CH2 network nonlocality

As pathways extend the amount of substance carried along at any given step is less than in the previous step due to dissipation. Therefore, pathways eventually end as they run out of originally introduced material. The rate of decay can be expressed as an exponential function, just as is the rate of pathway proliferation. Dissipation and pathway extension and growth in numbers are in conflict, but early in the transactional sequence following introduction the rate of the former exceeds that of the latter such that the total substance transferred between compartment pairs over the aggregate of pathways of a given length interconnecting them exceeds that of direct intercompartmental transfers. In other words, indirect pathways (those of lengths > 2) deliver more substance from any compartment to any other than a direct link between them. The influences carried by this transferred substance follows the substance itself in its being associated with pathways of particular lengths, and thus the conservative as well as non-conservative causes in the system can be said to be non-local. Indirect effects are dominant in systems, and this is especially true for complex systems, like ecosystems. The limit process that carries introduced conservative substance throughout the system to ultimate dissipation ensures that direct energy-matter links are quantitatively insignificant in comparison with the total. These links, provided by direct interactions such as feeding, serve only to structure the network; they make little contribution to intrasystem determination once this structuring is established. Dominant indirect effects in nature—that is a very different proposition from what we have in ecology at the present time. It is only a hypothesis, but robust in the mathematics of steady-state environ analysis. And each extended pathway that collectively provides its basis begins with openness at the boundary—either reception of input followed by forward passage of material in output environs to ultimate dissipation, or exhaustion from outputs preceded by the traceback of substance in input environs to its boundary points of original introduction.

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