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Games and cooperation
Eörs Szathmáry
Eötvös University Collegium Budapest
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Molecular hypercycle (Eigen, 1971)
autocatalysis
heterocatalytic aid
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Parasites in the hypercycle (Maynard Smith, 1979)
parasite
short circuit
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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.
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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
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Bubbles and permeability
We do not know where lipids able to form membranes had come from!!!
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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
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A trait-group model for viruses
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DI: V game
Payoff matrix for two players
V DIV 2a aDI b 0
There is protected polymorphism when b > 2a
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Another rendering of the DIV game
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Chicken and Hawk-Dove gamesSwerve Straight
Swerve Tie, Tie Lose, Win
Straight Win, Lose Crash, Crash
Hawk DoveHawk (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.
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Evolutionarily Stable Strategy (ESS)
Hawk DoveHawk -1/2 1
Dove 0 1/2
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
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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.
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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).
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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)
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Nature 420, 360-363 (2002).
Kin selection of molecules on the rocks
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Maximum as a function of molecule length
• Target and replicase efficiency
• Copying fidelity• Trade-off among
all three traits: worst case
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Evolution of replicases on the rocks
• All functions coevolve and improve despite the tradeoffs
• Increased diffusion destroys the system
• Kin selection on the rocks
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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!!!
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Evolving population
Error rate Replicase activity
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A cellular automaton simulation
• Reaction: template replication
• Diffusion (Toffoli-Margolus algorithm)
Black: empty site
X: potential mothers
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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)
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‘Stationary’ population
parasites
efficient replicases
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Slime mould fruiting body
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Slime mold sexual reproduction
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One amoeboid cells
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Slime mould aggregation
• Amoebas assemble around one focus• Amoeboid shape changes into bipolar
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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
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Formation of Dictyostelium fruiting body
• In the slug pre-stalk cells go first
• Finally, pre-spores make it to the top
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Cheaters in myxobacteria (Lenski & Velicer, 2000)
• P developmentally proficient• C cheater (goes to stalk)
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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
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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.
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Experimental data on E. coli populations
An autoinducer of antibiotic resistance
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Simpson’s paradox
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Playing with yeast
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Yeast snowdrift game
• Sucrose degraded by invertase to yield glucose in the periplasmic space
• Only 1% of glucose captured by the same cell
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The possible games
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Both can invade when rare
f
Pc-Pd
{c=0.02, ϵ=0.01}
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Extinction of cooperators
• By histidine concentration we can manipulate the cost of cooperation
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Population structure and relatedness in a bacterial
subpopulation• Proteins for
cooperation secreted or located on the outer membrane
• Can be on mobile elements
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Relatedness, transfer and migration
• Transfer of cooperation genes increases relatedness
• Spreads cooperating elements
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External protein genes are highly mobile
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Robustness in biology
Eörs Szathmáry
Eötvös University Collegium Budapest
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A genotype-phenotype model
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Robustness and adaptation time
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The explanation
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Robustness and diversity