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

A trait-group model for viruses

DI: V game

Payoff matrix for two players

V DI

V 2a a

DI b 0

There is protected polymorphism when b > 2a

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

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)

Prisoner’s Dilemma

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 fruiting body

Schematic drawing of slime mould life cycle

Slime mold sexual reproduction

One amoeboid cells

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.

Simpson’s paradox

Experimental data on E. coli populations

An autoinducer of antibiotic resistance

Yeast snowdrift game

• Sucrose degraded by invertase to yield glucose in the periplasmic space

• Only 1% of glucose captured by the same cell

Both can invade when rare

f

Pc-Pd

{c=0.02, b=0.01}

{c=0.02, ϵ=0.01}

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

Relatedness, transfer and migration

External protein genes are highly mobile