Cooperation: A Natural Law of the Universe?

Martin Nowak

The mathematics of cooperation

'As soon as I saw the pattern, I thought there’s something great here, but I don’t fully understand it and I don’t fully understand the implications. But the sheer beauty of it made it clear there was something amazing.'

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THE MATHEMATICS OF COOPERATION

MN: So here we have a sea of co-operators in blue and a single defector.

David: Tell me what you mean by co-operator and defector.

MN: A co-operator is somebody who pays a cost to help somebody else. So, for example, I pay a certain cost and you have a benefit. That’s cooperation.

David: Okay.

MN: And a defector does not do that. A defector does nothing: does not pay the cost, refuses to pay the cost, but also does not distribute benefit.

Ard: The defector’s selfish.

David: Is it selfish?

MN: Defectors are selfish and the co-operator does something very strange. The co-operator…

David: More generous?

MN: They’re generous, but kind of generous to a competitor, because everybody here is a competitor to everybody else. And the co-operator helps a competitor. It reduces its own potential in order to augment the potential of somebody else.

David: Which you wouldn’t expect natural selection to allow.

MN: Yes, natural selection should basically make sure those co-operators who do this strange thing, they get wiped out.

David: Yeah.

MN: We would expect them to get wiped out. Okay.

David: So what happens?

MN: Yeah, let us start the game. And we see, yes, these defectors, they are spreading, you know. So the colours that we are observing here are: red are defectors and blue are co-operators, and yellow and green are changing sides.

So yellow is now a new defector: it was a co-operator before. And green is a new co-operator: it was a defector before. We see the pattern is spreading. A kind of symmetry is being maintained here because they are deterministic of the rules, and the initial symmetry is never broken. But the amazing thing is these co-operators, they are persistent. They just refuse to get wiped out and they survive in those clusters. And if you watch very carefully, you see the clusters, they are actually growing until they collide with other clusters, and then they’re shrinking, and then they grow.

David: But they never go out of business.

MN: But they never get out of business. And the amazing thing is the average abundance of co-operators in this pattern is very close to 12log2-8.

David: What does that mean?

Ard: It’s close to constant.

MN: It converges to a constant which is approximately 31%, and this is a mathematical curiosity.

Ard: Natural selection would say the co-operators would get wiped out, because they are paying a cost to help their competitors. And yet it’s not happening. So why?

MN: The reason why it’s not happening is because the co-operators form clusters and in those clusters of co-operators, they actually get a high payoff. They have a high fitness.

David: So they do better?

MN: They do better than the defectors that are surrounded by other defectors. So we always have to ask, on the edge between a co-operator and defector cluster, who is actually winning?

MN: Because the co-operator, even though sitting on the edge, is still getting all the help from other co-operators inside, but a defector is, sort of, getting no help from his defectors. And therefore the co-operators form these clusters that can persist and can even grow in the presence of defectors.

Ard: So this is a bit like, if I’m with my neighbours and we help each other, then we’ll, in the end, be better off than the neighbours one block down who don’t help one another.

MN: Yes, that’s right. So the neighbours that help each other, they form a community that is cooperative, and the neighbours who don’t help each other, they form a community that is defective. And the first can prosper and the other one will kind of perish.

David: Is this, sort of, an addition to the rule of competition in natural selection. Is this a natural law of cooperation?

MN: I think the very interesting observation is the following: going back to first principles, natural selection favours defectors over co-operators. Yet we have cooperation in nature, and we need to find a reason why there is cooperation in nature. And thousands of papers have been written on that topic, actually, and I have been trying to classify all those different propositions into five mechanisms.

And what we’re seeing here is one of those five mechanisms, for the evolution of cooperation, that I call spatial selection.

The other four are… The most important mechanisms for humans, in my opinion, are indirect reciprocity and direct reciprocity. Direct reciprocity is the fundamental idea that we have repeated interaction between two people: I help you, you help me.

And indirect reciprocity is where there’s a repeated interaction in the group: I help you, somebody will help me. I help you, I gain the reputation of a helpful person and I receive help.

Spatial selection, that’s the third mechanism.

The fourth mechanism is group selection. Groups of co-operators out-compete other groups.

And the last one is kin selection: you help relatives. So J.B.S. Haldane said, ‘I will jump into the river to save two brothers or eight cousins.’

Ard: And these five, you call them laws or principles? What would you call them?

MN: They are mechanisms for the evolution of cooperation. So a mechanism is an interaction structure.

David: And this is a different part of nature from… We’re always taught in school of nature red in tooth and claw. This isn’t that, is it?

MN: I would say nature red in tooth and claw is the first, simple, interpretation of Darwinian selection, of Darwinian evolution, and this is now the add-on. I think this is the modern view. And the modern view is somehow also the one that I’ve wanted to promote over the last twenty years: that cooperation is a fundamental principal of the living world, of evolution. And cooperation is necessary whenever evolution makes a step to a higher level of organisation. So whenever evolutions leads from a simple level of organisation to a higher level of organisation, cooperation is essentially involved. And this is the emergence of the first cell; the emergence of eukaryotic cells that have actually organised inside; the emergence of multi-cell organisms, of social insects and of human society.

Ard: So these principles are what explain how very complex societies or organisms arose from evolution?

MN: I think that’s the fundamental step. So I call cooperation an architect, a master architect of complexity.

Ard: And without cooperation, this wouldn’t happen?

MN: I would expect that without cooperation, it is very likely that you would be stuck on a certain level of organisation. So, for example, just a world of single cell bacteria.

David: So, it’s really a very creative…?

MN: I think this is what makes evolution creative.

David: Yes. If you just had competition, then you would just repeat versions of whatever simple thing you started with.

MN: Yes, I think so. And also, competition would lead to the most selfish, to the most successful type dominating.

David: Ah.

MN: Everything would also be more impoverished.

David: So this is going to give you a richer kind of…?

MN: Yes, that is what I definitely, what I…

Ard: And more beautiful?

MN: Yes, more beautiful.

David: When you first had the idea, did you realise then what effect it would have on your life, or how powerful an idea it has become? Was it clear, or was it something you felt like you were just, sort of, exploring?

MN: As soon as I saw the pattern, I thought there’s something great here, but I don’t fully understand it and I don’t fully understand the implications. But the sheer beauty of it made it clear there was something amazing.

Ard: Something true?

MN: Something true.

Ard: You think the beauty of it told you there was something true about it?

MN: Something true. Something extremely relevant, yes, because this beauty emerged from that game in a completely simple way.

Ard: And was that a surprising emergence?

MN: Yeah, once we had it, you know, one could explain it, but when I set out I wouldn’t have expected something like this.

Frans de Waal

Cooperation throughout nature

‘Most animals cannot survive without cooperation. If competition is stronger as an instinct than cooperation, it would all fall apart.’

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COOPERATION THROUGHOUT NATURE

Ard: So when you first made these discoveries, what did the scientific community… how did they react to this?

FdW: Well, that's an interesting historical question because when I was a student all we could talk about was violence and aggression, and in that context I discovered, by accident, it was not necessarily my intention, but I discovered that chimpanzees reconcile after their fights. So they may have a big fight, two males for example, and then ten minutes later one of them approaches the other and they kiss and embrace, and then they groom each other for an hour, and I thought this was awfully interesting. I found that more interesting than the fight itself. And so when I first presented that at meetings, scientific meetings, first of all people didn't know what to do with it, because they'd never heard of something like this, and second they would say, ‘Well, maybe chimps do that, but my animals certainly don't do it.’

So they wanted to make an exception for chimps, maybe, but they really didn't buy into it as an important problem. Now we know that lots of social animals reconcile after fights. It's actually very common behaviour, and it’s related to the fact that they have competition, but they also depend on each other, so it's just as in humans.

Ard: So they have cooperation?

FdW: I would say most animals cannot survive without cooperation. So cooperation occurs between single-cell organisms, between insects, all the mammals – well, there's some solitary mammals, but the majority live in either troops or groups or herds. So the level of cooperation, it's all sorts of different levels, but it's everywhere.
Ard: So it's like an instinct? Would you say cooperation is an instinct as much as competition is?

FdW: Yes, of course.

David: Why do you think we haven't seen it before?

FdW: I think after World War II there was this obsession with competition and aggression and selfishness that lasted until the 1980s or so. So our genes were selfish, we were selfish, and cooperation was a special case that we needed to explain, and we had a lot of trouble explaining it.

But now I think it's very well recognised that not just humans, but all sorts of animals, are cooperative, and there are all these tests of cooperation. So you can set up a test with chimpanzees, as we did… This was actually developed a hundred years ago here at Yerkes Primate Centre by Robert Yerkes and his people.
So they would set up a box that is too heavy for one chimp to pull in, and they would put food on the box. So you put two chimps who have ropes, – so they will have to cooperate – and they will have to synchronise and pull it in at the same time, and then they can share the food afterwards.

And we recently set it up in our group of chimps where, instead of just having two chimps, we used fifteen chimps. So now you have the potential of competition. So you have a box with food that they can pull into, two chimps or three chimps at a time. But everyone is present, and so the highest ranking members of the group, they can kick you away or they can steal your food, or someone can sit next to you and try to steal your food, free-loading basically, the free-loading problem.

And so we wanted to see how the chimps handle this situation where they have the options between competition and cooperation. If competition is stronger as an instinct, so to speak, then cooperation would all fall apart and there would be bickering and fighting. But actually we had 3,500 cooperative pulls in our test. So basically they were cooperating all the time, and they handled the competition very well. They were very good at either alternating positions or getting rid of free-loaders, or not working with someone who's too competitive so that he learns to become cooperative. And all these things were happening at that time.

David: That's terribly sophisticated behaviour.

FdW: Yeah, but they do that in the field also. We were not particularly surprised because in the field we know the chimpanzees hunt together for monkeys, for example, and they share the meat afterwards. So it's not like a totally new thing, but now we had sort of formalised it and shown that that's what's possible.

I wrote a book, Chimpanzee Politics, which is all about how chimpanzees compete for power, but it is cooperative, otherwise we wouldn't call it politics – then it would be just a pecking order like among chickens, and the biggest, meanest chicken is top. But that's not how chimpanzees operate.

In chimpanzees it’s very well possible for the smallest male to be the alpha-male. Now how is that possible? That's only because that male is maybe very diplomatic and grooms particular partners and gives them particular favours after he has reached the top. And so you don't need to be a big, heavy, strong male to be the alpha-male, and that is because the system is basically a cooperative system where you pick out your partners and your partners support you, as long as you’re useful for them, because why would they support you if you withhold all the benefits from them and so on?

Martin Nowak

Competition and cooperation in evolution

‘Competition and cooperation are always totally locked together. There’s never the pure form of cooperation, like the utopia, this is never there. Cooperation is never fully stable.'

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COMPETITION AND COOPERATION in evolution

Ard: Some people of faith would be very nervous that you could explain altruistic behaviour by the laws of nature. What would you say?

MN: That they give a mathematical explanation for why these actions can actually be the ones preferred by natural selection, that’s very good.

Ard: Yeah.

MN: And I’m not nervous, but curiously, long ago, when Newton had the mathematical description of gravity, he asked himself briefly the question, you know, by having a mathematical description of gravity, do I take away from God? Does this take away from God? And he made the remark ‘Hypotheses non fingo’ – I make no hypothesis as to why there is gravity. This could as well be the action of God. So just by having a mathematical description of gravity, it doesn’t take away God as a reason for why there is gravity.

Ard: And the same is true for…

MN: For anything we could learn about the living world: for natural selection, for the mathematical description of natural selection.

David: What was the view of moral behaviour before your work, about whether people could cooperate; whether nature could generate cooperative behaviour?

MN: I think in the realm of evolutionary biology the idea really is that natural selection favours selfishness: that natural selection would promote defectors over co-operators. And, therefore, it is actually difficult to explain the emergence of cooperation. And that was realised as a problem, already, by Darwin: in some sense, he actually said, ‘If you would find a trait in a species that is just there for the benefit of another species, that would invalidate my theory,’ something like that.

David: So he knew it was a problem?

MN: He might have sensed it. Not having had access to the mathematical description of evolution, I would argue that his understanding was partial. But now our understanding is very rigorous, very quantitative.

So natural selection favours defectors over co-operators. That is now the starting point. But now we realise that cooperation is abundant in nature and is kind of needed to explain complex life. So, we have to ask the question, why is it that sometimes natural selection favours cooperation?

David: Yes, because the simple view of natural selection would be…

MN: It won’t.

David: That it can’t.

MN: Yes, and so, then, that is where the mechanisms for the evolution of cooperation come into play, and mechanisms and interaction structure in the population, such that natural selection sees the advantage of cooperation – favours co-operators over defectors.

David: In your work it’s very evident that two are, sort of, locked together. Would you describe that relation like that?

MN: Competition and cooperation are always totally locked together, yes, intertwined. There’s always competition, and there’s sometimes cooperation: competition and cooperation. There’s never the pure form of cooperation, like the utopia. This is never there. Cooperation is never fully stable.

David: And it’s dynamic? It’s constantly switching?

MN: It is dynamic, always changing. Cooperation is never fully stable. Cooperation always gets destroyed, and then you have to worry, ‘How do I rebuild cooperation once it’s destroyed?’

Ard: So, do you think that is also a metaphor for ourselves, our own lives?

MN: Yes, very much so. Theirs is like the cycles, you know, of cooperation and defection, of like friendship and loss of friendship.

Ard: And then it brings me to another question. I’ve heard you speak about the various evolutionary transitions from no life to life, etc. How important do you think the emergence of language was?

MN: So, I consider language the most interesting thing that happened in the last 600 million years.

Ard: Okay.

MN: So 600 million years ago, you know, it was the evolution of complex multi-cellularity on Earth.

Ard: Animals.

MN: Yes, gave rise to animals

Ard: Plants

MN: Plants, the nervous system, the immune system. But ever since then, what was the greatest thing that happened? Arguably human language, because it leads to a new mode of evolution.

Ard: Okay.

MN: So before human language, evolution is almost exclusively limited to genetic evolution. So the information that is being transferred from one generation to the next is coded in genetic structures. But with humans, we have both genetic evolution and cultural evolution: a linguistic evolution, so we can actually have an evolutionary process where one person has an idea and then talks about it and others sort of copy that idea so the idea spreads in the population.

Ard: And why is that such an important… Why do you consider it the most important thing in the last 600 million years?

MN: Because it leads to a new mode of evolution – to a very fast way of evolution. So humans, in a much, much faster time scale, discover, invent all sorts of new things: they don’t have to wait for a new idea to fix that genetic evolution.

Ard: Because new ideas are much more powerful because of language?

MN: Language is a vehicle to transmit, to replicate new ideas in an unlimited fashion.

Ard: And if we now think about cooperation, does language… is that a big step, is that important for cooperation?

MN: Yes, very much. Language is very important for cooperation. Once we go to the mechanism of indirect reciprocity, which I think was a key mechanism for humans, because we have to be able to talk to each other about others.

Ard: So, you think language has hugely changed our ability to cooperate?

MN: Yes, language gives us access to use all five mechanisms, and, in particular, indirect reciprocity, in an unlimited way. So animals without language can still use indirect reciprocity but they have to observe… They have to observe something directly, but humans can talk about things.

David: I just wanted to ask you, when we were sitting here, that you suggested that the cooperative side of natural selection was the side that was responsible for making things, making leaps of… I was going to say leaps forward, but to make things more complex.

MN: Yeah, I believe…

David: Why? Why is that? Why do you think that is?

MN: I think natural selection, competition, gives you better adaptation on a certain level of organisation. But then to move from one level of organisation to a higher level of organisation, so for example from single-cellular organism to multi-cellular organism, cooperation is involved. Even the emergence of human language is somehow based on cooperation, because the two people who want to share some information by communication, they want to do so because they are already in a cooperative relationship.

David: So that cooperative force is more creative in its…

MN: I believe cooperation is the master architect of the complexity of biological life that we see around us.

Gwendolyn Patton

The Montgomery bus boycott

‘We’re all interdependent, and I think that’s also very natural. Cooperation to me is natural, not competition. Cooperation makes you whole.’

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THE MONTGOMERY BUS BOYCOTT

GP: And now we got the Montgomery bus boycott, which I’m completely conscious of. And I become, really, the youth: go-get-me, go-bring-me, go-fetch-me, in the summer.

David: During the boycott?

GP: During the boycott. The summer of ’56. One night the family church on my daddy’s side was bombed.

David: Was bombed?

GP: In ’57, yes.

David: Who bombed it?

GP: The Kluxers.

David: The Ku Klux Klan?

GP: Yeah, along with all of the other bombings that were going on. So I was very much a part of… organically a part of the struggles, and I grew up that way.

David: The boycott, for those who don’t know, that was simply that you refused to get on the bus?

GP: Yeah, we refused to get on the bus and we walked everywhere. Now you have to understand, too, our tradition. You know, we weren’t that far removed, but we did a lot of walking anyhow; as African people we walk. The rural people, we walked as part of our own tradition.

Ard: And how did you feel when the bus boycott started? Did you…?

GP: I was just absolutely electrified. We’re gonna win this.

Ard: You felt… You already knew you were going to win?

GP: Yeah, we were gonna win this.

Ard: Why did you think you were going to…?

GP: However, coming from my granddaddy’s side, why are we fighting about sitting in the front of the bus? Why aren’t we fighting about owning the bus or the bus company? And then that’s when I began to really start doing some deep thinking. But you have to remember this struggle for human rights and dignity had been going on ever since we were first enslaved. And the fear! See, part of the vote, fighting for the vote, people were just afraid to go down to the Registrar’s office.

You have to remember the Dred Scott decision: a black person had no rights that a white person was bound to respect. You really have to understand that indelible… that fear. And then you try to avoid being insulted: you try to minimise that, so you kind of withdrew. And part of that withdrawal also cemented the black community to be reliant upon each other. And then it found its fullest magnification, organisationally, during the Montgomery bus boycott. You know what I mean ‒ this community was organised.

David: I want to ask you another question, which just picks up again on what someone else said ‒ you talked about how it’s important to have a movement. Do you think one of the things that made the movement, the black movement here, strong, was that you stuck with each other, that you cooperated with each other?

GP: Competition is the downfall of humanity. Again, I wanna be the only A. All that that’s about is competition. I’m gonna cheat… I’m gonna take from you. You know it’s that needless competition. I consider it needless, unless competition is about advancing yourself and your community. If that’s not the purpose, then it becomes horrific, dangerous, frightening.

David: And what’s better than competition?

GP: Cooperation. Cooperation makes you whole. You know, where I had my strength and innate talent. You know, born talent or spiritual-given talent. And like, in another, and you have it, then let’s cooperate and bring it together for the uplift of all of us. And that’s part of the equation.

Ard: And in the Montgomery bus boycott, is that what made you strong?

GP: Yes, knowing that my relatives who had cars would go and grocery shop for people of my community, that made me feel strong. And to know that my neighbours are walking because they had no cars, that kind of determination made me strong. Yes, we’re all interdependent. And I think that’s also very natural. Cooperation to me is natural, not competition: that’s unnatural.

And then when the bus boycott ended, and I get on the bus – ’57, I reckon it is – with my maternal grandmother who put me on the bus back in ’52, and she always went to the back. And I would always sit up front, because I thought that was the victory. And don’t let a white person be up there. Oh, my Lord! I would squirm and scoot, and all of that. Get a reaction, or, as we would say, to get a rise.

And so one time there were no white people on the bus, and I decided I’d go all the way in the back and sit with Mommy. Not all the way in the back seat, but in the back. And I finally asked Mommy, I said, ‘Mommy, why do you sit in the back of the bus? You know, we walked over a year and… Why? You know what I mean?’ And she was always very proper, and she said, ‘Gwendolyn, it was not about sitting next to white people on the bus, or even sitting in the front of the bus, it was about sitting anywhere you please.’ And I was not able to conceptualise the word, but I knew there was a word, that I later learned was called self-determination.