iEMSs 2008: International Congress on Environmental Modelling and Software Integrating Sciences and Information Technology for Environmental Assessment and Decision Making 4 th Biennial Meeting of iEMSs, http://www.iemss.org/iemss2008/index.php?n=Main.Proceedings M. Sànchez-Marrè, J. Béjar, J. Comas, A. Rizzoli and G. Guariso (Eds.) International Environmental Modelling and Software Society (iEMSs), 2008 Monitoring the effects of human activities and environmental change on a population system M. Gámez a , I. López a , J. Garay b and Z. Varga c a Departamento de Estadística y Matemática Aplicada, Universidad de Almería, La Cañada de San Urbano, 04120 Almería, España ( mgamez@ual.es ) b Ecological Modelling Research Group of the Hungarian Academy of Science and Department of Plant Taxonomy and Ecology, Eötvös Lorand University, Budapest, Hungary.(garayj@ludens.elte.hu) c Institute of Mathematics and Informatics, Szent István University, Páter K. u. 1., H-2103 Godollo, Hungary. ( Varga.Zoltan@gek.szie.hu ) Abstract: The monitoring and analysis of the processes taking place in an ecosystem is a key issue for a sustainable human activity. A system of populations, as the biotic component of a complex ecosystem is usually affected by the variation of its abiotic environment. Even in nearly natural ecosystems an abiotic effect like climatic implications of global warming may cause important changes in the dynamics of the population system. In ecosystems involving field cultivation or any industrial activity, the abiotic parameter in question may be the concentration of a substance, changing e.g. as a result of pollution, application of a pesticide or a fertilizer, etc. In many cases the observation of the densities of each population may be technically complicated or expensive, therefore the question arises whether from the observation of the densities of certain (indicator) populations, the whole state process of the population system can be uniquely recovered. The paper is aimed at a methodological development of state monitoring, under the conditions of a changing environment. It is shown, how the technique of mathematical systems theory can be applied not only for the approximate calculation of the state process on the basis of the observed data, even under the effect of an exogene abiotic change with known dynamics; but in certain cases, also for the estimation of the unknown biological effect of the change of an abiotic parameter. The proposed methodology is applied to simple illustrative examples concerning a three-species predator-prey system. Keywords: environmental monitoring, observer system, ecosystem 1. INTRODUCTION Detection of the effect of human activities (e.g. pollution) and environmental change such as climatic variation, is an important part of the analysis of a composite system, including ecological, human and environmental subsystems. The effect of such factors on the parameters of population system models has been studied by several authors, see e.g. Gragnani [2002], Xia [2007]. The problem we consider is the following: Suppose we know that an abiotic change has an effect on the parameters of a population system, we want to estimate, at the same time both the whole state process and the change of the mentioned parameters, observing the densities of certain indicator populations. For the solution of this problem a constructive method is proposed. Mathematical systems theory offers appropriate concepts and technique for the development such a methodology. The methodological foundations of the application of controllability and observability to frequency-dependent population models (described by systems with invariant manifold), 1877