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Evolution of CooperationPowerPoint Presentation

Evolution of Cooperation

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### Evolution of Cooperation

The importance of being suspicious

Do we see cooperation in Nature?

If I give you some DNA

will you give me some?

Ya, Sure.

Just promise it won’t get

complicated between us

Small

Picture:

Bacteria Sex

Martin A. Nowak (2006):

- Genes cooperate in genomes.

Martin A. Nowak (2006):

- Genes cooperate in genomes.
- Chromosomes cooperate in eukaryotic cells.

Martin A. Nowak (2006):

- Genes cooperate in genomes.
- Chromosomes cooperate in eukaryotic cells.
- Cells cooperate in multicellular organisms.

Martin A. Nowak (2006):

- Genes cooperate in genomes.
- Chromosomes cooperate in eukaryotic cells.
- Cells cooperate in multicellular organisms.
- There are many examples of cooperation among animals.

Martin A. Nowak (2006):

- Genes cooperate in genomes.
- Chromosomes cooperate in eukaryotic cells.
- Cells cooperate in multicellular organisms.
- There are many examples of cooperation among animals.
- Humans are the champions of cooperation: From hunter-gatherer societies to nation-states, cooperation is the decisive organizing principle of human society.

Martin A. Nowak (2006):

- Genes cooperate in genomes.
- Chromosomes cooperate in eukaryotic cells.
- Cells cooperate in multicellular organisms.
- There are many examples of cooperation among animals.
- Humans are the champions of cooperation: From hunter-gatherer societies to nation-states, cooperation is the decisive organizing principle of human society.
- The question of how natural selection can lead to cooperative behavior has fascinated evolutionary biologists for several decades.

Cooperation as a “paradox”:The Tragedy of the Commons

- Take a fishing lake where there is an upper limit on how much harvest can be taken in a sustainable manner.

- Above this limit, the fish pop. eventually crashes and everyone is worse off.

Cooperation as a “paradox”:The Tragedy of the Commons

- And they have to wait for someone to come and give them fish...

Cooperation as a “paradox”:The Tragedy of the Commons

- And they have to wait for someone to come and give them fish...

Tragedy of the Commons What should you do?

Best: Everyone fishes below the limit, but you cheat and fish more.

Tragedy of the Commons What should you do?

Best: Everyone fishes below the limit, but you cheat and fish more.

Next best: Everyone fishes below the limit, and you do too.

Tragedy of the Commons What should you do?

Best: Everyone fishes below the limit, but you cheat and fish more.

Next best: Everyone fishes below the limit, and you do too.

Pretty bad: Everyone fishes above the limit, and you do too.

Tragedy of the Commons What should you do?

Best: Everyone fishes below the limit, but you cheat and fish more.

Next best: Everyone fishes below the limit, and you do too.

Pretty bad: Everyone fishes above the limit, and you do too.

Worst: Everyone fishes above the limit, but you don’t for some reason.

Tragedy of the Commons What should you do? Results.

Lesson: No matter what everyone else is doing, you always do better by cheating.

Tragedy of the Commons What should you do? Results.

Lesson: No matter what everyone else is doing, you always do better by cheating.

Conclusion: Everyone cheats. Everyone does pretty bad.

Tragedy of the Commons Assigning score

(5)Best (T): temptation to cheat

(3)Next best (R): reward for cooperating

(1)Pretty bad (P): punishment for everyone cheating

(0)Worst (S): suckers payoff for cooperating against cheaters

**Scores are arbitrary, while obeying T > R > P > S, and an additional

condition: (T+P)/2 > R. These scores are the convention.

Tragedy of the Commons Simplified to two people

Tragedy of the Commons Simplified to two people

***This is the Prisoner’s Dilemma

The Prisoner’s Dilemma (PD)

If you are playing a cooperator, you can do best

by defecting

If you are playing a defector, you can do best

by defecting

The Prisoner’s Dilemma (PD)

- No matter what type of strategists are in a population, the best response is always to defect.

The Prisoner’s Dilemma (PD)

- No matter what type of strategists are in a population, the best response is always to defect.
- If we consider score to be a measure of fitness, then we should expect defectors to leave more offspring.

The Prisoner’s Dilemma (PD)

- No matter what type of strategists are in a population, the best response is always to defect.
- If we consider score to be a measure of fitness, then we should expect defectors to leave more offspring.
- Defectors take over, and can’t be invaded by a cooperator.

Nice guys finish last...

- So defection dominates, even though everyone does worse than if everyone cooperated.

Nice guys finish last...

- So defection dominates, even though everyone does worse than if everyone cooperated.
- “Everyone cooperating” is an optimal strategy for the population, but it is unstable. Defectors invade and take over.

Nice guys finish last...

- So defection dominates, even though everyone does worse than if everyone cooperated.
- “Everyone cooperating” is an optimal strategy for the population, but it is unstable. Defectors invade and take over.
- How can we explain the emergence of cooperation?

Achieving Cooperation: Direct Reciprocity

- When there is a potential for future rewards, cooperation could evolve via reciprocity (Trivers).

Achieving Cooperation: Direct Reciprocity

- When there is a potential for future rewards, cooperation could evolve via reciprocity (Trivers)
- We could have two agents repeat the game. Call this the Iterated PD (IPD).

Achieving Cooperation: Direct Reciprocity

- When there is a potential for future rewards, cooperation could evolve via reciprocity (Trivers)
- We could have two agents repeat the game. Call this the Iterated PD (IPD).
- Axelrod (1980a, b) hosted two round-robin tournaments of the IPD. A wide range of complex strategies were submitted...

Achieving Cooperation: Direct Reciprocity

- Amazingly, the winner of both tournaments was the simplest strategy entered: tit-for-tat (TFT).

Achieving Cooperation: Direct Reciprocity

- Amazingly, the winner of both tournaments was the simplest strategy entered: tit-for-tat (TFT).
- TFT cooperates on the first turn then copies its opponent’s previous move.

Achieving Cooperation: Direct Reciprocity

- Amazingly, the winner of both tournaments was the simplest strategy entered: tit-for-tat (TFT).
- TFT cooperates on the first turn then copies its opponent’s previous move.
- TFT can be considered as a special case of a “reactive strategy.”

Reactive Strategies for the IPD

- Reactive strategies are given by an ordered triple (y,p,q) that define their behaviour in the IPD.

Reactive Strategies for the IPD

- Reactive strategies are given by an ordered triple (y,p,q) that define their behaviour in the IPD.
y – probability of C on the 1st turn

p – probability of C following a C

q – probability of C following a D

Reactive Strategies for the IPD

- Thus TFT is (1,1,0). Other interesting strategies at the vertices are:
Always defect AllD = (0,0,0)

Always cooperate AllC = (1,1,1)

Reactive Strategies for the IPD

- Thus TFT is (1,1,0). Other interesting strategies at the vertices are:
Always defect AllD = (0,0,0)

Always cooperate AllC = (1,1,1)

- (0,1,0) is “Suspicious TFT” since it defects on the first turn (nervous of strangers) then has TFT behaviour.

Evolution of TFT in the IPD.

- Many models consider the infinitely iterated version, or a sufficiently long version of the IPD (Nowak & Sigmund, 1992; 1994; Imhof et al., 2005)

Evolution of TFT in the IPD.

- Many models consider the infinitely iterated version, or a sufficiently long version of the IPD (Nowak & Sigmund, 1992; 1994; Imhof et al., 2005)
- This completely discounts the effects of the first turn, which allows for the reduction of strategy space from (y,p,q) to a strategy square: (p,q).

Is this biologically reasonable?

- At some levels of organization, the assumption of long games may be founded.

Is this biologically reasonable?

- At some levels of organization, the assumption of long games may be founded.
- For multi-cellular organisms, this assumption seems hard to justify.

Is this biologically reasonable?

- At some levels of organization, the assumption of long games may be founded.
- For multi-cellular organisms, this assumption seems hard to justify.
- Also, if encounters are infrequent the agents may not recognize each other when they play again (and remember their opponents “last move”). Or end interactions early with defectors.

Let’s make a model

- Let ‘N’ individuals play the PD iterated ‘m’ times (m = 10 for results).
- Let each individual be given by (y,p). ‘y’ matters in short games.
- Start the population always defecting.
- Have many generations of: selection, reproduction, mutation, death.

Selection: First Play

- Probability of cooperating on the first turn is defined by each player’s ‘y’ value

Probability y2

Probability 1 - y2

Probability 1 – y4

Probability y4

Selection: Subsequent Plays

- Probability of p2 cooperating on round i given that p4 cooperated on round i-1 is p2.

Probability p2

Probability 1 - p2

- p4 defects in round i if p2 defected in round i - 1

Reproduction, Mutation, Death

- Based on their cumulative scores, an individual is selected stochastically for reproduction.
- Another individual is selected randomly to be replaced.
- The reproducing individual produces an offspring with the same ‘y’ and ‘p’ value with a small chance of a random mutation.
- All results are for population size N = 30, number of iterations m = 10, number of populations D = 50, and number of generations = 10000

Results: no noise, weak selection

Results: no noise,strong selection

Results: noise = 0.00001,strong selection (10)

Results: noise = 0.0001,strong selection (10)

Results: noise = 0.0001,very strong selection (30)

I have time for discussion?

- Without noise, a population can evolve toward TFT for sufficiently strong selection – even though the game is iterated a short amount
- With even a modest amount of noise, selection must be increased in strength to see natural selection (as opposed to drift)

I have time for discussion?

- For high noise (0.1%) A population must be under very strong selection to reach TFT from always defect
- A population accomplishes this using a trajectory close to STFT.

Thanks,

- Students, organizers, and mentors for your discussions!
- Special thanks to Alex and Lou for your help and patience.

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