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Input/Output
Analysis: Input/output analysis quantifies
direct and indirect trophic effects for each component in the network.
From this analysis, one can determine the full dependency of one compartment
relative to all other compartments. For example, input/output analysis
would quantify the degree to which a fish species relies on pelagic as
opposed to benthic resources.
Trophic
Status: The complexity of the structure of food webs can be simplified
by mapping their trophic exchanges into a simple linear chain of composite
trophic levels (Lindeman 1942) by weighting and averaging the trophic
position at which each compartment feeds. The advantage of such a transformation
is that food chain length and overall trophic efficiencies are easily
discernible.
Cycling:
A cycle is defined as a pathway in which material and energy travels
through the food web to arrive at where it began (also known as an "arc").
Cycling of material and energy is an important property of ecosystems,
particularly as it relates to autonomous system behavior, i.e., reduced
dependency on outside energy inputs. Ecosystem properties important in
cycling include the number of cycles, whether cycles occur over short
and fast pathways vs. long and slow pathways, and the percentage of material
and energy that is recycled. Other measures include: 1) information about
each arc, such as the amount of material and energy recycled through that
arc and other pathways using that same arc (a "nexus"), and,
2) separation of cyclic and noncyclic pathways.
Ecosystem
Indices: Ulanowicz (1986) has developed a suite of ecosystem level
indices based on information theory. These indices characterize the state
of a food web. They include total system throughput, ascendency, developmental
capacity, overhead, and redundancy. Total system throughput
is simply the sum of all the flows that occur in that food web; it
characterizes the overall activity of the ecosystem. Ascendency
is a measure of the size and organization of flows and can be interpreted
as the tightness of the constraints that channel trophic linkages. Higher
values for ascendency represent a food web with more trophic specialists,
increased cycling, and higher efficiency, while lower values for ascendency
represent a more generalist-based food web, decreased cycling, and lower
transfer efficiencies. The limit, or upper bound, to ascendency is the
developmental capacity. Developmental capacity is proportional
to the variety of flows in a network, and is a surrogate for the complexity
of an ecosystem. Developmental capacity minus ascendency equals overhead.
Overhead represents the amount of developmental capacity
that does not appear as organized structure or constraints. That is, overhead
represents all the ambiguities of connection and incoherencies of flow
(i.e., disordered activity) that are available to be reorganized as an
ecosystem develops. Redundancy is that component of the
overhead that reflects parallelisms in the internal pathways of trophic
transfers so that any two compartments cannot be severed by elimination
of a single intervening link.

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