Mathematical Basis of Complex Ecological Evaluation

Andrew Adamatzky (Intelligent Autonomous Systems Lab University of the West of England Bristol BS16 1QY, UK E‐mail:


ISSN: 0368-492X

Article publication date: 1 April 2000




Adamatzky, A. (2000), "Mathematical Basis of Complex Ecological Evaluation", Kybernetes, Vol. 29 No. 3, pp. 392-398.



Emerald Group Publishing Limited

The book is a surprising combination of classical techniques for analysis of large scale ecological systems with fresh concepts of biomolecular computing. A problem is to efficiently implement an integral evaluation of an ecological systems, i.e. identification of integral parameters of a state of environment from data of ecological monitoring. The authors make a couple of remarkable transformations of the problem. The problem of integral ecological evaluation is thought of in terms of an image recognition problem. The image recognition itself is implemented in a mathematical model of molecular recognition (Tarakanov, 1998a), i.e. with the help of formal peptides. The model of molecular recognition is derived from concepts of artificial peptide and artificial immune networks, where change of a topology of a peptide as a reaction on an external stimulus is considered as a prototype of biological recognition (Tarakanov, 1998b,c, 1999). Authors of the book hope that this approach will successfully compete with artificial neural networks (Dasgupta, 1998; Tarakanov and Dasgupka, 1999).

The first chapter introduces a problem of many‐component ecological evaluations. A focus is made on the choice of a unique integral criterion of an ecological system. The criterion represents numerous partial values and parameters derived from real life measurements. The chapter presents a case study of the development of an ecological atlas of St Petersburg (Govelik et al., 1992). The atlas consists of ten specialised maps (atmosphere, aquatic resources, flora and fauna etc.). Each of the maps employs a unique factor of reactive dynamic of the ecological system. These maps may be aggregated into an integral map, which will represent the ecological situation in general; this would ease comparing ecological zones and making computer analysis of the ecological situation. However, before publication of the book, there was no sensible technique for merging several specialised ecological maps into a single integral one. The authors try to fill the gap and to construct a rigorous mathematical background for heuristic approaches.

The second chapter presents a comparative study of contemporary mathematical techniques of analysis of ecological systems. Advantages of integral ecological evaluation are demonstrated there. The chapter results in representation of the problem in terms of image recognition.

A theoretical framework of the molecular recognition is given in the third chapter. A foundation of molecular recognition is built on the concept of a formal peptide, which employs known relations between free energy of a peptide molecule and its topology. The formal peptide can self‐organise its parameters during folding and binding with other formal peptides. This depends on the molecule’s own topology and states of the spatially neighbouring molecules. An artificial immune network emerges when several peptides are bound together. The entire network is capable of learning, recognition and decision making in uncertainty because binding links between molecules are variable and flexible.

The fourth chapter transforms the model of molecular recognition to a mathematical model of integral ecological evaluation. Basic formulae, criteria and recognition procedures are discussed. Namely, the authors analyse folding of initial data into a matrix (to increase selectivity of the recognition); supervised learning and recognition; unsupervised learning and data classification.

A bunch of applications is studied in the fifth chapter. We should mention their computation of maps for ecological atlases of St Petersburg and Kaliningrad, determination of correlation between pollution and health in the city of Tula, and investigation of similarities in a dynamic of infectious diseases in Russia for the period of 1996‐1997.

This small but capacious book exhibits nontrivial ideas, concepts and techniques and will certainly attract experts in biological computing, artificial intelligence, applied mathematics and ecology[1].


  1. 1.

    1. The book is written in English, which excludes annoying deviations in terminology so usual in non‐authorised translations. Those interested in the book may contact one of the authors – Dr Alexander Tarakanov on


Dasgupta, D. (Ed.) (1998), Artificial Immune Systems and Their Applications, Springer‐Verlag, New York, NY.

Gorelik, D.O., Kuznetsov, V.I. and Khrovov, G.V. (Eds) (1992), Ecological Atlas of St Petersburg, Monitoring Press, St Petersburg (in Russian).

Tarakanov, A.O. (1998a), “Complex ecological evaluation by mathematical model of molecular recognition”, in Proc. Int. Workshop Tools for Mathematical Modelling, St Petersburg, pp. 62‐7.

Tarakanov, A.O. (1998b), “Mathematical models of biomolecular information processing: formal peptide instead of formal neurone”, Problems of Informatization, Vol. 1, pp. 46‐51 (in Russian).

Tarakanov, A.O. (1998c), Mathematical Models of Basic Biomolecular Mechanisms of Information Processing”, SPIIRAN Press, St Petersburg.

Tarakanov, A.O. (1999), “Formal peptide as a basis agent of immune networks: from natural prototype to mathematical theory and applications”, in Proc. 1st Int. Workshop of Central and Eastern Europe on Multi‐Agent Systems, St. Petersburg, pp. 281‐92.

Tarakanov, A. and Dasgupta D. (1999), “A formal immune system”, in Proc. 3rd Int. Workshop Information Processing in Cells and Tissues, Indianopolis.

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