Zoltán Varga^*, Manuel Gámez, Inmaculada López

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Institute of Mathematics and Informatics, Szent István University, Godollo, Hungary.
Department of Mathematics, University of Almería, Almería, Spain.
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Abstract: The paper is an update of two earlier review papers concerning the application of the methodology of mathematical systems theory to population ecology, a research line initiated two decades ago. At the beginning the research was concentrated on basic qualitative properties of ecological models, such as observability and controllability. Observability is closely related to the monitoring problem of ecosystems, while controllability concerns both sustainable harvesting of population systems and equilibrium control of such systems, which is a major concern of conservation biology. For population system, observability means that, e.g. from partial observation of the system (observing only certain indicator species), in principle the whole state process can be recovered. Recently, for different ecosystems, the so-called observer systems (or state estimators) have been constructed that enable us to effectively estimate the whole state process from the observation. This technique offers an efficient methodology for monitoring of complex ecosystems (including spatially and stage-structured population systems). In this way, from the observation of a few indicator species the state of the whole complex system can be monitored, in particular certain abiotic effects such as environmental contamination can be identified. In this review, with simple and transparent examples, three topics illustrate the recent developments in monitoring methodology of ecological systems: stock estimation of a fish population with reserve area; and observer construction for two vertically structured population systems (verticum-type systems): a four-level ecological chain and a stage-structured fishery model with reserve area.

Keywords: Ecological Chain; Fishery with Reserve Area; Stable Coexistence; Ecosystem Monitoring; Verticum-Type System; Nonlinear System; Observer Design

Cite this paper: Z. Varga, M. Gámez and I. López, "Recent Developments in Monitoring of Complex Population Systems," American Journal of Operations Research, Vol. 3 No. 1, 2013, pp. 167-180. doi: 10.4236/ajor.2013.31A016.

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