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.