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. Nature 420, (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,
Grey, D., Hutson, V. & Szathmáry, E. (1995) A re-examination of the stochastic corrector model. Proc. R. Soc. Lond. B 262,

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