principle of minimum entropy production' the gross entropy
goes monotonically down under fixed constraints or forces. This should
not be confused or conflated with the decline in specific entropy
production as described above (although many years back did just
that). The best case to use for students is the case of the thermo
diffusion tube (e.g., find illustration in textbook by
Babloyantz). There are several forces one of which is a heat gr adient
which is held constant but very near equilibrium producing a steady
flow. The reservoirs used to maintain the gradients for several other
forces are not maintained and as they are used up the forces
disappear. Over time the change in the rate of entropy production goes
down monotonically until it reaches zero where the entropy production
is constant and maintained only by the remaining fixed heat gradient.
It is extremely important that the author not mistake the two and then
over claim, in particular for the second, which is what it seems he
may be doing. In particular, he rightly notes the problem of the
population of one being a problem for evolutionary theory reduced to
the consequences of natural selection, but the particular extremum he
invokes and then seems to imply explains natural selection simply
cannot work that way. The 'universal evolution..." he invokes says
that in (a very particular kind of) the rate of change of the entropy
production will be negative in sign to some minimum steady state or
zero. It is my hope that this is not what the author believes since if
so it is untenable. The reductio of such an argument as realized years
ago would be the claim that natural selection is the consequence of or
works to maximize death or the extinction of life since the true
minimum is death in this case. The general principle he would want in
this case (which refers in most general terms to the development or
selection of degrees of freedom in the expansion of in space-time) is
the one from Swenson he discusses on page 20.

With the issues addressed I think this could be an extremely
worthwhile and intelligible paper.

References:

Population of One:

SWENSON R. 1991. End-directed physics and evolutionary ordering:
obviating the problem of the population of one. In The Cybernetics of
Complex Systems: Self Organization, Evolution, and Social
Change. F. Geyer, Ed. :41-60. Intersystems Publications. Salinas, CA.

SWENSON, R. 1997. Autocatakinetics, evolution, and the law of maximum
entropy production: a principled foundation toward the study of human
ecology. Adv. Hum. Ecol. 6: 1-46.  http://www.spontaneousorder.net/

SWENSON, R. & M.T. TURVEY. 1991. Thermodynamic reasons for
perception-action cycles. Ecol. Psych. 4: 317-348
http://www.ecologicalpsychology.com

Swenson, R. 1996. "Thermodynamics and Evolution." In G. Greenberg and
M. Haraway, eds., The Encyclopedia of Comparative Psychology. New
York: Garland Publishers, Inc.
http://www.entropylaw.com/thermoevolution2.html

General Review Swenson's principle:

Swenson, R. (2000). Spontaneous Order, Autocatakinetic Closure, and
the Development of Space-Time. Annals New York Academy of Sciences,
vol. 901, pp. 311-319, 2000.
http://evolution.philosophyofscience.net/