# Dynamic Ecological System Analysis

## TL;DR

This paper introduces a comprehensive mathematical framework for analyzing nonlinear ecological systems dynamically, enabling detailed tracking of flows, storages, and interactions within complex ecological networks.

## Contribution

It develops a novel system decomposition and flow characterization method that extends static network analysis to nonlinear dynamic ecological systems.

## Key findings

- Analytical characterization of flow paths and interactions.
- Quantitative classification of interspecific interactions.
- Extension of static network concepts to dynamic settings.

## Abstract

This article develops a new mathematical method for holistic analysis of nonlinear dynamic compartmental systems through the system decomposition theory. The method is based on the novel dynamic system and subsystem partitioning methodologies through which compartmental systems are decomposed to the utmost level. The dynamic system and subsystem partitioning enable tracking the evolution of the initial stocks, environmental inputs, and intercompartmental system flows, as well as the associated storages derived from these stocks, inputs, and flows individually and separately within the system. Moreover, the transient and the dynamic direct, indirect, acyclic, cycling, and transfer (diact) flows and associated storages transmitted along a given flow path or from one compartment, directly or indirectly, to any other are analytically characterized, systematically classified, and mathematically formulated. Further, the article develops a dynamic technique based on the diact transactions for the quantitative classification of interspecific interactions and the determination of their strength within food webs. Major concepts and quantities of the current static network analyses are also extended to nonlinear dynamic settings and integrated with the proposed dynamic measures and indices within the proposed unifying mathematical framework. Therefore, the proposed methodology enables a holistic view and analysis of ecological systems. We consider that this 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.