Abstract
To explain higher-level heritability, we propose a dynamical systems approach, based on simulations of the high-dimensional replicator equation with mutation dynamics. We assume that all variants are generated from within the groups of variants through mutations. Simulating the equation with a random interaction matrix and possible variants, we report that this system tends to have many attractors, of fixed point, chaotic and quasiperiodic type. In a chaotic attractor, special gene-like variants appear to control the heritability ofthe system, in the sense that removal of the variants would easily enable the system to depart from the attractor. Those variants do not predominate in thepopulation size, but have the lowest net reproduction and mutation rates on average. Because their rate of growth is small, they are named neutral phenotypes. Additionally, combinatorial effects of these neutral variants to the entire system are reported.
Keywords: chaos, evolvability, neutral phenotype, replicator dynamics
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Contributor Information
T. Ikegami, Email: ikeg@sacral.c.u-tokyo.ac.jp
K. Hashimoto, Email: hasimoto@sacral.c.u-tokyo.ac.jp
References
- 1.Goodnight C.J. PNAS. 2000;97(17):9365–9366. doi: 10.1073/pnas.97.17.9365. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 2.Swenson W., Wilson D.S., Elias R. PNAS. 2000;97(16):9110–9114. doi: 10.1073/pnas.150237597. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 3.Yokoyama, K.:presented at the Mathematical Biology Meeting, Hamamatsu, Oct, 2000.
- 4.Ikegami T.J. Artificial Life and Robotics. 1999;3(4):242–245. [Google Scholar]
- 5.Smith, J.M.: Evolution and the Theoryof Games, Cambridge University Press, 1982.
- 6.Hofbauer, J.:Nonlinear Analysis5 (1981), 1003.
- 7.Tokita K., Yasutomi A. Physical Review E. 1999;60:682. doi: 10.1103/physreve.60.842. [DOI] [PubMed] [Google Scholar]
- 8.Ikegami R., Yoshikawa E. I. In: Towards the Harnessing of Chaos. Yamaguchi M., editor. Tokyo: Springer-Verlag; 1995. p. 63. [Google Scholar]
- 9.Hashimoto K., Ikegami T. J. Phys.Soc. Japan. 2001;70:349. [Google Scholar]
- 10.Brown, J.H. et al.:Science 2001 July 27, 293(5530): p. 643–650.
- 11.Kaneko, K.: presented at the 4th Int'l Conf. on BiologicalPhysics, Kyoto, 2001.
- 12.Hogeweg, P.: In: C. Adami et al.(eds.), Artificial Life VI, MIT Press, 1998, pp. 285–294.