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Fitness landscapes

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Biological Evolution and Statistical Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 585))

Abstract

Fitness landscapes are a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. A fitness landscape is a mapping from a configuration space that is equipped with some notion of adjacency, nearness, distance or accessibility, into the real numbers. Landscape theory has emerged as an attempt to devise suitable mathematical structures for describing the “static” properties of landscapes as well as their influence on the dynamics of adaptation. This chapter gives a brief overview on recent developments in this area, focusing on “geometrical” properties of landscapes.

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References

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

    Google Scholar 

  2. K. Binder, A.P. Young: Rev. Mod. Phys. 58, 801–976 (1986)

    Article  CAS  Google Scholar 

  3. M. Mézard, G. Parisi, M. Virasoro: Spin Glass Theory and Beyond (World Scientific, Singapore, 1987)

    Google Scholar 

  4. H.S. Chan, K.A. Dill: J. Chem. Phys. 95, 3775–3787 (1991)

    Article  CAS  Google Scholar 

  5. K.A. Dill, S. Bromberg, K. Yue, K.M. Fiebig, D.P. Yeo, P.D. Thomas, H.S. Chan: Prot. Sci. 4, 561–602 (1995)

    Article  CAS  Google Scholar 

  6. J.N. Onuchic, H. Nymeyer, A.E. Garcia, J. Chahine, N.D. Socci: Adv. Protein Chem. 53, 87–152 (2000)

    Article  PubMed  CAS  Google Scholar 

  7. C. Flamm, I.L. Hofacker, P.F. Stadler: Adv. Complex Syst. 2, 65–90 (1999)

    Article  Google Scholar 

  8. C. Flamm, W. Fontana, I. Hofacker, P. Schuster: RNA 6, 325–338 (2000)

    Article  PubMed  CAS  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  11. K. Kollman, J.H. Miller, S.E. Page: Amer. Pol. Sci. Rev. 86, 929–937 (1992)

    Article  Google Scholar 

  12. B.M. Stadler: Adv. Complex Syst. 2, 101–116 (1999)

    Article  Google Scholar 

  13. M. Garey, D. Johnson: Computers and Intractability. AGuide to the Theory of NP Completeness (Freeman, San Francisco, 1979)

    Google Scholar 

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

    Google Scholar 

  15. J.R. Koza: Genetic Programming: On the Programming of Computers by Means of Natural Selection (MIT Press, Cambridge, MA, 1992)

    Google Scholar 

  16. J.H. Holland: Adaptation in Natural and Artificial Systems (MIT Press, Cambridge, MA, 1993)

    Google Scholar 

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

    Google Scholar 

  18. D.B. Fogel: Evolutionary Computation (IEEE Press, New York, 1995)

    Google Scholar 

  19. P. Schuster, W. Fontana, P.F. Stadler, I.L. Hofacker: Proc. Roy. Soc. Lond. B 255, 279–284 (1994)

    Article  CAS  Google Scholar 

  20. A.S. Perelson, S.A. Kauffman (Eds.): Molecular Evolution on Rugged Landscapes: Proteins, RNA, and the Immune System (Addison-Wesley, Reading, MA, 1991) (1991)

    Google Scholar 

  21. H. Frauenfelder, A.R. Bishop, A. Garcia, A. Perelson, P. Schuster, D. Sherrington, P.J. Swart (Eds.): Landscape Paradigms in Physics and Biology: Concepts, Structures, and Dynamics (Elsevier, Amsterdam, 1997), special Issue of Phyica D vol. 107(2–4)

    Google Scholar 

  22. J.P. Crutchfield, P. Schuster (Eds.): Evolutionary Dynamics-Exploring the Interplay of Selection, Neutrality, Accident, and Function (Oxford Univ. Press, Oxford UK, 2000), to appear

    Google Scholar 

  23. J. Hofbauer, K. Sigmund: Dynamical Systems and the Theory of Evolution (Cambridge University Press, Cambridge U.K., 1988)

    Google Scholar 

  24. R. Bürger: The Mathematical Theory of Selection, Recombination, and Mutation (John Wiley & Sons, Chichester UK, 2000)

    Google Scholar 

  25. L. Altenberg, M.W. Feldman: Genetics 117, 559–572 (1987)

    PubMed  CAS  Google Scholar 

  26. Y.I. Lyubich: Mathematical structures in population genetics (Springer-Verlag, Berlin, 1992)

    Google Scholar 

  27. J.W. Weibull: Evolutionary Game Dynamics (MIT Press, Cambridge MA, 1996)

    Google Scholar 

  28. A. Dress, D. Rumschitzki: Acta Appl. Math. 11, 103–111 (1988)

    Article  Google Scholar 

  29. P.F. Stadler: J. Math. Chem. 20, 1–45 (1996)

    Article  CAS  Google Scholar 

  30. J.S. Farris: “The logical basis of phylogenetic analysis” in Advances in Cladistics, ed. by N.I. Platnick, V.A. Funk (Columbia University Press, New York, 1983), pp. 1–36

    Google Scholar 

  31. J. Felsenstein: J. Mol. Evol. 17, 368–376 (1981)

    Article  PubMed  CAS  Google Scholar 

  32. L.R. Foulds, R.L. Graham: Adv. Appl. Math. 3, 43–49 (1982)

    Article  Google Scholar 

  33. W.H.E. Day, D.S. Johnson, D. Sanko.: Math. Biosci. 81, 33–42 (1986)

    Article  Google Scholar 

  34. D.F. Robinson: J. Combin. Theory B 11, 105–119 (1971)

    Article  Google Scholar 

  35. M. Li, J. Tromp, L. Zhang: J. Theor. Biol. 182, 463–467(1996)

    Article  PubMed  CAS  Google Scholar 

  36. O. Bastert, D. Rockmore, P.F. Stadler, G. Tinhofer: (2000), “Landscapes on spaces of trees” submitted, SFI preprint 01-01-006

    Google Scholar 

  37. J. Kececioglu, D. Sanko.: Algorithmica 13, 180–210 (1995)

    Article  Google Scholar 

  38. D. Sanko., G. Sundaram, J. Kececioglu: Internatl. J. Foundations Computer Sci. 7, 1–9 (1996)

    Article  Google Scholar 

  39. J.C. Culberson: Evol. Comp. 2, 279–311 (1995)

    Article  Google Scholar 

  40. T. Jones: (1995), “One operator, one landscape” Tech. Rep. #95-02-025, Santa Fe Institute

    Google Scholar 

  41. P. Gitcho., G.P. Wagner: Complexity 2, 47–43 (1996)

    Article  Google Scholar 

  42. P.F. Stadler, G.P. Wagner: Evol. Comp. 5, 241–275 (1998)

    Article  Google Scholar 

  43. G.P. Wagner, P.F. Stadler: “Complex adaptations and the structure of recombination spaces” in Algebraic Engineering, ed. by C. Nehaniv, M. Ito (World Scientific, Singapore, 1999), pp. 96–115, proceedings of the Conference on Semi-Groups and Algebraic Engineering, University of Aizu, Japan

    Google Scholar 

  44. P. Larrañaga, C.M.H. Kuijpers, R.H. Murga, I. Inza, S. Dizdarevic: Articial Intelligence Review 13, 129–170 (1999)

    Article  Google Scholar 

  45. A. Brouwer, A. Cohen, A. Neumaier: Distance-regular Graphs (Springer Verlag, Berlin, New York, 1989)

    Google Scholar 

  46. M. Shpak, G.P. Wagner: Artificial Life 6, 25–43 (2000)

    Article  PubMed  CAS  Google Scholar 

  47. L. Lovasz: “Random walks on graphs: A survey” in Combinatorics, Paul Erdős is Eighty Vol.2 Budapest (1996), pp. 353–398, keszthely (Hungary) 1993

    Google Scholar 

  48. E.D. Weinberger: Biol. Cybern. 63, 325–336 (1990)

    Article  Google Scholar 

  49. E.D. Weinberger: Biol. Cybern. 65, 321–330 (1991)

    Article  Google Scholar 

  50. W. Hordijk: Evolutionary Computation 4(4), 335–360 (1996)

    Article  Google Scholar 

  51. W. Hordijk: Physica D 107, 255–264 (1997)

    Article  Google Scholar 

  52. P.F. Stadler, R. Seitz, G.P. Wagner: Bull. Math. Biol. 62, 399–428 (2000)

    Article  PubMed  CAS  Google Scholar 

  53. H.R. Fischer: Math. Annalen 137, 269–303 (1959)

    Article  Google Scholar 

  54. D.C. Kent: Fund. Math. 54, 125–133 (1964)

    Google Scholar 

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

    Google Scholar 

  56. D.C. Kent: Fund. Math. 62, 95–100 (1968)

    Google Scholar 

  57. B.M.R. Stadler, P.F. Stadler, W. Fontana, G.P. Wagner: J. Theor. Biol. (2001). Submitted, SFI preprint 00-12-070

    Google Scholar 

  58. B.M.R. Stadler, P.F. Stadler, M. Shpak, G.P. Wagner: Artificial Life (2001). Submitted, SFI preprint 01-02-011

    Google Scholar 

  59. R. Palmer: “Optimization on rugged landscapes” in Molecular Evolution on Rugged Landscapes: Proteins, RNA, and the Immune System, ed. by A.S. Perelson, S.A. Kauffman (Addison Wesley, Redwood City, CA, 1991), pp. 3–25

    Google Scholar 

  60. P.F. Stadler, W. Schnabl: Phys. Lett. A 161, 337–344 (1992)

    Article  Google Scholar 

  61. P.F. Stadler, B. Krakhofer: Rev. Mex. Fis. 42, 355–363 (1996)

    Google Scholar 

  62. R. García-Pelayo, P.F. Stadler: Physica D 107, 240–254 (1997)

    Article  Google Scholar 

  63. D.J. Thouless, P.W. Anderson, R.G. Palmer: Phil. Mag. 35, 593–601 (1977)

    Article  CAS  Google Scholar 

  64. F. Tanaka, S.F. Edwards: J. Phys. F 10, 2769–2778 (1980)

    Article  Google Scholar 

  65. A.J. Bray, M.A. Moore: J. Phys. C 14, 1313–1327 (1981)

    Article  CAS  Google Scholar 

  66. D.J. Gross, M. Mézard: Nucl. Phys. B 240, 431–452 (1984)

    Article  Google Scholar 

  67. B. Derrida, E. Gardner: J. Physique 47, 959–965 (1986)

    Article  Google Scholar 

  68. H. Rieger: Phys. Rev. B 46, 14655–14661 (1992)

    Google Scholar 

  69. V.M. de Oliveira, J.F. Fontanari, P.F. Stadler: J. Phys. A: Math. Gen. 32, 8793–8802 (1999)

    Article  Google Scholar 

  70. F.F. Ferreira, J.F. Fontanari, P.F. Stadler: J. Phys. A: Math. Gen. 33, 8635–8647 (2000)

    Article  CAS  Google Scholar 

  71. J. Garnier, L. Kallel: SIAM J. Discr. Math. (2000). Submitted

    Google Scholar 

  72. E.D. Weinberger: Phys. Rev. A 44, 6399–6413 (1991)

    Article  PubMed  Google Scholar 

  73. W. Fontana, P.F. Stadler, E.G. Bornberg-Bauer, T. Griesmacher, I.L. Hofacker, M. Tacker, P. Tarazona, E.D. Weinberger, P. Schuster: Phys. Rev. E 47, 2083–2099 (1993)

    Article  CAS  Google Scholar 

  74. J.H. Gillespie: Evolution 38, 1116–1129 (1984)

    Article  CAS  Google Scholar 

  75. S.A. Kauffman, S. Levin: J. Theor. Biol. 128, 11–45 (1987)

    Article  PubMed  CAS  Google Scholar 

  76. H. Flyvbjerg, B. Lautrup: Phys. Rev. A 46, 6714–6723 (1992)

    Article  PubMed  Google Scholar 

  77. C.A. Macken, A.S. Perelson: Proc. Natl. Acad. Sci. USA 86, 6191–6195 (1989)

    Article  PubMed  CAS  Google Scholar 

  78. C.A. Macken, P.S. Hagan, A.S. Perelson: SIAM J. Appl. Math. 51, 799–827 (1991)

    Article  Google Scholar 

  79. A.S. Perelson, C.A. Macken: Proc. Natl. Acad. Sci. USA 92, 9657–9661 (1995)

    Article  PubMed  CAS  Google Scholar 

  80. K.J. Niklas: Amer. J. Botany 84, 16–25 (1997)

    Article  Google Scholar 

  81. R. Rammal, G. Toulouse, M.A. Virasoro: Rev. Mod. Phys. 58, 765–788 (1986)

    Article  Google Scholar 

  82. A.M. Vertechi, M.A. Virasoro: J. Phys. France 50, 2325–2332 (1989)

    Google Scholar 

  83. S.R. Morgan, P.G. Higgs: J. Phys. A 31, 3153–3170 (1998)

    Article  CAS  Google Scholar 

  84. C. Flamm, I.L. Hofacker, S. Maurer-Stroh, P.F. Stadler, M. Zehl: RNA 7, 254–265 (2001)

    Article  PubMed  CAS  Google Scholar 

  85. W. Kern: Discr. Appl. Math. 43, 115–129 (1993)

    Article  Google Scholar 

  86. R. Azencott: Simulated Annealing (John Wiley & Sons, New York, 1992)

    Google Scholar 

  87. O. Catoni: Ann. Probab. 20, 1109–1146 (1992)

    Article  Google Scholar 

  88. O. Catoni: “Simulated annealing algorithms and Markov chains with rate transitions” in Seminaire de Probabilites XXXIII, ed. by J. Azema, M. Emery, M. Ledoux, M. Yor (Springer, Berlin/Heidelberg, 1999), Vol. 709 of Lecture Notes in Mathematics, pp. 69–119

    Google Scholar 

  89. B. Hajek: Math. Operations Res. 13, 311–329 (1988)

    Article  Google Scholar 

  90. J. Ryan: Discr. Appl. Math. 56, 75–82 (1995)

    Article  Google Scholar 

  91. G.B. Sorkin: (1988), “Combinatorial optimization, simulated annealing, and fractals” Tech. Rep. RC13674 (No.61253), IBM Research Report

    Google Scholar 

  92. M. Eigen, J. McCaskill, P. Schuster: Adv. Chem. Phys. 75, 149–263 (1989)

    Article  CAS  Google Scholar 

  93. P.F. Stadler: Discr. Math. 145, 229–238 (1995)

    Article  Google Scholar 

  94. P. Schuster, P.F. Stadler: Computers & Chem. 18, 295–314 (1994)

    Article  CAS  Google Scholar 

  95. P.F. Stadler, R. Happel: J. Math. Biol. 38, 435–478 (1999)

    Article  Google Scholar 

  96. P.F. Stadler, W. Schnabl: Phys. Letters A 161, 337–344 (1992)

    Article  Google Scholar 

  97. B. Krakhofer, P.F. Stadler: Europhys. Lett. 34, 85–90 (1996)

    Article  CAS  Google Scholar 

  98. B. Mohar: “The Laplacian spectrum of graphs” in Graph Theory, Combinatorics, and Applications, ed. by Y. Alavi, G. Chartrand, O. Ollermann, A. Schwenk (John Wiley and Sons, Inc., New York, 1991), pp. 871–898

    Google Scholar 

  99. R. Merris: Lin. Alg. Appl. 39, 19–31 (1995)

    Google Scholar 

  100. F.R.K. Chung: Spectral Graph Theory, Vol. 92 of CBMS (American Mathematical Society, Providence RI, 1997)

    Google Scholar 

  101. B. Mohar: “Some applications of Laplace eigenvalues of graphs” in Graph Symmetry: Algebraic Methods and Applications, ed. by G. Hahn, G. Sabidussi (Kluwer, Dordrecht, 1997), Vol. 497 of NATO ASI Series C, pp. 227–275

    Google Scholar 

  102. D. Rockmore: “Some applications of generalized FFTs” in Groups and Computation II, ed. by L. Finkelstein, W. Kantor (American Mathmatical Society, Providence, RI, 1995), Vol. 28 of DIMACS, pp. 329–370

    Google Scholar 

  103. D. Rockmore, P. Kostelec, W. Hordijk, P.F. Stadler: Appl. Comput. Harmonic Anal. (2000). In press Santa Fe Institute preprint 99-10-068

    Google Scholar 

  104. T.J. Schaefer: “The complexity of satisfiability problems” in Proceedings of the 10th Annual ACM Symposium on Theory of Computing, ed. by N.N. (Association for Computing Machinery, New York, 1978), pp. 216–226

    Google Scholar 

  105. D.E. Goldberg: Complex Systems 3, 129–152 (1989)

    Google Scholar 

  106. D.E. Goldberg: Complex Systems 3, 153–176 (1989)

    Google Scholar 

  107. S.E. Page, D.E. Richardson: Complex Systems 6, 125–136 (1992)

    Google Scholar 

  108. M.D. Vose, A.H. Wright: Evol. Comp. 6, 253–274 (1998)

    Article  CAS  Google Scholar 

  109. M.D. Vose, A.H. Wright: Evol. Comp. 6, 275–289 (1998)

    Article  CAS  Google Scholar 

  110. L.K. Grover: Oper. Res. Lett. 12, 235–243 (1992)

    Article  Google Scholar 

  111. B. Codenotti, L. Margara: (1992), “Local properties of some np-complete problems” Tech. Rep. TR 92-021, International Computer Science Institute, Berkeley, CA

    Google Scholar 

  112. E. Angel, V. Zissimopoulos: Discr. Appl. Math. 99, 261–277 (2000)

    Article  Google Scholar 

  113. I. Chavel: Eigenvalues in Riemannian Geometry (Academic Press, Orlando Fl., 1984)

    Google Scholar 

  114. Y.C. de Verdière: Rendiconti di Matematica 13, 433–460 (1993)

    Google Scholar 

  115. J. Friedman: Duke Math. J. 69(3), 487–525 (1993)

    Article  Google Scholar 

  116. H. van der Holst: (1996), “Topological and spectral graph characterizations” Ph.D. thesis, Universiteit van Amsterdam

    Google Scholar 

  117. A.M. Duval, V. Reiner: Lin. Alg. Appl. 294, 259–268 (1999)

    Article  Google Scholar 

  118. E.B. Davies, G.M.L. Gladwell, J. Leydold, P.F. Stadler: Lin. Alg. Appl. (2001). In press, see also: math.SP/0009120

    Google Scholar 

  119. R. Happel, P.F. Stadler: Complexity 2, 53–58 (1996)

    Article  Google Scholar 

  120. W. Hordijk, P.F. Stadler: J. Complex Systems 1, 39–66 (1998)

    Article  Google Scholar 

  121. Y. Davidor: Complex Systems 4, 369–383 (1990)

    Google Scholar 

  122. M. Whitlock, P.C. Phillips, F.B.G. Moore, S. Tonsor: Ann. Review Ecol. Systematics 26, 601–629 (1995)

    Article  Google Scholar 

  123. J.B. Wolf, E.D. Brodie III, M.J. Wade (Eds.): Epistasis and the Evolutionary Process (Oxford Univ. Press, Oxford, UK, 2000)

    Google Scholar 

  124. C.M. Reidys, P.F. Stadler: Appl. Math. & Comput. 117, 321–350 (2001)

    Article  Google Scholar 

  125. C.M. Reidys: Adv. Appl. Math. 19, 360–377 (1997)

    Article  Google Scholar 

  126. S. Gavrilets, J. Gravner: J. Theor. Biol. 184, 51–64 (1997)

    Article  PubMed  CAS  Google Scholar 

  127. C.M. Reidys, P.F. Stadler, P. Schuster: Bull. Math. Biol. 59, 339–397(1997 )

    Article  PubMed  CAS  Google Scholar 

  128. S. Gavrilets, H. Li, M.D. Vose: Proc. Roy. Soc. London B 265, 1483–1489 (1998)

    Article  CAS  Google Scholar 

  129. S. Kopp, C.M. Reidys: Adv. Complex Syst. 2, 283–301 (1999)

    Article  Google Scholar 

  130. P.F. Stadler: J. Mol. Struct. (THEOCHEM) 463, 7–19 (1999)

    Article  CAS  Google Scholar 

  131. W. Fontana, D.A.M. Konings, P.F. Stadler, P. Schuster: Biopolymers 33, 1389–1404 (1993)

    Article  PubMed  CAS  Google Scholar 

  132. W. Fontana, P. Schuster: Science 280, 1451–1455 (1998)

    Article  PubMed  CAS  Google Scholar 

  133. D.E. Goldberg, M. Rudnik: Complex Systems 5, 265–278 (1991)

    Google Scholar 

  134. G.E. Liepins, M.D. Vose: Complex Systems 5, 45–61 (1991)

    Google Scholar 

  135. P. Field: Complex Systems 9, 11–28 (1995)

    Google Scholar 

  136. L. Altenberg: “The schema theorem and the Price’s theorem” in Foundations of Genetic Algorithms 3, ed. by L.D. Whitley, M.D. Vose (Morgan Kauffman, San Francisco CA, 1995), pp. 23–49

    Google Scholar 

  137. A.D. Bethke: (1991), “Genetic algorithms and function optimizers” Ph.D. thesis, University of Michigan

    Google Scholar 

  138. J.H. Holland: “Genetic algorithms and classifier systems: foundations and future directions” in Proceedings of the 2nd International Conference on Genetic Algorithms (1987), pp. 82–89

    Google Scholar 

  139. S. Forrest, M. Mitchell: “Relative building block fitness and the building block hypothesis” in Foundations of Genetic Algorithms 2, ed. by L.D. Whitley (Morgan Kaufmann, San Mateo, CA, 1993), pp. 109–126

    Google Scholar 

  140. C.R. Stephens, H. Waelbroeck: Phys. Rev. E 57, 3251–3264 (1998)

    Article  CAS  Google Scholar 

  141. L.D. Whitley: “Fundamental principles of deception in genetic search” in Foundations of Genetic Algorithms, ed. by G. Rawlins (Morgan Kaufmann, San Mateo, CA, 1991), pp. 221–241

    Google Scholar 

  142. K. Deb, D.E. Goldberg: “Analyzing deception in trap functions” in Foundations of Genetic Algorithms 2, ed. by L.D. Whitley (Morgan Kaufmann, San Mateo, CA, 1993), pp. 93–108

    Google Scholar 

  143. P.F. Stadler: “Spectral landscape theory” in Evolutionary Dynamics-Exploring the Interplay of Selection, Neutrality, Accident, and Function, ed. by J.P. Crutchfield, P. Schuster (Oxford University Press, New York, 2001), in press

    Google Scholar 

  144. B. Naudts, L. Kallel: IEEE Trans. Evol. Comp. (2000). To appear

    Google Scholar 

  145. M. Mitchell: An Introduction to Genetic Algorithms (MIT Press, Cambridge MA, 1996)

    Google Scholar 

  146. D.F. T. Baeck, Z. Michalewicz (Eds.): Handbook of Evolutionary Computation (Oxford University Press, New York, 1997)

    Google Scholar 

  147. E. Angel, V. Zissimopoulos: Theor. Computer Sci. 191, 229–243 (1998)

    Article  Google Scholar 

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  1. Institut für Theoretische Chemie und Molkulare Strukturbiologie, Universität Wien, Währingerstrasse 17, A-1090, Wien, Austria

    Peter F. Stadler

  2. The Santa Fe Institute, 1399 Hyde Park Rd., 87501, Santa Fe, NM

    Peter F. Stadler

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  1. Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937, Köln, Germany

    Michael Lässig

  2. Theory Division, MPI for Colloids and Interfaces, 14424, Potsdam, Germany

    Angelo Valleriani

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Stadler, P.F. (2002). Fitness landscapes. In: Lässig, M., Valleriani, A. (eds) Biological Evolution and Statistical Physics. Lecture Notes in Physics, vol 585. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45692-9_10

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