Four-state quantum chain as a model of sequence evolution

Journal of Statistical Physics

Volumn 102, Issue 1-2, 2001, Pages 315-343

  Hermisson, Joachim ^a,b,c   Wagner, Holger ^d   Baake, Michael ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b UNIVERSITY OF KARLSRUHE   (Germany)

^c YALE UNIVERSITY   (United States)

^d MAX PLANCK INSTITUTE FOR BIOPHYSICAL CHEMISTRY   (Germany)

Author keywords

Biological evolution; Error threshold; Mean held model; Mutation; Phase transition; Quantum chain; Selection

Indexed keywords

EID: 0035218314     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026577012763     Document Type: Article

References (28)

1. 1. E. Baake, Diploid models on sequence space, J. Biol. Syst. 3:343-349 (1995).
2. 2. E. Baake, M. Baake, and H. Wagner, Ising quantum chain is equivalent to a model of biological evolution, Phys. Rev. Lett. 78:559-562 (1997): Erratum: Phys. Rev. Lett. 79:1782 (1997).
3. 3. E. Baake, M. Baake, and H. Wagner, Quantum mechanics versus classical probability in biological evolution, Phys. Rev. E 57:1191-1192 (1998).
4. 4. E. Baake and W. Gabriel, Biological evolution through mutation, selection, and drift: An introductory review, Ann. Rev. Comput. Phys. 7:203-264 (1999) (condmat/9907372).
5. 5. J. Crow and M. Kimura, An Introduction to Population Genetics Theory (Harper & Row, New York, 1970).
6. 6. N. G. Duffield and R. Kühn, The thermodynamics of site-random mean-field quantum spin systems, J. Phys. A 22:4643-4658 (1989).
7. 7. M. Eigen, Selforganization of matter and the evolution of biological macromolecules, Naturwiss. 58:465-523 (1971).
8. 8. M. Eigen, J. McCaskill, and P. Schuster, The molecular quasi-species, J. Chem. Phys. 75:149-263 (1989).
9. 9. R. A. Fisher, The Genetical Theory of Natural Selection (Clarendon Press, Oxford, 1930).
10. 10. S. Franz and L. Peliti, Error threshold in simple landscapes, J. Phys. A 26:4481-4487 (1993).
11. 11. S. Franz. L. Peliti, and M. Sellitto, An evolutionary version of the random energy model, J. Phys. A 26:L1195-1199 (1993).
12. 12. S. Galluccio, Exact solution of the quasispecies model in a sharply-peaked landscape, Phys. Rev. E 56:4526-4539 (1997).
13. 13. S. A. Kauffmann and S. A. Levin, Towards a general theory of adaptive walks on rugged landscapes, J. Theor. Biol. 128:11-45 (1987).
14. 14. J. Kogut, An introduction to lattice gauge theory and spin systems, Rev. Mod. Phys. 51:656-713 (1979).
15. 15. I. Leuthäusser, An exact correspondence between Eigen's evolution model and a two-dimensional Ising system, J. Chem. Phys. 84:1884-1885 (1986).
16. 16. I. Leuthäusser, Statistical mechanics of Eigen's evolution model, J. Stat. Phys. 48: 343-3460 (1987).
17. 17. W.-H. Li, Molecular Emlution (Sinauer, Sunderland, 1997).
18. 18. K. Malarz and D. Tiggemann, Dynamics in Eigen's evolution model, Int. J. Mod. Phys. C 9:481-490 (1997).
19. 19. M. Nowak and P. Schuster, Error thresholds of replication in finite populations. Mutation frequencies and the onset of Muller's ratchet, J. Theor. Biol. 137:375-395 (1989).
20. 20. P. O'Brien, A genetic model with mutation and selection, Math. Biosci. 73:239-251 (1985).
21. 21. O. Redner, private communication (1999).
22. 22. P. Stadler, Landscapes and their correlation functions, J. Math. Chem. 20:1-45 (1996).
23. 23. D. Swofford, G. Olsen, P. Waddell, and D. Hillis, Phylogenetic inference, in Molecular Systematics, M. Hillis, C. Moritz, and E. Mable. eds. (Sinauer, Sunderland, 1995). pp. 407-517.
24. 24. P. Tarazona, Error thresholds for molecular quasispecies as phase transitions: From simple landscapes to spin-glass models, Phys. Rev. A 45:6038-6050 (1992).
25. 25. C. J. Thompson and J. L. McBride, On Eigen's theory of the self-organization of matter and the evolution of biological macromolecules, Math. Biosci. 21:127-142 (1974).
26. 26. H. Wagner, Biologische Sequenzraummodelle and Statische Mechanik, Ph.D. thesis, University of Tübingen, Dissertations Druck (Darmstadt, 1998).
27. 27. H. Wagner, E. Baake, and T. Gerisch, Ising Quantum chain and sequence evolution, J. Stat. Phys. 92:1017-1051 (1998).
28. 28. T. Wiehe, Model dependency of error thresholds: the role of the fitness functions and contrasts between the finite and infinite sites models, Genet. Res. Camb. 69:127-136 (1997).