## Agencies Imparting Directionality

It remains to identify the agency behind any directionality that ecosystems might exhibit. Our natural inclination is such a search would be to look for agencies that conform to our notions of "lawful" behaviors. But such a scope could be too narrow. It would behoove us to broaden our perspective and attempt to generalize the notion of "law" and consider as well the category of "process". A process resembles a law in that it consists of rulelike behaviors, but whereas a law always has a determinate outcome, a process is guided more by its interactions with aleatoric events.

The indeterminacy of such action is perhaps well illustrated by the artificial example of Polya's Urn (Eggenberger and Polya, 1923). Polya's process consists of picking from an urn containing red and blue balls. The process starts with one red ball and one blue ball. The urn is shaken and a ball is drawn at random. If it is a red ball, then the ball is returned to the urn with yet another red ball; if a blue ball is picked, then it likewise is returned with another blue ball. The question then arises whether the ratio of red to blue balls approaches a fixed value. It is rather easy to demonstrate that the law of large number takes over and that after a sufficient number of draws, the ratio changes only within bounds that progressively shrink as the process continues. Say the final ratio is 0.3879175. The second question that arises is whether that ratio is unique? If the urn is emptied and the process repeated, then will the ratio once again converge to 0.3879175? The answer is no. The second time it might converge to 0.81037572. It is rather easy to show in Monte-Carlo fashion that the final ratios of many successive runs of Polya's process are uniformly distributed over the interval from 0 to 1.

One sees in Polya's Urn how direction can evolve out of a stochastic background. The key within the process is the feedback that is occurring between the history of draws and the current one. Hence, in looking for the origins of directionality in real systems, we turn to consider feedback within living systems. Feedback, after all, has played a central role in much of what is known as the theory of "self-organization" (e.g. Eigen, 1971; Maturana and Varela, 1980; DeAngelis et al., 1986; Haken, 1988; Kauffman, 1995). Central to control and directionality in cybernetic systems is the concept of the causal loop. A causal loop, or circuit is any concatenation of causal connections whereby the last member of the pathway is a partial cause of the first. Primarily because of the ubiquity of material recycling in ecosystems, causal loops have long been recognized by ecologists (Hutchinson, 1948).

It was the late polymath, Gregory Bateson (1972) who observed "a causal circuit will cause a non-random response to a random event at that position in the circuit at which the random event occurred." But why is this so? To answer this last question, let us confine further discussion to a subset of causal circuits that are called autocatalytic (Ulanowicz, 1997). Henceforth, autocatalysis will be considered any manifestation of a positive feedback loop whereby the direct effect of every link on its downstream neighbor is positive. Without loss of generality, let us focus our attention on a serial, circular conjunction of three processesâ€”A, B, and C (Figure 4.2) Any increase in A is likely to induce a corresponding increase in B, which in turn elicits an increase in C, and whence back to A.1

A didactic example of autocatalysis in ecology is the community that builds around the aquatic macrophyte, Utricularia (Ulanowicz, 1995). All members of the genus Utricularia are carnivorous plants. Scattered along its feather-like stems and leaves are small bladders, called utricles (Figure 4.3a). Each utricle has a few hair-like triggers at its

Figure 4.2 Simple autocatalytic configuration of three species.

Figure 4.2 Simple autocatalytic configuration of three species.

Figure 4.3 The Utricularia system. (a) View of the macrophyte with detail of a utricle. (b) The three flow autocatalytic configuration of processes driving the Utricularia system.

'The emphasis in this chapter is on positive feedback and especially autocatalysis. It should be mentioned in passing that negative feedback also plays significant roles in complex ecosystem dynamics (Chapter 7), especially as an agency of regulation and control.

terminal end, which, when touched by a feeding zooplankter, opens the end of the bladder, and the animal is sucked into the utricle by a negative osmotic pressure that the plant had maintained inside the bladder. In nature the surface of Utricularia plants is always host to a film of algal growth known as periphyton. This periphyton in turn serves as food for any number of species of small zooplankton. The autocatalytic cycle is closed when the Utricularia captures and absorbs many of the zooplankton (Figure 4.3b).

In chemistry, where reactants are simple and fixed, autocatalysis behaves just like any other mechanism. As soon as one must contend with organic macromolecules and their ability to undergo small, incremental alterations, however, the game changes. With ecosystems we are dealing with open systems (see Chapter 2), so that whenever the action of any catalyst on its downstream member is affected by contingencies (rather than being obligatory), a number of decidedly non-mechanical behaviors can arise (Ulanowicz, 1997). For the sake of brevity, we discuss only a few:

Perhaps most importantly, autocatalysis is capable of exerting selection pressure on its own, ever-changing, malleable constituents. To see this, one considers a small spontaneous change in process B. If that change either makes B more sensitive to A or a more effective catalyst of C, then the transition will receive enhanced stimulus from A. In the Utricularia example, diatoms that have a higher P/B ratio and are more palatable to microheterotrophs would be favored as members of the periphyton community. Conversely, if the change in B makes it either less sensitive to the effects of A or a weaker catalyst of C, then that perturbation will likely receive diminished support from A. That is to say the response of this causal circuit is not entirely symmetric, and out of this asymmetry emerges a direction. This direction is not imparted or cued by any externality; its action resides wholly internal to the system. As one might expect from a causal circuit, the result is to a degree tautologousâ€”autocatalytic systems respond to random events over time in such a way as to increase the degree of autocatalysis. As alluded to above, such asymmetry has been recognized in physics since the mid-1960s, and it transcends the assumption of reversibility. It should be emphasized that this directionality, by virtue of its internal and transient nature cannot be considered teleological. There is no externally determined or pre-existing goal toward which the system strives. Direction arises purely out of immediate response by the internal system to a novel, random event impacting one of the autocatalytic members.

To see how another very important directionality can emerge in living systems, one notes in particular that any change in B is likely to involve a change in the amounts of material and energy that are required to sustain process B. As a corollary to selection pressure we immediately recognize the tendency to reward and support any changes that serve to bring ever more resources into B. Because this circumstance pertains to any and all members of the causal circuit, any autocatalytic cycle becomes the epi-center of a centripetal flow of resources toward which as many resources as possible will converge (Figure 4.4). That is, an autocatalytic loop defines itself as the focus of centripetal flows. One sees didactic example of such centripetality in coral reef communities, which by their considerable synergistic activities draw a richness of nutrients out of a desert-like and relatively inactive surrounding sea. Centripetality is obviously related to the more commonly recognized attribute of system growth (Chapter 6).

Centripetality

Figure 4.4 The centripetality of an autocatlytic system, drawing progressively more resources unto itself.