If ecology is to be discussed at the ecosystem level, for reasons, how can this complex and formidable system level be dealt with? We begin by describing simplified versions that encompass only the most important or basic, properties and functions. Because, in science, simplified versions of the real world are called models, it is appropriate now to introduce this concept.
Ecological model (by definition) is a formulation that mimics a real-world phenomenon and by which predictions can be made. In their simplest form, models may be verbal or graphic (informal). Ultimately, however, models must be statistical and mathematical (formal) if their quantitative predictions are to be reasonably good.
For example, a mathematical formulation that mimics numerical changes in a population of insects and that predicts the numbers in the population at some time would be considered a biologically useful model. If the insect population in question is a pest species, the model could have an economically important application.
Computer-simulated models permit one to predict probable outcomes as parameters in the model are changed, as new parameters are added, or as old ones are removed. Thus, a mathematical formulation can often be “tuned” or refined by computer operations to improve the “fit” to the real-world phenomenon. Above all, models summarize what is understood about the situation modeled and thereby delimit aspects needing new or better data, or new principles.
When a model does not work—when it poorly mimics the real world—computer operations can often provide clues to the refinements or changes needed. Once a model proves to be a useful mimic, opportunities for experimentation are unlimited, because one can introduce new factors or perturbations and see how they would affect the system. Even when a model inadequately mimics the real world, which is often the case in its early stages of development, it remains an exceedingly useful teaching and research tool if it reveals key components and interactions that merit special attention.
Contrary to the feeling of many who are skeptical about modeling the complexity of nature, information about only a relatively small number of variables is often a sufficient basis for effective models because key factors, or emergent and other integrative properties, often dominate or control a large percentage of the action. Watt (1963), for example, stated, “We do not need a tremendous amount of information about a great many variables to build revealing mathematical models.” Though the mathematical aspects of modeling are a subject for advanced texts, we should review the first steps in model building.
Modeling usually begins with the construction of a diagram, or “graphic model,” which is often a box or compartment diagram, as illustrated in Figure 1-5. Shown are two properties, P1 and P2, that interact, I, to produce or affect a third property, P3, when the system is driven by an energy source, E. Five flow pathways, F, are shown, with F1 representing the input and F6 the output for the system as a whole.
Thus, at a minimum, there are five ingredients or components for a working model of an ecological situation, namely, (1) an energy source or other outside forcing function, E; (2) properties called state variables, P1; P2, … Pn; (3) flow pathways, F1, F2, … Fn, showing where energy flows or material transfers connect properties with each other and with forces; (4) interaction functions, I, where forces and properties interact to modify, amplify, or control flows or create new “emergent” properties; and (5) feedback loops, L.
Figure 1-5 could serve as a model for the production of photochemical smog in the air over Los Angeles. In this case, Pi could represent hydrocarbons and P2 nitrogen oxides, two products of automobile exhaust emission. Under the driving force of sunlight energy, E, these interact to produce photochemical smog, P3. In this case, the interaction function, I, is a synergistic or augmentative one, in that P3 is a more serious pollutant for humans than is P1 or P2 acting alone.
Alternatively, Figure 1-5 could depict a grassland ecosystem in which Pi represents the green plants that convert the energy of the Sun, E, to food. P2 might represent herbivorous animal that eats plants, and P3 an omnivorous animal that can eat either the herbivores or the plants. In this case, the interaction function, I, could represent several possibilities. It could be a no-preference switch if observation in the real world showed that the omnivore P3 eats either P1 or P2, according to availability.
Or I could be specified to be a constant percentage value if it was found that the diet of P3 was composed of, say, 80 percent plant and 20 percent animal matter, irrespective of the state of P1 or P2. Or I could be a seasonal switch if P3 feeds on plants during one part of the year and on animals during another season. Or I could be a threshold switch if P3 greatly prefers animal food and switches to plants only when P2 is reduced to a low level.
Feedback loops are important features of ecological models because they represent control mechanisms. Figure 1-6 is a simplified diagram of a system that features a feedback loop in which “downstream” output, or some part of it, is fed back or recycled to affect or perhaps control “upstream” components.
For example, the feedback loop could represent predation by “downstream” organisms, C, that reduce and thereby tend to control the growth of “upstream” herbivores or plants B and A in the food chain. Often, such a feedback actually promotes the growth or survival of a downstream component, such as a grazer enhancing the growth of plants (a “reward feedback,” as it were).
Figure 1-6 could also represent a desirable economic system in which resources, A, are converted into useful goods and services, B, with the production of wastes, C, that are recycled and used again in the conversion process (A —> B), thus reducing the waste output of the system. By and large, natural ecosystems have a circular or loop design rather than a linear structure. Feedback and cybernetics, the science of controls.
Figure 1-7 illustrates how positive and negative feedback can interact in the relationship between atmospheric CO2 concentration and climatic warming. An increase in CO2 has a positive greenhouse effect on global warming and on plant growth. However, the soil system acclimates to the warming, so soil respiration does not continue to increase with warming. This acclimation results in a negative feedback on carbon sequestration in the soil, thus reducing emission of CO2 to the atmosphere, according to a study by Luo et al. (2001).
Compartment models are greatly enhanced by making the shape of the “boxes” indicate the general function of the unit. In Figure 1-8, some of the symbols from the H. T. Odum energy language are depicted. In Figure 1-9, these symbols are used in a model of a pine forest located in Florida. Also, in this diagram estimates of the amount of energy flow through the units are shown as indicators of the relative importance of unit functions.
In summary, good model definition should include three dimensions:
(1) The space to be considered (how the system is bounded);
(2) The subsystems (components) judged to be important in overall function; and
(3) The time interval to be considered. Once an ecosystem, ecological situation, or problem has been properly defined and bounded, a testable hypothesis or series of hypotheses is developed that can be rejected or accepted, at least tentatively, pending further experimentation or analysis. For more on ecological modeling, see Patten and Jorgensen (1995), H. T. Odum and E. C. Odum (2000), and Gunderson and Holling (2002).