Introduction

The ever-increasing interest toward ecosystem status and performance stimulates the application of tools for whole-system assessment; a prominent collection of quantitative methods to achieve this aim consists of ecosystem network analysis (ENA).

The apparatus of ENA comprises indices, derived from information theory, that quantify global attributes, and, in particular, ascendency (A) measures growth (size) and development (organization of flows) of ecosystems.

Ascendency is estimated as the product of average mutual information (AMI) by total system throughput (TST). It measures the ability of a system to prevail over alternative configurations. AMI evaluates how the system is developed, defining flow articulation, and TST expresses the size of an ecosystem as the sum of all the flows.

Since growth and development are natural processes, they possess finite limits: the minimum value for ascendency is 0, while its upper boundary, defined as development capacity (C), is affected by system topology.

As a consequence, with a given number of nodes and TST, the highest development capacity is assigned to a wholly connected network (with all flows of equal intensity), while a balanced and completely articulated topology (linear and closed chain) shows the minimum development capacity, corresponding, only in this case, to the system ascendency.

The remaining fraction preventing ascendency from reaching its theoretical maximum is called total overhead ($), and it is calculated as the difference between development capacity (C) and system ascendency (A).

The article briefly sketches on information theory principles and probabilistic approach applied to the study of ecological networks, introducing an explanation of development capacity and associated overhead definitions.

Then, it shows an alternative equation to define development capacity, described as a function of the effective number of ecosystem roles (a measure of the degree to which the system is differentiated into distinct functions).

Finally, through the comparison between ascendency, overhead, and development capacity, examples of applications to real ecosystems are introduced, strengthening the important part ascendency plays as a whole-system index.

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