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Games and cooperation

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.

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Games and cooperation

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  1. Games and cooperation Eörs Szathmáry Collegium Budapest Eötvös University

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

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

  4. 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.

  5. 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

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

  7. 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

  8. A trait-group model for viruses

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

  10. Another rendering of the DIV game

  11. Chicken and Hawk-Dove games 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.

  12. Evolutionarily Stable Strategy (ESS) 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:

  13. 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.

  14. 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).

  15. 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)

  16. Nature420, 360-363 (2002). Kin selection of molecules on the rocks

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

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

  19. 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!!!

  20. Evolving population Error rate Replicase activity

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

  22. 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)

  23. ‘Stationary’ population efficient replicases parasites

  24. Slime mould fruiting body

  25. Slime mold sexual reproduction

  26. One amoeboid cells

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

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

  29. Formation ofDictyosteliumfruiting body • In the slug pre-stalk cells go first • Finally, pre-spores make it to the top

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

  31. 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

  32. Public goods and E. coli • We constructed two Escherichia coli strainsthat recapitulate the interaction of producers andnonproducers . The common goodin this system is a membrane-permeableRhlautoinducer molecule, rewired to activateantibiotic (chloramphenicol; Cm) resistance geneexpression. • Otherwise isogenic, green fluorescentprotein (GFP)–marked producers synthesize theRhl autoinducer constitutively, whereas nonfluorescentnonproducers do not. • The systemexhibited the expected propertiesfor public-good producers and nonproducers. • First, in antibiotic-containingmedia, producers grewin a density-dependent manner thatwas abolished when a synthetic autoinducer wasexogenously supplied, indicating thatautoinducer production was limiting. • Second, whenstarted from the same initial density, pure culturesof nonproducers grew slower than pure culturesof producers in antibiotic • However, additionof either synthetic autoinducer or cell-freeconditioned medium (containing autoinducer madeby producers) increased nonproducer growth in antibiotic-containing media.

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

  34. Simpson’s paradox

  35. Playing with yeast

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

  37. The possible games

  38. Both can invade when rare {c=0.02, ϵ=0.01} Pc-Pd f

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

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

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

  42. External protein genes are highly mobile

  43. Robustness in biology Eörs Szathmáry Collegium Budapest Eötvös University

  44. A genotype-phenotype model

  45. Robustness and adaptation time

  46. The explanation

  47. Robustness and diversity

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