An Ecosystem As A Configuration Space

In my most recent posting, I've been exploring a quite classic mathematical model of an ecosystem: the Salt Marsh ecosystem model developed at Sapelo Island and described in the fascinating 1981 volume, "The Ecology of a Salt Marsh". For those of us who are devoted to grasping the "wholeness" of an ecosystem, the question arises whether matching such a system to a mathematical model helps in grasping this wholeness - or whether it may even detract. The concern would be that true unity is broken when a whole is described in terms of relationships among discrete parts: as if the "whole" were no more than a summation of parts - in Parmenides' distinction, an ‘ALL" (TO PAN), exactly the wrong approach to a true "WHOLE" (TO HOLON). An excellent guide in these matters is James Clerk Maxwell, who faced this question as he searched for equations that would characterize the electromagnetic field in its wholeness. As soon as he learned of them, he embraced Lagrange's equations of motion, and as he formulated them, his equations derive from Lagrange's equations, not from Newton's. For Lagrange, the energy of the whole system is the primary quantity, while the motions of parts derive from it by way of a set of partial differential equations. Fundamentally, it is the whole which moves, the moving entity, while the motions of the parts are quite literally, derivate.

The components of such a system may be any set of measurable variables, independent of one another and sufficient in number to characterize the state of the system as a whole. Various sets of such variables may serve to characterize the same system, and each set is thought of as representing the whole and its motions by way of a configuration space. If we have such a space with the equations of its motion, we've caught the original system in its wholeness: not as a summation of the components we happen to measure, but in that overall function in which their relationships inhere.

Now, it seems to me that a mathematical model of an ecosystem, to the extent that it is successful, is exactly such a configuration space, capturing the wholeness of the ecosystem whose states and motions it mirrors. Specifically, the authors of the Sapelo Island Marsh Model were if effect working toward just this goal, though it may not have appeared to them in just these terms. All their research on this challenging project was directed toward discovering and measuring those connections, and the integrity of the resulting mathematical system was exactly their goal.

They had chosen to construct their model in terms of carbon sinks and flows; the measures of these quantities were sufficient to characterize the state of the system and its motions, and therefore constituted a carbon-configuration space of the marsh. A different set of measures might have been chosen, and would have constituted a second configuration space for the same system: for example, they might have constructed an energy-model, which have been equivalent and represented in other terms the same wholeness of the marsh. Carbon serves in essence as a representative of the underlying energy flows through the system.

I recognize that this discussion may raise more questions than it answers, and I would be delighted to receive responses which challenged this idea. But I think it sets us on a promising track in the search for the wholeness of an ecosystem - an effort, indeed, truly compatible with the wisdom of Parmenides!

Can An Ecosystem Model Help Us Think About Wholeness?

Readers of this website will be aware of my preoccupation with the question of "wholeness". The more I observe the world's current struggle to find its way through complex economic structures or global systems, the more convinced I become of the degree to which our deep-rooted commitment to individualism is betraying us. Individualism is both an ethic, which we are determined to impart to the world, and a habit of thought. This is not the moment to follow that line of thought further; it has been the subject of other postings, and it will be of more in the future. My concern at the moment is to offer a new approach to this issue. On a visit to the Key School in Annapolis recently, on the shores of the Chesapeake, I was struck by the widespread awareness there that the Bay is sick: 27% of true health was the figure I was hearing. That led me to wonder about the concept of "health" of an ecosystem, and how it might be grasped. With the aid of the computer, I knew, the human mind is today able to reason about problems hitherto too complex to analyze. Could I find a computer model of an ecosystem?

By good luck, I've found not only such an ecosystem model, but a revealing account of a team project by which it was achieved. Teams of experienced scientists agreed to set aside their normal researches into separate compartments of the ecosystem, and direct their efforts  instead to a different kind of learning: to the common goal of constructing a coherent computer model which would capture the intricate interrelationships of these many components of one single system.

The system to which fortune had led me was a salt marsh at Sapelo Island on the coast of Georgia. The Book, edited by L. R.Pomeroy and R.G.  Wiegert, is "The Ecology of a Salt Marsh" (New York, 1981). Its innocent title fails to suggest the very special interest of the project it narrates. Quite elegantly, the book pulls together a fascinating account of the scientists' experience in disciplining their work to this goal.

An aesthetic of wholeness is invoked at the outset, with lines from  Sydney Lanier's poem, "The Marshes of Glynn". We learn much about this new sort of scientific endeavor when the book closes with a section on the aesthetic of the marsh, and a final quotation from that same poem.

Though a layman in matters of biology, I've since been making an effort to follow the turns of this inquiry. I won't say more how, beyond the remark that the effort proved successful only after the scientists had learned of a fundamental error they had been making, and accepted correction from the computer.

People whose judgment I very much respect have expressed their doubts as to the whether such a computer model is an appropriate means for approaching wholeness, or whether at this point I'm confusing true wholeness with a mere assemblage of parts by complicated aggregation. (My thoughts go back to Plato's "Parmenides", and the paradigm there of Hesiod's wagon: I agree that the "wagon" is something quite other than an assemblage of its parts!) In these terms, is a working computer model helping us to grasp the wholeness of a system, or betraying us into confusing true wholeness with a merely clever example of aggregation? In the case of a living ecosystem, in which the wholeness is manifestly organic, is the computer misleading us, tempting us to confuse organism with a complex structure of inherently inorganic parts?

My case for the computer as a welcome aid in advancing toward a  grasp of true wholeness must be made in future remarks which I plan to post soon.