Dear John, I came across the article and wrote to John Harte. My email to him and his kind response are appended below.
I brief, I believe John is on the correct pathway, and it is one that I have been treading for some 35 years now. I think, however, that one cannot simply apply statistical entropy in an unconditional way. Like physical entropy, statistical entropy has meaning only in a relative sense. That is, it can only be measured with respect to some reference situation (cf., the third law of thermodynamics). (We've been over this together in connection with the Brooks and Wiley hypothesis.) By invoking a reference state (even if that state should be reflexive, as is done with weighted networks), one discovers that statistical entropy alone does not parse out order from disorder. Once such parsing has been made, one may then follow the course of order and disorder, in the context of the chosen reference state. <http://people.biology.ufl.edu/ulan/pubs/FISPAP.pdf> John did not suggest a solution to my ignorance about the almost constant proportion between constraint and indeterminism in ecosystem trophic networks. Maybe someone on FIS can suggest one? Peace, Bob Subject: Re: Ecological thermodynamics From: "John HARTE" <jha...@berkeley.edu> Date: Fri, September 26, 2014 9:03 am To: "Robert Ulanowicz" <u...@umces.edu> Dear Bob, I am in South Africa, Cape Town region, on sabbatical and enjoying immensely the wildlife and botanical preserves, and especially traipsing through the fynbos. Off to Chile next week for a month. I have thought about trophic networks and maxent only to the extent that I realized that the linkage distribution across nodes in most real networks does indeed follow (with some scatter of course)) a Boltzmann distribution. But I have shied away from looking at what theory has to say about flow rates between nodes because the data are so spotty. Recently I have been working with a graduate student on a state-counting approach, a la Boltzmann,to understanding competitive coexistence. It turns out the method actually predicts the dependence of demographic rates on population sizes. The outcome differs somewhat from the variety of dependences found in the usual Lotka-Volterra type models. What's interesting to me is that, as in your work, a quantitative and testable tradeoff arises for populations, in this case between the capacity to adapt under evolution and capacity to survive under competition. I enjoy reading your papers! Cheers, John John Harte Professor of Ecosystem Sciences ERG/ESPM 310 Barrows Hall University of California Berkeley, CA 94720 USA On Thu, Sep 25, 2014 at 7:06 AM, Robert E. Ulanowicz <u...@umces.edu> wrote: > Dear John, > > I notice that you have made considerable headway with applying MAXENT to > ecological theory. I was thinking you might find interesting some results > we have observed that might be of help in your search for global metrics. > > In particular, we have discovered that weighted networks of trophic > exchanges fall within a very narrow range as regards the ratio of mutual > information and conditional entropy. (See Figure 7 on p1089 of > <http://people.biology.ufl.edu/ulan/pubs/Dual.pdf>.) Admittedly, this > observation is based on sketchy data, but if it does hold up, then > Equations (5) below the figure might suggest a method superior to MAXENT > (for ecosystems only, of course) for estimating missing data? > > On the other hand, notice that the variable F as defined in Equation (4) > bears strong resemblance to the entropy formalism, except it is defined on > the basis of a global variable, "a", rather than the weighted sum of token > properties. Ecosystems also plot out near the maximum of F. I have puzzled > about the resemblance and come to no conclusions. Possibly, your deeper > interest in MAXENT might allow you an insight that eludes me. > > Here's wishing you the best of continued success with your work! > > Peace, > Bob > > P.S. I have also mulled over the relationship between ecosystems and > thermodynamics. Some ruminations can be found in my paper with Bruce > Hannon <http://people.biology.ufl.edu/ulan/pubs/Prodent.pdf> and in the > early chapters of my first two books > (<http://people.biology.ufl.edu/ulan/pubs/GandD.htm> and > <http://people.biology.ufl.edu/ulan/pubs/EcolAsc.htm>). My latest > speculations appeared in > <http://people.biology.ufl.edu/ulan/pubs/Harmony.pdf>. > > > List, > > I am curious what people think of this. > > http://www.wired.com/2014/09/information-theory-hold-key-quantifying-nature/ > > From the article: > > MaxEnt is based on principles of simplicity and consistency, but it has > additional assumptions baked into it, starting with the fact that > researchers must choose just a few variables to feed into the procedure. > In 2008, when Harte first considered the idea, he decided to try it out > using the size of an area, the number of species there, the number of > individuals, and the total metabolic rate of all those organisms. He didnt > pick these characteristics at random; he had an inkling, from reading work > on metabolic theory, that these had promise for describing biological > systems. In some cases, they do very well. > > The simplification of a complex ecosystem into just a handful of variables > has fueled criticisms of MaxEnt, because it assumes that those numbers and > whatever processes generate them are the only things shaping the > environment. In essence, it generates predictions of biodiversity without > taking into account how that diversity arises. It implies that the details > many ecologists focus on might not matter if you want to understand the > larger patterns of an ecosystem. Harte said he usually gets two responses: > Youve opened up a whole new theory, and youre an idiot, because we all > know that mechanism matters in ecology. > > > Other extrapolation methods are mentioned in the article that I am also > curious about. > > John > > > > _______________________________________________ > Fis mailing list > Fis@listas.unizar.es > http://listas.unizar.es/cgi-bin/mailman/listinfo/fis > _______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
