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The Topology of Evolutionary Biology

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Modelling in Molecular Biology

Part of the book series: Natural Computing Series ((NCS))

Summary

Central notions in evolutionary biology are intrinsically topological. This claim is perhaps most obvious for the discontinuities associated with punctuated equilibrium. Recently, a mathematical framework has been developed that derives the concepts of phenotypic characters and homology from the topological structure of the phenotype space. This structure in turn is determined by the genetic operators and their interplay with the properties of the genotype-phenotype map.

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References

  1. Futuyma, D.J.: Evolutionary Biology. Sinauer Associates, Sunderalnd, Massachusetts (1998)

    Google Scholar 

  2. Graur, D., Li, W.H.: Fundamentals of Molecular Evolution. Sinauer Associates, Sunderland, Massachusetts (2000)

    Google Scholar 

  3. Schlichting, C.D., Pigliucci, M.: Phenotypic Evolution: A Reaction Norm Perspective. Sinauer Associates, Sunderland, Massachusetts (1998)

    Google Scholar 

  4. Eldredge, N., Gould, S.J.: no title. In Schopf, T.J.M., ed.: Models in Paleobiology. Freeman, San Francisco (1972) 82–115

    Google Scholar 

  5. Maynard-Smith, J., Burian, R., Kauffman, S.A., Alberch, P., Campbell, J., Goodwin, B., Lande, R., Raup, D., Wolpert, L.: Developmental constraints and evolution. Quart. Rev. Biol. 60 (1985) 265–287

    Article  Google Scholar 

  6. Schwenk, K.: A utilitarian approach to evolutionary constraint. Zoology 98 (1995) 251–262

    Google Scholar 

  7. Müller, G.B., Wagner, G.P.: Novelty in evolution: Restructuring the concept. Annu. Rev. Ecol. Syst. 22 (1991) 229–256

    Article  Google Scholar 

  8. Wagner, G.P.: The biological homology concept. Annu. Rev. Ecol. Syst. 20 (1989) 51–69

    Article  Google Scholar 

  9. Wagner, G.P.: The origin of morphological characters and the biological basis of homology. Evolution 43 (1989) 1157–1171

    Article  Google Scholar 

  10. Fontana, W., Buss, L.W.: “The arrival of the fittest”: Towards a theory of biological organization. Bull. Math. Biol. 56 (1994) 1–64

    MATH  Google Scholar 

  11. Schuster, P.: Artificial life and molecular evolutionary biology. In Moran, F., Moreno, A., Merelo, J.J., Chacon, P., eds.: Advances in artificial life. Proceedings of Third European Conference on Artificial Life, Canada 1995. Volume 929 of Lecture Notes in Artificial Intelligence. Springer-Verlag, Berlin (1995) 3–19

    Google Scholar 

  12. Lewontin, R.C.: The Genetic Basis of Evolutionary Change. Columbia University Press, New York (1974)

    Google Scholar 

  13. Wagner, G.P., Altenberg, L.: Complex adaptations and the evolution of evolvability. Evolution 50 (1996) 967–976

    Article  Google Scholar 

  14. Fontana, W., Schuster, P.: Continuity in evolution: On the nature of transitions. Science 280 (1998) 1451–1455

    Article  Google Scholar 

  15. Fontana, W., Schnabl, W., Schuster, P.: Physical aspects of evolutionary optimization and adaption. Phys. Rev. A 40 (1989) 3301–3321

    Article  Google Scholar 

  16. Schuster, P., Fontana, W., Stadler, P.F., Hofacker, I.L.: From sequences to shapes and back: A case study in RNA secondary structures. Proc. R.Soc. B 255 (1994) 279–284

    Article  Google Scholar 

  17. Huynen, M.A., Stadler, P.F., Fontana, W.: Smoothness within ruggedness: The role of neutrality in adaptation. Proc. Natl. Acad. Sci. USA 93 (1996) 397–401

    Article  Google Scholar 

  18. Fontana, W., Schuster, P.: Shaping space: The possible and the attainable in RNA genotype-phenotype mapping. J. Theor. Biol. 194 (1998) 491–515

    Article  Google Scholar 

  19. Ancel, L., Fontana, W.: Plasticity, evolvability and modularity in RNA. J. Exp. Zool. (Mol. Dev. Evol.) 288 (2000) 242–283

    Article  Google Scholar 

  20. Spiegelman, S.: An approach to experimental analysis of precellular evolution. Q. Rev. Biophys. 4 (1971) 213–253

    Article  Google Scholar 

  21. Lenski, R.E., Travisano, M.: Dynamics of adaptation and diversification: A 10,000-generation experiment with bacterial populations. Proc. Natl. Acad. Sci. USA 91 (1994) 6808–6814

    Article  Google Scholar 

  22. Szostak, J.W., Ellington, A.D.: In Vitro selection of functional RNA sequences. In Gesteland, R.F., Atkins, J.F., eds.: The RNA World. Cold Spring Harbor Laboratory Press, Plainview, New York (1993) 511–533

    Google Scholar 

  23. Cupal, J., Kopp, S., Stadler, P.F.: RNA shape space topology. Artif. Life 6 (2000) 3–23

    Article  Google Scholar 

  24. Stadler, B.M.R., Stadler, P.F., Wagner, G.P., Fontana, W.: The topology of the possible: Formal spaces underlying patterns of evolutionary change. J. Theor. Biol. 213 (2001) 241–274

    Article  MathSciNet  Google Scholar 

  25. Stadler, B.M.R., Stadler, P.F., Shpak, M., Wagner, G.P.: Recombination spaces, metrics, and pretopologies. Z. Phys. Chem. 216 (2002) 217–234

    Article  Google Scholar 

  26. Stadler, B.M.R., Stadler, P.F.: Generalized topological spaces in evolutionary theory and combinatorial chemistry. J. Chem. Inf. Comput. Sci. 42 (2002) 577–585

    Article  Google Scholar 

  27. Maynard-Smith, J.: Natural selection and the concept of a protein space. Nature 225 (1970) 563–564

    Article  Google Scholar 

  28. Eigen, M., Schuster, P.: The Hypercycle. Springer-Verlag, New York, Berlin (1979)

    Book  Google Scholar 

  29. Gitchoff, P., Wagner, G.P.: Recombination induced hypergraphs: a new approach to mutation-recombination isomorphism. Complexity 2 (1996) 37–43

    Article  MathSciNet  Google Scholar 

  30. Shpak, M., Wagner, G.P.: Asymmetry of configuration space induced by unequal crossover: Implications for a mathematical theory of evolutionary innovation. Artif. Life 6 (2000) 25–43

    Article  Google Scholar 

  31. Changat, M., Klavžar, S., Mulder, H.M.: The all-path transit function of a graph. Czech. Math. J. 51 (2001) 439–448

    Article  MATH  Google Scholar 

  32. Stadler, P.F., Wagner, G.P.: The algebraic theory of recombination spaces. Evol. Comput. 5 (1998) 241–275

    Article  Google Scholar 

  33. Stadler, P.F., Seitz, R., Wagner, G.P.: Evolvability of complex characters: Population dependent Fourier decomposition of fitness landscapes over recombination spaces. Bull. Math. Biol. 62 (2000) 399–428

    Article  Google Scholar 

  34. Page, W.: Topological Uniform Structures. Dover Publications, Mineola, New York (1994)

    Google Scholar 

  35. Gaal, S.A.: Point Set Topology. Academic Press, New York (1964)

    MATH  Google Scholar 

  36. Steen, L.A., Seebach, Jr., J.A.: Counterexamples in Topology. Holt, Rinehart & Winston, New York (1970)

    MATH  Google Scholar 

  37. Davey, B.A., Priestley, H.A.: Introduction to Lattice and Order. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  38. Kuratowski, C.: Sur la notion de limite topologique d’ensembles. Ann. Soc. Polon. Math. 21 (1949) 219–225

    MathSciNet  MATH  Google Scholar 

  39. Eckhardt, U., Latecki, L.: Digital topology. Technical Report 89, Hamburger Beitr. z. Angew. Math. A (1994)

    Google Scholar 

  40. Smyth, M.B.: Semi-metric, closure spaces and digital topology. Theor. Comput. Sci. 151 (1995) 257–276

    Article  MathSciNet  MATH  Google Scholar 

  41. Pfaltz, J.: Closure lattices. Discrete Math. 154 (1996) 217–236

    Article  MathSciNet  MATH  Google Scholar 

  42. Galton, A.: Continuous motion in discrete space. In Cohn, A.G., Giunchiglia, F., Selman, B., eds.: Principles of Knowledge Representation and Reasoning: Proceedings of the Seventh International Conference (KR2000), Morgan Kaufmann, San Francisco (2000) 26–37

    Google Scholar 

  43. Marchand-Maillet, S., Sharaiha, Y.M.: Discrete convexity, straightness, and the 16-neighborhood. Comput. Vision Image Understanding 66 (1997) 316–329

    Article  Google Scholar 

  44. Largeron, C., Bonnevay, S.: A pretopological approach for structural analysis. Inf. Sci. 144 (2002) 169–185

    Article  MathSciNet  MATH  Google Scholar 

  45. F. LeBourgeois, M. Bouayad, H.E.: Structure relation between classes for supervised learning using pretopology. In Fifth International Conference on Document Analysis and Recognition (1999) 33–36

    Google Scholar 

  46. Speroni di Fenizio, P., Banzhaf, W., Ziegler, J.: Towards a theory of organizations. In Proceedings of the Fourth German Workshop on Artificial Life GWAL’00. (2002)

    Google Scholar 

  47. Čech, E.: Topological Spaces. Wiley, London (1966)

    MATH  Google Scholar 

  48. Jablonka, E., Lamb, R.M.: Epigenetic Inheritance and Evolution. Oxford University Press, Oxford (1995)

    Google Scholar 

  49. Schultes, E., Bartel, D.: One sequence, two ribozymes: Implications for the emergence of new ribozyme folds. Science 289 (2000) 448–452

    Article  Google Scholar 

  50. Mills, D., Peterson, R., Spiegelman, S.: An extracellular Darwinian experiment with a self-duplicating nucleic acid molecule. Proc. Natl. Acad. Sci. USA 58 (1967) 217

    Article  Google Scholar 

  51. Klug, S.J., Famulok, M.: All you wanted to know about SELEX. Mol. Biol. Rep. 20 (1994) 97–107

    Article  Google Scholar 

  52. Zuker, M., Sankoff, D.: RNA secondary structures and their prediction. Bull. Math. Biol. 46 (1984) 591–621

    MATH  Google Scholar 

  53. Hofacker, I.L., Fontana, W., Stadler, P.F., Bonhoeffer, L.S., Tacker, M., Schuster, P.: Fast folding and comparison of RNA secondary structures. Monatsh. Chem. 125 (1994) 167–188

    Article  Google Scholar 

  54. Shelton, V.M., Sosnick, T.R., Pan, T.: Applicability of urea in the thermodynamic analysis of secondary and tertiary RNA folding. Biochemistry 38 (1999) 16831–16839

    Article  Google Scholar 

  55. Mathews, D., Sabina, J., Zucker, M., Turner, H.: Expanded sequence dependence of thermodynamic parameters provides robust prediction of RNA secondary structure. J. Mol. Biol. 288 (1999) 911–940

    Article  Google Scholar 

  56. Babajide, A., Hofacker, I.L., Sippl, M.J., Stadler, P.F.: Neutral networks in protein space: A computational study based on knowledge-based potentials of mean force. Folding Des. 2 (1997) 261–269

    Article  Google Scholar 

  57. Stadler, P.F.: The genotype phenotype map. Konrad Lorenz Institute Workshop on Biological Information. (2002)

    Google Scholar 

  58. Hammer, P.C.: Extended topology: Continuity I. Port. Math. 25 (1964) 77–93

    MathSciNet  Google Scholar 

  59. Gnilka, S.: On continuity in extended topologies. Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 37 (1997) 99–108

    MathSciNet  MATH  Google Scholar 

  60. Wright, S.: The roles of mutation, inbreeding, crossbreeeding and selection in evolution. In Jones, D.F., ed.: Proceedings of the Sixth International Congress on Genetics. Volume 1. (1932) 356–366

    Google Scholar 

  61. Wright, S.: “Surfaces” of selective value. Proc. Natl. Acad. Sci. USA 58 (1967) 165–172

    Article  Google Scholar 

  62. Reidys, C.M., Stadler, P.F.: Combinatorial landscapes. SIAM Rev. 44 (2002) 3–54

    Article  MathSciNet  MATH  Google Scholar 

  63. Flamm, C., Hofacker, I.L., Stadler, P.F., Wolfinger, M.T.: Barrier trees of degenerate landscapes. Z. Phys. Chem. 216 (2002) 155–173

    Article  Google Scholar 

  64. Stadler, P.F.: Fitness landscapes. In Lässig, M., Valleriani, A., eds.: Biological Evolution and Statistical Physics. Springer-Verlag, Berlin (2002) 187–207

    Google Scholar 

  65. Rechenberg, I.: Evolutionstrategie. Frommann-Holzboog, Stuttgart (1973)

    Google Scholar 

  66. Heidrich, D., Kliesch, W., Quapp, W.: Properties of Chemically Interesting Potential Energy Surfaces. Volume 56 of Lecture Notes in Chemistry. Springer-Verlag, Berlin (1991)

    Book  Google Scholar 

  67. Mezey, P.G.: Potential Energy Hypersurfaces. Elsevier, Amsterdam (1987)

    Google Scholar 

  68. Schuster, P.: Evolution in silico and in vitro: The RNA model. Biol. Chem. 382 (2001) 1301–1314

    Article  Google Scholar 

  69. Fontana, W.: Modelling “evo-devo” with RNA. BioEssays 24 (2002) 1164–1177

    Article  Google Scholar 

  70. Kauffman, S.A.: The Origin of Order. Oxford University Press, New York, Oxford (1993)

    Google Scholar 

  71. Wagner, G., Stadler, P.F.: Quasi-independence, homology and the unity of type: A topological theory of characters. J. Theor. Biol. 220 (2003) 505–527

    Article  MathSciNet  Google Scholar 

  72. Lewontin, R.C.: Adaptation. Sci. Am. 239 (1978) 156–169

    Article  Google Scholar 

  73. Imrich, W., Klavžar, S.: Product Graphs: Structure and Recognition. Wiley, New York (2000)

    MATH  Google Scholar 

  74. Dörfler, W., Imrich, W.: über das starke Produkt von endlichen Graphen. ö sterreich. Akad. Wiss. Math.-Natur. Kl. S.-B. II 178 (1970) 247–262

    MATH  Google Scholar 

  75. McKenzie, R.: Cardinal multiplication of structures with a reflexive multiplication. Fundam. Math. 70 (1971) 59–101

    MathSciNet  MATH  Google Scholar 

  76. Feigenbaum, J., Schäffer, A.A.: Finding the prime factors of strong direct products of graphs in polynomial time. Discrete Math. 109 (1992) 77–102

    Article  MathSciNet  MATH  Google Scholar 

  77. Imrich, W.: Factoring cardinal product graphs in polynomial time. Discrete Math. 192 (1998) 119–144

    Article  MathSciNet  MATH  Google Scholar 

  78. Lovász, L.: Operations with structures. Acta Math. Acad. Sci. Hung. 18 (1967) 321–328

    Google Scholar 

  79. Lovász, L.: Unique factorization in certain classes of structures. In: Mini-Conference on Universal Algebra, Szeged 1971, Bolyai Janos Math. Soc. (1971) 24–25

    Google Scholar 

  80. Wagner, G.P.: Homology and the mechanisms of development. In Hall, B.K., ed.: Homology: The Hierarchical Basis of Comparative Biology. Academic Press, San Diego, California (1994) 273–299

    Google Scholar 

  81. Wagner, G.P.: What is the promise of developmental evolution? Part II: a causal explanation of evolutionary innovations may be impossible. J. Exp. Zool. (Mol. Dev. Evol.) 291 (2001) 305–309

    Article  Google Scholar 

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Stadler, B.M.R., Stadler, P.F. (2004). The Topology of Evolutionary Biology. In: Ciobanu, G., Rozenberg, G. (eds) Modelling in Molecular Biology. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18734-6_12

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  • DOI: https://doi.org/10.1007/978-3-642-18734-6_12

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