Ascendency in itself, thus, combines two factors each of which quantifies a core attribute of ecological flow networks: the first is the system size or system activity, measured by its TST; the other is the level of constraints imposed on matter circulation by the articulation of flows, and it is quantified by the AMI. As said before, ecological flow networks are ecosystem images. Given the high number of actors that play the game in an ecosystem, processes such as feeding, decay, excretion, and so forth give rise to a vast array of matter and energy passages between species or nutrient pools. This multiplicity of exchanges can be captured by a network representation, whose connections are in terms of some currency that is either material (nitrogen, carbon, phosphorus) or energetic (joule).
In this scenario, it is straightforward to ask in what way ascendency can contribute to characterize ecosystem status. Each arrow in network represents a flow of a given currency and the magnitude associated to the link quantifies the intensity of that passage. The summation of all the flows in a network yields the total amount of material or energy that the ecosystem handles. This quantity estimates the level of activity that pertains to the ecosystem, exactly as the sum of monetary flows estimates the overall economic activity of a society. As more material becomes available to an ecosystem, more compartments likely can be sustained. Both the number of compartments and magnitude of flows define the size of a system. The process that is directly linked with size is growth. By measuring TST, thus, one quantifies the growth of an ecosystem, which depends on both magnitude of flows and number of compartments. Growth is extensive in nature. That is, it pertains to the 'extension' of a system but does not provide detail about how material and energy are distributed within the ecosystem. It might well happen that two systems with the same TST are characterized by totally different flow structures.
As it has been shown in the calculation section, higher values of AMI pertain to flow structures that are maximally constrained with respect to matter and energy movement within the system. These ecosystems are considered also to be highly organized. Energy distribution, in fact, takes place along few efficient routes and, as a consequence, the cost of maintenance for the whole ecosystem decreases. From this, it follows that highly redundant flow networks are said to be less organized. They possess lower AMI values. What determines the level of flow redundancy in an ecological network? To answer this question, it is necessary to consider the situation depicted in Figure 6.
In the upper graph, the four components of the ecosystem exchange matter using numerous equiponderant links. However, if it happens that links a, b, and c are more efficient in transferring energy, at every cycle they will become more and more important so that more energy will pass along the route a—b—c, which will become predominant. The ultimate consequence is that this positive feedback will select this route against all the others, pruning away less-efficient links. The final configuration for the system could be the one depicted in the lower graph, in which the route a—b—c is the only active one in the system.
Figure 6 Hypothetical mechanism for ecosystem development. More efficient connections become dominant and channels medium throughout the system. The final configuration is less redundant and more developed.
The presence of positive-feedback cycles (autocatalytic cycles), in synthesis, would force ecological networks toward less-redundant, more-efficient configuration. In other words, ecosystems would develop in the direction of more organized structure of exchanges, and development is identified as any increase in the mutual information of the exchange configuration. AMI, thus, quantifies development for ecosystems. Ascendency measures the fraction of matter or energy that an ecosystem distributes in an efficient way; combining ecosystem activity and organization, it provides a unique measure of growth and development.
What ecosystems undergo during time is a series of orderly and sometimes repeatable states called succession. It is commonplace that during succession several attributes or properties change following well-defined patterns. Given that ascendency is a measure of ecosystem development, the next question to be answered is to what extent ascendency captures the changes typical of ecosystem succession. Ecosystem ecologists use several attributes to classify ecosystems during the course of succession. Mature ecosystems (late succession stages) would show greater species richness, greater internalization ofmedium (less dependency on external exchanges) through higher level of cycling and finer trophic specialization. All these major tendencies would be reflected in a higher ascendency. Greater species richness and niche specialization in fact may result in more constrained network of flows (increased AMI); the improved cycling function would increase the magnitude of the flows, thus boosting the system throughput. Thus, the expected outcome of succession is an increase of both system throughput and mutual information of the exchange configuration, from which one deduces that ascendency would increase during succession. However, this trend is not without limit. Every ecosystem possesses a development capacity which constitutes an upper limit for ascendency. Also, an increase in TST and AMI likely occurs in different phases of the succession process. If we imagine ecosystem succession as subdivided into stages such as (1) growth, (2) development, and (3) maturation, it is likely that the increase in activity dominates the first stage and declines as the ecosystem becomes more organized. In this latter phase, instead, the throughput accumulated at the beginning is redistributed and organized so that the mutual information of flows increases. The potential for ecosystem organization, quantified by the development capacity, however is never expressed completely during succession. Some encumbered complexity is retained basically because of thermodynamic constraints and the rigor of the environment. Dissipation in fact may never equal zero, and pruning away redundant connections is convenient only when the risk of disrupting the remaining connections is low, that is when the 'external environment' is more benign.
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