Games and cooperation

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. Prisoner’s Dilemma

17. Bacteriophage game • Using bacteriophage φ6, an RNA viral parasite of E. coli. • Their ancestral stock of φ6 had been propagated at low density, such that usually only a single phage infected each host. • By propagating φ6 for 250 generations at higher density, so that approximately five phage infected each cell, they derived a strain, φH2, which had evolved higher competitive ability at the expense of a lower efficiency of transmission. • The competitive advantage of this strain as a function of its frequency was determined to have a roughly twofold advantage over its ancestor when rare and a smaller advantage when common

18. Other viruses play the Prisoners’ Dilemma game F(A) The fitness of φH2 relative to its ancestor φ6 decreases with frequency, but is still greater than 1 when it is common (red dots). Thus, φH2 will invade a population of φ6, but φ6 cannot invade φH2. Red dots show mean ± s.e.m.; dashed lines are regressions with 95% confidence intervals. The blue dots and lower lines show a control experiment, in which φ6 was competed against another clone identical except for the presence of a marker gene used in the fitness assay. (B) The payoff matrix estimated from A. Each entry gives the fitness of φ6 (top row) or φH2 (bottom row) when either φ6 (left) or φH2 (right) is common.

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

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

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

22. 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!!!

23. Evolving population Error rate Replicase activity

24. ‘Stationary’ population efficient replicases parasites

25. Slime mould fruiting body

26. Schematic drawing of slime mould life cycle

27. Slime mold sexual reproduction

28. One amoeboid cells

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

30. 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

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

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

33. 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.

34. Simpson’s paradox

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

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

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

39. Population structure and relatedness in a bacterial subpopulation • Proteins for cooperation secreted or located on the outer membrane

40. Relatedness, transfer and migration

41. External protein genes are highly mobile