Ecological Applications

Development capacity is estimated as the product of the ecosystem size (TST) and the diversity of flow structure, calculated using the Shannon information formula. Though information indices depend on arbitrary choices of what constitute a compartment, ascendency, overhead, and development capacity remain efficient indicators and they are widely applied in ENA.

In case studies, the ascendency measures how network structure and form reflect constraints to potential indeterminacy, while the potential degree of freedom preserved by an ecosystem is defined as overhead. Ascendency and overhead are the constitutive terms of the development capacity.

Development capacity of a system may rise when the scaling factor TST is augmented or through an increasing number of compartments with unarticulated flows. In presence of few limiting factors, TST tends to augment, but, in real systems, nutrient availability and respiration flows contribute to limit both its rise and a finer partition of transfers.

Level of resolution in building networks, on which ecosystem topology depends, affects both ascendency and development capacity. So, the same network could

Table 4 Total system throughput (TST), average mutual information (AMI), ascendency (A), and development capacity (C) are summarized for 14 ecosystems. Number of roles related to ascendency and development capacity are computed (Roles (A) and Roles (C)) adopting formula [43] as a reference

TST

AMI

A

C

Roles (A)

Roles (C)

Charca de Maspalomas

7 496 600 mg C m"

4d-1

2.250487

16 871 000

39886000

9.492356

204.495366

Chesapeake Bay mesohaline

4116200 mgCm"

2 —1 2 sum 1

2.087 799

8593800

19655000

8.067143

118.514489

Crystal River Creek (control)

22 420 mgCm"2d

"1

1.264 050

28340

70712

3.539728

23.428885

Crystal River Creek (delta temp.)

18050 mgCm"2d

"1

1.242 881

22 434

56 315

3.465583

22.645125

Everglades graminoids

19949 gCm"2yr"

1

1.937 090

38643

79572

6.938528

53.988517

Florida Bay

3459gCm"2yr1

2.024571

7 004

18 540

7.572859

212.578400

Lower Chesapeake Bay

1 451 200 mgCm"

21 2 sum 1

2.044170

2 966 500

7 713700

7.722 749

203.444686

Middle Chesapeake Bay

1 879000 mgCm"

21 2 sum 1

2.060990

3872 600

9328300

7.853740

143.237 257

Upper Chesapeake Bay

854330 mgCm"2

sum"1

2.133017

1 822 300

4583700

8.440289

213.846183

St. Marks River

2 064 mgCm"2d"

1

1.804 825

3 726

11264

6.078907

234.292711

Lake Michigan

36985 mgCm"2d

"1

1.775 017

65 649

140690

5.900381

44.879207

Mondego Estuary

10 852 g AFDW m"

2yr"1

1.524 788

16 547

39126

4.594170

36.797 075

Final Narragansett

4611 300 mgCm"

V"1

1.627 892

7 506 700

20464000

5.093129

84.588144

Ythan Estuary

5 440 gCm"2yr"1

1.592273

8663

23397

4.914906

73.744240

show a high detailed representation with many compartments and transfers, or it could be depicted with few nodes grouping several species that were separated in the previous case. When TST is assigned, in the first hypothesis, development capacity and ascendency are higher than in the latter since a lot of flows collapse in presence of few bigger nodes including many species, with a consequent reduction of articulation.

This is a sort of scale-resolution sensitivity, reflecting the importance of flow structure on C.

Once we know relationships among system components together with their weight (i.e., in presence of a network at a given level of resolution), development capacity and its constitutive terms, ascendency (indicator of organized flow structure), and overhead (index of potential resiliency) can be estimated. The only requirement is that all measurements have the same currency. In ecological applications, these three indices provide a sort of 'snapshot' of the developmental status of the system and their variations in time can give clues about ecosystem health and integrity.

In what follows, very general and theoretical patterns in information index variations are sketched out, but to test their predictive adequacy sufficient data sets describing ecosystem trophic relations before and after perturbation are required. At present, time series are exceedingly rare.

In general, in presence ofnovel perturbations, we expect ascendency to decrease, depending on a reduction ofsystem size (TST) and flow articulation (AMI), while for unim-pacted ecosystems a trend toward increasing ascendency, in both its constituent terms, would be detected.

Also, development capacity reflects changes occurring to the system status, showing a tendency to decrease in case of impacted conditions.

In contrast to the ascendency falling down in disturbed ecosystems, both overhead related to internal flows (redundancy) and respiration (dissipative overhead) exhibit increasing trends, as one would expect in response to stress. Overhead on imports and overhead on exports may instead change in an apparently not characteristic fashion, with slight drops in their values. This could be caused by the strong influence of TST component that overwhelms, with its falling down in presence of perturbation (lower level of total system activity intended as less medium processed), the effects produced by higher flow disorder and incoherence.

Therefore, final values of information indices could be deeply affected by system size (TST), as described above in the case of overhead on imports and on exports, hiding the contribution of system flow organization (AMI). Because of this tendency, a detailed analysis of the flow structure status could be stressed dividing C, A, and $ by TST. It should be noted, however, that differences in the AMI component of these information indices represent logarithms of variations in actual probabilities and are, consequently, much-attenuated indicators of change.

Besides theoretical patterns, trends outlined by studies on eutrophication (system overenrichment of nutrients, usually nitrogen and phosphorus) show apparently strange increasing values in ascendency and development capacity.

In fact, information indices exhibit characteristic behaviors in case of eutrophication and the most evident consequence of the ecosystem growth (augmented system activity - TST) is the rise of C and A, in spite of an oversimplified and degraded web structure.

The higher ascendency in presence of eutrophication is due to the exclusive effect of TST that more than compensates for a concomitant fall in the degrees of freedom remaining in the system. It is then obvious that not every increase in system ascendency represents healthy change.

In addition to ecosystem networks, urban systems can also be depicted with compartments and flows connecting them, adopting different currencies: water, energy, metals, wood, and many others. When size of flows is increased, there is a simple growth of TST without any change in network articulation and, accordingly, ascendency and development capacity rise. Often, in urban networks, this growth of system size is confused with system development. A great insight into this misleading idea is supplied scaling ascendency with C. In fact, there are many examples of urban water network with ascendency set around the 40% of development capacity, while this percentage is considerably higher in ecosystems, reaching till 55% and 60% of the maximum capacity (data available from the Florida Bay data set; http:// www.cbl.umces.edu/~atlss/).

These data contradict the common perception that human systems are well organized, highlighting the need for increasing ascendency through a more efficient transfer organization and use of resources. A more articulated topology could be obtained, for instance, by reducing dissipations, increasing internal recycling, and process efficiencies or limiting exports.

The importance of development capacity as an ascendency and overhead scaling factor is strengthened by its application to assess both system performance and integrity.

Homeostasis, transfer efficiency, opportunity for growth, stability, sustainability, and minimal external support are many attributes commonly grasped into the definition of ecosystem health, that addresses how well the system is functioning, assessing its performance. For example, if the ratio between overhead on imports and development capacity decreases, over a sufficiently wide time lag, the ecosystem under analysis shows a trend toward organization and minimization of its dependence on external supports. This inclination could be confirmed by a more efficient transfer organization of internal flows (IA scaled with internal capacity) and by an increased amount of recycled matter.

At the same time, another ecosystem health property as transfer efficiency increases when the network becomes more articulated and this is the case when ascendency exceeds a given threshold (i.e., 50% of the development capacity).

The integrity concept endorses how well a system performs on a temporal scale, being associated to: capability for future developmental options, capacity to withstand stress (i.e., resilience and resistance), and ability for change and development. Integrity preservation can be estimated, for example, by scaling overhead indices with C. When a stabilized and sufficiently high percentage of redundancy is showed, the ecosystem offers a multiplicity of pathways. This aspect may produce a good ability to overcome the perturbations: the more unarticulated is the system, the higher is the number of available pathways that energy can experience to flow through the network. In this way, if a species is no more, the multiplicity of trophic relations (that is variety of routes) reduces risks of indirect extinction of other species. In fact, it is quite unlikely that, in presence of high redundancy percentage, many species exclusively feed on the extinguished node.

Also, the simple calculation of development capacity appears as an appropriate measure of ecological integrity, being the sum of a term describing the tendency to an organized and well-performing behavior (A), with its complement that represents the degrees of freedom remaining in the system for reconfiguration in response to injury ($).

Therefore, development capacity cannot be simply seen as an ascendency and redundancy scaling factor. Rather, its interplay with ascendency and overhead, giving rise to the percentage of organized complexity (A/C) and not constrained flows ($R/C), is an effective approach to check complex properties as ecosystem health and integrity. As a consequence, the action of ascendency and overhead might be described as balanced result between two antagonistic tendencies than being explained in a rigorous and algorithmic fashion.

Sufficient amounts of both attributes (A and $) should be preserved for the persistence of each system over the long term, and a monitoring process to quantitatively track changes in these two partitions over time should be planned to trace ecological dynamics.

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