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Definition
A hypercycle is a catalytic network of autocatalysts (Ik) that are functionally coupled in a dynamical cycle: \( \Rightarrow {\mathrm{I}}_1\Rightarrow {\mathrm{I}}_2\Rightarrow \dots \Rightarrow {\mathrm{I}}_{\mathrm{n}}\Rightarrow {\mathrm{I}}_1\Rightarrow \). Hypercycle dynamics is described by means of nonlinear differential equations of replicator equation type (Fig. 1).
The catalytic interactions in a hypercycle with n members. The individual elements, 1, 2, 3, 4, …, n, are coupled by cyclic catalysis (black arrows): 1→2, 2→3, 3→4, 4→n, n→1. Every member is an autocatalyst as indicated by cycles (small circular arrows)
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References and Further Reading
Eigen M (1971) Self-organization of matter and the evolution of biological macromolecules. Naturwissenschaften 58:465–523
Eigen M, Schuster P (1977) The hypercycle. A principle of natural self-organization. Part A: emergence of the hypercycle. Naturwissenschaften 64:541–565
Eigen M, Schuster P (1978a) The hypercycle. A principle of natural self-organization. Part B: the abstract hypercycle. Naturwissenschaften 65:7–41
Eigen M, Schuster P (1978b) The hypercycle. A principle of natural self-organization. Part C: the realistic hypercycle. Naturwissenschaften 64:341–369
Hofbauer J, Sigmund K (1998) Evolutionary games and replicator dynamics. Cambridge University Press, Cambridge
Maynard Smith J, Szathmáry E (1995) The major transitions in evolution. WH Freeman, Oxford
Nowak MA (2006) Evolutionary dynamics. The Belknap Press of Harvard University Press, Cambridge, MA, Exploring the equations of life
Phillipson PE, Schuster P (2009) Modeling by nonlinear differential equations. Dissipative and conservative processes. World Scientific, Singapore, pp 61–75
Schuster P (1996) How does complexity arise in evolution? Complexity 2(1):22–30
Vaidya N, Manapat ML, Chen IA, Xulvi-Brunet R, Hayden EJ, Lehman N (2012) Spontaneous network formation among cooperative RNA replicators. Nature 491:72–77
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Schuster, P. (2014). Hypercycle. In: Amils, R., et al. Encyclopedia of Astrobiology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27833-4_765-3
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DOI: https://doi.org/10.1007/978-3-642-27833-4_765-3
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