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(Super)systems and selection dynamics

(Super)systems and selection dynamics. Eörs Szathmáry & Mauro Santos. Collegium Budapest. Eötvös University Budapest. Haldane’s intellectual son: John Maynard Smith (1920-2004). Units of evolution. multiplication heredity variation. hereditary traits affecting survival and/or reproduction.

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(Super)systems and selection dynamics

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  1. (Super)systems and selection dynamics Eörs Szathmáry & Mauro Santos Collegium Budapest Eötvös University Budapest

  2. Haldane’s intellectual son: John Maynard Smith (1920-2004)

  3. Units of evolution • multiplication • heredity • variation hereditary traits affecting survival and/or reproduction

  4. Parabolic replicators: survival of everybody Szathmáry & Gladkih (1987) Even a Lyapunov function could be proven: Varga & Szathmáry (1996) Bull. Math. Biol.

  5. Growth laws and selection consequences Szathmáry (1989) Trend Ecol. Evol. • Parabolic: p < 1  survival of everybody • Exponential: p = 1  survival of the fittest • Hyperbolic: p > 1  survival of the common

  6. Why would one do such a model?

  7. A crucial insight: Eigen’s paradox (1971) • Early replication must have been error-prone • Error threshold sets the limit of maximal genome size to <100 nucleotides • Not enough for several genes • Unlinked genes will compete • Genome collapses • Resolution???

  8. Simplified error threshold x + y = 1

  9. Molecular hypercycle (Eigen, 1971) autocatalysis heterocatalytic aid

  10. Parasites in the hypercycle (JMS) short circuit parasite

  11. The Lotka-Volterra equation

  12. The replicator equation

  13. Game dynamics

  14. Permanence

  15. “Hypercyles spring to life”… • Cellular automaton simulation on a 2D surface • Reaction-diffusion • Emergence of mesoscopic structure • Conducive to resistance against parasites • Good-bye to the well-stirred flow reactor

  16. Mineral surfaces are a poor man’s form of compartmentation (?) • A passive form of localisation (limited diffusion in 2D) • Thermodynamic effect (when leaving group also leaves the surface) • Kinetic effects: surface catalysis (cf. enzymes) • How general and diverse are these effects? • Good for polymerisation, not good for metabolism (Orgel) • What about catalysis by the inner surface of the bilayer (composomes)?

  17. Surface metabolism catalysed by replicators(Czárán & Szathmáry, 2000) I1-I3: metabolic replicators(template and enzyme) M: metabolism (not detailed) P:parasite (only template)

  18. Elements of the model • A cellular automaton model simulating replication and dispersal in 2D • ALL genes must be present in a limited METABOLIC neighbourhood for replication to occur • Replication needs a template next door • Replication probability proportional to rate constant (allowing for replication) • Diffusion

  19. Robust conclusions • Protected polymorphism of competitive replicators (cost of commonness and advantage of rarity) • This does NOT depend on mesoscopic structures (such as spirals, etc.) • Parasites cannot drive the system to extinction • Unless the neighbourhood is too large (approaches a well-stirred system) • Parasites can evolve into metabolic replicators • System survives perturbation (e.g. when death rates are different in adjacent cells), exactly because no mesocopic structure is needed.

  20. An interesting twist • This system survives with arbitrary diffusion rates • But metabolic neighbourhood size must remain small • Why does excessive dispersal not ruin the system? • Because it convergences to a trait-group model!

  21. The trait group model (Wilson, 1980) Mixed global pool Random dispersal Harvest Mixed global pool Applied to early coexistence: Szathmáry (1992)

  22. Why does the trait group work? • It works only for cases when the “red hair theorem” applies • People with red hair overestimate the frequency of people with red hair, essentially because they know this about themselves • “average subjective frequency” • In short, molecules must be able to scratch their own back!

  23. Error rates and the origin of replicators

  24. Nature420, 360-363 (2002). Replicase RNA Other RNA

  25. Increase in efficiency • Target efficiency: the acceptance of help • Replicase efficiency: how much help it gives • Copying fidelity • Trade-off among all three traits: worst case The dynamics becomes interesting on the rocks!

  26. Evolving population Error rate Replicase activity • Molecules interact with their neighbours • Have limited diffusion on the surface

  27. The stochastic corrector model for compartmentalized genomes Szathmáry, E. & Demeter L. (1987) Group selection of early replicators and the origin of life. J. theor Biol.128, 463-486. Grey, D., Hutson, V. & Szathmáry, E. (1995) A re-examination of the stochastic corrector model. Proc. R. Soc. Lond. B 262, 29-35.

  28. The stochastic corrector model (1986, ’87, ’95, 2002) metabolic gene replicase membrane

  29. The mathematical model • Inside compartments, there are numbers rather than concentrations • Stochastic kinetics was applied: • Master equations instead of rate equations: P’(n, t) = ……. Probabilities • Coupling of two timescales: replicator dynamics and compartment fission • A quasipecies at the compartment level appears • Characterized by gene composition rather than sequence

  30. Dynamics of the SC model • Independently reassorting genes (ribozymes in compartments) • Selection for optimal gene composition between compartments • Competition among genes within the same compartment • Stochasticity in replication and fission generates variation on which natural selection acts • A stationary compartment population emerges

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