  The system decomposition theory has recently been developed for the dynamic
analysis of nonlinear compartmental systems. The application of this theory to
the ecosystem analysis has also been introduced in a separate article. Based on
this methodology, multiple new dynamic ecological system measures and indices
of matrix, vector, and scalar types are systematically introduced in the
present paper. These mathematical system analysis tools are quantitative
ecological indicators that monitor the flow distribution and storage
organization, quantify the direct, indirect, acyclic, cycling, and transfer
(diact) effects and utilities of one compartment on another, identify the
system efficiencies and stress, measure the compartmental exposures to system
flows, determine the residence times and compartmental activity levels, and
ascertain the system resilience and resistance in the case of disturbances. The
proposed dynamic system measures and indices, thus, extract detailed
information about ecosystems' characteristics, as well as their functions,
properties, behaviors, and various other system attributes that are potentially
hidden in and even obscured by data. A dynamic technique for the quantitative
characterization and classification of main interspecific interactions and the
determination of their strength within food webs is also developed based on the
diact effect and utility indices. Moreover, major concepts and quantities in
the current static network analyses are also extended to nonlinear dynamic
settings and integrated with the proposed dynamic measures and indices in this
unifying mathematical framework. We consider that the proposed methodology
brings a novel complex system theory to the service of urgent and challenging
environmental problems of the day and has the potential to lead the way to a
more formalistic ecological science.
