# Static ecological system analysis

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## Abstract

In this article, a new mathematical method for static analysis of compartmental systems is developed in the context of ecology. The method is based on the novel system and subsystem partitioning methodologies through which compartmental systems are decomposed to the utmost level. That is, the distribution of environmental inputs and intercompartmental system flows as well as the organization of the associated storages generated by these flows within the system is determined individually and separately. Moreover, the transient and the static 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. A quantitative technique for the categorization of interspecific interactions and the determination of their strength within food webs is also developed based on the diact transactions. The proposed methodology allows for both input- and output-oriented analyses of static ecological networks. The input- and output-oriented analyses are introduced within the proposed mathematical framework and their duality is demonstrated. Major flow- and stock-related concepts and quantities of the current static network analyses are also integrated with the proposed measures and indices within this unifying framework. This comprehensive methodology enables a holistic view and analysis of ecological systems.

## Keywords

Complex systems theory Ecological network analysis Compartmental systems System and subsystem partitioning Subsystem scaling Transient flows and storages diact flows and storages Food webs Interspecific interactions Input-output economics Epidemiology Infectious diseases Toxicology Pharmacokinetics Neural networks Chemical and biological systems Control theory Information theory Information diffusion Social networks Computer networks Malware propagation Traffic flow## Notes

### Acknowledgements

The author would like to thank Hasan Coskun for useful discussions and his helpful comments that improved the manuscript.

## Supplementary material

## References

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