Life After Newton: an Ecological Metaphysic

BioSystems 50 (1999) 127–142

Life after Newton: an ecological metaphysic

Robert E. Ulanowicz *

Uni6ersity of Maryland System, Chesapeake Biological Laboratory, PO Box 38, Solomons, MD 20688-0038, USA

Received 16 October 1998; received in revised form 29 November 1998; accepted 7 December 1998

Abstract

Ecology may indeed be ‘deep’, as some have maintained, but perhaps much of the mystery surrounding it owes more simply to the dissonance between ecological notions and the fundamentals of the modern synthesis. Comparison of the axioms supporting the Newtonian world view with those underlying the organicist and stochastic metaphors that motivate much of ecosystems science reveals strong disagreements—especially regarding the nature of the causes of events and the scalar domains over which these causes can operate. The late Karl Popper held that the causal closure forced by our mechanical perspective on nature frustrates our attempts to achieve an ‘evolutionary theory of knowledge.’ He suggested that the Newtonian concept of ‘force’ must be generalized to encompass the contingencies that arise in evolutionary processes. His reformulation of force as ‘propensity’ leads quite naturally to a generalization of Newton’s laws for ecology. The revised tenets appear, however, to exhibit more scope and allow for change to arise from within a system. Although Newton’s laws survive (albeit in altered form) within a coalescing ecological metaphysic, the axioms that Enlightenment thinkers appended to Newton’s work seem ill-suited for ecology and perhaps should yield to a new and coherent set of assumptions on how to view the processes of nature. © 1999 Elsevier Science Ireland Ltd. All rights reserved.

Keywords: Aristotelian causalities; Ascendency; Autocatalysis; Indeterminacy; Information theory; Irreversible thermodynamics; Newtonian laws; Nominalism; Organicism; Postmodern constructivism; Propensity; Stochasticism; Telos

1. Introduction ogy was characterized by Naess, 1988, when he wrote about ‘deep ecology’ as something that Ecology has never nestled comfortably among affects one’s life and perception of the natural the traditional sciences. The uniqueness of ecol- world in a profound way. Numerous others sense that ecology is useful for addressing phenomena * Tel.: +1-410-3267266; fax: +1-410-3267378. in ﬁelds that are well-removed from the meadow E-mail address: [email protected] (R.E. Ulanowicz) or savannah. Thus, one encounters books on ‘the

0303-2647/99/$ - see front matter © 1999 Elsevier Science Ireland Ltd. All rights reserved. PII: S0303-2647(98)00097-5 128 R.E. Ulanowicz / BioSystems 50 (1999) 127–142 ecology of computational systems’ (Huberman, ganism’ is frequently used to characterize 1988) or discovers whole institutes devoted to the Clements’ ecology (although a perusal of his writ- ‘ecological study of perception and action’ (Gib- ings will reveal he used this neologism only son, 1979). rarely.) Clements credited Smuts, 1926 for his It is well and good to laud ecology through interest in holism, and Clements, in turn, moti- poetry or metaphor, but most scientists demand a vated two of ecology’s most renowned figures, G. more rational and systematic comparison of ideas Evelyn Hutchinson and Eugene P. Odum. We emerging from ecology with those comprising the note in passing that organic imagery hints broadly established modern synthesis. In what follows I of Aristotle, and that Francis Bacon devoted his will attempt to compare the historical lines of life to purging Aristotelian thought from natural ecosystems thinking against the axioms that un- philosophy. dergird the Newtonian treatment of natural phe- Organicism appears heterodox to most scien- nomena. I will argue that these elements of tists, because scientific orthodoxy demands a Newtonianism fail as a framework upon which to purely mechanical view of the world. Although hang the manifold facets of the process called life Darwin did introduce history into biology, he (i.e. life post-Newton.) It appears that a full and otherwise hewed closely to Newtonian strictures, coherent apprehension of living systems can be which he inherited via Thomas Malthus and achieved if one reconsiders, in addition to a cer- Adam Smith (Depew and Weber, 1994). In the tain Newtonian element, some ancient Aristote- US, this mechanical view of the living world was lian concepts in conjunction with the more bolstered by the technocratic movement of the contemporary notion of a world that is ontologi- 1920’s and 1930’s, which strongly influenced the cally open, as proposed by Peirce, 1877 and Pop- ecology of Odum, 1960. Clarke, 1954, for exam- per, 1982. The ensuing unitary description of ple, in his textbook on ecology, went so far as to natural dynamics is cast in the mold of Postmod- depict ecosystem populations and processes as the ern Constructivism (Griffin, 1996; Ferre´, 1996) figurative gears and wheels of a machine. Connell but nonetheless retains marked similarity to the and Slatyer, 1977 provide a more recent example fundamental laws outlined by Newton in his Prin- of the attempt to portray ecosystem succession as cipia (life in the image of Newton). The axioms a constellation of basic mechanisms. that later thinkers appended to Newton’s work, Inherent in the mechanical picture of ecosys- however, do not appear consonant with ecological tems is a rigidity and determinism not always thinking and perhaps should be replaced by a new found in organisms and other living systems. At set of assumptions. the other extreme stand the stochastics, or nominalists, who regard any notion of organization in ecosystems as pure illusion. For some, even 2. The ecological triptych ecosystems themselves appear as pure artifice (En- gleberg and Boyarsky, 1979; Cousins, 1987). The Conventional wisdom holds that there exists no stochastic vein in ecology runs deep and is at least single theoretical core to ecological thinking as, as old as the holist. Gleason, 1917, for example, say, Maxwell’s Laws provide for the study of published his contention that plant communities electricity and magnetism. The reason is that, are stochastic assemblies at about the same time historically, ecosystems theorists have divided that Clements, 1916 was advocating that ecosys- roughly into three camps: (1) organicists; (2) tems approach their climax configurations in vir- mechanists; and (3) nominalists, or stochastics tually deterministic fashion. Stochasticism was (Hagen, 1992). The rise of systems ecology early slow to catch on in American ecology until the in the 20th Century tracks closely the writings of 1950’s, when changing political fashions may have Frederic Clements, 1916 and his manifold analo- herded many into this camp (Barbour, 1996). The gies between ecosystems and organisms. The nominalist scenario seems to require fewer mathe- metaphor of ecological community as ‘superor- matical applications, so it is perhaps understand- R.E. Ulanowicz / BioSystems 50 (1999) 127–142 129 able that some of the more gifted ecological writ- influences. It was the revolutionary idea of ers are attracted to this movement (Simberloff, Descartes to accord primacy to straight-line mo- 1980; Shrader-Frechette and McCoy, 1993; tion over curvilinear pathways, such as the circle. Sagoff, 1997). The Greeks, for example, had regarded the circle Metaphors by definition are not precise, so it is as the most natural trajectory for heavenly bodies, not surprising that ecological descriptions often because it was considered to be the most perfect borrow from more than one of these analogies. geometrical form. Most renditions of ecological succession, for ex- (2) The rate of change of the momentum of a ample, include both organismal and stochastic body is proportional to the applied force: This elements. Other fields of inquiry also provide hy- law tells what happens when external agencies brid metaphors. Thus, neo-Darwinian evolution, intervene. The law is far more phenomenological ecosystem modeling and thermodynamics all in- than most seem willing to admit, and it is central clude both mechanisms and chance events, to the definitions of force and mass. whereas developmental biology, cybernetics and (3) Every action is opposed by an equal and teleonomy (sensu Mayr, 1992) combine propor- opposite reaction: Like most of his contempo- tions of organicism with mechanism. An example raries, Newton seemed to value conservation quite has yet to appear in ecology of any scientific highly, and one of the ways to impose conserva- model that amalgamates all three metaphors (see tion is to require symmetry. Salthe, 1993), yet such an admixture would be The mathematical forms of these three laws required of any theory that would coalesce ecol- were sufficient to prescribe all of classical mechan- ogy into a unified discipline. Such an overarching ics. It was their rigorous minimalism, more than paradigm would have seemed unthinkable several Newton’s three principles, that came to character- decades ago, but recent insights by both philoso- ize the ensuing ‘Newtonianism’. Somewhat sur- phers and ecologists have made the goal of a prisingly (given the legion of print that is devoted unified theory of ecosystems seem much closer. to the scientific method), one rarely finds the minimalist assumptions behind Newtonianism spelled out in any detail. One exception is by 3. The Newtonian metaphysic Kampis, 1991 and another is the attempt by De- pew and Weber, 1994 to formulate the Newtonian To begin a systematic comparison of the as- canon in terms of four fundamental postulates. sumptions behind the three prevailing ecological According to these latter authors: metaphors, we focus initially upon the most (1) Newtonian systems are deterministic. Given prevalent—the Newtonian or mechanical world the initial position of any entity in the system, a view. It is widely accepted that the foundations set of forces operating on it, and stable closure for the modern view of nature, which had its conditions, every subsequent position of each par- beginnings with Bacon, Galileo, Hobbes, ticle or entity in the system is in principle specific Gassendi and Descartes, were made fast by New- and predictable. This is another way of saying ton’s publication of Principia. (Less well-known is that mechanical causes are everywhere ascendant. how the actual format of Principia, which was (2) Newtonian systems are closed. They admit largely accidental, set the stage for the materialist/ of no outside influences other than those pre- mechanical revolution that was to follow Westfall, scribed as forces by Newton’s theory. 1993; Ulanowicz, 1995a). (3) Newtonian systems are re6ersible. The laws To review, the three laws that Newton himself specifying motion can be calculated in both tem- formulated can be summarized as: poral directions. There is no inherent arrow of (1) A body once set in motion continues in time in a Newtonian system. straight-line motion until acted upon by another (4) Newtonian systems are strongly decompos- force: This is a statement about what happens to able or atomistic. Reversibility presupposes that a body when it is isolated from any external larger units must be regarded as decomposable 130 R.E. Ulanowicz / BioSystems 50 (1999) 127–142 aggregates of stable least units—that which can (1994) put it, ‘Clements had it backwards. Ecosys- be built up can be taken apart again. Increments tems are not super-organisms; organisms are su- of the variables of the theory can be measured by per-ecosystems.’1 Certainly, the limits on how addition and subtraction. accurately one can predict the outcome of ecolog- Closer analysis reveals that implicit in the four ical succession are far broader than what is possi- items cited by Depew and Weber lies a fifth ble with ontogeny—too broad, in fact, to allow assumption that should be made explicit, namely, the claim that such succession is a deterministic (5) Newtonian laws are uni6ersal. They are ap- process. plicable everywhere, at all times and over all (2) Concerning causal closure, the point is al- scales (Ulanowicz, 1997). Not only is time consid- most moot in nominalism. Certainly, nominalism ered to be uniform throughout the universe (Mat- allows no cause other than the material or the suno and Salthe, 1995); but, in principle, no mechanical. But the nominalist would go further complications should arise if laws pertaining to and question whether it is useful, or even possible, very small dimensions, such as those governing to trace every event to its mechanical/material strong intranuclear forces, were to be applied at origins. Chance is, after all, the very crux of galactic scales, where gravitation operates. nominalism. All of which points directly at the It should be noted in passing that there are Achilles heel of Newtonianism, namely, that considerable overlaps among the five attributes of chance is an unwelcome interloper in a Newto- the Newtonian metaphysic, i.e. the Newtonian nian world. For, if there are only material and ideal itself is not strongly decomposable. mechanical causes at work, a chance event that cannot be subsumed by the law of averages would disrupt the reductionists’ scenario, making it im- 4. Broader horizons possible to predict higher level phenomena. What, then, keeps the world from coming apart? It took The advantage in spelling out the framework of some major backtracking for science to reconcile the Newtonian world view item-by-item is that we the idea of chance at the microscopic level with may now proceed to compare these five assump- predictable Newtonian behaviors at macroscopic tions with any counterparts that might pertain to levels. Fisher (1930) pointed out, however, that the other two ecosystem metaphors: such reconciliations are predicated on the assump- (1) As for determinism, we recognize immedi- tion that ‘the reliability of physical material flows ately that the other viewpoints do not share this not necessarily from the reliability of its ultimate Newtonian assumption. Stochasticism is tau- components, but simply from the fact that these tologous with chance. Of course, the Newtonian is components are very numerous and largely inde- likely to counter immediately with the belief that pendent’. Fact? The real fact is there is no guaran- such chaos is only apparent and can always be tee that components at very small scales act resolved by analyzing the system with greater independently of each other—only the desire on precision and in finer detail. Ultimately, however, the part of some to cling to the Newtonian such reductionistic regression leads to a dead-end metaphysic. as one approaches the scale of molecular or sub- It is worth noting that the assumption of inde- atomic particles, where indeterminism reigns. pendence is favored by individuals who, like most Ontogenists might question whether the organic biologists, profess a falsificationist stance regard- analogy is anything but deterministic. Within cer- ing scientific propositions. That is, one is expected tain bounds (Griffiths and Knight, 1998), one can to pull no punches whatsoever in a continuing predict how a specific instance of organic develop- attempt to falsify hypotheses. However, cherished ment will play out. But one should note that the Newtonian beliefs appear to be exempt from such type of organic development ascribed to ecosystems is decidedly weaker than what is normally 1 Clements actually referred to ecological communities, as observed in ontogeny. As Depew and Weber the term ‘‘ecosystem’’ was not coined until 1937 by Tansley. R.E. Ulanowicz / BioSystems 50 (1999) 127–142 131 scrutiny. It is far better to focus upon a narrow and final agencies are capable of exerting top– range of conditions under which Newtonian pos- down selection upon stochastic events below tulates can be retained and the rest can be (Salthe, 1985), both mitigating the detrimental ignored. consequences of micro events and nurturing those If the nominalists preserve the logical coherence random happenings that enhance functioning. In- of their beliefs by boldly proclaiming all order evitably, the rehabilitation of formal, and espe- (except that imposed by observation) to be illu- cially final, causalities will elicit strong, but sory, what options are available to the organicist, misdirected criticism from those who abhor teleol- for whom form and function are essential at- ogy in biology. tributes of the systems they study? One possibility (3) It should be apparent that reversibility has would be to borrow from antiquity and explicitly no place in the chaotic world painted by the acknowledge form and function as agents behind nominalist. Although, in the organic world view, development. That is, they could return to the formal and final agencies can contain the effects ideas of Aristotle, so fervently eschewed by Ba- of disturbance and restore functioning, it does not con, and reconsider opening the window of necessarily follow that the system always can be causality to admit once again the existence of returned to its original state. Organic systems are natural formal and final causalities (Rosen, 1985, not fully reversible; most chance events leave be- 1991; Ulanowicz, 1990). For these two types of hind finite alterations in systems structure. Or- cause are capable of restraining the disordering ganic systems are historical in nature (Brooks and effects of chance events at lower levels from un- Wiley, 1986). bridled propagation up the hierarchy of scales (see (4) Nominalists regard ensembles as atomistic Salthe, 1985, 1993; Wimsatt, 1994 for related by definition. The antithesis to this view is the formulations). organic system, which it is assumed can function That formal and final causes occur over longer (exhibit an intrinsic telos) only by acting as a times and larger scales can be seen from the whole. The Newtonian ideal, as espoused in ele- (unsavory) example of a military battle. The ma- mentary systems theory, is to break the system terial causes of a battle include the weapons and into parts, study the behaviors of the parts in munitions that the armies employ against each isolation and to reconstitute the behavior of the other. The soldiers who use these implements of whole from the combined descriptions of such destruction comprise the efficient causes behind atomistic behavior. This stratagem does not seem the conflict. The juxtaposition of the armies in the to apply to biological systems for several reasons. context of the physical landscape constitute two First, the component processes may simply cease formal agencies that strongly influence the course to function once an element is separated from the and outcome of the fray. Lastly, the final causes whole. Even if they should continue, the reper- for the battle appear among the set of social, toire of component responses that can be elicited political and economic events that initiated the in isolation most likely will not include those most war. That the temporal and spatial scales associ- relevant when the unit is imbedded in its organic ated with each cause are hierarchically ordered matrix. Finally, any adaptation that a component should be obvious and becomes literal when one might undergo when under the selective influence notes that efficient, formal and final causes are the of the ensemble is simply unknowable whenever domains of the private, general and prime minis- the element is observed in isolation (Abrams, ter, respectively. The legitimate interests of these 1996). agents map onto progressively broader geographic (5) Universality is antithetical to nominalism areas over longer times. (stochasticism), and its relevance to organic sys- The existence of higher level causes means that tems seems dubious as well. The idea that a law or a chance event at any level need no longer set phenomenon formulated within a particular win- organization at larger scales collapsing like some dow of time and space should be applicable all the house of cards. As will be argued below, formal time and everywhere seems limited to circum- 132 R.E. Ulanowicz / BioSystems 50 (1999) 127–142 stances where system parts are rarefied and inter- Popper, regarded by many as a conservative act weakly. Only a theoretical physicist would philosopher of science, likewise has suggested that dare to imagine the coupling of quantum phe- practitioners of science need to reconsider their nomena, relevant at atomic scales, with the gravi- views on basic causality if they are ever to achieve tational forces exerted over light years (Hawking, a truly ‘evolutionary theory of knowledge’ (Pop- 1988). Ecology teaches its practitioners somewhat per, 1990). His own opinion was that the universe more humility. When objects and processes crowd is causally open: that chance operates, not only in upon one another, it becomes difficult to project the netherworld of quantum phenomena, but at the influence of one event at a particular scale all levels (Popper, 1982). Popper was no icono- over remote domains of time and space. Too clast, however, and he urged not that we abandon many other elements and processes interfere along Newtonian forms, but rather that we expand the way, and it has just been argued how recourse upon them. In his view, Newtonian forces are but to atomism is unlikely to salvage matters. a small subset of a more general universe of Under these considerations, the most realistic agents he called ‘propensities.’ Briefly, a propen- stance for the organicist appears to be the hierar- sity is the tendency for a certain event to occur in chical approach (Allen and Starr, 1982; Salthe, a particular context. Propensities are related to, 1985). While the organic approach is more likely but not identical with, conditional probabilities. to encompass rules and laws than is nominalism, Suppose, for example, that one is considering a organic principles seem to pertain to limited Newtonian force that relates antecedent A with ranges of space and time. One must remain wary consequence B. Then every time that A occurs, it of any attempt to stretch explanations across is followed by B, without exception. In the lan- scales, as, for example, when the reasons behind guage of probabilities, one may say that the con- all social behavior are sought in genetics, or when ditional probability that B will occur, given that A the autonomy of human thought processes is pur- has happened, is unity (1) or certainty. This is ported to arise in the quantum phenomena occur- written as ring in molecules of the brain. Although through p(B A) 1, the hierarchical perspective one perceives an or- = ganic world that is more loosely coupled than the where p(B A) is the conditional probability that B Newtonian clockwork universe, the picture is cer- will result, given that A has occurred. In the larger tainly not one without a modicum of order. non-Newtonian world, we might observe that Whenever a rule or principle wanes in explanatory whenever A happens, B usually ensues—but not power as the scale of observation shifts, another is always. Whenever the coupling between A and B sure to emerge that maintains structure at the new is not isolated, interferences can intervene to af- level. Although such a ‘granular’ view of reality is fect the outcome. Whence, the conditional proba- at odds with the Newtonian vision, it is wholly bility that B will occur, given that A has consistent with the picture of organic causality happened, is usually less than unity. This means portrayed above. that the probabilities for other outcomes, e.g. C, D, E, … are not zero. In symbols, B 5. Enlarging the Newtonian edifice p(B A) 1 p(C A)\0 Ecology is not the sole heterodox discipline in science. Dissatisfaction with the rigidity that New- p(D A)\0 tonianism forces upon the neo-Darwinian synthe- p(E A)\0, … sis itself has been expressed by Chomsky, 1996 and also has been voiced by notable developmen- As an example, we consider an event frequency tal biologists, such as Sidney Brenner and Guen- table (Table 1) that reports the number of times ther Stent (Lewin, 1984). The late Sir Karl each ‘cause’, a1, a2, a3 or a4 is followed by any of R.E. Ulanowicz / BioSystems 50 (1999) 127–142 133

Table 2 ﬁve possible outcomes, b1, b2, b3, b4 or b5. From among the 1000 events recorded in Table 1, one Frequency table as in Table 1, except that care was taken to isolate causes from each other sees that the ‘joint probability’ that, say a1 and b3 occur together is 16 out of 1000 events. b1 b2 b3 b4 b5 Sum p(a1, b3)=16/1000 a1 0 269 0 0 0 269 a2 0 0 0 0 227 227 a 2630000 263 where p(a1, b3) is the joint probability that a1 and 3 a4 0 0 241 0 0 241 b3 occur together. The joint probability is not the same as the conditional probability, however. To calculate the latter, one must, according to Bayes, Sum 263 269241 0 227 1000 normalize the joint probability by the probability, p(a1), that a1 occurs under any circumstances, i.e. Interestingly, b4 never occurs under isolated (rareﬁed or laboratory) conditions. It arises purely p(b3 a1)=p(a1, b3)/p(a1). as a result of interferences among propensities.

One can see from the far right-hand column of That the propensity associated with p(b4 a3) de- Table 1 that p(a1)=269/1000, so that pends entirely upon its proximity to (ability to interact with) other system propensities is an illus- p(b3 a1)=16/269. tration of Popper’s assertion that propensities, unlike forces, never occur in isolation, nor are From Table 1 it is apparent that whenever a 1 they inherent in an object. They always arise out happens, there is a good likelihood that b will 2 of a context, which almost invariably includes follow. Similarly, b is likely to result from a and 5 2 other propensities. Thus, Popper concludes that b from a . The situation is less clear as to what 3 4 the fall of an apple is a decidedly non-Newtonian ensues from a3, but b1 and b4 are more likely to occur than the rest. The events not mentioned event. The tendency for an apple to fall and where it might land depend, not just upon the weight of ([a1, b3], [a1, b4], etc.) result from what Popper terms ‘interference’. Presumably, if it were possi- the apple and the gravitational constant, but also ble to isolate phenomena, then each of the 269 upon biochemical conditions in the stem, the speed of the blowing wind, etc. times that a1 happens, it would be followed by b2. Similarly, if all phenomena could be strictly iso- One concludes that whenever propensities occur lated, the results might look something like those in propinquity, interferences and new propensities shown in Table 2. Under isolation, propensities are likely to arise. Conversely, one must add degenerate into mechanical-like forces, e.g. constraints in order to ‘organize’ the more indeterminate configuration represented in Table 1 p(b2 a1)=1. into the more mechanical-like system depicted in Table 1 Table 2. That is, the transition from the loose Frequency table of the hypothetical number of joint occur- configuration into its rigid counterpart is an ex- rences that four ‘causes’ (a … a ) were followed by five ‘ef- 1 4 ample of what is meant by ‘organization’ (Sky- fects’ (b … b ) 1 5 rms, 1980; Matsuno, 1986). However, conditional

b1 b2 b3 b4 b5 Sum probabilities by themselves do not quantify propensities in any way that bears analogy with a 40 193 1611 9 269 1 Newtonian laws. Popper was quite aware of this a 18 7 0 27 175 227 2 lack of connection, and so he noted simply that a3 104 0 38 118 3 263 a4 46161 20 50 241 ‘we need to develop a calculus of conditional probabilities.’ We will attempt such a calculus Sum166 206 215 176 237 1000 presently, but we turn our attention first to elabo- rating what sort of natural agency conceivably 134 R.E. Ulanowicz / BioSystems 50 (1999) 127–142 might be behind the transition from the behavior It is important to note two things about auto- inherent in Table 1 to that shown in Table 2. catalytic loops: (1) The members are not always What causes systems to grow and develop? linked in a rigid fashion, i.e. the action of A does not have to augment that of B at every instant— just most of the time. There is simply a propensity 6. Autocatalysis: a unitary agency for A to augment B; (2) The members of the cycles, being biotic elements and processes, are A clue to one agency behind growth and devel- capable of variation. Whereas autocatalysis in opment comes from considering what happens simple chemical systems can justifiably be re- when propensities act in close proximity to each garded as a mechanism (discrete stoichiometry of other. Any one process will either abet (+), the reactions and simple, unchangeable reactants diminish (−) or not affect (0) another. The sec- keep the process mostly mechanical in nature), as ond process in turn can have any of the same soon as chance and variation enter the scene, three effects upon the first. Out of the nine possi- autocatalysis begins to exhibit some behaviors ble combinations for reciprocal actions, one is that are decidedly nonmechanical in nature. very different from all the rest—mutualism (+ Autocatalysis among indeterminate processes , +). There is a growing consensus that some gives rise to a form of selection pressure that the form of positive feedback is responsible for much ensemble exerts upon its components. If, for ex- of the order and structure we perceive in living ample, some characteristic of process B should systems (Eigen, 1971; Haken, 1988; Kauffman, change in some chance way, and if that change 1995; DeAngelis et al., 1986). Sometimes the posi- should either increase the catalytic effect of B tive feedback is considered to take a particular upon C or make B more sensitive to catalysis by form, such as autopoeisis (Maturana and Varela, A, then the change in B will be rewarded and 1980) or autocatalysis (Ulanowicz, 1986, 1997). It retained. If, however, the change should decre- is this latter form of mutualism that we wish to ment B’s effect upon C or make B less sensitive to consider here. A, then B subsequently will receive less support Autocatalysis means any cyclical concatenation from A and the change is most likely to atrophy. of processes wherein each member has the Formally, such selection is unlike what normally propensity to accelerate the activity of the suc- is considered under the rubric of natural selection. ceeding link. Suppose, for example, that the ac- In particular, such a selection in autocatalytic tion of some process A has a propensity to systems engenders a centripetal movement of ma- augment a second process B. B, in turn, tends to terial and energy toward the loop itself. For any accelerate a third process C, which then promotes change in a constituent process that happens to the initial action A. The consequence of any pro- bring in more material or energy to abet that cess, when followed around the cycle, is self-stim- process will be rewarded. This selection applies to ulation. An ecological example of autocatalysis any and all elements of the loop, so that the cycle exists among the biotic associations formed itself becomes the focus of an inward migration of around aquatic plants belonging to the genus material and energy that is actively induced by the Utricularia (Ulanowicz, 1995b). The surface of the kinetic configuration. Utricularia plant supports the growth of a fast- The centripetal flow of resources represents a growing film of diatomaceous algae, generically siphoning of vital materials away from system called ‘periphyton’. This periphyton is consumed members that do not engage as effectively in by any number of water-borne heterotrophs re- autocatalysis. There will also be competition be- ferred to as ‘zooplankton’. The cycle is completed tween autocatalytic loops. The net result is that when the Utricularia captures and absorbs many the topology of the exchanges connecting system of the zooplankton in small bladders or utricules elements is gradually pruned of those members that are scattered along its feather-like leaves and that least effectively participate in autocatalysis. stems. As the same time, flows over the links that remain R.E. Ulanowicz / BioSystems 50 (1999) 127–142 135 will increase appreciably, due to the acceleration fully to an open universe, the effects of autocatal- that is inherent in autocatalysis. An example of ysis just described must be given concrete the growth and development of a network engen- mathematical expression. Toward this end, we dered by autocatalysis is depicted schematically in note how the terms ‘growth’ and ‘development’, Fig. 1. In Fig. 1(a), the system begins with many although their meanings overlap considerably, largely equiponderant connections. As autocataly- nonetheless emphasize different aspects of a uni- sis prunes the system, however, some of the links tary process. ‘Growth’ highlights the increase in shrink or disappear, and an overall greater level system size or activity, whereas ‘development’ lays of activity is channeled (constrained) along these more stress upon the increase in system pathways that most effectively engage in auto- organization. catalysis. (Fig. 1(b)). The extensive nature of growth is rather easy to quantify. To do so, we denote the magnitude of any transfer of material or energy from any donor

7. Quantifying growth and development (prey) i to its receptor (predator) j by Tij. Then one measure of total system activity is the sum of It is paramount among the advantages of New- all such exchanges, a quantity referred to in eco- tonian science that it is strictly quantitative. If nomic theory as the ‘total system throughput’, T. Newtonian dynamics are to be extended success- % % T= Tij i j

If reckoning the ‘size’ of a system by its level of activity seems at ﬁrst a bit strange, one should recall that such is common practice in economic theory, where the size of a country’s economy is gauged by its ‘gross domestic product’. Quantifying the intensive process of development is somewhat more complicated. The object here is to quantify the transition from a very loosely coupled, highly indeterminate collection of exchanges to one in which exchanges are more constrained along the most efﬁcient pathways. We begin, as did Boltzmann, 1872, who anticipated information theory by quantifying the indetermi-

nacy, hj, of category j,

hj =−k log p(Bj),

where p(Bj) is the marginal probability that event

Bj will happen, and k is a scalar constant. Roughly speaking, hj is correlated with how surprised the observer will be when Bj occurs. If Bj is almost certain to happen, p(Bj) will be a fraction Fig. 1. Schematic representation of the major effects that near 1, and hj will be quite small. Conversely, if Bj autocatalysis exerts upon a system: (a) Original system happens only rarely, p(B ) will be a fraction very conﬁguration with numerous equiponderant interactions; (b) j Same system after autocatalysis has pruned some interactions, near zero, and hj will become a large positive strengthened others, and increased the overall level of system number. In the latter instance, the observer is very activity (indicated by the thickening of the arrows). surprised to encounter Bj. 136 R.E. Ulanowicz / BioSystems 50 (1999) 127–142

Constraint removes indeterminacy. Therefore, terms of measurable quantities. If we focus upon the indeterminacy of a system with constraints trophic exchanges, a convenient interpretation of should be less than what it would be in uncon- Ai is ‘a quantum of medium leaves compartment strained circumstances. Suppose, for example, i’ and of Bj, ‘a quantum enters compartment j’. that an a priori event Ai exerts some constraint The Tij may be regarded as entries in a square upon whether or not Bj subsequently occurs. The events matrix, similar to Tables 1 and 2. The joint probability that Bj will happen in the wake of Ai probabilities can be estimated by the quotients is by definition the conditional probability Tij/T, and the marginal probabilities become the p(Bj Ai), so that the (presumably smaller) inde- normalized sums of the rows and columns terminacy of Bj under the influence of Ai (call it % h*),j will be measured by the Boltzmann formula p(Ai) jTij /T as and h* k log p(B A ) j =− j i % It follows that one may use the decrease in p(Bj) iTij /T indeterminacy, hj −h*,j as one measure of the intensity of the constraint that Ai exerts upon Bj. In terms of the measurable exchanges, the esti- Call this constraint hij, where mated average mutual constraint takes the form h h h* [ k log p(B )] [ k log p(B A )] ij = j − j = − j − − j i < = T T A=k% % (T /T) log ij . =k log[p(Bj Ai)/p(Bj)]. i j ij % T % T We note here for future reference that the con- k ik l lj straint that Ai exerts upon Bj is formally equal to (Note: In estimating probabilities by palpable the constraint that Bj exerts on Ai. Using Bayes’ Theorem, we see that flows, one avoids the criticism leveled against Popper’s propensities that one cannot infer cause hij =k log[p(Bj Ai)/p(Bj)] from probability. At a minimum, there will always exist a material cause linking i to j.) =k log[p(B , A )/p(A )p(B )] j i i j That A indeed captures the extent of organiza-

=k log[p(Ai Bj)/p(Ai)]=hij tion created by autocatalysis can be see from the example in Fig. 2. In Fig. 2(a), there is equiproba- Hence, one may speak of the mutual constraint bility that a quantum will find itself in the next that Ai and Bj exert on each other. time step in any of the four compartments. Little One may use this measure of constraint be- is constraining where medium may flow. The av- tween any arbitrary pair of events Ai and Bj to erage mutual constraint in this kinetic configura- calculate the amount of constraint inherent in the tion is appropriately zero. One infers that some system as a whole: one simply weights the mutual constraints are operating in Fig. 2(b), because constraint of each pair of events by the associated medium that leaves any compartment can flow to joint probability, p(Ai, Bj) that the two will co-oc- only two other locations. These constraints regis- cur and then sums over all possible pairs. This ter as k units of A. Finally, Fig. 2(c) is maximally yields the expression for the average mutual con- constrained. Medium leaving a compartment can straint A,as flow to one and only one other node. p(A , B ) n The reader may be puzzled as to why we con- A=k% % p(A , B ) log i j . i j i j p(A )p(B ) tinue to measure constraint in units of k. The i j conventional practice in information theory is to In order to apply A to evaluate constraint in designate the base to be used in calculating the ecosystems, it remains to estimate p(Ai, Bj)in logarithms (usually 2, e or 10) and set the value of R.E. Ulanowicz / BioSystems 50 (1999) 127–142 137

tributes that were observed to change during the course of ecological succession. His list of 24 properties can be subgrouped as pertaining to speciation, specialization, internalization or cy- cling—all of which tend to increase during system development. However, increases in these same four features of network conﬁgurations lead, ce- teris paribus, to increases in ascendency. Whence, Odum’s phenomenology can be quantiﬁed and condensed into the following principle:

In the absence of major perturbations, ecosystems exhibit a propensity towards conﬁgurations of ever-greater network ascendency.

The reader may correctly object that real ecosystems are never free of perturbations, and Fig. 2. (a) The most equivocal distribution of 96 units of under many natural conditions a rise in systems transfer among four system components; (b) A more con- ascendancy hardly even seems probable. That is strained distribution of the same total flow; (c) The maximally constrained pattern of 96 units of transfer involving all four because ascendancy tells only half of the story. A components. complementary narrative that quantifies the free- dom and indeterminacy of a given network can be formulated with the help of other variables from information theory in terms of what has been k=1. The units of A would then appear as ‘bits’, called the systems ‘overhead’. Components of the ‘napiers’ or ‘hartleys’, respectively. The problem system overhead play very important roles in the with this convention is that the calculated value evolution and sustainability of ecosystems, but conveys no indication as to the physical size of the elaboration on this topic would only distract from system. The goal here, however, is to capture both the search here for generalized Newtonian images. the extensive and intensive consequences of auto- Those interested in the persistence of ecosystems catalysis in a single measure. One convenient way are encouraged to read about the significance of of incorporating size is to give physical dimen- adaptability in ecosystems (Conrad, 1983) and sions to k (Tribus and McIrvine, 1971), i.e. we set about the importance of overhead (Ulanowicz k=T, and the dimensions of A will contain the and Norden, 1990; Ulanowicz, 1986, 1997). units used to measure the exchanges. For example, if the transfers in Fig. 2 had been measured as g/m2/d, and the base of the logarithm was 2, then the values of A would be expressed in the units 8. Propensities as generalized forces g-bits/m2/d. To signify that the scaled measure is now qual- Returning to the notion of propensity, the itatively different, we choose to rename A. Ac- reader may recall how propensity was explicitly cordingly, it will be called the system ‘ascendency’ folded into the definition of autocatalysis. We (Ulanowicz, 1980). It measures both the size and now ask whether it is possible to extract an ex- the organizational status of the network of expression for propensities from the resulting for- changes that occur in an ecosystem. In an attempt mulae for ascendency? As a first step in this to characterize what it means for an ecosystem to search, it is helpful to rewrite the last formula develop, Odum (1969) catalogued ecosystem at- with T substituted for k: 138 R.E. Ulanowicz / BioSystems 50 (1999) 127–142 < = be impossible to identify. Nonetheless, there re- T T mains great appeal in the notion that the commu- A k% % T log ij = i j ij nity power function is a significant indicator of % % kTik lTlj overall system status. As was noted, ascendency has the form of a power function (James Kay, The reader should note in this last formula that personal communication). In fact, if the medium the ascendency is the sum of exactly m terms, used to calculate the ascendency is energy, the where m is the number of individual transfers, Tij. index takes on the dimensions of ‘power-bits’. All That is, to calculate A one multiplies each flow, of which suggests that the logarithmic factors in

Tij, by a corresponding logarithmic factor and the formula for ascendency may stand as formal sums over m such products. analogs to the thermodynamic forces. However, To anyone with a passing familiarity of irre- Popper has criticized the concept of ‘force’ as too versible thermodynamics, the procedure just de- narrow in scope. This leads us to speculate that scribed should be very familiar. It is exactly how the logarithmic factors represent the ‘generalized one calculates the total dissipation in an ensemble forces’, i.e. the ‘propensities’ conjugate to their of processes. For, very near to thermodynamic respective flows. equilibrium, the theory of irreversible thermody- Popper, 1990 appealed for the development of namics postulates that, for each observable pro- ‘a calculus of conditional probabilities’. We note cess or flow, one may identify a conjugate here that it is conditional probabilities, not mar- ‘thermodynamic force’. For example, mass diffu- ginal or unconditional probabilities, that are most sion is assumed to flow ‘downhill’ along any germane to the meaning of information (Tribus spatial gradient in the chemical potential of the and McIrvine, 1971). Hence, I wish to suggest medium in question. Similarly, thermal conduc- that information theory already satisfies Popper’s tion flows down a gradient in temperature of the desiderata for a calculus of conditional probabili- conducting medium, electrical current follows a ties (Ulanowicz, 1996). Accordingly, we may cal- gradient in voltage, chemical reaction occurs in culate the propensity pij, for flow from i to j, response to a difference in Gibbs free energy, etc. according to the formula It is assumed that these ‘forces’ all can be cast in appropriate dimensions such that the product of < = T T each flow times its conjugate ‘force’ yields a p log ij . ij = product with the dimensions of power (Onsager, % % kTik lTlj 1931). The sum of all such products pertaining to each process in a system yields what is known as It is worth noting that deriving an explicit the power (or dissipation) function, which is be- formula for Popper’s propensities renders his con- lieved to characterize the overall dynamics of the cept fully operational whenever all the Tij’s in a system. Prigogine (1945), for example, has hy- system are known. For example, Ulanowicz and pothesized that, very near to equilibrium, any Baird, 1999 estimated the transfers of carbon, ensemble of processes takes on the particular nitrogen and phosphorus among the major taxa configuration that results in the smallest value of of the ecosystem inhabiting the mesohaline reach the dissipation function. of Chesapeake Bay and utilized the resulting Unfortunately, there are problems with the for- propensities to identify those exchanges that most mulation of thermodynamic forces (Ulanowicz, influence the nutrient dynamics of that 1997). For one, the forces are defined opposite to community. Newton’s original conception. Because they relate to near equilibrium conditions, they pertain more to the first law conditions of non-intervention. In 9. In the image of Newton far-from-equilibrium systems, such as biological entities, the ‘forces’ remain elusive and even may This discovery of a convenient thermodynami- R.E. Ulanowicz / BioSystems 50 (1999) 127–142 139 cal analogy opens one’s eyes to still further Newton’s second law states that, in response to analogs. We recall that the measure of constraint an external interference, the system will follow the which a donor (Ai) exerts on its receptor (Bj)is disturbance, i.e. the response is positive. In the equal in value to that which the receptor imposes biological realm, after any immediate negative upon the donor. That is, Newton’s third law impact that a disturbance might have on an or- (symmetry) has its counterpart in our probabilis- ganic system, the system response looks at first tic reformulation. (Note: the propensities pij them- glance qualitatively indistinguishable from how it selves are not symmetric with respect to donor behaves when the ensemble is unperturbed, i.e. and recipient, any more than the force with which there is again a propensity for the system to one boxer striking a second is obliged by New- increase in ascendency. But closer scrutiny of the ton’s third law to equal the force with which the usual behaviors in perturbed and unperturbed second might simultaneously strike the first.) situations reveals that the dynamics in each case Still further analogies appear. Reconsideration differ significantly. of the formula for A in light of the new identifica- The scales of the responses with and without tion of propensities reveals that the community intervention usually differ markedly. What hap- ascendency takes the form of a flow-weighted pens after intervention (the analog to the second average propensity for the system as a whole. law) is likely to occur rapidly and in such a way Since A is itself a propensity, Odum’s phe- that the interference is absorbed locally and with nomenological principle can be restated as, minimal dissipation (Lubashevskii and Gafiychuk, 1995). Quite often, the operative control is via localized negative feedback. This response has In the absence of major perturbations, there been labeled ‘self-regulation’ (Gafiychuk and is a propensity for the flow-weighted ecosystem Ulanowicz, 1996) and is depicted as a Venn dia- propensity to increase in value. gram in Fig. 3. The system A had adapted to some extent to its environment, B, as represented The ‘propensity of a propensity’ relationship by the intersection between A and B. Suddenly, appearing in the restated principle is reminiscent the environment changes from B to B%, and some of Newton’s second law, which deals with the structural constraint is irretrievably lost, as indi- time rate of change of momentum. Momentum, in cated by the dotted region on the diagram. Adap- its turn, is a time rate of change of position, i.e. tation ensues, and ascendancy increases, however, the second law treats the rate-of-change of a by progressively greater overlap with the new rate-of-change (Ulanowicz, 1998). If at first this environment, as indicated by the striped area on resemblance should seem a bit far fetched, then Fig. 3. one should pause to consider the contexts of Newton’s first and second laws. As mentioned earlier, the first law tells what happens in the absence of external influence—the rate of change of the rate of change is identically zero. With mechanical systems, no input means no change. This differs from ecological phenomenology, which indicates that, in the absence of external disturbance, the propensity of the system propensity assumes a positive value. An organic system Fig. 3. Venn diagram depicting the process of self-regulation. can exhibit change from within. This is a radical System A had accommodated to environment B to an extent departure from Darwin, who, as intellectual indicated by the overlap of the two circles. Intervention brings about a changed environment, represented by B%. Some modes grandson of Newton, took great pains to locate of accommodation are irretrievably lost (dotted area), whereas selection pressure outside the developing system regulation proceeds by expanding the stippled area (and the (Depew and Weber, 1994). ascendency) as much as feasible. 140 R.E. Ulanowicz / BioSystems 50 (1999) 127–142

exposition, I propose below a set of rough counterparts to the five elements of the Newtonian metaphysic elaborated earlier (albeit in a different order): 1. Ecosystems are ontically open: Indetermina- cies, or ‘genetic events’ can arise anytime, at Fig. 4. Venn diagram depicting the process of semi-au- any scale. Mechanical, or efficient causes usu- tonomous development: (a) System A and environment B at a ally originate at scales inferior to that of ob- given time; (b) System at later time has developed to harmo- servation and propagate upwards; formal nize more with its environment, as indicated by increased overlap between A and B. agencies appear at the focal level; and final causes arise at higher levels and propagate A system in relative isolation (all living systems downward (Salthe, 1985; Ulanowicz, 1997). must remain open to some degree) will undergo 2. Ecosystems are contingent in nature: Biotic ‘development’ in a way that is qualitatively actions resemble propensities more than me- different from recovery from intervention. It will chanical forces. develop slowly over time and usually involve 3. The realm of ecological phenomena is granular positive feedbacks that span most of the system. (Allen and Starr, 1982) in the hierarchical Usually, development is accompanied by sense of the word: An event at any one scale progressively more overall dissipation (Ulanowicz can affect matters at other scales only with a and Hannon, 1987). In terms of Venn diagrams, magnitude that diminishes as the scale of the this slower transition resembles that shown in Fig. effect becomes farther removed from that of 4. the eliciting event. It follows that genetic events at lower levels do not propagate unim- peded up the hierarchical levels, because they 10. An ecological metaphysic become subject to constraint and selection by formal and final agencies extant at higher Just as Schroedinger used the form of Newton’s levels. second law as a point from which to embark upon 4. Ecosystems are historical entities: Genetic an entirely unmechanical view of the sub-micro- events often constitute discontinuities in the scopic world, we have just discerned formal con- behaviors of systems in which they occur. As nections between the laws that Newton himself such, they engender irreversibility and degrade exposited and at least one version of contempo- predictability. The effects of genetic events are rary ecosystems science. It does not follow, how- retained in the material and kinetic forms that ever, that the assumptions that were added by result from adaptation. The interactions of later practitioners of Newtonian science translate propensities in organic systems create a more as well into the biological realm, Darwin and his likely direction or telos in which the system successors notwithstanding. If one wishes to un- develops. derstand the development of biological systems in 5. Ecosystems are organic: Genetic events often full hierarchical detail and is not content with the appear simultaneously at several levels. abrupt juxtaposition of pure stochasticity and de- Propensities never exist in isolation from their terminism found in neo-Darwinism (Ulanowicz, context, which includes other propensities. 1997), then one must abandon the assumptions of Propensities in communication grow progres- closure, determinism, universality, reversibility sively more interdependent, so that the obser- and atomism and replace them by the ideas of vation of any part in isolation (if possible) openness, contingency, granularity, historicity and reveals ever less about its behavior when act- organicism, respectively. That is, one must formu- ing within the ensemble. late a new metaphysic for how to view living None of the foregoing statements is entirely phenomena. By way of summarizing the foregoing new to ecology. Most have appeared in the litera- R.E. 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