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
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
b
DI
a
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
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:
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
br>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
efficient
replicases
parasites
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 membranepermeable 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
{c=0.02, ϵ=0.01}
{c=0.02, b=0.01}
Pc-Pd
f
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