## Limitations of FCI

FCI considers only the diagonal coefficients of the Leontiefmatrix, accounting therefore only for paths starting and ending at the same node.

Using the notation introduced above, we see that FCI accounts for simple cycles and compound cycles, but does not consider the contribution of compound paths, as they never appear on the diagonal. Compound paths, however, contain cycles that should be included in the definition of cycling index. Unfortunately, there is no simple linear algebra technique that can account both for cycles and compound paths, and counting all the pathways in an ecological network is computationally very intense.

As an example of the limitation of the FCI, we see that in Figure 4 the pathway Plants ! Detritus ! Detritus feeders ! Detritus ! Bacteria will not contribute to any diagonal coefficient, even if it contains a cycle. Because each quantum of matter can be recycled into the same compartment many times, it will also move around compound paths many times. This may result in off-diagonal coefficients in the Leontief matrix that are greater than 1, stressing the need for counting compound paths in the cycling process.

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