# Groups, kin and self interest

In my last post on group selection, I described how multilevel selection differed from more traditional (and popular) concepts of group selection. One difference is that the multilevel selection framework defines groups as any subset of interacting individuals, such as a cooperating pair or family unit, rather than restricting the definition to population size groups.

There are few tangible examples available on how a multilevel selection framework works, so below is an attempt to offer an illustration of how the definition of group in a multilevel selection framework is used. It also serves as a test of how well I understand the concept myself. This numerical example also illustrates why it is generally the less intuitive approach, which is also the reason I consider that inclusive fitness – the sum of direct and indirect (kin) fitness – has proven to be the more fruitful approach in evolutionary biology. At the end, I place the discussion in an economic context to draw out my point.

This numerical example is loosely based on the approach David Sloan Wilson used in his 1975 and 1977 papers, which might be seen as the beginning of modern multilevel selection theory. The maths in the multilevel selection debate has moved on since this time, but this illustration works for the point I want to make.

Suppose there are 200 agents in a population, of which half are cooperators and half are defectors. Cooperators always seek to cooperate and engage in a mutual trade (say, making an alert sound or entering into a transaction), while the defector will always shirk.

Agents live for one generation during which they are randomly paired with another agent. From a multilevel selection perspective, we will describe these pairs as groups. This gives us 100 groups, each comprising two agents. From random pairing, we expect that 50 of the cooperators will be paired with other cooperators, and the other 50 will be paired with defectors. Similarly, 50 of the defectors are paired with other defectors, and 50 with cooperators.

A cooperator will seek to cooperate with whoever they are paired, generating a benefit of one fitness unit for themselves, but donating two fitness units to whoever they cooperate with. Thus, if a cooperator meets another cooperator, they both cooperate and generate a surplus, from which they each get a pay-off of three fitness units (one from their own action and two from their partner). If a cooperator pairs with a defector, the group still generates a surplus through the efforts of the cooperator, but the cooperator only receives one fitness unit while the defector receives two. Finally, if a defector is paired with another defector, there is no cooperation or surplus generated, so both defectors receive zero.

Within the groups of all cooperators and all defectors, both agents get the same pay-off (three or zero), so there is no individual level selection. Within mixed groups of cooperators and defectors, the defectors get double the fitness units of the cooperator, so there is individual level selection against the cooperators. Therefore, on average, there is individual selection against cooperators within groups. Within the group, the cooperator’s action appears to be an altruistic act. David Sloan Wilson has called this situation where an agent’s absolute fitness increases but their relative fitness is decreased within a group “weak altruism”.

Now for the competition between groups. The groups of cooperators get a total pay-off of six, mixed groups both get a total pay-off of three, while the groups of all defectors receive a pay-off of zero. There is selection for groups comprising solely of cooperators relative to the other two groups, and selection for mixed groups relative to groups of defectors. Group success increases with the proportion of cooperators.

Group and individual selection are operating in different directions – individual selection favours defectors while group level selection favours cooperators. Which one wins? Across all cooperators, they receive an average of two fitness units each, while defectors receive an average of one fitness unit each. Competition between groups is the dominant force and cooperators increase in prevalence despite being selected against within groups. Wilson showed in his papers that all it requires in this case of random assortment is that the cooperator have positive absolute fitness – then the group selection will overcome the relative fitness disadvantage within groups.

Now, let’s reframe this from an inclusive fitness perspective. An cooperator’s action gives them a pay-off of one, and a pay-off of two to whomever they are paired with. If we ignore kin for a moment, that pay-off of two to their partner represents an average fitness increase of 0.01 for the rest of the population (two fitness units across a population of 199). One is more than 0.01, so the cooperator’s relative fitness in the population is increased due to the transaction (the transaction also increases cooperators fitness relative to 198 of the 199 others in the population). It is in the cooperators self-interest to conduct a transaction with their partner, no matter who the partner is.

Factoring in kin, the random assortment means that the two donated fitness units will on average increase the fitness of receiving defectors (non-kin) or cooperators (their kin) by an equal amount, so the effect of that donation nets out to zero instead of 0.01. Thus, the mere fact that the cooperator receives a positive pay-off is sufficient for them to increase in prevalence. Further, if there is any assortment by type, the cooperators’ pay-off can even be negative as their kin are even more likely to benefit from their cooperative acts.

The benefit of the inclusive fitness approach is that we are not left asking why someone enters a transaction when their partner obtains a fitness advantage relative to them. The reason is that this partner is not the relevant benchmark. Rather, it is the broader population. When looked at from the population level, the situation described above involves no altruism in the ordinary sense that we define it – it is pure self-interest or benefit to kin. So what if your particular partner does well from dealing with you? The deal still makes sense. The label of weak altruism appears out of place.

If we frame this example in an economic context, the inclusive fitness approach appears even more intuitive. In economics, there is a concept known as consumer and producer surplus, which is the benefit one receives from a transaction. In the case of a consumer, if you value a good at \$2 but only have to pay \$1, then your consumer surplus is \$1. Similarly, if a producer is willing to sell a good for \$1 but receives \$2 for it, there is \$1 of producer surplus. Every economic transaction involves a distribution of surplus between the two parties.

Now, imagine we have a population of economic agents, some of whom are cooperators and others are defectors. When two cooperators get together, a transaction occurs and each receives \$3 of consumer or producer surplus. If a cooperator meets a defector, the defector rips them off, but not so much that the transaction does not occur. A defecting producer might use sub-standard materials, while a defecting consumer might try to shortchange the purchaser. The net result is that the defector walks away from the transaction with \$2 of surplus, while the cooperator receives \$1. If two defectors meet, their mutual attempts to get the better of the transaction results in it collapsing and no surplus is gained by either party.

Obviously, this is just a slightly different framing of my earlier example. If we treat each consumer-producer pair as a group, there is within group selection against cooperators, but group selection for cooperators. The net effect is that cooperators prosper. Similarly, if looked at from an inclusive fitness perspective, the cooperators will end up better off as their fitness gain is higher than that for the rest of the population.

Now, an economist looking at these exchanges would say they are obviously beneficial, regardless of any group framing. This is partly a consequence of the economic focus on absolute and not relative gains, but it also reflects the general fact that the majority of transactions do not have a perfectly equal division of the surplus. If you limit your group to the two people conducting the transaction, there is almost always “weak altruism” within the group. But is the cooperator being altruistic in any ordinary sense? No. Of course the altruist would enter into the transaction, even if the relative share of the benefits is not perfectly equal. We enter into transactions of this type every day because we benefit from the exchange. Ask yourself how often you consider yourself to be altruistic when you enter into an economic exchange. The only time we would not agree to enter such an exchange is spite, which Alan Grafen noted when he said that “a self interested refusal to be spiteful” was a far better description than “weak altruism” of what is occurring when we do transact.

The above is a simple example, but it captures a fundamental issue with the multilevel selection approach. The groupings are often less intuitive and, in my opinion (and I suspect most biologists’ opinion), less insightful than simply looking at the issue from an inclusive fitness angle to begin with. Group selection tends to be a more intuitive concept when the groups are population size groups. But then we find ourselves back in the old group selection debate and discussing factors such as the degree of migration between groups and whether intergroup competition can override the spread of cheaters within them. But to be realistic, that is where much of the popular debate about human altruism is anyhow.

1. Bret Beheim says:

Hi Jason,

I was following the discussion on Andrew Gelman’s blog, and I thought I would add my two cents to your above exercise.

If I understand your payoff structure correctly, a “cooperator” always has a higher payoff than a noncooperator, other things equal. If Jane the cooperator is paired with a non-cooperator, she gets a payoff of 1 for her efforts. Sally the defector would get 0 in the same situation. If Jane is paired with a cooperator, she gets 3 units of payoff (1 from herself and 2 from her partner). Sally only gets 2. So, it’s not a cooperative dilemma at all – cooperators always have a higher expected fitness, and cooperation will always invade such an evolutionary game structure over many generations, regardless of how you do the bookkeeping.

The interesting stuff about multilevel selection happens the cooperator may do better than if he was a non-cooperator, or worse, conditional on the action of the other guy. For example, two castaways agree to specialize and trade (one catches the fish, the other collects firewood) but the fisher renegs on the deal, collecting fish and firewood just for himself, leaving the cooperator with no food. That’s a Stag Hunt situation. Or, they both specialize as planned, and once the feast is all set up, one of them takes it all for himself. That’s a Prisoner’s Dilemma. Each of these is different from your example because it’s not clear how cooperation could get established in a population of defectors (in the case of the Stag Hunt), and in the PD it’s not clear how cooperation can be maintained even in a world of cooperators, since a lone defector will always have higher fitness.

1. Thanks for your comment Bret. On the first part, you are right and you have provided an explanation that is even simpler than mine. But that again highlights the issue with the multilevel selection approach. By framing the groups in a certain way, what is clearly the optimal strategy is instead framed as “weak altruism”. By looking across the population and not within and between groups, you have cut to the core of the example.

Things do get more interesting when you move to a prisoner’s dilemma or stag hunt game. On the prisoner’s dilemma, cooperators lose out where there is random assortment as in Wilson’s model, so some form of positive assortment is required for cooperators to have higher fitness. The question then becomes what is the motivation for or basis of that assortment – and that is where kin becomes an obvious factor for consideration. Regardless of the scenario, we can then calculate the inclusive fitness and determine which strategy will increase in prevalence.

Personally, I am not a big fan of the prisoner’s dilemma as a tool for examining the origins of human cooperation and/or group selection, and consider that the stag hunt game is probably a better proxy for human interaction (a topic for another post). I could manufacture the same result as my example using certain parameters, and expand the scope of potential parameters by introducing some positive assortment.

On the dynamics and the establishment of the first cooperator in the Stag Hunt, that is a problem that neither inclusive fitness or multilevel selection approach helps with. I suppose that is the time to drop the strict game theory and ask whether intelligence, drift, luck etc could result in a few cooperators emerging. Once there is more than one cooperator, positive assortment by kin then provides an avenue for further growth.

2. Thanks for the example, which I *think* I’ve properly understood; I do agree that Bret Beheim’s reformulation is more clear on what’s actually going on.

Re your comment “I am not a big fan of the prisoner’s dilemma as a tool for examining the origins of human cooperation and/or group selection”, John Hawks expressed a similar sentiment recently (“I think the Prisoner’s Dilemma has been overemphasized in the discussion of the evolution of human cooperation, as many kinds of social interactions in ancient hunter-gatherers would not have fit that dynamic.”). That makes two people whose opinions I respect who think this, so I’d definitely be interested in seeing a follow-up post from you addressing this general topic.

1. One thing to note with Bret’s approach is that it only works in the case of random assortment. Suppose a cooperator is always paired with a defector. In that case, defectors would have higher fitness. Positive assortment also creates the possibility that a dominant strategy of defecting (as in the prisoner’s dilemma) could have lower fitness.

On the prisoner’s dilemma, I’ll whip up a post at some point in the next couple of weeks. Following your suggestion has been fruitful in the past – the reading list that I created on your prompting a few months ago is easily my most visited page.

1. “Following your suggestion has been fruitful in the past” — I’m glad to hear it. I hope that in return you won’t mind my imposing on you a bit to test my understanding:

The main sentence that confused me on first reading was the following one in the inclusive fitness discussion: “If we ignore kin for a moment, that pay-off of two to their partner represents an average fitness increase of 0.01 for the rest of the population (two fitness units across a population of 199).” Where does this come from? My initial guess is that it reflects a simplified perspective (“[ignoring] kin for a moment”) in which everyone is assumed equally related to everyone else in the population (due to random mating?), so the payoff of two to the cooperator’s partner can be thought of as a fitness increase spread out equally among the entire rest of the population (i.e., minus the cooperator).

Am I on the right track here, or I am missing something?

2. Yes, you’re on the right track. The assumption you made would do the trick – although the one I half had in mind was that no-one is related at all. I was simply trying to ignore the consequences of the distribution of the other fitness units for a few moments.

3. Thanks for the clarification!

3. Hi Jason,

Thanks for the post.

Brian Skryms has written a lot about the stag hunt as a more fitting model of the origins of human cooperation than the PD. http://www.amazon.com/Stag-Hunt-Evolution-Social-Structure/dp/0521533929

Coordination games, like the stag hunt, are in some ways better than the PD for illustrating the utility of multilevel selection models. The stag hunt has two evolutionarily stable equilibria – one that is risk-dominant and one that is payoff-dominant. If the population is divided into isolated groups of n-individuals playing n-person stag hunt games, then one would expect, through stochastic forces, initial conditions, etc., that some groups would be coordinating at one equilibrium and some groups would be coordinating at another equilibrium. Selection within the groups would be zero since everyone would be at the same strategy. But let the groups compete and groups at the the payoff-dominant equilibrium should do better.

Here is a related model by Boyd and Richerson: http://www.sscnet.ucla.edu/anthro/faculty/boyd/BoydRichersonJTB90.pdf

To me, the Boyd and Richerson model would be difficult to reframe in an inclusive fitness framework and probably less intuitive.

Matt

As an aside: it seems that you are defining “kin” as “individuals-with-the-same-strategy.” However, this definition seems different than how most biologists use it – which has more to do with being related by descent.

1. Thanks for the tip on Skyrms’s book. My library has an electronic copy, so it is already in hand.

On the Boyd and Richerson model, I don’t understand gene-culture evolution models well enough to critique them from the inclusive fitness and multilevel selection angles, but am trying to get to that point. Maybe that article can be a benchmark for me – I’ll develop a post at some point to see if I can look at it from both sides (that is likely to be a few months away). However, I do recall a reference to this Boyd and Richerson model in an article by West et al. They wrote:

More recently, over the last decade, group selection has been used in a third “newer” way. In these models, it is argued that a key factor favouring cooperation is direct competition between groups, and this is referred to as group selection (Binmore, 2005a; Bowles, 2006, 2009; Bowles et al., 2003; Boyd & Richerson, 1990, 2002; Boyd et al., 2003; Gintis, 2003; Gintis et al., 2003; Henrich, 2004). For example, as discussed in Misconception 2, when groups compete for territories, and territories are won by the groups with the most cooperators. However, these models do not provide an alternative to inclusive fitness or kin selection — individuals gain a direct fitness benefit through cooperating because they increase the success of their group (including themselves), and an indirect fitness benefit in the cases where the models also assume limited dispersal, which leads to significant relatedness between the individuals in a group.

On my loose use of “kin”, a better (broader) word might have been “relatedness” to capture the genetic similarity without common descent – however in hindsight I could have almost of left the kin part out given how strong the direct fitness benefits to cooperation are.

1. Bret Beheim says:

Matt’s right about the 2002 Boyd and Richerson model being a real key to understanding what cultural group selection is all about. The process of selection between the two equilibria can be described in multiple ways, but the causal mechanism is rooted in the differential influence of individuals across groups. My guess is that this captures the essence of many rapid institutional shifts in the real world, like the spread of the nation-state, or the collapse of Soviet system. West, El Mouden, Gardner’s review paper grossly misrepresents this result by bringing up limited dispersal and altruism (which are just nonsense in that context). That’s pretty much par for the course with that paper, unfortunately.

2. Thanks for reading the blog! Bret alerted me to your blog last night and I’ve also added it to my feed. There are some earlier posts I’d like to look at too.

One of the many frustrations with the West et al. article is that they do these laundry-list citations and when you actually go and look at the papers they cite it is difficult to see how their criticism applies.

For example, for “Misconception 2” the first two citations are to works by Boyd and Richerson. The first is a book which reprints 20 separate articles that could easily have been reprinted individually and, to my knowledge, none make the “misconception” they claim. The second mentions reciprocity briefly, but says it is not a very good explanation for altruism in large groups – which is exactly the opposite of what West et. al implies it says. To me, this makes the whole thing smell like straw.

In the section you quote, I think the misconception West et. al makes is thinking about inclusive fitness, kin selection and multilevel selection as different mechanisms instead of different ways of modeling the world.

I seem to remember that Sam Bowles’s Microeconomics book has an equilibrium-selection model in it somewhere. Bret and I ran a seminar where we worked through it. There were a a couple of economics grad students in the seminar that thought it was a good introduction from the economics perspective.

2. “Brian Skryms has written a lot about the stag hunt as a more fitting model of the origins of human cooperation than the PD.” I read this book many years ago (along with Skryms’s “Evolution of Cooperation”); I’ll have to look into it again. I wonder though how one would address Herbert Gintis’s criticism in his Amazon review that “Skyrms’ major point in this book is just dead wrong”; I lack the expertise to evaluate his arguments.

4. Charles Goodnight says:

As somebody who has spent much of my adult life thinking about multilevel selection I appreciate your enlightened view on the subject. I would like to alert you to a body of literature that rarely gets discussed in the popular press. Mostly because it is based on statistical genetics, and is much less flashy than talk of cooperaters, cheaters, and altruists. It turns out that there has been extensive experimental and theoretical research on multilevel selection using this genetic approach, and that the results are illuminating, not to mention useful (the eggs you ate for breakfast were probably laid by chickens developed using protocols from this school ). In short, it is unfortunate that more attention is not paid to the genetic school of multilevel selection. Below are a few papers that might be useful.

Wade, M. J. (1976). “Group selection among laboratory populations of Tribolium.” Proc. Nat. Acad. Sci. USA 73: 4604-4607. An oldie, but goodie that explains what the early group selection models were missing

Goodnight, C. J. and L. Stevens (1997). “Experimental Studies of Group Selection: What do they tell us about group selection in nature?” American Naturalist 150(Supplement): S59-S79.
An article I wrote on the implications of experimental studies of group selection. It is actually pretty readable.

Wade, M. J. et al. (2010). “Multilevel and kin selection in a connected world.” Nature 463(18): E8-E9. You have probably seen this, but it is important if for no other reason than the list of authors represents a lot of people that are important in the field.

The bottom line on all this is that multilevel selection is perhaps a superset of group selection, but it is not a different creature. It also turns out that there is a lot of multilevel selection out there, and, Coyne and Dawkins not withstanding, it IS different than selection on individual genes. To give the punchline away, context is everything. Group selection cannot be reduced to selection on genes because individuals interact, as do genes, and as complexity theory tells us, this means that the whole is more than the sum of its parts.

1. Thanks for the references, Charles. I’ve come across them before but haven’t given them a proper read. I suppose it’s time that I did.

I’m still coming to grips with the argument that group selection is not able to be reduced to genes in some contexts. How does that reconcile with D.S. Wilson’s (and others) line that inclusive fitness and multilevel selection are just different accounting methods? Is it a case that the accounting method works but you lose information? Or are there cases where the accounting transition cannot be done?