Cooperation Flashcards
group living 3
Game theory model: Games with repeated encounters and the evolution of cooperation
–repeated encounters with same individuals provides the conditions for learning.
–e.g: consider a game where individuals can cooperate or defect – the prisoners dilemma
The prisoner’s dilemma
*2 people arrested for a crime
*insufficient evidence to tie either to the crime but both are armed, & either/both could be imprisoned for possession of illegal firearm.
*Each independently offered choice of:
–confessing (and implicating the other)
-> if one defects then the other serves 3 years and they go free
-> if both defect then both serve 2 years
–or staying silent -> if both stay silent both will serve 1 year
Prisoner’s dilemma (PD) in the context of prisoners A & B encountering each other once:
What should A do?
- If B cooperates, A should defect, since going free is better than serving 1 year.
* If B defects, A should also defect, since serving 2 years is better than serving 3.
* So either way, A should defect.
* Same reasoning for B’s choices.
* so, regardless Of what the Other decides, each prisoner gets a higher pay-off by betraying the other (“defecting”).
To be a prisoner’s dilemma game the following condition must hold for the payoffs
Temptation > cooperation reward > punishment payoff > sucker’s payoff
T > R > P > S
R > P : mutual cooperation is superior to mutual defection,
T > R and P > S : defection is the dominant strategy for both.
i.e., mutual defection is the only outcome from which each player could only do worse by unilaterally changing strategy
-> Dilemma = pursuing individual, selfish reward leads the prisoners to both defect, but they would get a better reward if they both cooperated!!
But what about repeated encounters? Iterated PD (IPD)
both prisoners continuously have opportunity to penalize the other for previous decisions.
If number repeat encounters is known to the players, then (by backward induction) both will betray each other repeatedly, for the same reasons as in PD.
In infinite or unknown repeats: always defect may no longer be a strictly dominant strategy
Iterated prisoners dilemma (IPD)
Axelrod and Hamilton (1981).
–computer strategies to compete in an IPD tournament.
–greedy strategies do poorly in the long run
–altruistic strategies did better, judged purely by self-interest.
Shows possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by natural selection.
*The winning strategy was tit for tat,
–cooperate on the first iteration
–then do what opponent did on the previous move.
A mechanism for the evolution of cooperation and reciprocal altruism in a ‘model’ world.
Cooperation: Joint action that is mutually beneficial in terms of fitness to all protagonists.
Altruism: A behaviour that is a priori paradoxical from the evolutionary point of view because it reduces the fitness of the actor while increasing the fitness of one or more conspecific recipients i.e. the action imposes a cost to the actor.
Reciprocal altruism: where altruistic acts are exchanged among individuals. One individual acts altruistically towards other(s) that are likely to reciprocate in future
IPD also requires that 2R > T + S
preventing alternating cooperation and defection giving a greater reward than mutual cooperation.
So IPD can explain the evolution of cooperation and reciprocal altruism in a ‘model’ world – but what about in the real world??
IPD and the evolution of cooperation (reciprocal altruism)
Reciprocity can only evolve if:
–Donor and recipient can recognise one another
–Repayment is likely
–Benefit to recipient is greater than cost to donor
e.g. –Vampire Bats (Desmodus rotundus, Wilkinson 1984):
Food sharing in vampire bats- Individuals recognise each other, repayment likely
Conditions that favour evolution of reciprocal altruism:
–Stable social groups (so individuals are involved in repeated interactions, and hence many opportunities for altruistic acts, and reciprocation)
–Good memory
–Symmetry of interactions between potential altruists
Vampire bat reciprocity study
- Vampire bats forage at night for the blood of other mammals with varying success
- The bats can starve if they go without nourishment for 68 hours
- Weight shift and risk of starvation correlate
- Hungry bats will beg a bat that has fed and if that bat chooses to be a donor it regurgitates blood
- Hungry bats that have been fed by a donor will often reciprocate and donate to their donor when they have a successful night
- Donator loses 5% of weight brings that donor six hours closer to starvation whereas the recipient starving bat gains 16 hours longer of survival – gain is greater than cost
Reviewing the basic assumptions of ESS
- infinite, random mixing population:
Infact most populations are finite with non-random mixing:
– individuals will have some degree of genetic relatedness,
–Individuals may live near (& interact with) close relatives thus should behave more dove-like.
–individuals may have repeated contests against same opponents (iterated prisoner’s dilemma) - Asexual reproduction:
as long as ‘like begets like’ to some extent, the fact that players are sexual, diploid & that heritability is complex shouldn’t change the nature of the model, only the time it takes to reach an ESS. - Pairwise contests:
Sometimes an individual competes against rest of the population or group, e.g: lekking birds.
*called ‘playing the field’:
–If pure ESS is a single strategy, then the solution is as before
*i.e: the strategy that can’t be invaded by a mutant strategy.
–If mixed ESS, then the ratio can be determined as described in Maynard-Smith (beyond this lecture).
4.Symmetry:
most contests are actually asymmetrical:
–contestants differ in size, strength, sex, age, etc.
–individuals differ in their fighting ability = Resource Holding Potential (RHP) - see later lecture re: dominance relationships
–Fighting behaviour also be affected by the (perceived) value of the contested resource - expect higher intensity fights over more valuable resources.
–Models to examine this:
*e.g: Hawk-Dove-Bourgeois Game
*e.g: Hawk-Dove-Assessor
- Finite set of alternative strategies :
*Models that have more strategies and conditional strategies:
–e.g: Hawk-Dove-Retaliator Game
–e.g: Hawk-Dove-Bourgeois Game
–e.g: Hawk-Dove-Assessor
*But in reality often continuous range of (potential) strategies.
Alternative mating strategy
Involves individual variation of strategies within mating patterns Behavioural, morphological, physiological & life history differences.
*Tactic: a phenotype that results from a strategy e.g.
tactic 1 = to fight for access to mates,
tactic 2 = to sneak copulations.
*Strategy: genetically based ‘decision rules’ for allocation of effort among alternative tactics.
–i.e: mechanism that ‘decides’ which tactic is expressed & when.
*3 categories of strategies:
1)Alternative strategies: genetic polymorphisms - 2 or more strategies, rare
2) Mixed strategies: theoretical – probabilistic allocation amongst alternative tactics, no known examples.
3)Conditional strategies: tactics adopted depend on status/condition of individual.
Typically:
–Aggressive males, polygynous males.
–Monogamous males.
–Sneaker or Satellite males.
*Possibilities depend upon Parental care & Dispersion again.
*Evolutionary Stable Strategies (ESS).
Alternative mating strategies — e.g. 1: Marine Isopods
Paracerceis sculpta: (Shuster & Wade 1991).
Live in chambers in inter-tidal sponges.
3 male size morphs with different behavioural strategies:
1)Alpha dom males larger than females – dominate to gain females
2)Beta males similar size to females – sneak in by pretending to be female
3)Gamma males very small – sneak
- Genetic control:
— - traits controlled by one locus with 3 alternative alleles. - Equal number of matings achieved by each morph — ESS.
- But variance in success within morphs - still strong sexual
selection.
Alternative mating strategies — e.g. 2: Bluegill Sunfish
Gravel nest dug by male, female lays eggs, male fertilises and protects eggs
3 male morphs:
1)Parental - larger, aggressive territory holders
2)Satellite - 100k like females - spawn with pair
3) Satellite/Sneaker - smaller - rush in before parental male
& fertilize eggs
Genetic polymorphism similar to marine isopods parental – alpha aggressive, satellite – smaller and look like females, sneaker v. small nales rush in before parental male can fertilise eggs
*Satellite morphs cannot exist alone, but territorial male can.
*Satellite morphs may successfully invade large territorial male.
*Males of all 3 strategies have approx. equal fitness - ESS.
*Male types mature at different ages.
–territorial males mature in 6-7 years
–both satellite types 2-3 years.
*Condition dependent: all males have capability to become any morph - depends upon condition during development.
Alternative mating strategies — e.g. 3: Side-blotched lizards
* Rock-paper-scissors’ game (Sinervo & Livley 1996).
- Three male morphs & tactics:
— O - Orange throated males - dominant, polygynous.
— B - Blue throated males - monogamous, mate guarding.
— Y - Yellow throated males - sneaker, female mimics. - Contests morphs are more symmetric.
- But strong asymmetries in contests
between morphs.
Each genetic morph has a benefit and a weakness against other morphs – a rock paper scissors type situation:
- Y sneakers can deceive O dominants
- Monogamous B not fooled by Y.
— B chase off Y
— B vs B = ritualised displays — low aggression. - O aggressively attack intruding B
- O & B defend territories.
- Y cluster around territories Of O (more successful in sneaking copulations from females on O cf. B territories).
Blue and orange maintain territory whilst yellow morph sneaks around and generally inhabits orange territory as they are less capable of identifying these sneaker males.
Game theory models summary
1) Density dependent fitness gained, or lost through interaction of others in population, e.g. contests & aggression. Implies a limiting resource.
2) An ESS is an evolutionary strategy that can’t be invaded by a more successful strategy. Basic model assumes infinite population size, asexual reproduction, pairwise symmetrical contests between 2 opponents & finite set of alternative strategies.
3) In a mixed ESS the strategy is to do H with probability p and D with probability 1- p, or a stable polymorphism could exist where some individuals always do H, and some always do D.
4) Games with repeated encounters with same individuals provide the conditions for learning. If games can be repeated & you’re likely to encounter the same opponent again, then reciprocal altruism can be an ESS.
