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.

中文翻译：

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静态生态系统分析

在本文中，在生态学的背景下开发了一种新的数学方法来对车厢系统进行静态分析。该方法基于新颖的系统和子系统划分方法，通过该方法，可将分区系统最大程度地分解。也就是说，环境投入和部门间系统流的分布以及系统中这些流所生成的关联存储的组织是分别确定的。此外，瞬时和静态的直接，间接，非循环，循环和转移（精确沿给定的流动路径或从一个隔间直接或间接传递给任何其他隔间的流动和相关的存储装置经过分析表征，系统分类和数学公式化。还基于干果，开发了一种对种间相互作用进行分类并确定其在食物网中强度的定量技术。交易。所提出的方法可以对静态生态网络进行面向输入和面向输出的分析。在建议的数学框架内引入了面向输入和输出的分析，并证明了它们的对偶性。在此统一框架内，当前静态网络分析的主要与流量和存量相关的概念和数量也与拟议的措​​施和指标整合在一起。这种全面的方法可以对生态系统进行整体观察和分析。