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

Published online by Cambridge University Press:  27 November 2009

A. N. Gorban ,
E. V. Smirnova  and
T. A. Tyukina
A. N. Gorban*
Affiliation:
Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK
E. V. Smirnova
Affiliation:
Siberian Federal University, Krasnoyarsk, 660041, Russia
T. A. Tyukina
Affiliation:
Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK
*
ag153@le.ac.uk
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Abstract

We study ensembles of similar systemsunder load of environmental factors. The phenomenon of adaptationhas similar properties for systems of different nature. Typically,when the load increases above some threshold, then the adaptingsystems become more different (variance increases), but thecorrelation increases too. If the stress continues to increasethen the second threshold appears: the correlation achievesmaximal value, and start to decrease, but the variance continue toincrease. In many applications this second threshold is a signalof approaching of fatal outcome.
This effect is supported by many experiments and observation ofgroups of humans, mice, trees, grassy plants, and on financialtime series. A general approach to explanation of the effectthrough dynamics of adaptation is developed. H. Selye introduced“adaptation energy" for explanation of adaptation phenomena. Weformalize this approach in factors – resource models anddevelop hierarchy of models of adaptation. Different organizationof interaction between factors (Liebig's versus synergisticsystems) lead to different adaptation dynamics. This gives anexplanation to qualitatively different dynamics of correlationunder different types of load and to some deviation from thetypical reaction to stress.
In addition to the “quasistatic" optimization factor – resourcemodels, dynamical models of adaptation are developed, and asimple model (three variables) for adaptation to one factor loadis formulated explicitly.

Keywords

adaptationfactorcorrelationsprincipal componentsdynamicscrisis
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 6: Ecology (Part 1) , 2009 , pp. 1 - 53
Copyright
© EDP Sciences, 2009

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