# Total System Throughput and Average Mutual Information

Besides the graphical and mathematical representation of 'who eats whom' and 'at what rate', ENA performs calculus focusing both on single-compartment and whole-system levels.

TST and AMI are basal indices advocating a systemic approach.

The total amount of flows occurring in the system is called TST, and for Cone Spring is equal to 42 445 kcalm _2yr_1:

TST defines ecosystem activity (size) and it conceptually corresponds to what in economy is known as gross national product (GDP), an indicator of economic community size.

Ecosystem development is connected to flow organization and it increases when uncertainty is diminishing. Mathematically, uncertainty (H), related to a distribution of probability over n categories (with scalar constant K), is equivalent to

System flow disorganization is measured by uncertainty and its amount can be distinguished into output H(a) and input H(b) contributions:

With completely independent events, total system uncertainty becomes H(a) + H(b). However, inputs and outputs in ecosystems are not always independent and the associated uncertainty can be computed adopting joint probabilities p(a ¡,bj):

Therefore, with inputs and outputs that are not completely independent,

and, in this case, the degree of system organization is defined as

yielding to

To measure transfer uncertainty with network analysis notation, the probability that a quantum of matter (or energy) would flow from compartment to j is computed as p{a» j

with output and input probabilities that can be written as marginal sums of joint probabilities:

pj ffiE

AMI is the index measuring system organization (ecosystem development intended as flow articulation). Using the expressions provided by formulas — into , and simplifying, one obtains for this quantity the following representation: 