Fitness landscapes
Inhaltsverzeichnis
Referenz
Stadler, P.F.: Fitness landscapes. In: Biological Evolution and Statistical Physics, pp. 183–204. Springer, Heidelberg (2002)
DOI
http://dx.doi.org/10.1007/3-540-45692-9_10
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.
Extended Abstract
Bibtex
@Inbook{Stadler2002, author="Stadler, Peter F.", editor="L{\"a}ssig, Michael and Valleriani, Angelo", title="Fitness landscapes", bookTitle="Biological Evolution and Statistical Physics", year="2002", publisher="Springer Berlin Heidelberg", address="Berlin, Heidelberg", pages="183--204", isbn="978-3-540-45692-6", doi="10.1007/3-540-45692-9_10", url="http://dx.doi.org/10.1007/3-540-45692-9_10 http://de.evo-art.org/index.php?title=Fitness_landscapes" }
Used 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
2. K. Binder, A.P. Young: Rev. Mod. Phys. 58, 801–976 (1986)CrossRef
3. M. Mézard, G. Parisi, M. Virasoro: Spin Glass Theory and Beyond (World Scientific, Singapore, 1987)
4. H.S. Chan, K.A. Dill: J. Chem. Phys. 95, 3775–3787 (1991)CrossRef
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)CrossRef
6. J.N. Onuchic, H. Nymeyer, A.E. Garcia, J. Chahine, N.D. Socci: Adv. Protein Chem. 53, 87–152 (2000)PubMedCrossRef
7. C. Flamm, I.L. Hofacker, P.F. Stadler: Adv. Complex Syst. 2, 65–90 (1999)CrossRef
8. C. Flamm, W. Fontana, I. Hofacker, P. Schuster: RNA 6, 325–338 (2000)PubMedCrossRef
9. P.G. Mezey: Potential Energy Hypersurfaces (Elsevier, Amsterdam, 1987)
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)
11. K. Kollman, J.H. Miller, S.E. Page: Amer. Pol. Sci. Rev. 86, 929–937 (1992)CrossRef
12. B.M. Stadler: Adv. Complex Syst. 2, 101–116 (1999)CrossRef
13. M. Garey, D. Johnson: Computers and Intractability. A Guide to the Theory of NP Completeness (Freeman, San Francisco, 1979)
14. I. Rechenberg: Evolutionstrategie (Frommann-Holzboog, Stuttgart, 1973)
15. J.R. Koza: Genetic Programming: On the Programming of Computers by Means of Natural Selection (MIT Press, Cambridge, MA, 1992)
16. J.H. Holland: Adaptation in Natural and Artificial Systems (MIT Press, Cambridge, MA, 1993)
17. S.A. Kauffman: The Origin of Order (Oxford University Press, New York, Oxford, 1993)
18. D.B. Fogel: Evolutionary Computation (IEEE Press, New York, 1995)
19. P. Schuster, W. Fontana, P.F. Stadler, I.L. Hofacker: Proc. Roy. Soc. Lond. B 255, 279–284 (1994)CrossRef
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)
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)
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
23. J. Hofbauer, K. Sigmund: Dynamical Systems and the Theory of Evolution (Cambridge University Press, Cambridge U.K., 1988)
24. R. Bürger: The Mathematical Theory of Selection, Recombination, and Mutation (John Wiley & Sons, Chichester UK, 2000)
25. L. Altenberg, M.W. Feldman: Genetics 117, 559–572 (1987)PubMed
26. Y.I. Lyubich: Mathematical structures in population genetics (Springer-Verlag, Berlin, 1992)
27. J.W. Weibull: Evolutionary Game Dynamics (MIT Press, Cambridge MA, 1996)
28. A. Dress, D. Rumschitzki: Acta Appl. Math. 11, 103–111 (1988)CrossRef
29. P.F. Stadler: J. Math. Chem. 20, 1–45 (1996)CrossRef
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
31. J. Felsenstein: J. Mol. Evol. 17, 368–376 (1981)PubMedCrossRef
32. L.R. Foulds, R.L. Graham: Adv. Appl. Math. 3, 43–49 (1982)CrossRef
33. W.H.E. Day, D.S. Johnson, D. Sanko.: Math. Biosci. 81, 33–42 (1986)CrossRef
34. D.F. Robinson: J. Combin. Theory B 11, 105–119 (1971)CrossRef
35. M. Li, J. Tromp, L. Zhang: J. Theor. Biol. 182, 463–467(1996)PubMedCrossRef
36. O. Bastert, D. Rockmore, P.F. Stadler, G. Tinhofer: (2000), “Landscapes on spaces of trees” submitted, SFI preprint 01-01-006
37. J. Kececioglu, D. Sanko.: Algorithmica 13, 180–210 (1995)CrossRef
38. D. Sanko., G. Sundaram, J. Kececioglu: Internatl. J. Foundations Computer Sci. 7, 1–9 (1996)CrossRef
39. J.C. Culberson: Evol. Comp. 2, 279–311 (1995)CrossRef
40. T. Jones: (1995), “One operator, one landscape” Tech. Rep. #95-02-025, Santa Fe Institute
41. P. Gitcho., G.P. Wagner: Complexity 2, 47–43 (1996)CrossRef
42. P.F. Stadler, G.P. Wagner: Evol. Comp. 5, 241–275 (1998)CrossRef
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
44. P. Larrañaga, C.M.H. Kuijpers, R.H. Murga, I. Inza, S. Dizdarevic: Articial Intelligence Review 13, 129–170 (1999)CrossRef
45. A. Brouwer, A. Cohen, A. Neumaier: Distance-regular Graphs (Springer Verlag, Berlin, New York, 1989)
46. M. Shpak, G.P. Wagner: Artificial Life 6, 25–43 (2000)PubMedCrossRef
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
48. E.D. Weinberger: Biol. Cybern. 63, 325–336 (1990)CrossRef
49. E.D. Weinberger: Biol. Cybern. 65, 321–330 (1991)CrossRef
50. W. Hordijk: Evolutionary Computation 4(4), 335–360 (1996)CrossRef
51. W. Hordijk: Physica D 107, 255–264 (1997)CrossRef
52. P.F. Stadler, R. Seitz, G.P. Wagner: Bull. Math. Biol. 62, 399–428 (2000)PubMedCrossRef
53. H.R. Fischer: Math. Annalen 137, 269–303 (1959)CrossRef
54. D.C. Kent: Fund. Math. 54, 125–133 (1964)
55. E. Čech: Topological Spaces (Wiley, London, 1966)
56. D.C. Kent: Fund. Math. 62, 95–100 (1968)
57. B.M.R. Stadler, P.F. Stadler, W. Fontana, G.P. Wagner: J. Theor. Biol. (2001). Submitted, SFI preprint 00-12-070
58. B.M.R. Stadler, P.F. Stadler, M. Shpak, G.P. Wagner: Artificial Life (2001). Submitted, SFI preprint 01-02-011
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
60. P.F. Stadler, W. Schnabl: Phys. Lett. A 161, 337–344 (1992)CrossRef
61. P.F. Stadler, B. Krakhofer: Rev. Mex. Fis. 42, 355–363 (1996)
62. R. García-Pelayo, P.F. Stadler: Physica D 107, 240–254 (1997)CrossRef
63. D.J. Thouless, P.W. Anderson, R.G. Palmer: Phil. Mag. 35, 593–601 (1977)CrossRef
64. F. Tanaka, S.F. Edwards: J. Phys. F 10, 2769–2778 (1980)CrossRef
65. A.J. Bray, M.A. Moore: J. Phys. C 14, 1313–1327 (1981)CrossRef
66. D.J. Gross, M. Mézard: Nucl. Phys. B 240, 431–452 (1984)CrossRef
67. B. Derrida, E. Gardner: J. Physique 47, 959–965 (1986)CrossRef
68. H. Rieger: Phys. Rev. B 46, 14655–14661 (1992)
69. V.M. de Oliveira, J.F. Fontanari, P.F. Stadler: J. Phys. A: Math. Gen. 32, 8793–8802 (1999)CrossRef
70. F.F. Ferreira, J.F. Fontanari, P.F. Stadler: J. Phys. A: Math. Gen. 33, 8635–8647 (2000)CrossRef
71. J. Garnier, L. Kallel: SIAM J. Discr. Math. (2000). Submitted
72. E.D. Weinberger: Phys. Rev. A 44, 6399–6413 (1991)PubMedCrossRef
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)CrossRef
74. J.H. Gillespie: Evolution 38, 1116–1129 (1984)CrossRef
75. S.A. Kauffman, S. Levin: J. Theor. Biol. 128, 11–45 (1987)PubMedCrossRef
76. H. Flyvbjerg, B. Lautrup: Phys. Rev. A 46, 6714–6723 (1992)PubMedCrossRef
77. C.A. Macken, A.S. Perelson: Proc. Natl. Acad. Sci. USA 86, 6191–6195 (1989)PubMedCrossRef
78. C.A. Macken, P.S. Hagan, A.S. Perelson: SIAM J. Appl. Math. 51, 799–827 (1991)CrossRef
79. A.S. Perelson, C.A. Macken: Proc. Natl. Acad. Sci. USA 92, 9657–9661 (1995)PubMedCrossRef
80. K.J. Niklas: Amer. J. Botany 84, 16–25 (1997)CrossRef
81. R. Rammal, G. Toulouse, M.A. Virasoro: Rev. Mod. Phys. 58, 765–788 (1986)CrossRef
82. A.M. Vertechi, M.A. Virasoro: J. Phys. France 50, 2325–2332 (1989)
83. S.R. Morgan, P.G. Higgs: J. Phys. A 31, 3153–3170 (1998)CrossRef
84. C. Flamm, I.L. Hofacker, S. Maurer-Stroh, P.F. Stadler, M. Zehl: RNA 7, 254–265 (2001)PubMedCrossRef
85. W. Kern: Discr. Appl. Math. 43, 115–129 (1993)CrossRef
86. R. Azencott: Simulated Annealing (John Wiley & Sons, New York, 1992)
87. O. Catoni: Ann. Probab. 20, 1109–1146 (1992)CrossRef
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
89. B. Hajek: Math. Operations Res. 13, 311–329 (1988)CrossRef
90. J. Ryan: Discr. Appl. Math. 56, 75–82 (1995)CrossRef
91. G.B. Sorkin: (1988), “Combinatorial optimization, simulated annealing, and fractals” Tech. Rep. RC13674 (No.61253), IBM Research Report
92. M. Eigen, J. McCaskill, P. Schuster: Adv. Chem. Phys. 75, 149–263 (1989)CrossRef
93. P.F. Stadler: Discr. Math. 145, 229–238 (1995)CrossRef
94. P. Schuster, P.F. Stadler: Computers & Chem. 18, 295–314 (1994)CrossRef
95. P.F. Stadler, R. Happel: J. Math. Biol. 38, 435–478 (1999)CrossRef
96. P.F. Stadler, W. Schnabl: Phys. Letters A 161, 337–344 (1992)CrossRef
97. B. Krakhofer, P.F. Stadler: Europhys. Lett. 34, 85–90 (1996)CrossRef
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
99. R. Merris: Lin. Alg. Appl. 39, 19–31 (1995)
100. F.R.K. Chung: Spectral Graph Theory, Vol. 92 of CBMS (American Mathematical Society, Providence RI, 1997)
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
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
103. D. Rockmore, P. Kostelec, W. Hordijk, P.F. Stadler: Appl. Comput. Harmonic Anal. (2000). In press Santa Fe Institute preprint 99-10-068
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
105. D.E. Goldberg: Complex Systems 3, 129–152 (1989)
106. D.E. Goldberg: Complex Systems 3, 153–176 (1989)
107. S.E. Page, D.E. Richardson: Complex Systems 6, 125–136 (1992)
108. M.D. Vose, A.H. Wright: Evol. Comp. 6, 253–274 (1998)CrossRef
109. M.D. Vose, A.H. Wright: Evol. Comp. 6, 275–289 (1998)CrossRef
110. L.K. Grover: Oper. Res. Lett. 12, 235–243 (1992)CrossRef
111. B. Codenotti, L. Margara: (1992), “Local properties of some np-complete problems” Tech. Rep. TR 92-021, International Computer Science Institute, Berkeley, CA
112. E. Angel, V. Zissimopoulos: Discr. Appl. Math. 99, 261–277 (2000)CrossRef
113. I. Chavel: Eigenvalues in Riemannian Geometry (Academic Press, Orlando Fl., 1984)
114. Y.C. de Verdière: Rendiconti di Matematica 13, 433–460 (1993)
115. J. Friedman: Duke Math. J. 69(3), 487–525 (1993)CrossRef
116. H. van der Holst: (1996), “Topological and spectral graph characterizations” Ph.D. thesis, Universiteit van Amsterdam
117. A.M. Duval, V. Reiner: Lin. Alg. Appl. 294, 259–268 (1999)CrossRef
118. E.B. Davies, G.M.L. Gladwell, J. Leydold, P.F. Stadler: Lin. Alg. Appl. (2001). In press, see also: math.SP/0009120
119. R. Happel, P.F. Stadler: Complexity 2, 53–58 (1996)CrossRef
120. W. Hordijk, P.F. Stadler: J. Complex Systems 1, 39–66 (1998)CrossRef
121. Y. Davidor: Complex Systems 4, 369–383 (1990)
122. M. Whitlock, P.C. Phillips, F.B.G. Moore, S. Tonsor: Ann. Review Ecol. Systematics 26, 601–629 (1995)CrossRef
123. J.B. Wolf, E.D. Brodie III, M.J. Wade (Eds.): Epistasis and the Evolutionary Process (Oxford Univ. Press, Oxford, UK, 2000)
124. C.M. Reidys, P.F. Stadler: Appl. Math. & Comput. 117, 321–350 (2001)CrossRef
125. C.M. Reidys: Adv. Appl. Math. 19, 360–377 (1997)CrossRef
126. S. Gavrilets, J. Gravner: J. Theor. Biol. 184, 51–64 (1997)PubMedCrossRef
127. C.M. Reidys, P.F. Stadler, P. Schuster: Bull. Math. Biol. 59, 339–397(1997 )PubMedCrossRef
128. S. Gavrilets, H. Li, M.D. Vose: Proc. Roy. Soc. London B 265, 1483–1489 (1998)CrossRef
129. S. Kopp, C.M. Reidys: Adv. Complex Syst. 2, 283–301 (1999)CrossRef
130. P.F. Stadler: J. Mol. Struct. (THEOCHEM) 463, 7–19 (1999)CrossRef
131. W. Fontana, D.A.M. Konings, P.F. Stadler, P. Schuster: Biopolymers 33, 1389–1404 (1993)PubMedCrossRef
132. W. Fontana, P. Schuster: Science 280, 1451–1455 (1998)PubMedCrossRef
133. D.E. Goldberg, M. Rudnik: Complex Systems 5, 265–278 (1991)
134. G.E. Liepins, M.D. Vose: Complex Systems 5, 45–61 (1991)
135. P. Field: Complex Systems 9, 11–28 (1995)
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
137. A.D. Bethke: (1991), “Genetic algorithms and function optimizers” Ph.D. thesis, University of Michigan
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
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
140. C.R. Stephens, H. Waelbroeck: Phys. Rev. E 57, 3251–3264 (1998)CrossRef
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
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
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
144. B. Naudts, L. Kallel: IEEE Trans. Evol. Comp. (2000). To appear
145. M. Mitchell: An Introduction to Genetic Algorithms (MIT Press, Cambridge MA, 1996)
146. D.F. T. Baeck, Z. Michalewicz (Eds.): Handbook of Evolutionary Computation (Oxford University Press, New York, 1997)
147. E. Angel, V. Zissimopoulos: Theor. Computer Sci. 191, 229–243 (1998)CrossRef
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