In such cybernetic systems the course is not maintained by rigid control, but flexibly. Thus the ship does not move unwaveringly on its path, but actually follows it in a wavelike motion that swings equally to both sides of the true course. The frequency of these swings depends on the relative speeds of the various steps in the cycle, such as the rate at which the ship responds to the rudder.
Ecological systems exhibit similar cycles, although these are often obscured by the 15 effects of daily or seasonal variations in weather and environmental agents. The most famous examples of such ecological oscillations are the periodic fluctuations of the size of fur-bearing animal populations. For example, from trapping records in Canada it is known that the populations of rabbits and lynx follow ten-year fluctuations. When there are many rabbits the lynx prosper; the rising population of lynx increasingly ravages the rabbit population, reducing it; as the latter become scarce, there is insufficient food to support the now numerous lynx; as the lynx begin to die off, the rabbits are less fiercely hunted and increase in number. And so on. These oscillations are built into the operation of the simple cycle, in which the lynx population is positively related to the number of rabbits and the rabbit population is negatively related to the number of lynx.
In such an oscillating system there is always the danger that the whole system will collapse when an oscillation swings so wide of the balance point that the system can no longer compensate for it. Suppose, for example, in one particular swing of the rabbit—lynx cycle, the lynx manage to eat all the rabbits (or, for that matter, all but one). Now the rabbit population can no longer reproduce. As usual, the lynx begin to starve as the rabbits are consumed; but this time the drop in the lynx population is not followed by an increase in rabbits. The lynx then die off. The entire rabbit—lynx system collapses.
This is similar to the ecological collapse which accompanies what is called "eutrophication."[164] If the nutrient level of the water becomes so high as to stimulate the rapid growth of algae, the dense algal population cannot be long sustained because of the intrinsic limitations of photosynthetic efficiency. As the thickness of the algal layer in the water increases, the light required for photosynthesis that can reach the lower parts of the algal layer becomes sharply diminished, so that any strong overgrowth of algae very quickly dies back, releasing organic debris. The organic matter level may then become so great that its decay totally depletes the oxygen content of the water. The bacteria of decay then die off, for they must have oxygen to survive. The entire aquatic cycle collapses.
The dynamic behavior of a cybernetic system—for example, the frequency of its natural oscillations, the speed with which it responds to external changes, and its over-all rate of operation—depends on the relative rates of its constituent steps. In the ship system, the compass needle swings in fractions of a second; the helmsman's reaction takes some seconds; the ship responds over a time of minutes. These different reaction times interact to produce, for example, the ship's characteristic oscillation frequency around its true course.
In the aquatic ecosystem, each biological step also has a characteristic reaction time, which depends on the metabolic and reproductive rates of the organisms involved. The time to produce a new generation of fish may be some months; of algae, a matter of days; decay bacteria can reproduce in a few hours. The metabolic rates of these organisms—that is, the rates at which they use nutrients, consume oxygen, or produce waste—is inversely related to their size. If the metabolic rate of a fish is 1, the algal rate is about 100, and the bacterial rate about 10,000.
If the entire cyclical system is to remain in balance, the over-all rate of turnover 20 must be governed by the slowest step—in this case, the growth and metabolism of the fish. Any external effect that forces part of the cycle to operate faster than the over-all rate leads to trouble. So, for example, the rate of waste production by fish determines the rate of bacterial decay and the rate of oxygen consumption due to that decay. In a balanced situation, enough oxygen is produced by the algae and enters from the air to support the decay bacteria. Suppose that the rate at which organic waste enters the cycle is increased artificially, for example, by dumping sewage into the water. Now the decay bacteria are supplied with organic waste at a much higher level than usual; because of their rapid metabolism they are able to act quickly on the increased organic load. As a result, the rate of oxygen consumption by the decay bacteria can easily exceed the rate of oxygen production by the algae (and its rate of entry from the air) so that the oxygen level goes to zero and the system collapses. Thus, the rates of the separate processes in the cycle are a natural state of balance which is maintained only so long as there are no external intrusions on the system. When such an effect originates outside the cycle, it is not controlled by the self-governing cyclical relations and is a threat to the stability of the whole system.
Ecosystems differ considerably in their rate characteristics and therefore vary a great deal in the speed with which they react to changed situations or approach the point of collapse. For example, aquatic ecosystems turn over much faster than soil ecosystems. Thus, an acre of richly populated marine shoreline or an acre of fish pond produces about seven times as much organic material as an acre of alfalfa annually. The slow turnover of the soil cycle is due to the rather low rate of one of its many steps—the release of nutrient from the soil's organic store, which is very much slower than the comparable step in aquatic systems.
The amount of stress which an ecosystem can absorb before it is driven to collapse is also a result of its various interconnections and their relative speeds of response. The more complex the ecosystem, the more successfully it can resist a stress. For example, in the rabbit-lynx system, if the lynx had an alternative source of food they might survive the sudden depletion of rabbits. In this way, branching—which establishes alternative pathways—increases the resistance of an ecosystem to stress. Most ecosystems are so complex that the cycles are not simple circular paths, but are crisscrossed with branches to form a network or a fabric of interconnections. Like a net, in which each knot is connected to others by several strands, such a fabric can resist collapse better than a simple, unbranched circle of threads—which if . cut anywhere breaks down as a whole. Environmental pollution is often a sign that ecological links have been cut and that the ecosystem has been artificially simplified and made more vulnerable to stress and to final collapse.
The feedback characteristics of ecosystems result in amplification and intensification processes of considerable magnitude. For example, the fact that in food chains small organisms are eaten by bigger ones and the latter by still bigger ones inevitably results in the concentration of certain environmental constituents in the bodies of the largest organisms at the top of the food chain. Smaller organisms always exhibit much higher metabolic rates than larger ones, so that the amount of their food which is oxidized relative to the amount incorporated into the body of the organism is thereby greater. Consequently, an animal at the top of the food chain depends on the consumption of an enormously greater mass of the bodies of organisms lower down in the food chain. Therefore, any nonmetabolized material present in the lower organisms of this chain will become concentrated in the body of the top one. Thus, if the concentration of DDT[165] (which is not readily metabolized) in the soil is 1 unit, earthworms living in the soil will achieve a concentration of from 10 to 40 units, and in woodcocks feeding on the earthworms the DDT level will rise to about 200 units.