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

52 Pages Posted: 28 May 2009

See all articles by Alexander N. Gorban

Alexander N. Gorban

University of Leicester, UK

Elena V. Smirnova

affiliation not provided to SSRN

Tatiana A. Tyukina

affiliation not provided to SSRN

Date Written: May 28, 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.

Keywords: Correlations, Factor, Principal components, Adaptation, Dynamics, Crisis Indicator

JEL Classification: C32, C69

Suggested Citation

Gorban, Alexander N. and Smirnova, Elena V. and Tyukina, Tatiana A., General Laws of Adaptation to Environmental Factors: From Ecological Stress to Financial Crisis (May 28, 2009). Available at SSRN: https://ssrn.com/abstract=1411127 or http://dx.doi.org/10.2139/ssrn.1411127

Alexander N. Gorban (Contact Author)

University of Leicester, UK ( email )

University Road
Leicester, LE1 7RH
United Kingdom

Elena V. Smirnova

affiliation not provided to SSRN

Tatiana A. Tyukina

affiliation not provided to SSRN

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