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.