Static ecological system measures

A holistic analysis of compartmental systems
  • Huseyin CoskunEmail author


A new mathematical method for the static analysis of ecological systems has recently been developed by the author and was presented in a separate article. Based on this methodology, multiple new 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—directly or indirectly—on another, and determine the residence times and compartmental activity levels. 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 novel and unifying mathematical framework. This comprehensive framework enables a holistic view and analysis of static ecological systems. A quantitative technique for the classification and characterization of interspecific interactions and the determination of their strength within food webs is also developed. The proposed methodology allows for both input- and output-oriented analyses of ecological networks. The holistic perspective of the proposed methodology is extended further from the input-oriented to the output-oriented analysis. The proposed system measures and indices, thus, extract detailed information about ecosystems’s characteristics, as well as their functions, properties, behaviors, and various other system attributes that are potentially hidden in and even obscured by data.


Complex systems theory Ecological network analysis Compartmental systems System and subsystem partitioning Subsystem scaling diact flows and storages diact effect measures and indices diact utility measures and indices diact residence times 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 



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


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA

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