Games and cooperation Eörs Szathmáry Collegium Budapest Eötvös

Games and cooperation Eörs Szathmáry Collegium Budapest Eötvös University

Molecular hypercycle (Eigen, 1971) autocatalysis heterocatalytic aid

Parasites in the hypercycle (Maynard Smith, 1979) short circuit parasite

The stochastic corrector model for compartmentation 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.

Group selection of early replicators • Many more compartments than templates within any compartment • No migration (fusion) between compartments • Each compartment has only one parent • Group selection is very efficient • Selection for replication synchrony

Bubbles and permeability We do not know where lipids able to form membranes had come from!!!

A case study: defective interfering particles (DIPs) • DIP is a hyperparasite of the standard virus (SV) • Gains a replicative advantage when complemented • Usually shorter molecule • Would be the winner in a well-mixed flow reactor • No chance to fix in structured populations

A trait-group model for viruses

DI: V game Payoff matrix for two players V DI V 2 a b DI a 0 There is protected polymorphism when b > 2 a

Another rendering of the DIV game

Chicken and Hawk-Dove games Swerve Straight Swerve Tie, Tie Lose, Win Straight Win, Lose Crash, Crash Hawk Dove Hawk (V-C)/2, (V-C)/2 V, 0 Dove 0, V V/2, V/2 In the biological literature, this game is referred to as Hawk-Dove. The earliest presentation of a form of the Hawk-Dove game was by John Maynard Smith and George Price in their 1973 Nature paper, "The logic of animal conflict". The traditional payoff matrix for the Hawk-Dove game is given here, where V is the value of the contested resource, and C is the cost of an escalated fight. It is (almost always) assumed that the value of the resource is less than the cost of a fight is, i. e. , C > V > 0. If C ≤ V, the resulting game is not a game of Chicken.

Evolutionarily Stable Strategy (ESS) Hawk Dove Hawk -1/2 1 Dove 0 1/2 V=1, C=2 If an invader plays Hawk (P=1) or Dove (P=0), the payoff to the invader is ¼ in both cases An invader plays hawk with probability P and dove with probability 1 – P; and the residents play hawk and dove with equal probability. So, the four possible outcomes when a resident meets an invader have probabilities:

ESS II. Multiplying these by the payoffs for each of the four cases, we find that when a resident meets an invader, it wins the following payoff on average: Payoff invader against invader: Because this is never greater than the payoff to a resident, no strategy can invade: The resident strategy P = 1/2 is therefore an ESS.

Evolutionary Stability in the Hawk-Dove game The expected payoff for different kinds of contests in the hawk– dove game, when the resident population is at the evolutionarily stable strategy (ESS) (P = 0. 5, where P is the probability that an individual plays hawk rather than dove).

The ESS, verbally • The ESS is the best reply to itself (Nash equilibrium) • If there is an alternative best reply, then the reply of the ESS to the invader must be better than the invader’r reply to itself (stability condition)

Nature 420, 360 -363 (2002). Kin selection of molecules on the rocks

Maximum as a function of molecule length • Target and replicase efficiency • Copying fidelity • Trade-off among all three traits: worst case

Evolution of replicases on the rocks • All functions coevolve and improve despite the tradeoffs • Increased diffusion destroys the system • Kin selection on the rocks

Hamilton’s rule b r > c • b: help given to recipient • r: degree of genetic relatedness between altruist and recipient • c: price to altruist in terms of fitness • Formula valid for INVASION and MAINTENANCE • APPLIES TO THE FRATERNAL TRANSITIONS!!!

Evolving population Error rate Replicase activity

A cellular automaton simulation • Reaction: template replication • Diffusion (Toffoli. Margolus algorithm) Black: empty site X: potential mothers

Strong and weak altruism • Strong altruist pays an absolute cost • Weak altruist pays a relative cost (it increases its own fitness less than that of the others) • Weak altruist can spread with random group assortment • Strong altruism requires nonrandom group assortment (kin selection)

‘Stationary’ population efficient replicases parasites

Slime mould fruiting body

Slime mold sexual reproduction

One amoeboid cells

Slime mould aggregation • Amoebas assemble around one focus • Amoeboid shape changes into bipolar

Propagation of c. AMP signal • Focal cell releases a dose of c. AMP and then becomes inactive for a while • Surrounding cells move towards higher c. AMP and they release c. AMP also

Formation of Dictyostelium fruiting body • In the slug pre-stalk cells go first • Finally, pre-spores make it to the top

Cheaters in myxobacteria (Lenski & Velicer, 2000) • P developmentally proficient • C cheater (goes to stalk)

Facultative cheaters • Many cheaters are cheating only on the wild type • They cooperate among themselves • Conflict selects for measures and countermeasures • Drives fast molecular evolution • Similar to hybrid dysgenesis

Public goods and E. coli • • • We constructed two Escherichia coli strains that recapitulate the interaction of producers and nonproducers. The common good in this system is a membranepermeable Rhl autoinducer molecule, rewired to activate antibiotic (chloramphenicol; Cm) resistance gene expression. Otherwise isogenic, green fluorescent protein (GFP)–marked producers synthesize the Rhl autoinducer constitutively, whereas nonfluorescent nonproducers do not. The system exhibited the expected properties for public-good producers and nonproducers. First, in antibiotic-containing media, producers grew in a density-dependent manner that was abolished when a synthetic autoinducer was exogenously supplied, indicating that autoinducer production was limiting. Second, when started from the same initial density, pure cultures of nonproducers grew slower than pure cultures of producers in antibiotic However, addition of either synthetic autoinducer or cell-free conditioned medium (containing autoinducer made by producers) increased nonproducer growth in antibiotic-containing media.

Experimental data on E. coli populations An autoinducer of antibiotic resistance

Simpson’s paradox

Playing with yeast

Yeast snowdrift game • Sucrose degraded by invertase to yield glucose in the periplasmic space • Only 1% of glucose captured by the same cell

The possible games

Both can invade when rare {c=0. 02, ϵ=0. 01} Pc-Pd f

Extinction of cooperators • By histidine concentration we can manipulate the cost of cooperation

Population structure and relatedness in a bacterial subpopulation • Proteins for cooperation secreted or located on the outer membrane • Can be on mobile elements

Relatedness, transfer and migration • Transfer of cooperation genes increases relatedness • Spreads cooperating elements

External protein genes are highly mobile

Robustness in biology Eörs Szathmáry Collegium Budapest Eötvös University

A genotype-phenotype model

Robustness and adaptation time

The explanation

Robustness and diversity