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Issue Math. Model. Nat. Phenom.
Volume 4, Number 6, 2009
Ecology (Part 1)
Page(s) 1 - 53
DOI 10.1051/mmnp/20094601
Published online 27 November 2009

Math. Model. Nat. Phenom. Vol. 4, No. 6, 2009, pp. 1-53
DOI: 10.1051/mmnp/20094601

General Laws of Adaptation to Environmental Factors: from Ecological Stress to Financial Crisis

A.N. Gorban1, E.V. Smirnova2 and T.A. Tyukina1

1  Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK
2  Siberian Federal University, Krasnoyarsk, 660041, Russia

ag153@le.ac.uk

Published online: 27 November 2009

Abstract
We study ensembles of similar systems under load of environmental factors. The phenomenon of adaptation has similar properties for systems of different nature. Typically, when the load increases above some threshold, then the adapting systems become more different (variance increases), but the correlation increases too. If the stress continues to increase then the second threshold appears: the correlation achieves maximal value, and start to decrease, but the variance continue to increase. In many applications this second threshold is a signal of approaching of fatal outcome.
This effect is supported by many experiments and observation of groups of humans, mice, trees, grassy plants, and on financial time series. A general approach to explanation of the effect through dynamics of adaptation is developed. H. Selye introduced “adaptation energy" for explanation of adaptation phenomena. We formalize this approach in factors – resource models and develop hierarchy of models of adaptation. Different organization of interaction between factors (Liebig's versus synergistic systems) lead to different adaptation dynamics. This gives an explanation to qualitatively different dynamics of correlation under different types of load and to some deviation from the typical reaction to stress.
In addition to the “quasistatic" optimization factor – resource models, dynamical models of adaptation are developed, and a simple model (three variables) for adaptation to one factor load is formulated explicitly.


Mathematics Subject Classification. 92D40, 93C40, 91B84, 62M10

Key words: adaptation -- factor -- correlations -- principal components -- dynamics -- crisis


© EDP Sciences 2009


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