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Punctuated Equilibrium in Statistical Models of Generalized Coevolutionary Resilience: How Sudden Ecosystem Transitions Can Entrain Both Phenotype Expression and Darwinian Selection

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Transactions on Computational Systems Biology IX

Part of the book series: Lecture Notes in Computer Science ((TCSB,volume 5121))

Abstract

We argue that mesoscale ecosystem resilience shifts akin to sudden phase transitions in physical systems can entrain similarly punctuated events of gene expression on more rapid time scales, and, in part through such means, slower changes induced by selection pressure, triggering punctuated equilibrium Darwinian evolutionary transitions on geologic time scales. The approach reduces ecosystem, gene expression, and Darwinian genetic dynamics to a least common denominator of information sources interacting by crosstalk at markedly differing rates. Pettini’s ‘topological hypothesis’, via a homology between information source uncertainty and free energy density, generates a regression-like class of statistical models of sudden coevolutionary phase transition based on the Rate Distortion and Shannon-McMillan Theorems of information theory which links all three levels. A mathematical treatment of Holling’s extended keystone hypothesis regarding the particular role of mesoscale phenomena in entraining both slower and faster dynamical structures produces the result. A main theme is the necessity of a cognitive paradigm for gene expression, mirroring I. Cohen’s cognitive approach to immune function. Invocation of the necessary conditions imposed by the asymptotic limit theorems of communication theory enables us to penetrate one layer more deeply before needing to impose an empirically-derived phenomenological system of ‘Onsager relation’ recursive coevolutionary stochastic differential equations. Extending the development to second order via a large deviations argument permits modeling the influence of human cultural structures on ecosystems as ‘farming’.

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References

  1. Adami, C., Cerf, N.: Physical complexity of symbolic sequences. Physica D 137, 62–69 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Adami, C., Ofria, C., Collier, T.: Evolution of biological complexity. Proceedings of the National Academy of Sciences 97, 4463–4468 (2000)

    Article  Google Scholar 

  3. Albert, R., Barabasi, A.: Statistical mechanics of complex networks. Reviews of Modern Physics 74, 47–97 (2002)

    Article  MathSciNet  Google Scholar 

  4. Ancel, L.: A quantitative model of the Simpson-Baldwin effect. Journal of Theoretical Biology 196, 197–209 (1999)

    Article  Google Scholar 

  5. Ash, R.: Information Theory. Dover Publications, New York (1990)

    MATH  Google Scholar 

  6. Atlan, H., Cohen, I.: Immune information, self-organization and meaning. International Immunology 10, 711–717 (1998)

    Article  Google Scholar 

  7. Auslander, L.: Differential Geometry. Harper and Row, New York (1967)

    MATH  Google Scholar 

  8. Avital, E., Jablonka, E.: Animal Traditions: Behavioral inheritance in evolution. Cambridge University Press, New York (2000)

    Book  Google Scholar 

  9. Baker, M., Stock, J.: Signal transduction: networks and integrated circuits in bacterial cognition. Current Biology 17(4), R1021–R1024 (2007)

    Article  Google Scholar 

  10. Barkow, J., Cosmides, L., Tooby, J. (eds.): The Adapted Mind: Biological Approaches to Mind and Culture. University of Toronto Press (1992)

    Google Scholar 

  11. Beck, C., Schlogl, F.: Thermodynamics of Chaotic Systems. Cambridge University Press, Cambridge (1995)

    MATH  Google Scholar 

  12. Binney, J., Dowrick, N., Fisher, A., Newman, M.: The theory of critical phenomena. Clarendon Press, Oxford (1986)

    Google Scholar 

  13. Bonner, J.: The evolution of culture in animals. Princeton University Press, Princeton (1980)

    Google Scholar 

  14. Burago, D., Burago, Y., Ivanov, S.: A Course in Metric Geometry. American Mathematical Society, Providence (2001)

    MATH  Google Scholar 

  15. Byrk, A., Raudenbusch, S.: Hierarchical Linear Models: Applications and Data Analysis Methods. Sage Publications, New York (2001)

    Google Scholar 

  16. Champagnat, N., Ferriere, R., Meleard, S.: Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models. Theoretical Population Biology 69, 297–321 (2006)

    Article  MATH  Google Scholar 

  17. Cohen, I.: The cognitive principle challenges clonal selection. Immunology Today 13, 441–444 (1992)

    Article  Google Scholar 

  18. Cohen, I.: Tending Adam’s Garden: Evolving the Cognitive Immune Self. Academic Press, New York (2000)

    Google Scholar 

  19. Cohen, I.: Immune system computation and the immunological homunculus. In: Nierstrasz, O., Whittle, J., Harel, D., Reggio, G. (eds.) MoDELS 2006. LNCS, vol. 4199, pp. 499–512. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  20. Cohen, I., Harel, D.: Explaining a complex living system: dynamics, multi-scaling and emergence. Journal of the Royal Society: Interface 4, 175–182 (2007)

    Article  Google Scholar 

  21. Cover, T., Thomas, J.: Elements of Information Theory. John Wiley and Sons, New York (1991)

    Book  MATH  Google Scholar 

  22. Dembo, A., Zeitouni, O.: Large Deviations: Techniques and Applications, 2nd edn. Springer, New York (1998)

    MATH  Google Scholar 

  23. Dercole, F., Ferriere, R., Gragnani, A., Rinaldi, S.: Coevolution of slow-fast populations: evolutionary sliding, evolutionary pseudo-equilibria and complex Red Queen dynamics. Proceedings of the Royal Society, B 273, 983–990 (2006)

    Article  Google Scholar 

  24. Diekmann, U., Law, R.: The dynamical theory of coevolution: a derivation from stochastic ecological processes. Journal of Mathematical Biology 34, 579–612 (1996)

    Article  MathSciNet  Google Scholar 

  25. Dimitrov, A., Miller, J.: Neural coding and decoding: communication channels and quantization. Computation and Neural Systems 12, 441–472 (2001)

    MATH  Google Scholar 

  26. Dretske, F.: The explanatory role of information. Philosophical Transactions of the Royal Society A 349, 59–70 (1994)

    Article  Google Scholar 

  27. Durham, W.: Coevolution: Genes, Culture, and Human Diversity. Stanford University Press, Palo Alto (1991)

    Google Scholar 

  28. Eldredge, N., Gould, S.: Punctuated equilibrium: an alternative to phyletic gradualism. In: Schopf, T. (ed.) Models in Paleobiology, pp. 82–115. Freeman, Cooper and Co., San Francisco (1972)

    Google Scholar 

  29. Eldredge, N.: Time Frames: The Rethinking of Darwinian Evolution and the Theory of Punctuated Equilibria. Simon and Schuster, New York (1985)

    Google Scholar 

  30. Emery, M.: Stochastic Calculus in Manifolds. Universitext series. Springer, New York (1989)

    MATH  Google Scholar 

  31. English, T.: Evaluation of evolutionary and genetic optimizers: no free lunch. In: Fogel, L., Angeline, P., Back, T. (eds.) Evolutionary Programming V: Proceedings of the Fifth Annual Conference on Evolutionary Programming, pp. 163–169. MIT Press, Cambridge (1996)

    Google Scholar 

  32. Fath, B., Cabezas, H., Pawlowski, C.: Regime changes in ecological systems: an information theory approach. Journal of Theoretical Biology 222, 517–530 (2003)

    MathSciNet  Google Scholar 

  33. Feller, W.: An Introduction to Probability Theory and Its Applications. John Wiley and Sons, New York (1971)

    MATH  Google Scholar 

  34. Feynman, R.: Feynman Lectures on Computation. Addison-Wesley, Reading (1996)

    Google Scholar 

  35. Fleming, R., Shoemaker, C.: Evaluating models for spruce budworm-forest management: comparing output with regional field data. Ecological Applications 2, 460–477 (1992)

    Article  Google Scholar 

  36. Forlenza, M., Baum, A.: Psychosocial influences on cancer progression: alternative cellular and molecular mechanisms. Current Opinion in Psychiatry 13, 639–645 (2000)

    Article  Google Scholar 

  37. Franzosi, R., Pettini, M.: Theorem on the origin of phase transitions. Physical Review Letters 92, 060601 (2004)

    Article  Google Scholar 

  38. Fredlin, M., Wentzell, A.: Random Perturbations of Dynamical Systems. Springer, New York (1998)

    Google Scholar 

  39. Glazebrook, J., Wallace, R.: Rate distortion manifolds as model spaces for cognitive information (submitted, 2007)

    Google Scholar 

  40. Goubault, E.: Some geometric perspectives in concurrency theory. Homology, Homotopy, and Applications 5, 95–136 (2003)

    MATH  MathSciNet  Google Scholar 

  41. Goubault, E., Raussen, M.: Dihomotopy as a tool in state space analysis. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 16–37. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  42. Gould, S.: The Structure of Evolutionary Theory. Harvard University Press, Cambridge (2002)

    Google Scholar 

  43. Grossman, Z.: Round 3. Seminars in Immunology 12, 313–318 (2000)

    Article  Google Scholar 

  44. Gunderson, L.: Ecological resilience – in theory and application. Annual Reviews of Ecological Systematics 31, 425–439 (2000)

    Article  Google Scholar 

  45. Gunderson, L.: Personal communication (2007)

    Google Scholar 

  46. Hartl, D., Clark, A.: Principles of Population Genetics. Sinaur Associates, Sunderland (1997)

    Google Scholar 

  47. Holling, C.: Resilience and stability of ecological systems. Annual Reviews of Ecological Systematics 4, 1–23 (1973)

    Article  Google Scholar 

  48. Holling, C.: Cross-scale morphology, geometry and dynamics of ecosystems. Ecological Monographs 41, 1–50 (1992)

    Google Scholar 

  49. Jimenez-Montano, M.: Formal languages and theoretical molecular biology. In: Goodwin, B., Saunders, P. (eds.) Theoretical Biology: Epigenetic an Evolutionary Order in Complex Systems. Edinburgh University Press (1989)

    Google Scholar 

  50. Kastner, M.: Phase transitions and configuration space topology (2006) (ArXiv preprint cond-mat/0703401)

    Google Scholar 

  51. Khinchin, A.: Mathematical Foundations of Information Theory. Dover Publications, New York (1957)

    MATH  Google Scholar 

  52. Laland, K., Odling-Smee, F., Feldman, M.: Evolutionary consequences of niche construction and their implications for ecology. Proceedings of the National Academy of Sciences 96, 10242–10247 (1999)

    Article  Google Scholar 

  53. Lee, J.: Introduction to Topological Manifolds. Springer, New York (2000)

    MATH  Google Scholar 

  54. Levin, S.: Ecology in theory and application. In: Levin, S., Hallam, T., Gross, L. (eds.) Applied Mathematical Ecology biomathematics Texts, vol. 18. Springer, New York (1989)

    Google Scholar 

  55. Lewontin, R.: Biology as Ideology: The Doctrine of DNA. Harper Collins, New York (1993)

    Google Scholar 

  56. Lewontin, R.: The Triple Helix: gene, organism, and environment. Harvard University Press (2000)

    Google Scholar 

  57. Liao, J., Biscolo, R., Yang, Y., My Tran, L., Sabatti, C., Roychowdhury, V.: Network component analysis: Reconstruction of regulatory signals in biological systems. Proceedings of the National Academy of Sciences 100, 15522–15527 (2003)

    Article  Google Scholar 

  58. Liu, Y., Ringner, M.: Revealing signaling pathway deregulation by using gene expression signatures and regulatory motif analysis. Genome Biology 8, R77 (2007)

    Article  Google Scholar 

  59. Luchinsky, D.: On the nature of large fluctuations in equilibrium systems: observations of an optimal force. Journal of Physics A 30, L577–L583 (1997)

    Article  Google Scholar 

  60. Matsumoto, Y.: An Introduction to Morse Theory, Translations of Mathematical Monographs, vol. 208. American Mathematical Society (2002)

    Google Scholar 

  61. Michel, L., Mozrymas, J.: Application of Morse Theory to the symmetry breaking in the Landau theory of the second order phase transition. In: Kramer, P., Rieckers, A. (eds.) Group Theoretical Methods in Physics: Sixth International Colloquium. Lecture Notes in Physics, vol. 79, pp. 447–461. Springer, New York (1977)

    Chapter  Google Scholar 

  62. Milnor, J.: Morse Theory. Annals of Mathematical Studies, vol. 51. Princeton University Press, Princeton (1963)

    MATH  Google Scholar 

  63. Nunney, L.: Lineage selection and the evolution of multistage carcinogenesis. Proceedings of the London Royal Society B 266, 493–498 (1999)

    Article  Google Scholar 

  64. Odling-Smee, F., Laland, K., Feldman, M.: Niche construction. The American Naturalist 147, 641–648 (1996)

    Article  Google Scholar 

  65. Ofria, C., Adami, C., Collier, T.: Selective pressures on genomes in molecular evolution. Journal of Theoretical Biology 222, 477–483 (2003)

    MathSciNet  Google Scholar 

  66. Onsager, L., Machlup, S.: Fluctuations and irreversible processes. Physical Review 91, 1505–1512 (1953)

    Article  MATH  MathSciNet  Google Scholar 

  67. O’Nuallain, S.: Code and context in gene expression, cognition, and consciousness. In: Barbieri, M., Hoffmeyer, J. (eds.) Biosemiotics: The codes of life. Springer, New York (2008)

    Google Scholar 

  68. Pettini, M.: Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics. Springer, New York (2007)

    Book  MATH  Google Scholar 

  69. Pettini, M., Franzosi, R., Spinelli, L.: Topology and phase transitions I. Preliminary results. Nuclear Physics B 782, 189–218 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  70. Pielou, E.C.: Mathematical Ecology. John Wiley and Sons, New York (1977)

    Google Scholar 

  71. Podolsky, S., Tauber, A.: The generation of diversity: Clonal selection theory and the rise of molecular biology. Harvard University Press (1998)

    Google Scholar 

  72. Pratt, V.: Modeling concurrency with geometry. In: Proceedings of the 18th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 311–322 (1991)

    Google Scholar 

  73. Priami, C.: Computational thinking in biology. In: Priami, C. (ed.) Transactions on Computational Systems Biology VIII. LNCS (LNBI), vol. 4780, pp. 63–76. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  74. Ricotta, C.: Additive partition of parametric information and its associated β-diversity measure. Acta Biotheoretica 51, 91–100 (2003)

    Article  Google Scholar 

  75. Ridley, M.: Evolution, 2nd edn. Blackwell Science/Oxford University Press (1996)

    Google Scholar 

  76. Rojdestvensky, I., Cottam, M.: Mapping of statistical physics to information theory with applications to biological systems. Journal of Theoretical Biology 202, 43–54 (2000)

    Article  Google Scholar 

  77. Sayyed-Ahmad, A., Tuncay, K., Ortoleva, P.: Transcriptional regulatory network refinement and quantification through kinetic modeling, gene expression microarray data and information theory. BMC Bioinformatics 8, 20 (2007)

    Article  Google Scholar 

  78. Shirkov, D., Kovalev, V.: The Bogoliubov renormalization group and solution symmetry in mathematical physics. Physics Reports 352, 219–249 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  79. Soyer, O., Salathe, M., Bonhoeffer, S.: Signal transduction networks: Topology, response and biochemical processes. Journal of Theoretical Biology 238, 416–425 (2006)

    Article  MathSciNet  Google Scholar 

  80. Tauber, A.: Conceptual shifts in immunology: Comments on the ‘two-way paradigm’. Theoretical Medicine and Bioethics 19, 457–473 (1998)

    Article  Google Scholar 

  81. Volney, W., Fleming, R.: Spruce budworm (Choristoneura spp.) biotype reactions to forest and climate characteristics. Global Change Biology 13, 1630–1643 (2007)

    Article  Google Scholar 

  82. Waddington, C.: Epilogue. In: Waddington, C. (ed.) Towards a Theoretical Biology: Essays. Aldine-Atherton, Chicago (1972)

    Google Scholar 

  83. Wallace, R., Wallace, R.G.: Psychopathica Automatorum: A cognitive neuroscience perspective on highly parallel computation and its dysfunctions (to appear, 2008)

    Google Scholar 

  84. Wallace, R., Fullilove, M.T.: Collective Consciousness and its Discontents: Institutional Distributed Cognition, Racial Policy and Public Health in the United States. Springer, New York (2008)

    Google Scholar 

  85. Wallace, R., Wallace, R.G.: Information theory, scaling laws and the thermodynamics of evolution. Journal of Theoretical Biology 192, 545–559 (1998)

    Article  Google Scholar 

  86. Wallace, R., Wallace, R.G.: Organisms, organizations, and interactions: an information theory approach to biocultural evolution. BioSystems 51, 101–119 (1999)

    Article  Google Scholar 

  87. Wallace, R., Wallace, R.G.: Immune cognition and vaccine strategy: beyond genomics. Microbes and Infection 4, 521–527 (2002)

    Article  MathSciNet  Google Scholar 

  88. Wallace, R., Wallace, D., Wallace, R.G.: Toward cultural oncology: the evolutionary information dynamics of cancer. Open Systems and Information Dynamics 10, 159–181 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  89. Wallace, R.: Language and coherent neural amplification in hierarchical systems: renormalization and the dual information source of a generalized stochastic resonance. International Journal of Bifurcation and Chaos 10, 493–502 (2000)

    Article  Google Scholar 

  90. Wallace, R.: Immune cognition and vaccine strategy: pathogenic challenge and ecological resilience. Open Systems and Information Dynamics 9, 51–83 (2002)

    Article  MATH  Google Scholar 

  91. Wallace, R.: Adaptation, punctuation and rate distortion: non-cognitive ‘learning plateaus’ in evolutionary process. Acta Biotheoretica 50, 101–116 (2002)

    Article  Google Scholar 

  92. Wallace, R.: Consciousness: A Mathematical Treatment of the Global Neuronal Workspace Model. Springer, New York (2005)

    Google Scholar 

  93. Wallace, R.: A global workspace perspective on mental disorders. Theoretical Biology and Medical Modelling 2, 49 (2005)

    Article  Google Scholar 

  94. Whitham, T.: A framework for community and ecosystem genetics: from genes to ecosystems. Nature Reviews: genetics 7, 510–523 (2006)

    Article  Google Scholar 

  95. Wilson, K.: Renormalization group and critical phenomena. I Renormalization group and the Kadanoff scaling picture. Physical Review B 4, 3174–3183 (1971)

    Article  MATH  Google Scholar 

  96. Wymer, C.: Structural nonlinear continuous-time models in econometrics. Macroeconomic Dynamics 1, 518–548 (1997)

    Article  MATH  Google Scholar 

  97. Zhu, R., Riberio, A., Salahub, D., Kauffman, S.: Studying genetic regulatory networks at the molecular level: Delayed reaction stochastic models. Journal of Theoretical Biology 246, 725–745 (2007)

    Article  MathSciNet  Google Scholar 

  98. Zurek, W.: Cosomological experiments in superfluid helium? Nature 317, 505–508 (1985)

    Article  Google Scholar 

  99. Zurek, W.: Shards of broken symmetry. Nature 382, 296–298 (1996)

    Article  Google Scholar 

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  1. The New York State Psychiatric Institute,  

    Rodrick Wallace

  2. Consumers Union,  

    Deborah Wallace

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  1. Rodrick Wallace
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  1. The Microsoft Research, University of Trento, Centre for Computational and Systems Biology, Piazza Manci, 17, 38050, Povo (TN), Italy

    Corrado Priami

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Wallace, R., Wallace, D. (2008). Punctuated Equilibrium in Statistical Models of Generalized Coevolutionary Resilience: How Sudden Ecosystem Transitions Can Entrain Both Phenotype Expression and Darwinian Selection. In: Priami, C. (eds) Transactions on Computational Systems Biology IX. Lecture Notes in Computer Science(), vol 5121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88765-2_2

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