Aggregation of variables and system decomposition: Applications to fitness landscape analysis

Theory in Biosciences

Volumn 123, Issue 1, 2004, Pages 33-68

  Shpak, Max ^a   Stadler, Peter ^b   Wagner, Gunter P ^a   Hermisson, Joachim ^c  

^a UNIVERSITY OF TENNESSEE   (United States)

^b UNIVERSITY OF LEIPZIG   (Germany)

^c UNIVERSITY OF MUNICH   (Germany)

Author keywords

Aggregation of variables; Decomposability; Fitness landscapes; Mutation selection

Indexed keywords

CALCULATION; DATA ANALYSIS; DECOMPOSITION; HYPOTHESIS; LINEAR SYSTEM; MATHEMATICAL ANALYSIS; MOLECULAR DYNAMICS; MOLECULAR EVOLUTION; MUTATIONAL ANALYSIS; NATURAL SELECTION; PARAMETER; PHASE TRANSITION; REVIEW; SYSTEM ANALYSIS; TECHNIQUE;

EID: 3142632025     PISSN: 14317613     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.thbio.2004.02.001     Document Type: Article

References (35)

1. Altenberg, L., 1995. The schema theorem and Price's theorem. In: Whitley, D., Vose, M. (Eds.), Foundations in Genetic Algorithms. Morgan Kauffman, San Francisco, pp. 23-49.
2. Ando, A., Fisher, F., 1963. Near-decomposability: partition and aggregation, and the relevance of stability discussions. International Economic Review 4, 53-67.
3. Bogart, K.P., 2000. Introductory Combinatorics 3rd Edition. Harcourt/Academic Press, San Diego, CA.
4. Buerger, R., 1998. Mathematical properties of mutation-selection models. Genetica 103, 279-298.
5. Buerger, R., 2001. The Mathematical Theory of Selection, Recombination, and Mutation. Wiley, New York, NY.
6. Burke, C.J., Rosenblatt, M., 1958. A markovian function of a markov chain. Annals of Mathematical Statistics 29, 1112-1122.
7. Crow, J., Kimura, M., 1970. An Introduction to Population Genetics Theory. Harper and Row, New York, NY.
8. Dress, A.W.M., Rumschitzki, D.S., 1987. Evolution on sequence space and tensor products of representation spaces. Acta Applicandae Mathematicae 11, 103-115.
9. Eigen, M., McCaskill, J., Schuster, P., 1989. The molecular quasis-species. Advances in Chemistry and Physics 75, 149-263.
10. Godsil, C., 1993. Algebraic Combinatorics. Chapman & Hall, New York, NY.
11. Goldberg, D.E., 1989. Genetic Algorithms. Reading, MA.
12. Haken, H., 1977. Synergetics. Springer, Berlin.
13. Hermisson, J., Redner, O., Wagner, H., Baake, E., 2002. Mutation-selection blance: ancestry, load, and maximum principle. Theoretical Population Biology 62, 9-46.
14. Holland, J.P., 1975. Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI.
15. Jones, B.L., 1978. Some principles governing selection in self-reproducing macromo-lecular systems. Journal of Mathematical Biology 6, 169-175.
16. Kauffman, S.A., 1993. The Origins of Order. Oxford University Press, Oxford, UK.
17. Laubichler, M., Wagner, G.P., 2000. Organisms and character decomposition: steps towards and intergrated theory of biology. Philosophy of Science 66 (Suppl.).
18. Levins, R., 1970. Extinction. In: Gersten-haber, M. (Ed.), Some Mathematical Questions in Biology. Lectures on Mathematical Analysis of Fundamental Biological Phenomena. Annals of NY Academy of Sciences 231, 123-138
19. Lewontin, R.C., Kojima, K., 1960. The evolutionary dynamics of complex polymorphisms. Evolution 14, 458-472.
20. Lewontin, R.C., 1970. The units of selection. Annual Review of Ecology and Systematics 1, 1-14.
21. Moran, P.A.P., 1976. Global stability of genetic systems governed by mutation and selection. Mathematical Proceedings of the Cambridge Philosophical Society 81, 435-441.
22. Nowak, Schuster, 1989. Error thresholds of replication in finite poulations. Journal of Theoretical Biology 137, 375-395.
23. Rosen, R., 1984. Fundamentals of Measurement and Representation of Natural Systems. New York, North Holland.
24. Schank, J.C., Wimsatt, W.C., 1988. Generative entrenchment and evolution. In: Fine, A., Machamer, P.K. (Eds.), PSA-186, 2:33-60, Philosophy of Science Association
25. Schuster, P., Swetina, J., 1989. Stationary mutant distributions and evolutionary optimization. Bulletin of Mathematical Biology 50, 635-660.
26. Schwenk, A.J., 1974. Computing the characteristic polynomial of a graph. In: Bari, R., Harary, F. (Eds.), Graphs and Combinatorics. Springer, Berlin, pp. 153-172.
27. Simon, H.A., Ando, J., 1961. Aggregation of variables in dynamic systems. Econometrica 29, 111-138.
28. Stadler, P.P., 1996. Landscapes and their correlation functions. Journal of Mathematical Chemistry 20, 1-45.
29. Stadler, P.P., Tinhofer, G., 2000. Equitable partitions, coherent algebras, and random walks: applications to the correlation structure of landscapes. MATCH 40, 215-261
30. Thompson, C.J., McBride, J.L., 1974. On eigen's theory of sel-organization of matter and evolution of biological macromolecules. Mathematical Biosciences 27, 127-142.
31. Wagner, G.P., Booth, G., Bagheri, H., 1997. A population genetic theory of canalization. Evolution 51, 329-347.
32. Wagner, G.P., Laubichler, M., 2000. Character identificiation in evolutionary biology: the role of the organism. Theory of Biosceinces 119, 20-40.
33. Wilke, C., 2001. Adaptive evolution on neutral networks. Bulletin of Mathematical Biology 63, 715-730.
34. Wimsatt, W., 1981. Units of selection and the structure of the multi-level genome. In Asquith, P.D., Grere, R.N. (Eds.), PSA-180, 2:122-183. Philosophy of Science Association.
35. Wright, S., 1932. The roles of mutation, inbreeding, cross-breeding, and selection in evolution. Proceedings of the VI International Congress of Genetics, vol 1, pp. 356-366