Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-21T13:48:09.576Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

S. Breznitz (Ed.). The denial of stress. New York: International Universities Press, Inc., 1983.
Bomze, I.M.. Regularity vs. degeneracy in dynamics, games, and optimization: a unified approach to different aspects. SIAM Review, 44 (2002), 394-414. CrossRef
G.V. Bulygin, A.S. Mansurov, T.P. Mansurova, A.A. Mashanov, E.V. Smirnova. Impact of health on the ecological stress dynamics. Institute of Biophysics, Russian Academy of Sciences, Preprint 185B, Krasnoyarsk, 1992.
G.V. Bulygin, A.S. Mansurov, T.P. Mansurova, E.V. Smirnova. Dynamics of parameters of human metabolic system during the short-term adaptation. Institute of Biophysics, Russian Academy of Sciences, Preprint 180B, Krasnoyarsk, 1992.
Cade, B.S., Terrell, J.W., Schroeder, R.L.. Estimating effects of limiting factors with regression quantiles. Ecology, 80 (1999), 311–323. CrossRef
R. Cangelosi, A. Goriely. Component retention in principal component analysis with application to cDNA microarray data. Biology Direct, 2 (2007). Online: http://www.biology-direct.com/content/2/1/2 CrossRef
T. Colborn, D. Dumanoski, J.P. Meyers. Our stolen future: are we threatening our fertility, intelligence, and survival? – A Scientific Detective Story. Dutton, Peguin Books, NY, 1996.
Çukur, S., Eryigit, M., Eryigt, R.. Cross correlations in an emerging market financial data. Physica A, 376 (2007), 555–564. CrossRef
Daly, H.E.. Population and economics – a bioeconomic analysis. Population and Environment, 12 (1991), 257–263. CrossRef
T. De Donder, P. Van Rysselberghe. Thermodynamic theory of affinity. A book of principles. Stanford: University Press, 1936.
S. Drożdż, F. Grümmer , A.Z. Górski, F. Ruf, J. Speth. Dynamics of competition between collectivity and noise in the stock market. Physica A, 287 (2000) 440–449.
A.C. Eliasson, C. Kreuter. On currency crisis: a continuous crisis definition (Deutsche Bank Research Quantitative Analysis Report), Conference paper, X International “Tor Vergata" Conference on Banking and Finance, December 2001.
Feinberg, M.. Chemical kinetics of a sertain class. Arch. Rat. Mech. Anal., 46 (1972), 1–41. CrossRef
G.F. Gause. The struggle for existence. Williams and Wilkins, Baltimore, 1934. Online: http://www.ggause.com/Contgau.htm.
W.N. Goetzmann, L. Li, K.G. Rouwenhorst. Long-term global market correlations (October 7, 2004). Yale ICF Working Paper No. 08-04. Available at SSRN: http://ssrn.com/abstract=288421
B. Goldstone. The general practitioner and the general adaptation syndrome. S. Afr. Med. J. 26 (1952), 88–92, 106–109. PMID: 14901129, 14913266.
Gopikrishnan, P., Rosenow, B., Amaral, L.A.N., Stanley, H.E.. Universal and Nonuniversal Properties of cross correlations in financial time series. Phys. Rev. Lett., 83 (1999), 1471–1474.
A.N. Gorban. Selection theorem for systems with inheritance. Math. Model. Nat. Phenom., 2, No. 4, 2007, 1–45.
A.N. Gorban, V.T. Manchuk, E.V. Petushkova (Smirnova). Dynamics of physiological parameters correlations and the ecological-evolutionary principle of polyfactoriality. Problemy Ekologicheskogo Monitoringa i Modelirovaniya Ekosistem [The Problems of Ecological Monitoring and Ecosystem Modelling], Vol. 10. Gidrometeoizdat, Leningrad, 1987, pp. 187–198.
A.N. Gorban, O. Radulescu. Dynamic and static limitation in multiscale reaction networks, Revisited. Adv. Chem. Eng., 34 (2008), 103–173.
A.N. Gorban, E.V. Smirnova, T.A. Tyukina. Correlations, risk and crisis: from physiology to finance. Physica A, submitted. arXiv preprint: http://arxiv.org/abs/0905.0129 (May 1, 2009).
J.B.S. Haldane. The causes of evolution. Princeton Science Library, Princeton University Press, 1990.
G.G. Judge, W.E. Griffiths, R.C. Hill, H. Lütkepohl, T.-C. Lee. The theory and practice of econometrics. Wiley Series in Probability and Statistics, # 49 (2nd ed.), Wiley, New York 1985.
Karmanova, I.V., Razzhevaikin, V.N., Shpitonkov, M.I.. Application of correlation adaptometry for estimating a response of herbaceous species to stress loadings. Doklady Botanical Sciences, 346–348 (1996), 4–7. [Translated from Doklady Akademii Nauk SSSR, 346, 1996.]
F. Lillo, R.N. Mantegna. Variety and volatility in financial markets. Phys. Rev. E, 62 (2000), 6126 (2000).
G. L. Litvinov, V. P. Maslov (Eds.). Idempotent mathematics and mathematical physics. Contemporary Mathematics, AMS, Providence, RI, 2005.
F. Longin, B. Solnik. Is the correlation in international equity returns constant: 1960-1990? J. Internat. Money and Finance, 14, No. 1 (1995), 3–26.
A.S. Mansurov, T.P. Mansurova, E.V. Smirnova, L.S. Mikitin, A.V. Pershin. How do correlations between physiological parameters depend on the influence of different systems of stress factors? In: Global & Regional Ecological Problems, R.G. Khlebopros (Ed.), Krasnoyarsk State Technical University Publ., 1994, 499–516.
A.S. Mansurov, T.P. Mansurova, E.V. Smirnova, L.S. Mikitin, A.V. Pershin. Human adaptation under influence of synergic system of factors (treatment of oncological patients after operation). Institute of Biophysics Russian Academy of Sciences, Preprint 212B Krasnoyarsk, 1995.
R.N. Mantegna. Hierarchical structure in financial markets. The European Physical Journal B, 11, No. 1 (1999), 193–197.
Markose, S.M.. Computability and evolutionary complexity: markets as complex adaptive systems (CAS). Economic Journal, 115 (2005), F159–F192. Available online at SSRN: http://ssrn.com/abstract=745578 CrossRef
R.N. Mantegna, H.E. Stanley. An introduction to econophysics: correlations and complexity in finance. Cambridge University Press, Cambridge, 1999.
D. Matesanz, G.J. Ortega. Network analysis of exchange data: Interdependence drives crisis contagion, MPRA Paper No. 7720, posted 12 March 2008, Online at http://mpra.ub.uni-muenchen.de/7720/
R. McCarty, K. Pasak. Alarm phase and general adaptation syndrome. In: Encyclopedia of Stress, George Fink (ed.), Vol. 1, Academic Press, 2000, 126–130.
I. Meric, G. Meric. Co-movements of European equity markets before and after the 1987 crash. Multinational Finance J., 1, No. 2 (1997), 137–152.
E.P. Odum. Fundamentals of ecology (3d ed.). W. B. Saunders, Comp., Philadelphia 96 - London – Toronto, 1971.
Oechssler, J., Riedel, F.. On the dynamic foundation of evolutionary stability in continuous models. J. of Economic Theory, 107 (2002), 223–252. CrossRef
Onnela, J.-P., Chakraborti, A., Kaski, K., Kertész, J., Kanto, A.. Dynamics of market correlations: Taxonomy and portfolio analysis. Physical Review E, 68 (2003), 056110. CrossRef
M.Y. Ozden. Law of the minimum in learning. Educational Technology & Society, 7 , No. 3 (2004), 5–8.
Q. Paris. The return of von Liebig's “Law of the minimum". Agron. J., 84 (1992), 1040–1046
K. Pearson. On lines and planes of closest fit to systems of points in space. Philosophical Magazine, 2, No. 6 (1901), 559–572.
Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L.A.N., Guhr, T., Stanley, H.E.. Random matrix approach to cross correlations in financial data. Phys. Rev. E, 65 (2002), 066126. CrossRef
L.I. Pokidysheva, R.A. Belousova, E.V. Smirnova. Method of adaptometry in the evaluation of gastric secretory function in children under conditions of the North. Vestn. Ross Akad Med Nauk, No. 5 (1996), 42–45. PMID: 8924826
L.D. Ponomarenko, E.V. Smirnova. Dynamical characteristics of blood system in mice with phenilhydrazin anemiya. Proceeding of 9th International Symposium “Reconstruction of homeostasis", Krasnoyarsk, Russia, March 15-20, 1998, vol. 1, 42–45.
M. Potters, J.P. Bouchaud, L. Laloux. Financial applications of random matrix theory: old laces and new pieces. Acta Phys. Pol. B, 36, No. 9 (2005), 2767–2784.
V.N. Razzhevaikin, M.I. Shpitonkov. Substantiation of correlation adaptometry based on evolutionary optimality principles. Computational Mathematics and Mathematical Physics, 43, No. 2 (2003), 296–307.
R.T. Rockafellar. Convex analysis. Princeton University Press, Princeton, NJ, 1970. Reprint: 1997.
F. Salisbury. Plant physiology (4th ed.). Wadsworth Belmont, CA, 1992.
J.K. Schkade, S. Schultz. Occupational adaptation in perspectives. Ch. 7 in: Perspectives in Human Occupation: Participation in Life, By Paula Kramer, Jim Hinojosa, Charlotte Brasic Royeen (eds), Lippincott Williams & Wilkins, Baltimore, MD, 2003, 181–221.
K.R. Sedov, A.N. Gorban', E.V. Petushkova (Smirnova), V.T. Manchuk, E.N. Shalamova. Correlation adaptometry as a method of screening of the population. Vestn. Akad Med Nauk SSSR, No. 10 (1988), 69–75. PMID: 3223045
H. Selye. Adaptation energy. Nature, 141 (3577) (21 May 1938), 926.
Selye, H.. Experimental evidence supporting the conception of “adaptation energy". Am. J. Physiol., 123 (1938), 758–765.
Sengupta, A.M., Mitra, P.P.. Distributions of singular values for some random matrices. Phys. Rev. E, 60 (1999), 3389–3392. CrossRef
F.N. Semevsky, S.M. Semenov. Mathematical modeling of ecological processes. Gidrometeoizdat, Leningrad, 1982.
P.G. Shumeiko, V.I. Osipov, G.B. Kofman. Early detection of industrial emission impact on Scots Pine needles by composition of phenolic compounds. In: Global & Regional Ecological Problems, R.G. Khlebopros (Ed.), Krasnoyarsk State Technical University Publ., 1994, 536–543.
R. Smith. The spread of the credit crisis: view from a stock correlation network (February 23, 2009). Available online at SSRN: http://ssrn.com/abstract=1325803
S.O. Strygina, S.N. Dement'ev, V.M. Uskov, G.I. Chernyshova. Dynamics of the system of correlations between physiological parameters in patients after myocardial infarction. In: Mathematics, Computer, Education, Proceedings of Conference, Issue 7, Moscow, 2000, 685–689.
G.N. Svetlichnaia, E.V. Smirnova, L.I. Pokidysheva. Correlational adaptometry as a method for evaluating cardiovascular and respiratory interaction. Fiziol. Cheloveka, 23, No. 3 (1997), 58–62. PMID: 9264951
A.V. Vasil'ev, G.Iu. Mal'tsev, Iu.V. Khrushcheva, V.N. Razzhevaikin, M.I. Shpitonkov. Applying method of correlation adaptometry for evaluating of treatment efficiency of obese patients. Vopr. Pitan., 76, No. 2 (2007), 36–38. PMID: 17561653
M.J. West-Eberhard. Developmental plasticity and evolution. Oxford University Press, US, 2003.
Zuckerkandl, E., Villet, R.. Concentration-affinity equivalence in gene regulation: convergence of genetic and environmental effects. PNAS USA, 85 (1988), 4784–4788. CrossRef