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theory have been developed and used in order to improve the parameter
estimation. 67,69,70
b. Artificial neural networks (ANNs) methods and especially the “multi-
layer feed-forward neural network” (BPN) and the “Kohonen self-
organizing mapping” (SOM) have been used extensively for ecological
modeling 71 and in particular for performing specific tasks in different
fields of applied ecology. These fields include soil hydrology; 72 mod-
eling the greenhouse effect; 73 modeling water and carbon fluxes above
European coniferous forests; 74 modeling phytoplankton primary pro-
duction; 75,76 applying ANNs tools to ocean color remote sensing; 77
predicting P/B ratio of animal populations; 78 predicting collembolan
diversity and abundance in riparian habitats; and predicting the
response of zooplankton biomass to climatic and oceanic changes. 79
The technique of stochastic dynamic programming, previously used in
agricultural economics 80 and in commercial fisheries, 81 has been improved.
This has been used to obtain solutions for maintaining a minimum viable
population size with minimum economic loss, and it suggests that this
approach can have a “universal applicability in conservation biology.” 82
The numerical method of analysis and input-output models also has
been used for the assessment of “ecological sustainability” of a regional
economy 83 or a national economy. 84
c. Despite many and persisting constraints, a great effort has been made
in recent years to develop and apply techniques for modeling structural
changes in ecological systems, based on the catastrophe theory 67,70 and
for mathematical modeling of the structural dynamic homomorph mod-
els describing ecological systems ( Figure 2.13) . Also promising are
the models consisting of linear differential equations with time varying
parameters 85 and especially the dynamic mathematical models devel-
oped by using the exergy as a goal function. 67
Above is a brief presentation of the main findings of a much more comprehensive
critical analysis of recent approaches and developments in the field of ecological
modeling. It can be concluded that there are strong concepts available enabling a
systemic approach to environment and an almost complete range of methods, mod-
eling tools and logistics for:
• Designing and implementing study programs for spatio-temporal identi-
fication of NC and SES s as well as quality assessments of historical data
and knowledge
• Designing and developing the initial structure for the information system
of knowledge and database for each category of identified ecological
systems ( Figure 2.14)
• Developing or adapting the most appropriate package of mathematical
models, integrating all types of a, b, and c models, in order to describe
specific phenomena, processes, or structural changes, and dynamics of
the whole system by using existing knowledge and data as well as the set
of hypotheses dealing with uncertainties and gaps in knowledge and data
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