## Adaptive Cycles On Multiple Scales

With the following argumentation we want to link these concepts with another approach to ecosystem theories: Ecosystems are organized hierarchically (see Box 2.2 in Chapter 2). Hereafter, we will assume that throughout complexification periods, the focal processes always are influenced by the lower levels' dynamics and the higher levels' development, forming a system of constraints and dynamics of biological potentials. Thus there are four general hierarchical determinants for ecosystem dynamics:

(i) The constraints from higher levels are completely effective for the fate of the focal variable. The constraints operate in certain temporal features, with specific regularities and intervals. Some examples for these temporal characteristics are:

• Day-night dynamics (e.g., determining ecosystem temperature, light, or humidity)

• Tides (e.g., determining organism locations in the Wadden Sea)

• Moon phases (e.g., determining sexual behavior)

• Annual dynamics (e.g., determining production phases of plants)

• Longer climatic rhythms (e.g., sun spots influencing production)

• Dynamics of human induced environmental stress factors o Typical periodic land use activities (e.g., crop rotation) o Land use change (structural and functional)

o Emission dynamics and environmental policy (e.g., sulfur emission in

Germany and their effects on forests) o Global change and greenhouse gas emissions (e.g., temperature rise) o Continuous climate change

• Biome transitions

These constraints are interacting and constantly changing; therefore, the maximum degree of mutual adaptation is a dynamic variable as well. This is a focal reason why the orientor approach is nominated as a "very theoretical outline" only. As ecosystems "always are recovering from the last disturbance," the orientor dynamics often are practically superseded by the interacting constraints dynamics.

(ii) The dynamics of the focal variables themselves exhibit certain natural frequencies. As in the patch dynamics concepts, there can be internal change dynamics on the observed level itself. For example, we can observe the undisturbed succession on the base of biological processes—from a lake to a fen. The system changes enormously due to its internal dynamics. Throughout this process often a limited number of species become dominant, e.g., stinging nettles in secondary successions on abandoned agricultural systems. This leads to an interruption of orientor dynamics because the dominant organisms do not allow competitors to rise.

(iii) The biological potential of the lower levels results from mostly filtered, smoothened, and buffered variables with high frequencies. They can only become effective if the system exceeds certain threshold values. This can happen if disturbances unfold their indirect effects, as has been described above.

(iv) Disturbances primarily meet elements that operate on similar spatial and temporal scales. Only after these components have been affected, indirect effects start influencing the interrelated scales and thus can provoke far-reaching changes.

Summarizing these points, we can state that ecosystems under steady state conditions are regulated by a hierarchy of interacting processes on different scales. The slow processes with large extents build up a system of constraints for the processes with high dynamics. Thereby limiting their degrees of freedom, steady states can be characterized by relatively low variability of low-level processes (O'Neill et al., 1986). Furthermore, under steady state conditions, these high dynamic processes cannot influence the system of constraints, resulting in a rather high resilience. Thus, the question arises, what will happen during disturbances?

This can be depicted by the concept of stability landscapes (see Walker et al., 2004) or hypothetical potential functions. In Figure 7.9 the system state is plotted on the x-axis, the z-axis represents the parameter values (may also be taken as a temporal development with changing parameter loadings), and the potential function is plotted on the y-axis. This function can be regarded as the slope of a hill, where the bottom of the valley

represents steady state conditions. If we throw a marble into this system, then it will find its position of rest after a certain period of time at the deepest point of the curve. If the parameter values change continuously (A — B — C), then a set of local attractors appear, symbolized by the longitudinal profile of the valley, or the broadscale bifurcation line (H) at level I. This manifold sketches a sequence of steady states referring to different parameter values. In Figure 7.9, the straight line below on level I may be interpreted as the sequence of a parameter of a high hierarchical level while the oscillating parameter value line L indicates the states of a lower level holon. The return times of this holon to its different steady states will be different if the states A, B, and C are compared: The steeper the slope the more rapidly a local steady state will be reached, and smaller amplitudes will be measured. When the parameter value is changed continuously within long-term dynamics we will find small variations near state A. As our parameter shifts from A via B toward C, the potential curve's slopes decrease, finding a minimum at B. In this indifferent state the amplitudes of the low-level holon will be very high (see level I). If there is a further change of the parameter value, a first-order phase transition takes place. The state can be changed radically passing the bifurcation point B before a more stable state is achieved again, finally reaching C. Passing B there are two potential states the system can take, and the direction our holon takes is determined by all levels of the broken hierarchy, including the high frequent (small scale) dyna-mics. This process is accompanied by temporal decouplings, by a predominance of positive feedbacks, and by autocatalytic cycles.

This makes it possible for ecosystems to operate at the edge of chaos, but frequently avoid chaos and utilize all the available resources at the same; see also Box 7.4.

### Box 7.4 Chaos in ecosystem models

The prevailing conditions including the abundance of other species determine which growth rate is optimal. If the growth rate is too high, then the resources (food) will be depleted and the growth will cease. If the growth rate is too low, then the species does not utilize the resources (food) to the extent that it is possible. The optimal growth rate also yields the highest system exergy. If, in a well-calibrated and validated eutrophi-cation model—state variables include phytoplankton, nitrogen, phosphorus, zooplankton, fish, sediment nitrogen, and sediment phosphorus—the zooplankton growth rate is changed, then exergy will show a maximum at a certain growth rate (which is frequently close to the value found by the calibration and approved by the validation). At both lower and higher growth rates, the average exergy is lower because the available phytoplankton is either not utilized completely or is overexploited. When overexploitation occurs the phytoplankton and zooplankton show violent fluctuations. When the resources are available the growth rate is very high but the growth stops and the mortality increases as soon as the resources are depleted, which gives the resources a chance to recover and so on. At a growth rate slightly higher than the value giving maximum exergy, the model starts to show deterministic chaos. Figure 7.10 illustrates the exergy as function of the zooplankton growth rate in the model referred to above, focusing on the time when the model starts to show deterministic chaos. These results are consistent with Kaufmann's (1993) statement: biological systems tend to operate at the edge of chaos to be able to utilize the resources at the optimum. In response to constraints, systems move away as far as possible from thermodynamic equilibrium under the prevailing conditions, but that implies that the system has a high probability to avoid chaos, although the system is operating close to chaos. Considering the enormous complexity of natural ecosystems, and the many interacting processes, it is surprising that chaos is not frequently observed in nature, but it can be explained by an operation at the edge of chaos to ensure a high utilization of the resources—to move as far away as possible from thermodynamic equilibrium under the prevailing conditions.

Figure 7.10 Exergy is plotted versus maximum growth rate for zooplankton in a well calibrated and validated eutrophication model. The shaded line corresponds to chaotic behavior of the model, i.e., violent fluctuations of the state variables and the exergy. The shown values of the exergy above a maximum growth rate of about 0.65-0.7 per day are therefore average values. By a minor change of the initial value of phytoplankton or zooplankton in the model, significant changes are obtained after 2 months simulations as an indication of deterministic chaos.

After having elucidated disturbance from the hierarchical viewpoint, one last aspect should be taken into consideration. As we have mentioned above, the adaptive cycle is a metaphor, which can be assigned to a multitude of interacting scales. There is a high normality in disturbance with adaptability as a key function. If this feature cannot reach sufficient quantities by low-scale flexibility, then the breakdown on a higher hierarchical level enables the system to start a reset under the new prevailing conditions. Thus, in the end, disturbance really can be understood as a part of ecosystem growth and development on a higher scale, as indicated in Figure 7.11; disturbance may even be extremely necessary to enable a continuation of the complexifying trajectory of the overall system.

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