Dominance of Indirect Effects

This property compares the contribution of flow along indirect pathways with those along direct ones. Indirect effects are any that require an intermediary node to mediate the transfer and can be of any length. The strength of indirectness has been measured in a ratio of the sum of the indirect flow intensities divided by the direct flow intensities:

where Sj, the Kronecker delta, is 1 if and only if i = j and is 0 otherwise. When the ratio is greater than 1, then dominance of indirect effects is said to occur. Analysis of many different models has shown that this ratio is often greater than 1, revealing the nonintuitive result that indirect effects have greater contribution than direct effects. Thus, each compartment influences each other, often significantly, by many indirect, nonobvious pathways. The implications of this important result are clear in that each compartment is embedded in and dependent on the rest of the network for its situation, thus calling for a true systems approach to understand such things as feedback and distributed control in the network.

utility: U = D0 + D1 + D2 + D3 + ■■■ ^ Dm = (I-D)-1

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