View More View Less
  • 1 Department of Biological Physics, Eötvös University H-1117 Budapest, Pázmány Péter sétány 1A, Hungary
  • 2 Department of Entomology, Faculty of Horticultural Science, Corvinus University of Budapest H-1118 Budapest, Ménesi út 44, Hungary
Restricted access

The growth of many artificial replicators is approximately parabolic (sub-exponential) in solution, due to the self-inhibition through duplex formation by the association of single-stranded molecules. This type of growth implies “survival of everybody” under a selection constraint. Parabolic growth requires high enough concentration so that the single strands can find one another. The selective outcome is more complicated when spontaneous decay of molecules is also taken into account. When double strands decompose at a slower rate than single strands, coexistence or survival of the fittest becomes a quantitative issue. Here we investigate the evolution of parabolic replicators by the methods of adaptive dynamics. Directional selection for higher replication rate in general results in a “parabolic quasi-species”, due to the fact that the fittest template is followed by a moving shadow of inferior templates that owe their presence to parabolic growth. Under the assumption of cross-hybridisation between non-identical templates molecular coexistence disappears when such pairing is sufficiently non-selective, because replicators do not inhibit themselves more than they limit the others. At intermediate specificity of pairing adaptive branching of the population becomes feasible, due to the fact that distant enough sequences are able to escape from cross-limitation by other sub-populations.

  • Dieckmann U. and Law, R. (1996): The dynamical theory of coevolution: a derivation from stochastic ecological processes. J. Math. Biol. 34:579-612.

    'The dynamical theory of coevolution: a derivation from stochastic ecological processes ' () 34 J. Math. Biol. : 579 -612.

    • Search Google Scholar
  • Doebeli, M. and Dieckmann, U. (2000): Evolutionary branching and sympatric speciation caused by different types of ecological interactions. Am. Nat. 156:S77.

    'Evolutionary branching and sympatric speciation caused by different types of ecological interactions ' () 156 Am. Nat. : S77.

    • Search Google Scholar
  • Eigen, M. (1971): Molecular selforganization and the early stages of evolution. Quart. Rev. Biophys. 4:149-212.

    'Molecular selforganization and the early stages of evolution ' () 4 Quart. Rev. Biophys. : 149 -212.

    • Search Google Scholar
  • Eigen, M. and Schuster, P. (1977): The hypercycle: A principle of natural self-organization. Part A: emergence of the hypercycle. Naturwiss. 64:541-565.

    'The hypercycle: A principle of natural self-organization. Part A: emergence of the hypercycle ' () 64 Naturwiss. : 541 -565.

    • Search Google Scholar
  • Geritz, S. A. H., Gyllenberg, M., Jacobs, F. J. A. and Par-vinen, K. (in press): Invasion dynamics and attractor inheritance. J. Math. Biol.

  • Geritz S. A. H., METZ, J. A. J., KISDI, É. and MESZÉNA, G. (1997): Dynamics of adaptation and evolutionary branching. Phys. Rev. Letters 78:2024-2027.

    'Dynamics of adaptation and evolutionary branching ' () 78 Phys. Rev. Letters : 2024 -2027.

    • Search Google Scholar
  • Geritz S. A. H., Kisdi, É., Meszéna and Metz, J. A. J. (1998): Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol. 12:35-57.

    'Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree ' () 12 Evol. Ecol. : 35 -57.

    • Search Google Scholar
  • Geritz, S. A. H., van der Meijden, E. and Metz, J. A. J. (1999): Evolutionary dynamics of seed size and seedling competitive ability. Theor. Popul. Biol. 55:324-343.

    'Evolutionary dynamics of seed size and seedling competitive ability ' () 55 Theor. Popul. Biol. : 324 -343.

    • Search Google Scholar
  • Jacobs, F. J. A., Metz, J. A. J., Geritz, S. A. H. and Meszéna, G. (in prep.): Invasion implies fixation.

  • Kisdi, É. (1999): Evolutionary branching under asymmetric competition. J. Theor. Biol. 197:149-162.

    'Evolutionary branching under asymmetric competition ' () 197 J. Theor. Biol. : 149 -162.

  • Kisdi, É. and Geritz, S. A. H.(1999): Adaptive dynamics in allele space: evolution of genetic polymorphism by small mutations in a heterogeneous environment. Evolution 53:993-1008.

    'Adaptive dynamics in allele space: evolution of genetic polymorphism by small mutations in a heterogeneous environment ' () 53 Evolution : 993 -1008.

    • Search Google Scholar
  • Levin, S. M. (1970): Community equilibria and stability, and an extension of the competitive exclusion principle. Amer. Nat. 104:413-423.

    'Community equilibria and stability, and an extension of the competitive exclusion principle ' () 104 Amer. Nat. : 413 -423.

    • Search Google Scholar
  • Lifson, S. and Lifson, H. (1999): Models of prebiotic replication: Survival of the fittest versus extinction of the unfit-test. J. Theor. Biol. 199:425-433.

    'Models of prebiotic replication: Survival of the fittest versus extinction of the unfit-test ' () 199 J. Theor. Biol. : 425 -433.

    • Search Google Scholar
  • MacArthur, R. and Levins, R. (1964): Competition, habitat selection and character displacement in a patchy environment. Proc. Natl. Acad. Sci. USA 51:1207-1210.

    'Competition, habitat selection and character displacement in a patchy environment ' () 51 Proc. Natl. Acad. Sci. USA : 1207 -1210.

    • Search Google Scholar
  • Mac Arthur, R. and Levins, R. (1967): The limiting similarity, convergence, and divergence of coexisting species. Amer. Nat. 101(921):377-385.

    'The limiting similarity, convergence, and divergence of coexisting species ' () Amer. Nat. : 377 -385.

    • Search Google Scholar
  • Mathias, A., Kisdi, É. and Olivieri, I. (2001): Divergent evolution of dispersal in a heterogeneous landscape. Evolution, 55:246-259.

    'Divergent evolution of dispersal in a heterogeneous landscape ' () 55 Evolution : 246 -259.

    • Search Google Scholar
  • Mathias, A. and Kisdi, É. (in press): Evolutionary branching and coexistence of germination strategies. In Dieckmann, U. and Metz, J. A. J. (eds): Elements of Adaptive Dynamics. Cambridge University Press.

    Elements of Adaptive Dynamics , ().

  • Meszena G., Czibula, I. and Geritz, S. A. H. (1997): Adaptive dynamics in a 2-patch environment: A toy model for allopatric and parapatric speciation. J. Biol. Syst. 5:265-284.

    'Adaptive dynamics in a 2-patch environment: A toy model for allopatric and parapatric speciation ' () 5 J. Biol. Syst. : 265 -284.

    • Search Google Scholar
  • Meszéna, G. and Metz, J. A. J. (in press): The role of effective environmental dimensionality. In: Metz, J. A. J. and Dieckmann, U. (eds): Elements of Adaptive Dynamics. Cambridge University Press.

    Elements of Adaptive Dynamics , ().

  • Metz, J. A. J., Nisbet, R. M. and Geritz, S. A. H. (1992): How should we define 'fitness' for general ecological scenarios? Trends Ecol. Evol. 7:198-202.

    'How should we define 'fitness' for general ecological scenarios ' () 7 Trends Ecol. Evol. : 198 -202.

    • Search Google Scholar
  • Metz, J. A. J., Geritz, S. A. H., Meszéna, G., Jacobs, F. J. A. and van Heerwaarden, J. S. (1996): Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. In Strien, S. J. van and Verduyn Lunel, S. M. (eds): Stochastic and Spatial Structures of Dynamical Systems. North Holland, Amsterdam, pp. 183-231.

    Stochastic and Spatial Structures of Dynamical Systems , () 183 -231.

  • Mylius, S. D. and Diekmann, O. (1995): On evolutionarily stable life histories, optimization and the need to be specific about density dependence. Oikos 74:218-224.

    'On evolutionarily stable life histories, optimization and the need to be specific about density dependence ' () 74 Oikos : 218 -224.

    • Search Google Scholar
  • Pásztor, E., Meszéna, G. and Kisdi, É. (1996): R0 or r: a matter of taste? J. Evol. Biol. 9:511-518.

    'R0 or r: a matter of taste ' () 9 J. Evol. Biol. : 511 -518.

  • Roughgarden, J. A. (1979): Theory of Population Genetics and Evolutionary Ecology: An introduction. Macmillan, New York.

    Theory of Population Genetics and Evolutionary Ecology: An introduction , ().

  • Sasaki, A. and Ellner, S. (1995): The evolutionary stable phenotype distribution in a random environment. Evolution 49(2):337-350.

    'The evolutionary stable phenotype distribution in a random environment ' () 49 Evolution : 337 -350.

    • Search Google Scholar
  • Scheuring, I. and Szathmáry, E. (2001): Survival of replicators with parabolic growth tendency and exponential decay. J. Theor. Biol. 212:99-105.

    'Survival of replicators with parabolic growth tendency and exponential decay ' () 212 J. Theor. Biol. : 99 -105.

    • Search Google Scholar
  • Von Kiedrowski, G. (1999): Molekulare Prinzipien der arti-fiziellen Selbstreplikation. In Ganten, D. (ed.): Gene, Nerone, Qubits & Co. Unsere Welten der Information. S. Hirzel Verlag, Stuttgart, pp. 123-145.

    Gene, Nerone, Qubits & Co. Unsere Welten der Information , () 123 -145.

  • Von Kiedrowski, G. and Szathmáry, E. (2000): Selection versus coexistence of parabolic replicators spreading on surfaces. Selection 1:173-179.

    'Selection versus coexistence of parabolic replicators spreading on surfaces ' () 1 Selection : 173 -179.

    • Search Google Scholar
  • Wang, B. and Sutherland, I. O. (1997): Self-replication in a Diels-Alder reaction. Chem. Commun 16:1495-1496.

    'Self-replication in a Diels-Alder reaction ' () 16 Chem. Commun : 1495 -1496.

  • Wills, P. R., Kauffman, S. A., Stadler, B. M. R. and Stadler, P. F. (1998): Selection dynamics in autocatalytic systems: Templates replicating through binary ligation. Bull. Math. Biol. 160:1073-1098.

    'Selection dynamics in autocatalytic systems: Templates replicating through binary ligation ' () 160 Bull. Math. Biol. : 1073 -1098.

    • Search Google Scholar
  • Czárán, T. and Szathmáry, E. (2000): Coexistence of replicators in prebiotic evolution. In Dieckmann, U., LAW, R. and Metz, J. A. J. (eds): The Geometry of Ecological Interactions: Simplifying Spatial Complexity. IIASA and Cambridge University Press, pp. 116-134.

    The Geometry of Ecological Interactions: Simplifying Spatial Complexity , () 116 -134.

    • Search Google Scholar
  • Darwin, Ch. (1859): On the Origin of Species by Means of Natural Selection, or The Preservation of Favoured Races in the Struggle for Life. First Edition. Harvard University Press.

    On the Origin of Species by Means of Natural Selection, or The Preservation of Favoured Races in the Struggle for Life , ().

    • Search Google Scholar
  • Fontana, W. and Schuster, P. (1998): Shaping space: The possible and the attainable in RNA genotype-phenotype mapping. J. Theor. Biol. 194:491-515.

    'Shaping space: The possible and the attainable in RNA genotype-phenotype mapping ' () 194 J. Theor. Biol. : 491 -515.

    • Search Google Scholar
  • Varga, Z. and Szathmáry, E. (1997): An extremum principle for parabolic competition. Bull. Math. Biol. 59:1145-1154.

    'An extremum principle for parabolic competition ' () 59 Bull. Math. Biol. : 1145 -1154.

  • Von Kiedrowski, G. (1986): A self-replicating hexadeoxy nucleotide. Angew. Chem. Int. Ed. Engl. 25:932-935.

    'A self-replicating hexadeoxy nucleotide ' () 25 Angew. Chem. Int. Ed. Engl. : 932 -935.

  • Von Kiedrowski, G. (1993): Mimimal replicator theory I: Parabolic versus exponential growth. Bioorg. Chem. Frontiers 3:113-146.

    'Mimimal replicator theory I: Parabolic versus exponential growth ' () 3 Bioorg. Chem. Frontiers : 113 -146.

    • Search Google Scholar
  • Szathmáry, E. (1991): Simple growth laws and selection consequences. Trends Ecol. Evol. 6:366-370.

    'Simple growth laws and selection consequences ' () 6 Trends Ecol. Evol. : 366 -370.

  • Szathmáry, E. and Gladkih, I. (1989): Sub-exponential growth and coexistence of non-enzymatically replicating templates. J. Theor. Biol. 138:55-58.

    'Sub-exponential growth and coexistence of non-enzymatically replicating templates ' () 138 J. Theor. Biol. : 55 -58.

    • Search Google Scholar

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Aug 2020 4 0 1
Sep 2020 0 0 0
Oct 2020 9 0 0
Nov 2020 6 20 5
Dec 2020 2 0 0
Jan 2021 0 0 0
Feb 2021 0 0 0