Network Biology, 2021, 11(1): 1-28
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Reliability analysis of flow networks with an ecological perspective

Ali Muhammad Ali Rushdi, Omar Mutab Alsalami
Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia

Received 5 October 2020;Accepted 10 November 2020;Published 1 March 2021

This paper attempts to set the stage for a prospective interplay between ecology and reliability theory concerning the common issue of the concept of a capacitated or flow network. The paper treats the problem of species survivability, which pertains to the ability of a specific species to avoid local extinction by migrating from a critical habitat patch to more suitable destination habitat patches via perfect stepping stones and heterogeneous imperfect corridors. The paper proposes various types of techniques for analyzing a capacitated ecological network for the process of migration in a metapopulation landscape network that arises when paths to destination habitat patches share common corridors. These techniques include (a) Karnaugh maps, which are crucial in providing not only the visual insight necessary to write better future software but also constitute an adequate means of verifying such software and, (b) a generalization of the max-flow min-cut theorem that is applicable through the identification of minimal cut-sets and minimal paths in the ecological flow network. Care is taken to ensure that the reliability expressions obtained are as compact as possible and to check them for correctness. The ecological network capacity is a random pseudo-Boolean (-switching) function of the corridor successes; and hence, its expected value is easily obtainable from its sum-of-products formula. This network capacity has obvious benefits in the representation of nonbinary discrete random functions, which commonly arise during the analysis of flow networks. A tutorial example demonstrates these methods and illustrates their computational merits with ample details.

Keywords capacitated networks;map method;max-flow min-cut theorem;pseudo-switching function;habitat patch;ecological corridor;species migration;species survivability.

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