Network environ theory, simulation, and EcoNet® 2.0

We introduce and codify the mathematics of Ecological Network Analysis (ENA) in general and Network Environ Analysis (NEA) in particular used by the web-based simulation software EcoNet® 2.0. Where ecosystem complexity continues to drive an increasingly vast environmental modeling effort, ENA and NEA represent maturation, in part, of the compartment modeling approach. Compartment modeling mathematically represents compartment storages with both internal-connecting and external-environmental flows as ordinary differential equations. ENA and NEA expand these mathematics into complex systems analysis and corresponding network theory. EcoNet was developed to facilitate the mathematical modeling, to enhance the overall presentation, and to improve the subsequent long-term progress of ENA and NEA systems analysis. Thus, as a continuing enhancement to the overall understanding, but more importantly, to the future growth of environmental modeling associated with ENA and NEA, we derive and summarize the canonical mathematics of ENA, NEA, and EcoNet, which facilitates their future use.