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

A. N. Gorban; E. V. Smirnova; T. A. Tyukina

Mathematical Modelling of Natural Phenomena (2009)

  • Volume: 4, Issue: 6, page 1-53
  • ISSN: 0973-5348

Abstract

top
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.

How to cite

top

Gorban, A. N., Smirnova, E. V., and Tyukina, T. A.. "General Laws of Adaptation to Environmental Factors: from Ecological Stress to Financial Crisis." Mathematical Modelling of Natural Phenomena 4.6 (2009): 1-53. <http://eudml.org/doc/222333>.

@article{Gorban2009,
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. },
author = {Gorban, A. N., Smirnova, E. V., Tyukina, T. A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {adaptation; factor; correlations; principal components; dynamics; crisis; principal components},
language = {eng},
month = {11},
number = {6},
pages = {1-53},
publisher = {EDP Sciences},
title = {General Laws of Adaptation to Environmental Factors: from Ecological Stress to Financial Crisis},
url = {http://eudml.org/doc/222333},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Gorban, A. N.
AU - Smirnova, E. V.
AU - Tyukina, T. A.
TI - General Laws of Adaptation to Environmental Factors: from Ecological Stress to Financial Crisis
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/11//
PB - EDP Sciences
VL - 4
IS - 6
SP - 1
EP - 53
AB - 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.
LA - eng
KW - adaptation; factor; correlations; principal components; dynamics; crisis; principal components
UR - http://eudml.org/doc/222333
ER -

References

top
  1. S. Breznitz (Ed.). The denial of stress. New York: International Universities Press, Inc., 1983.  
  2. I.M. Bomze. Regularity vs. degeneracy in dynamics, games, and optimization: a unified approach to different aspects.SIAM Review, 44 (2002), 394-414.  
  3. 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.  
  4. 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.  
  5. B.S. Cade, J.W. Terrell, R.L. Schroeder. Estimating effects of limiting factors with regression quantiles.Ecology, 80 (1999), 311–323.  
  6. R. Cangelosi, A. Goriely. Component retention in principal component analysis with application to cDNA microarray data. Biology Direct, 2 (2007). Online:  URIhttp://www.biology-direct.com/content/2/1/2
  7. 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.  
  8. S. Çukur, M. Eryigit, R. Eryigt. Cross correlations in an emerging market financial data.Physica A, 376 (2007), 555–564.  
  9. H.E. Daly. Population and economics – a bioeconomic analysis.Population and Environment, 12 (1991), 257–263.  
  10. T. De Donder, P. Van Rysselberghe. Thermodynamic theory of affinity. A book of principles. Stanford: University Press, 1936.  
  11. 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.  
  12. 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.  
  13. M. Feinberg. Chemical kinetics of a sertain class.Arch. Rat. Mech. Anal., 46 (1972), 1–41.  
  14. G.F. Gause. The struggle for existence. Williams and Wilkins, Baltimore, 1934. Online: .  URIhttp://www.ggause.com/Contgau.htm
  15. 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:  URIhttp://ssrn.com/abstract=288421
  16. B. Goldstone. The general practitioner and the general adaptation syndrome. S. Afr. Med. J. 26 (1952), 88–92, 106–109. PMID: 14901129, 14913266.  
  17. P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, H.E. Stanley. Universal and Nonuniversal Properties of cross correlations in financial time series.Phys. Rev. Lett., 83 (1999), 1471–1474.  
  18. A.N. Gorban. Selection theorem for systems with inheritance. Math. Model. Nat. Phenom., 2, No. 4, 2007, 1–45.  
  19. 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.  
  20. A.N. Gorban, O. Radulescu. Dynamic and static limitation in multiscale reaction networks, Revisited. Adv. Chem. Eng., 34 (2008), 103–173.  
  21. A.N. Gorban, E.V. Smirnova, T.A. Tyukina. Correlations, risk and crisis: from physiology to finance. Physica A, submitted. arXiv preprint: (May 1, 2009).  URIhttp://arxiv.org/abs/0905.0129
  22. J.B.S. Haldane. The causes of evolution. Princeton Science Library, Princeton University Press, 1990.  
  23. 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.  
  24. I.V. Karmanova, V.N. Razzhevaikin, M.I. Shpitonkov. 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.]  
  25. F. Lillo, R.N. Mantegna. Variety and volatility in financial markets. Phys. Rev. E, 62 (2000), 6126 (2000).  
  26. G. L. Litvinov, V. P. Maslov (Eds.). Idempotent mathematics and mathematical physics. Contemporary Mathematics, AMS, Providence, RI, 2005.  
  27. 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.  
  28. 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.  
  29. 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.  
  30. R.N. Mantegna. Hierarchical structure in financial markets. The European Physical Journal B, 11, No. 1 (1999), 193–197.  
  31. S.M. Markose. Computability and evolutionary complexity: markets as complex adaptive systems (CAS).Economic Journal, 115 (2005), F159–F192. Available online at SSRN:  URIhttp://ssrn.com/abstract=745578
  32. R.N. Mantegna, H.E. Stanley. An introduction to econophysics: correlations and complexity in finance. Cambridge University Press, Cambridge, 1999.  
  33. D. Matesanz, G.J. Ortega. Network analysis of exchange data: Interdependence drives crisis contagion, MPRA Paper No. 7720, posted 12 March 2008, Online at  URIhttp://mpra.ub.uni-muenchen.de/7720/
  34. R. McCarty, K. Pasak. Alarm phase and general adaptation syndrome. In: Encyclopedia of Stress, George Fink (ed.), Vol. 1, Academic Press, 2000, 126–130.  
  35. 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.  
  36. E.P. Odum. Fundamentals of ecology (3d ed.). W. B. Saunders, Comp., Philadelphia 96 - London – Toronto, 1971.  
  37. J. Oechssler, F. Riedel. On the dynamic foundation of evolutionary stability in continuous models.J. of Economic Theory, 107 (2002), 223–252.  
  38. J.-P. Onnela, A. Chakraborti, K. Kaski, J. Kertész, A. Kanto. Dynamics of market correlations: Taxonomy and portfolio analysis.Physical Review E, 68 (2003), 056110.  
  39. M.Y. Ozden. Law of the minimum in learning. Educational Technology & Society, 7 , No. 3 (2004), 5–8.  
  40. Q. Paris. The return of von Liebig's “Law of the minimum". Agron. J., 84 (1992), 1040–1046  
  41. K. Pearson. On lines and planes of closest fit to systems of points in space. Philosophical Magazine, 2, No. 6 (1901), 559–572.  
  42. V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, T. Guhr, H.E. Stanley. Random matrix approach to cross correlations in financial data.Phys. Rev. E, 65 (2002), 066126.  
  43. 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  
  44. 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.  
  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.  
  46. 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.  
  47. R.T. Rockafellar. Convex analysis. Princeton University Press, Princeton, NJ, 1970. Reprint: 1997.  
  48. F. Salisbury. Plant physiology (4th ed.). Wadsworth Belmont, CA, 1992.  
  49. 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.  
  50. 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  
  51. H. Selye. Adaptation energy. Nature, 141 (3577) (21 May 1938), 926.  
  52. H. Selye. Experimental evidence supporting the conception of “adaptation energy".Am. J. Physiol., 123 (1938), 758–765.  
  53. A.M. Sengupta, P.P. Mitra. Distributions of singular values for some random matrices.Phys. Rev. E, 60 (1999), 3389–3392.  
  54. F.N. Semevsky, S.M. Semenov. Mathematical modeling of ecological processes. Gidrometeoizdat, Leningrad, 1982.  
  55. 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.  
  56. R. Smith. The spread of the credit crisis: view from a stock correlation network (February 23, 2009). Available online at SSRN:  URIhttp://ssrn.com/abstract=1325803
  57. 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.  
  58. 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  
  59. 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  
  60. M.J. West-Eberhard. Developmental plasticity and evolution. Oxford University Press, US, 2003.  
  61. E. Zuckerkandl, R. Villet. Concentration-affinity equivalence in gene regulation: convergence of genetic and environmental effects.PNAS USA, 85 (1988), 4784–4788.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.