Other Concepts Of Control In Ecology And Engineering

Considerations of exotic species and their control relates to the broader topic of control in ecology and engineering. Exotic species are often said to cause problems because they have escaped from the natural processes that control or regulate their populations. Human managers of exotic species have attempted to reestablish this control but with uneven success. In this final section of the chapter, discussion of control is expanded because of its importance to ecological engineering in a general sense.

Historically, control in ecology has been discussed in many contexts and often with controversial positions. One of the earliest controversies involved the control or regulation of population sizes. One group led by David Lack (1954) believed in

FIGURE 7.9 Patterns of population growth. (A) Exponential growth. (B) Logistic growth.

density dependence in which the severity of mortality factors is correlated with population density (such as for mortality caused by disease, predators or parasites, and food shortage). Another group led by Andrewartha and Birch (1954) believed in density independence in which the severity of mortality is the same at all population densities (such as for mortality caused by extreme weather events). This is a critically important distinction because density dependence allows for a self-regulation mechanism within a population. Cole (1957) reviewed the subject in terms of the search for a "governor" or controlling influence on population size. He showed the governor as a term added to the population growth equation, which converts uncontrolled, exponential growth (Figure 7.9a) into controlled, logistic or limited growth (Figure 7.9b):

dN/dt = rN exponential growth equation (7.1)

where

N is the population size r is the reproductive rate and dN/dt = g(rN) logistic growth equation

where g is the governor

Cole explored various forms for the governor term, the simplest of which has evolved to be the carrying capacity term, which causes the population to be regulated by density dependence:

where K is the carrying capacity or the maximum size of the population that the environment can support the addition of this term (g) to the exponential growth equation causes population growth to stop and population numbers to level off when N = K (see Equation 3.4). Carrying capacity therefore is an important quality within this elementary theory of population ecology because it causes controlled growth of the logistic equation as opposed to the out-of-control growth of the exponential equation. Much argument occurred between members of the density dependence and density independence schools of thought from the 1950s onward and to some extent the controversy continues (Chitty, 1996). Reviews are given by Krebs (1995) and Tamarin (1978).

At the ecosystem scale, control has been considered to occur either due to resource limitations (i.e., bottom-up control) or due to harvesting by consumers (i.e., top-down control). Bottom-up control of food webs is determined by resources, specifically those resources that are required for primary productivity. This is the process whereby solar energy is transformed into the chemical energy of biomass and is at the base of most food webs (i.e., the bottom). A number of resources are required for primary productivity, such as water, carbon dioxide, and nutrients. Justus Liebig, a German agronomist, proposed his famous Law of the Minimum in the 1800s to describe how resources limit (i.e., control) primary productivity (E. P. Odum, 1971; see also the excerpts of Liebig's publications in Kormondy, 1965; and Pomeroy, 1974). Liebig's law states that the required resource in the least supply will limit production. Thus, resources that limit primary productivity are called limiting factors. The primary way to identify a limiting nutrient is with nutrient addition experiments. In this kind of experiment different nutrients are added to a system in controlled locations in order to test for increases in plant growth. Although traditionally it has been thought that only one factor at a time can limit primary production, there is a growing trend of examining how limiting factors are linked or dynamically related. Alfred Redfield was the first to consider this idea in his study of "The Biological Control of Chemical Factors in the Environment" (Redfield, 1958; see also Redfield et al., 1963). In particular, he studied the biogeochemical cycle of the photic zone of the open ocean and found that carbon, nitrogen, and phosphorus cycled in a constant proportion that was roughly equivalent to the ratio of these elements in the biomass of the plankton. This observation indicates that of these three elements, no single one limited production but rather they all simulta g = (K - N)/N

neously were limiting. The implication was that the plankton biota had coevolved with the ocean nutrient cycles so that the ratio of elements released by decomposition matched the ratio of elements taken up by primary production. This was judged to be a highly evolved state and the element ratio became known as the Redfield ratio. The coevolution of biota and macronutrient cycles was considered to be possible only in the open ocean where the variable geology of land masses have little influence on chemistry, but even here other micronutrients such as iron may limit primary production (see Chapter 9). H. T. Odum attempted to generalize Redfield's concept with the introduction of the "ecomix" which he defined as "the particular ratio of elemental substances being synthesized into biomass and subsequently released and recirculated" (H. T. Odum, 1960). He suggested that

Although shortage or excessive accumulation of any one element will stop or retard the system, there is a self-selection for compatibility of the photosynthesis and the regenerative respiration. The characteristic ratio of elements which tends to be stabilized in the average mix of the system is the chemical ecomix (H. T. Odum, 1970)

Although Odum's ecomix idea was not picked up by other ecologists, more recently a whole new area of study on ecological stoichiometry has arisen based on Redfield's nutrient ratio approach to understanding bottom-up control in ecosystems (Daufresne and Loreau, 2001; Elser et al., 1996; Hessen, 1997; Lampert, 1999; Lockaby and Conner, 1999; Sterner, 1995).

The top-down control of food webs by consumers has received a great deal of attention in ecology with review articles of field and empirical studies (Chew, 1974; Huntly, 1995; Kitchell et al., 1979; Naiman, 1988; Owen and Wiegert, 1976; Petrusewicz and Grodzinski, 1975; Zlotin and Khodashova, 1980) and with theoretical work (Lee and Inman, 1975; O'Neill, 1976). Consumers make up many categories of organisms including carnivores, herbivores, detritivores, and omnivores along with parasites and even diseases. In each of these categories the consumer consumes different things. When the thing being consumed is living, then the predator-prey theory applies. All predator-prey relationships have the potential for control of prey by predators (see experiments by Gause in Chapter 4), but the strength of the relationship varies significantly. The most dramatic examples are keystone predators which exert strong control over multispecies assemblages (i.e., from the top of the food web). The keystone species concept was introduced by Robert Paine based on his experimental studies of a rocky intertidal food web in Mukkaw Bay, WA. This system is composed of a diverse assemblage of macroscopic attached algae, mussels, barnacles, and a large predatory starfish (Pisaster ochraceus). Paine (1966) experimentally removed the starfish from a section of the intertidal zone and compared the dynamics with a control section that contained the starfish. The removal of the predator caused a succession of species to occur with eventual competitive exclusion of other species by the mussel Mytilus. This result demonstrated that the predator had diversified the system by regulating the population of an otherwise dominant competitor. Any kind of species can be a keystone species and several are noted throughout this text. The primary way to identify a keystone species is with species removal experiments, as Paine conducted in the rocky inter-

tidal zone. Paine's work is a benchmark in ecology which led to a generation of experimental studies and to the important keystone species concept (Mills et al., 1993; Paine, 1995; Power et al., 1996).

Bottom-up and top-down control are combined in the trophic cascade model (Carpenter et al., 1985; Carpenter and Kitchell, 1993) which uses a food chain approach to describe ecosystem control. These authors studied lake ecosystems and showed how productivity is controlled both by nutrient concentration in the lake water and its effect on phytoplankton, which are at the base of the food chain, and by the effects of the top predator fish species, which are at the top of the food chain. Thus, control can "cascade" either up or down the food chain. One generalization of this model suggests that in certain food chains the direction of control depends on the number of links (Fretwell, 1987) in such a way that top carnivores enhance primary productivity by reducing the intensity of herbivory in odd-numbered chains, while top carnivores reduce primary productivity by enhancing the intensity of herbivory in even-numbered chains. This generalization would be a useful design rule if ecological engineers were able to construct food chains of any significant length. Overall, the trophic cascade is an interesting theory which is much discussed in the literature (Hunter and Price, 1992; Perrson et al., 1996; Strong, 1992).

Another approach to control in ecology has been the application of cybernetics concepts to the ecosystem. Cybernetics as a discipline was first articulated by Norbert Wiener (1948) to cover examples of "control and communication in the animal and the machine." At the heart of cybernetics is an understanding of feedback pathways between components of a system that influence (i.e., control) its behavior. From the start, as envisioned by Wiener, cybernetics involved study of both machine controls developed by human designers and control systems in organisms that have evolved through natural selection, especially in terms of physiology. It was logical for ecologists to apply cybernetics because there seem to be many examples of self-regulation in nature.

Ramon Margalef (1968) was the first ecologist to embrace cybernetics as a foundation for describing control in ecosystems. He set out his ideas in his classic book whose first chapter had the title "The Ecosystem as a Cybernetic System." This chapter is filled with ideas of feedbacks, organization, diversity, stability, and energetics which are presented as general theory in Margalef's unique writing style. In his view ecosystems are composed of many feedback circuits mediated by species which collectively result in macroscopic behavior. E. P. Odum (1971) also added cybernetics to the introductory chapter on ecosystems in the third edition of his text. He uses the example of the heating of a room with a thermostat-controlled furnace to illustrate feedback and control concepts, but he also discusses several more complex ecological applications which contrast with the thermostat-heating system. For example, he states:

... control mechanisms operating at the ecosystem level include those which regulate the storage and release of nutrients and the production and decomposition of organic substances. The interplay of material cycles and energy flows in large ecosystems generates a self-correcting homeostasis with no control or set-point required.

The concept of homeostasis mentioned in E. P. Odum's quote has come to be important in cybernetics and has been applied to ecology. In a homeostatic system adjustments take place in components so that some property of the system remains constant despite changes in the surrounding environment. For example, a thermostat maintains room temperature by adjusting the amount of fuel used in heating. Adjustments occur because of feedback about the system property that is being homeo-statically controlled. The mechanisms of adjustment in ecology are diverse. Wynne-Edwards (1970) spoke of the "homeostatic machinery" involved in population regulation as including "changes in mutual tolerance or aggression, in territory size, the amount of emigration, the age of sexual maturation, changes in fertility and reproductive success, in cannibalism and other socially-promoted forms of mortality both of young stages and adults." Hardin (1993) spoke of a "demostat," using the thermostat as an analogy, for similar mechanisms. Levins (1998) listed systems-level factors of homeostasis including "the redundancy of the set of variables (if they are species, niche overlap expresses this property), self-damping of the variable, positive and negative feedbacks among variables, long and short pathways in the system, the connectivity of the network, time delays and sinks, the heterogeneity of flows and interactions and the 'shapes' of functional relationships." However, one problem with applying the concept of homeostasis to ecosystems is identifying the system property that is maintained at a constant level. This relates to the ecological notions of stability mentioned earlier (see Chapter 4). Stability has many meanings and there is no consensus among ecologists about which aspects are most important. Species composition and community structure of an ecosystem are not good candidates because species can move across landscapes and change relative abundances through time. More likely, species are the components that adjust within the homeostatic process. A microcosm experiment conducted by Copeland (1965) indicated homeostasis of ecosystem metabolism. He moved a turtle grass (Thalassia testudinum) microcosm that was at steady-state with a light regime of 1,500-ft candles to a new light regime of 230-ft candles. Under the lower light environment the turtle grass died back and was replaced by blue-green algae as the dominant primary producer. Ecosystem metabolism declined initially after the drop in light intensity, but it returned to the previous level within 3 months. This is a remarkable experiment that ought to be repeated. Schultz (1964, 1969) provides another example concerning the Arctic tundra as a homeostatic system. A feedback model of homeostasis is given which includes levels of the lemming population, plant biomass and nutrient content, and soil temperature. The overall system oscillates but the composition remains stable.

H. T. Odum (1971) developed ideas of cybernetics and homeostasis by differentiating between power and control circuits in ecosystems, as noted in the following quote:

In very highly organized natural systems the flows of power are much divided among the species circuits, but they can be roughly separated into power circuits and control circuits. Thus, if oak trees process 50 percent of the power budget of a forest system, they constitute a power circuit. The squirrels of that forest may be processing much less than 1 percent of the forest budget. Their procedures for gathering and planting acorns may, however, serve as a control on the patterns of the oaks. Thus, we must distinguish between the power flow in a circuit and the power being controlled by a circuit. ... Power circuits must be large and sluggish, whereas control circuits with small energies are easily insulated and can perform delicate operations and provide a directive influence on the power circuits. These principles are the same in electrical power distribution, in the forest, or in the complex industrial systems of man.

These generalizations were applied to a specific example of the grazing control system in the Puerto Rican rainforest study (H. T. Odum and Ruiz-Reyes, 1970). He further illustrated his ideas on control in terms of the maximum power theory. In this context work of consumer organisms in the forest increases total system energy flow through their dispersed control actions. In the following quote (H. T. Odum, 1978b), he suggests a demonstration of this aggregate control action by comparing a forest plantation, which lacks most of the complex consumer diversity, with the rain forest that grows side by side in the Luquillo Mountains of eastern Puerto Rico:

A tropical forest plantation of Cadam trees in Puerto Rico has a productive net yield of photosynthesis 20g/m2/day (80 Calories/m2/day wood equivalents) as a monoculture without many consumers. In contrast, a fully developed ecosystem nearby (with fully developed consumers feeding back in an organized manner) showed an increase in this basic primary production. An increase of 7 g/m2/day (28 Calories/m2/day), most of which was used by the consumers without any net energy, was measured. The system with consumers contained more energy flow (power) than the same system without consumers. Most of the web of producer-consumer interaction was required to maximize power.

In addition to the more or less classic approaches to cybernetics in ecology listed above, many other studies are noteworthy. Knight (1983) developed H. T. Odum's consumer-control hypothesis and made experimental tests with microcosms in Silver Springs, FL. He concluded that the stable population levels of aquatic organisms seen by tourists through the famous glass bottom boats of the springs were maintained by "a harmonious system of feedback controls." Mattson and Addy (1975) provided a review of insect herbivory with many examples of similarities between insects and cybernetic regulators. Further examples of cybernetics in ecology are Montague's (1980) model of feedback actions of fiddler crabs in temperate salt-marshes, Gutierrez and Fey's (1980) discussion of feedback and ecosystem succession, and the review of DeAngelis et al. (1986).

Other ecologists have criticized the application of cybernetics. Perhaps the most vehement has been Lawrence Slobodkin (1993) who provided the quote below in a review of a book on the Gaia hypothesis:

The idea of feedback and cybernetics was born in engineering and imported into environmental sciences and biology so long ago that there is a tendency to forget that organisms have not been constructed by, or even for, engineers. Biological systems may indeed be represented by diagrams that look like those of a cybernetic engineer, but they do not have the properties of engineered cybernetic systems.

For example, compare a temperature control system for a living room and the processes that regulate the number of animals in a population. The thermostat-furnace-air con ditioner system is designed by an engineer with the express purpose of keeping a comfortable temperature for humans despite ambient changes outside the living room. It has an engineered purpose. Population size, on the other hand, is an epiphenomenal consequence of the environment and the properties of the organisms in the environment. The properties of the organisms are an outcome of an evolutionary process in which absolute population size has no particularly important meaning except for the trivial stipulation that the organisms' ancestors did not die before they reproduced. Therefore, although population regulation may appear to be comparable to an engineered cybernetic system, the appearance is deceiving. But the deceptive appearance of effective feedback in nature extends well beyond the scale of a single population.

It was already clear 30 years ago that some of the processes carried out by organisms on Earth tended to negate deviations from existing properties that are of importance for organisms. The carbon cycle, for example, is portrayed in elementary biology texts as a set of boxes representing plants, animals, and microbes and little else. The boxes are connected by arrows representing flow. They are wired together as if they were a diagram of a negative feedback system, maintaining constancy of atmospheric oxygen and carbon dioxide. ... Despite the cybernetic appearance of the block-and-arrow diagrams, there is no guarantee that the carbon cycle actually is an effective feedback system, particularly in the context of anthropogenic returns of buried carbon to the atmosphere . .

Earlier in his career Slobodkin (1964, 1968) was a bit more generous towards cybernetics and he suggested that the optimal strategy for species was to maximize homeostatic ability. The context for this suggestion was a model of evolution as an "existential game" that he developed. Slobodkin contended that the only measure of success of a species playing the existential game of evolution was persistence, which was proportional to homeostatic ability. Conrad's (1995) model of the ecosystem as an "existential computer" is a systems-level expression of this same kind of behavior.

Other critiques of cybernetics in ecology are given by O'Neill et al. (1986) and DeAngelis (1995). An interesting dialogue involved a critique by Engelberg and Boyarsky (1979) that elicited a number of rebuttals (Jordan, 1981; Knight and Swaney, 1981; McNaughton and Coughenour, 1981; Patten and Odum, 1981). These arguments involved much semantics with the positive result of recording a number of opinions on the cybernetic nature of ecosystems.

Unlike ecology, control theory in engineering is noncontroversial and straightforward. Control theory is a technical field common to all engineering disciplines. Traditionally, controls were small machines (sometimes called servo-mechanisms) which used feedback information to regulate larger processes. These devices date back to nearly 5000 bc in Egypt with many applications (Mayr, 1970). One old version was called a "governor," because it governed the rate at which a larger machine (such as a steam engine) operated. As noted earlier in this section, Cole (1957) used the "governor" as a metaphor for the regulatory mechanism in population dynamics. Perhaps the most widely known example of a mechanical control is the thermostat, which is part of the heating system of all modern homes and in many types of industries. Cornelius Drebbel, a Dutch engineer, is credited with inventing the thermostat in the 17th century for controlling temperature in his alchemy exper-

FIGURE 7.10 Details of a typical thermostat. (From Sutton, D. B. and N. P. Harmon, 1973. Ecology: Selected Concepts. John Wiley & Sons, New York. With permission.)

iments (Angrist, 1973). The modern thermostat is a device which senses temperature with a bimetallic strip and opens or closes an electrical circuit to a fuel source with reference to a set-point temperature (Figure 7.10). It is therefore a small engineered device that processes information (i.e., about temperature) and controls the operation of a larger system. Figure 7.11 shows an engineering block diagram of a temperature control system along with a translation in the energy circuit language. In the block diagram the thermostat is shown as the comparator unit while in the energy circuit diagram it is shown with the switch symbol. Basically, the thermostat compares the temperature in the building against the set-point value and turns on the furnace if the building temperature is below the set-point or turns off the furnace if the building temperature is above the set-point. This operation stabilizes the entire system by maintaining a constant indoor temperature even if the outdoor temperature changes dramatically.

Mathematical techniques describing control in engineering have developed especially within the last 100 years to provide a quantitative basis for design. These techniques are standardized and described in a number of textbooks, variously titled Control Engineering (Murphy, 1959), Feedback Control System Analysis and Synthesis (D'Azzo and Houpis, 1960), etc. Analysis is performed on sets of equations that describe the system, and designs are modified to ensure stable performance. Frequency response is one example where system performance is evaluated against variations in input conditions, followed by design modification. These kinds of techniques along with others represent the powerful tools that have allowed engineers to design, build, and operate the amazing array of technologies characteristic of modern society.

Engineering control theory has been successfully applied in physiology (Grod-ins, 1963; Milhorn, 1966; Milsum, 1966; Toates, 1975). This is not surprising since there are many examples of self-regulation of physiological processes where steady-

Comparator Unit

Comparator Unit

Information Feedback

Information Feedback

FIGURE 7.11 Comparison of an engineering block diagram of a thermostat controlled system with a translation in the energy circuit language. The thermostat is the comparator unit in the block diagram above and the switch symbol in the energy diagram below. Note the role of feedback in each model.

state conditions are maintained, as in body temperature, breathing rates, etc. (Lan-gley, 1965, 1973). In fact, Walter Cannon, a physiologist and medical doctor, coined the important cybernetic term homeostasis to describe these systems in his classic work in 1932. However, the application of engineering control theory to ecology has not been nearly as successful. Some attempts were made in the 1960s and 1970s (Lowes and Blackwell, 1974; Mulholland and Sims, 1976), but the applications did not lead to advancements in ecological understanding. Clearly, ecological circuits do not behave very much like human-designed circuits such as the thermostat-furnace system. For example, on the one hand, if the thermostat is removed from the system in Figure 7.11, as Paine did in his experiment of the keystone predator of the rocky intertidal zone, then the heating system becomes unstable and basically stops functioning. On the other hand, removal of the keystone species in Paine's ecosystem changed the system dramatically but it continued to function. One hypothesis to explain the difference between ecological and engineering control systems may be that ecosystems are more complex. Hill and Wiegert (1980) indicate the difference in control mechanisms between ecosystems and human-designed systems in the following quote:

Applying feedback control theory to engineered system is often much more successful than applying it to ecosystems. One reason is that engineered systems and control theory are eminently compatible because they have coevolved.

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