Presentation on theme: "Games and cooperation Eörs Szathmáry Eötvös University Collegium Budapest."— Presentation transcript:
Games and cooperation Eörs Szathmáry Eötvös University Collegium Budapest
Molecular hypercycle (Eigen, 1971) autocatalysis heterocatalytic aid
Parasites in the hypercycle (Maynard Smith, 1979) parasite short circuit
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
Chicken and Hawk-Dove games SwerveStraight SwerveTie, TieLose, Win StraightWin, LoseCrash, Crash HawkDove Hawk(V-C)/2, (V-C)/2V, 0 Dove0, VV/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) HawkDove Hawk-1/21 Dove01/2 V=1, C=2 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: If an invader plays Hawk (P=1) or Dove (P=0), the payoff to the invader is ¼ in both cases
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)
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
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.
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
‘Stationary’ population parasites efficient replicases
Slime mould aggregation Amoebas assemble around one focus Amoeboid shape changes into bipolar
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
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)
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 membrane- permeable 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.