(Super)systems and selection dynamics Eörs Szathmáry & Mauro Santos Collegium BudapestEötvös University Budapest

Haldane’s intellectual son: John Maynard Smith ( )

Units of evolution hereditary traits affecting survival and/or reproduction 1.multiplication 2.heredity 3.variation

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

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

Why would one do such a model?

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???

Simplified error threshold x + y = 1

Molecular hypercycle (Eigen, 1971) autocatalysis heterocatalytic aid

Parasites in the hypercycle (JMS) parasite short circuit

The Lotka-Volterra equation

The replicator equation

Game dynamics

Permanence

“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

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)?

Surface metabolism catalysed by replicators ( Czárán & Szathmáry, 2000) I 1 -I 3 : metabolic replicators (template and enzyme) M: metabolism (not detailed) P: parasite (only template)

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

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.

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!

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

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!

Error rates and the origin of replicators

Nature 420, (2002). Replicase RNA Other RNA

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!

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

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,

The stochastic corrector model (1986, ’87, ’95, 2002) metabolic gene replicas e membrane

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

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