Law of the Minimum Paradoxes

Bulletin of Mathematical Biology

Volumn 73, Issue 9, 2011, Pages 2013-2044

  Gorban, Alexander N ^a   Pokidysheva, Lyudmila I ^b   Smirnova, Elena V ^b   Tyukina, Tatiana A ^a  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

^b SIBERIAN FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

Adaptation; Fitness; Liebig's Law; Stress

Indexed keywords

ADAPTATION; ARTICLE; BIOLOGICAL MODEL; ECOSYSTEM; POPULATION DYNAMICS;

ADAPTATION, PHYSIOLOGICAL; ECOSYSTEM; MODELS, BIOLOGICAL; POPULATION DYNAMICS;

EID: 79961028872     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-010-9597-1     Document Type: Article

References (91)

1. Aumont, O., Maier-Reimer, E., Blain, S., & Monfray, P. (2003). An ecosystem model of the global ocean including Fe, Si, P colimitations. Glob. Biogeochem. Cycles, 17(2), 1060. doi: 10. 1029/2001GB001745.
2. Austin, M. (2007). Species distribution models and ecological theory: A critical assessment and some possible new approaches. Ecol. Model., 200(1-2), 1-19.
3. Ballantyne, F. IV, Menge, D. N. L., Ostling, A., & Hosseini, P. (2008). Nutrient recycling affects autotroph and ecosystem stoichiometry. Am. Nat., 171(4), 511-523.
4. Bloom, A. J., Chapin, F. S. III, & Mooney, H. A. (1985). Resource limitation in plants-an economic analogy. Annu. Rev. Ecol. Syst., 16, 363-392.
5. Bomze, I. M. (2002). Regularity vs. degeneracy in dynamics, games, and optimization: a unified approach to different aspects. SIAM Rev., 44, 394-414.
6. Breznitz, S. (Ed.) (1983). The denial of stress. New York: International Universities Press.
7. Brown, G. C., & Cooper, C. E. (1993). Control analysis applied to a single enzymes: can an isolated enzyme have a unique rate-limiting step? Biochem. J., 294, 87-94.
8. Bulygin, G. V., Mansurov, A. S., Mansurova, T. P., & Smirnova, E. V. (1992a). Dynamics of parameters of human metabolic system during the short-term adaptation. Institute of Biophysics, Russian Academy of Sciences, Preprint 180B, Krasnoyarsk.
9. Bulygin, G. V., Mansurov, A. S., Mansurova, T. P., Mashanov, A. A., & Smirnova, E. V. (1992b). Impact of health on the ecological stress dynamics. Institute of Biophysics, Russian Academy of Sciences, Preprint 185B, Krasnoyarsk.
10. Cade, B. S., Terrell, J. W., & Schroeder, R. L. (1999). Estimating effects of limiting factors with regression quantiles. Ecology, 80(1), 311-323.
11. Campbell, J. Y., Lo, A.-W., & MacKinlay, A. C. (1997). The econometrics of financial markets. Princeton: Princeton University Press.
12. Chapin, F. S. III, Schulze, E., & Mooney, H. A. (1990). The ecology and economics of storage in plants. Annu. Rev. Ecol. Syst., 21, 423-447.
13. Chauvet, G. A. (1999). S-propagators: a formalism for the hierarchical organization of physiological systems. Application to the nervous and the respiratory systems. Int. J. Gen. Syst., 28(1), 53-96.
14. Chertov, O., Gorbushina, A., & Deventer, B. (2004). A model for microcolonial fungi growth on rock surfaces. Ecol. Model., 177(3-4), 415-426.
15. Colborn, T., Dumanoski, D., & Meyers, J. P. (1996). Our stolen future: are we threatening our fertility, intelligence, and survival?-A scientific detective story. Dutton: Peguin Books.
16. Crampin, E. J., Halstead, M., Hunter, P., Nielsen, P., Noble, D., Smith, N., & Tawhai, M. (2004). Computational physiology and the physiome project. Exp. Physiol., 89, 1-26.
17. Daly, H. E. (1991). Population and economics-a bioeconomic analysis. Popul. Environ., 12(3), 257-263.
18. Danger, M., Daufresne, T., Lucas, F., Pissard, S., & Lacroix, G. (2008). Does Liebig's law of the minimum scale up from species to communities? Oikos, 117(11), 1741-1751.
19. Droop, M. R. (1973). Some thoughts on nutrient limitation in algae. J. Phycol., 9, 264-272.
20. Drożdż, S., Grümmer, F., Górski, A. Z., Ruf, F., & Speth, J. (2000). Dynamics of competition between collectivity and noise in the stock market. Physica A, 287, 440-449.
21. Egli, T., & Zinn, M. (2003). The concept of multiple-nutrient-limited growth of microorganisms and its application in biotechnological processes. Biotechnol. Adv., 22(1-2), 35-43.
22. Fisher, R. A. (1930). The genetical theory of natural selection. Oxford: Oxford University Press.
23. Fusco, G., & Minelli, A. (2010). Phenotypic plasticity in development and evolution: facts and concepts. Philos. Trans. R. Soc. B, 365(1540), 547-556.
24. Gause, G. F. (1934). The struggle for existence. Baltimore: Williams and Wilkins. Online: http://www. ggause. com/Contgau. htm.
25. Goldstone, B. (1952). The general practitioner and the general adaptation syndrome. S. Afr. Med. J., 26, 88-92, 106-109. PMID: 14901129, 14913266.
26. Gorban, A. N. (1984). Equilibrium encircling. Equations of chemical kinetics and their thermodynamic analysis. Novosibirsk: Nauka.
27. Gorban, A. N. (2004). Singularities of transition processes in dynamical systems: qualitative theory of critical delays. Electron. J. Diff. Eqns. Monograph (Vol. 05). E-print: arXiv: chao-dyn/9703010.
28. Gorban, A. N. (2007). Selection theorem for systems with inheritance. Math. Model. Nat. Phenom., 2(4), 1-45. E-print: arXiv: cond-mat/0405451 [cond-mat. stat-mech].
29. Gorban, A. N., & Radulescu, O. (2008). Dynamic and static limitation in multiscale reaction networks, revisited. Adv. Chem. Eng., 34, 103-173.
30. Gorban, A. N., & Zinovyev, A. Y. (2009). Principal graphs and manifolds. In E. S. Olivas et al. (Eds.), Handbook of research on machine learning applications and trends: algorithms, methods, and techniques (pp. 28-59). Hershey: IGI Global. E-print: arXiv: 0809. 0490 [cs. LG].
31. Gorban, A. N., Manchuk, V. T., & Petushkova (Smirnova), E. V. (1987). Dynamics of physiological paramethers correlations and the ecological-evolutionary principle of polyfactoriality. In Problemy Ekologicheskogo Monitoringa i Modelirovaniya Ekosistem [The Problems of Ecological Monitoring and Ecosystem Modelling] (pp. 187-198). Leningrad: Gidrometeoizdat.
32. Gorban, A. N., Kegl, B., Wunsch, D., & Zinovyev, A. (2008). Principal manifolds for data visualisation and dimension reduction. Lecture notes in computational science and engineering (Vol. 58). Berlin-Heidelberg-New York: Springer.
33. Gorban, A. N., Smirnova, E. V., & Tyukina, T. A. (2009). Correlations, risk and crisis: from physiology to finance. E-print: arXiv: 0905. 0129 [physics. bio-ph].
34. Gorban, A. N., Radulescu, O., & Zinovyev, A. Y. (2010). Asymptotology of chemical reaction networks. Chem. Eng. Sci., 65, 2310-2324.
35. Greene, E. (1999). Phenotypic variation in larval development and evolution: polymorphism, polyphenism, and developmental reaction norms. In M. Wake & B. Hall (Eds.), The origin and evolution of larval forms (pp. 379-410). San Diego: Academic Press.
36. Haldane, J. B. S. (1932). The causes of evolution. London: Longmans Green.
37. Hennessy, D. A. (2009). Crop yield skewness under law of the minimum technology. Am. J. Agric. Econ., 91(1), 197-208.
38. Hoffman, R. J. (1978). Environmental uncertainty and evolution of physiological adaptation in colias butterflies. Am. Nat., 112(988), 999-1015.
39. Hutchinson, G. E. (1961). The paradox of the plankton. Am. Nat., 95, 137-145.
40. Jolliffe, I. T. (2002). Principal component analysis, series. Springer series in statistics (Vol. 2). New York: Springer.
41. Karmanova, I. V., Razzhevaikin, V. N., & Shpitonkov, M. I. (1996). Application of correlation adaptometry for estimating a response of herbaceous species to stress loadings. Dokl. Botanic. Sci., 346-348, 4-7. Translated from Dokl. Akad. Nauk SSSR, 346, 1996.
42. Kingsolver, J. G., & Pfennig, D. W. (2007). Patterns and power of phenotypic selection in nature. BioScience, 57(7), 561-572.
43. Kleene, S. C. (1956). Representation of events in nerve sets and finite automata. In J. McCarthy & C. Shannon (Eds.), Automata studies (pp. 3-40). Princeton: Princeton University Press.
44. Kobe, R. K. (1996). Intraspecific variation in sapling mortality and growth predicts geographic variation in forest composition. Ecol. Monogr., 66(2), 181-201.
45. Kolokoltsov, V., & Maslov, V. (1997). Idempotent analysis and applications. Dordrecht: Kluwer Academic.
46. Legović, T., & Cruzado, A. (1997). A model of phytoplankton growth on multiple nutrients based on the Michaelis-Menten-Monod uptake, Droop's growth and Liebig's law. Ecol. Model., 99(1), 19-31.
47. Lerner, H. R. (Ed.) (1999). Plant responses to environmental stresses: from phytohormones to genome reorganization. New York: Dekker.
48. Litvinov, G. L. (2007). The Maslov dequantization idempotent and tropical mathematics: a brief introduction. J. Math. Sci., 140(3), 426-444. arXiv: math/0507014 [math. GM].
49. Litvinov, G. L., & Maslov, V. P. (Eds.) (2005). Idempotent mathematics and mathematical physics. Contemporary mathematics (Vol. 377). Providence: AMS.
50. Mansurov, A. S., Mansurova, T. P., Smirnova, E. V., Mikitin, L. S., & Pershin, A. V. (1994). How do correlations between physiological parameters depend on the influence of different systems of stress factors. In R. G. Khlebopros (Ed.), Global & regional ecological problems (pp. 499-516). Krasnoyarsk: Krasnoyarsk State Technical University Publ.
51. Mansurov, A. S., Mansurova, T. P., Smirnova, E. V., Mikitin, L. S., & Pershin, A. V. (1995). 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.
52. Marmarelis, V. Z. (1997). Modeling methodology for nonlinear physiological systems. Ann. Biomed. Eng., 25(2), 239-251.
53. Marmarelis, V. Z. (2004). Nonlinear dynamic modeling of physiological systems. New York: Wiley.
54. Maynard-Smith, J. (1982). Evolution and the theory of games. Cambridge: Cambridge University Press.
55. McCarty, R., & Pasak, K. (2000). Alarm phase and general adaptation syndrome. In G. Fink (Ed.), Encyclopedia of stress (Vol. 1, pp. 126-130). San Diego: Academic Press.
56. McGill, B. (2005). A mechanistic model of a mutualism and its ecological and evolutionary dynamics. Ecol. Model., 187(4), 413-425.
57. Menge, D. N. L., & Weitz, J. S. (2009). Dangerous nutrients: Evolution of phytoplankton resource uptake subject to virus attack. J. Theor. Biol., 257(1), 104-115.
58. Metz, J. A. J., Nisbet, R. M., & Geritz, S. A. H. (1992). How should we define fitness for general ecological scenarios. Trends Ecol. Evol., 7, 198-202.
59. Milo, R., Hou, J. H., Springer, M., Brenner, M. P., & Kirschner, M. W. (2007). The relationship between evolutionary and physiological variation in hemoglobin. PNAS USA, 104(43), 16998-17003.
60. Nijland, G. O., Schouls, J., & Goudriaan, J. (2008). Integrating the production functions of Liebig Michaelis-Menten, Mitscherlich and Liebscher into one system dynamics model. NJAS-Wageningen J. Life Sci., 55(2), 199-224.
61. Odum, E. P. (1971). Fundamentals of ecology (3rd ed.). Philadelphia-London-Toronto: Saunders.
62. Oechssler, J., & Riedel, F. (2002). On the dynamic foundation of evolutionary stability in continuous models. J. Econ. Theory, 107, 223-252.
63. Ozden, M. Y. (2004). Law of the minimum in learning. Educ. Technol. Soc., 7(3), 5-8.
64. Paris, Q. (1992). The return of von Liebig's "Law of the Minimum". Agron. J., 84, 1040-1046.
65. Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L. A. N., Guhr, T., & Stanley, H. E. (2002). Random matrix approach to cross correlations in financial data. Phys. Rev. E, 65, 066126.
66. Ponomarenko, L. D., & Smirnova, E. V. (1998). Dynamical characteristics of blood system in mice with phenilhydrazin anemiya. In Proceeding of 9th international symposium "Reconstruction of homeostasis" (Vol. 1, pp. 42-45), March 15-20, Krasnoyarsk, Russia.
67. Rockafellar, R. T. (1997). Convex analysis. Princeton: Princeton University Press.
68. Saito, M. A., & Goepfert, T. J. (2008). Some thoughts on the concept of colimitation: Three definitions and the importance of bioavailability. Limnol. Oceanogr., 53(1), 276-290.
69. Salisbury, F. (1992). Plant physiology (4th ed.). Belmont: Wadsworth.
70. Schkade, J. K., & Schultz, S. (2003). Occupational adaptation in perspectives. In P. Kramer, J. Hinojosa & C. B. Royeen (Eds.), Perspectives in human occupation participation in life (pp. 181-221). Baltimore: Lippincott Williams & Wilkins. Chap. 7.
71. Sedov, K. R., Gorban', A. N., Petushkova (Smirnova), E. V., Manchuk, V. T., & Shalamova, E. N., (1988). Correlation adaptometry as a method of screening of the population. Vestn. Akad. Med. Nauk SSSR, 10, 69-75. PMID: 3223045.
72. Selye, H. (1938a). Adaptation energy. Nature, 141(3577), 926.
73. Selye, H. (1938b). Experimental evidence supporting the conception of "adaptation energy". Am. J. Physiol., 123, 758-765.
74. Semevsky, F. N., & Semenov, S. M. (1982). Mathematical modeling of ecological processes. Leningrad: Gidrometeoizdat.
75. Shaw, R. G., Geyer, C. J., Wagenius, S., Hangelbroek, H. H., & Etterson, J. R. (2008). Unifying life-history analyses for inference of fitness and population growth. Am. Nat., 172, E35-E47.
76. Shoresh, N., Hegreness, M., & Kishony, R. (2008). Evolution exacerbates the paradox of the plankton. PNAS USA, 105(34), 12365-12369.
77. Shumeiko, P. G., Osipov, V. I., & Kofman, G. B. (1994). Early detection of industrial emission impact on Scots Pine needles by composition of phenolic compounds. In R. G. Khlebopros (Ed.), Global & regional ecological problems (pp. 536-543). Krasnoyarsk: Krasnoyarsk State Technical University Publ.
78. Sih, A., & Gleeson, S. K. (1995). A limits-oriented approach to evolutionary ecology. Trends Ecol. Evol., 10(9), 378-382.
79. Strygina, S. O., Dement'ev, S. N., Uskov, V. M., & Chernyshova, G. I. (2000). Dynamics of the system of correlations between physiological parameters in patients after myocardial infarction. In Mathematics computer, education. Proceedings of conference (Vol. 7, pp. 685-689), Moscow.
80. Sudakov, K. V. (2004). Functional systems theory: a new approach to the question of the integration of physiological processes in the body. Neurosci. Behav. Physiol., 34(5), 495-500.
81. Svetlichnaia, G. N., Smirnova, E. V., & Pokidysheva, L. I. (1997). Correlational adaptometry as a method for evaluating cardiovascular and respiratory interaction. Fiziol. Chelov., 23(3), 58-62. PMID: 9264951.
82. Thomson, J. D., Weiblen, G., Thomson, B. A., Alfaro, S., & Legendre, P. (1996). Untangling multiple factors in spatial distributions: lilies, gophers and rocks. Ecology, 77, 1698-1715.
83. Tilman, D. (1980). Resources: a graphical-mechanistic approach to competition and predation. Am. Nat., 116(3), 362-393.
84. Tilman, D. (1982). Resource competition and community structure. Princeton: Princeton University Press.
85. van den Berg, H. A. (1998). Multiple nutrient limitation in unicellulars: reconstructing Liebig's law. Math. Biosci., 149(1), 1-22.
86. van der Ploeg, R. R., Böhm, W., & Kirkham, M. B. (1999). On the origin of the theory of mineral nutrition of plants and the law of the minimum. Soil Sci. Soc. Am. J., 63, 1055-1062.
87. Waxman, D., & Welch, J. J. (2005). Fisher's microscope and Haldane's ellipse. Am. Nat., 166, 447-457.
88. West-Eberhard, M. J. (2003). Developmental plasticity and evolution. Oxford: Oxford University Press.
89. Wutzler, T., & Reichstein, M. (2008). Colimitation of decomposition by substrate and decomposers-a comparison of model formulations. Biogeosci. Discuss., 5, 163-190.
90. Zinn, M., Witholt, B., & Egli, T. (2004). Dual nutrient limited growth: models experimental observations, and applications. J. Biotechnol., 113(1-3), 263-279.
91. Zuckerkandl, E., & Villet, R. (1988). Concentration-affinity equivalence in gene regulation: convergence of genetic and environmental effects. PNAS USA, 85, 4784-4788.