The Averaging Fallacy

I turn now to a different issue. Sober and Wilson (1998) argue that the importance of group selection in evolution has been obscured by what they call the 'averaging fallacy'. Those who commit this fallacy are prone to claim that certain selection processes involve only individual selection, when in fact they involve a component of group selection. Indeed, Sober and Wilson say 'the controversy over group selection and altruism in biology can be largely resolved simply by avoiding the averaging fallacy' (1998 p. 34).

The averaging fallacy occurs as follows. A population contains individuals of two types, living in groups. Overall (population-wide) fitness values for each type are calculated, by averaging across all the groups; it is then claimed that the type with the higher overall fitness spreads by individual selection. This is fallacious, Sober and Wilson argue, because it ignores the effects of group structure. The type that is fittest overall may actually be less fit within each group, if groups in which the type is common are fitter than groups in which it is rare. If so, then there is a component of both individual and group selection at work, they argue.

Sober and Wilson acknowledge that if we merely wish to predict the evolutionary outcome, averaging fitnesses across groups is fine. But if we wish to understand why one type has spread at the expense of the other, averaging is at best useless and at worst misleading. It is useless because it tells us nothing about the level(s) of selection; it is misleading because it invites the fallacious inference that the type that has spread has done so by individual selection, since its overall individual fitness must have been higher. To avoid the averaging fallacy, Sober and Wilson argue, it is essential to define 'individual selection' in terms of fitness differences within groups, a la Price, not averaged across groups.

The averaging fallacy is reminiscent of the 'bookkeeping objection' against the gene's-eye view, discussed in Chapter 5. According to the bookkeeping objection, gene's-eye theorists create the illusion that genic selection is the only causal force at work, by averaging the fitness of a gene across all the diploid genotypes in which it occurs. Similarly, opponents of group selection use averaging to create the illusion that individual selection is the only causal force at work, Sober and Wilson argue. So in both cases, averaging obscures the true level(s) of selection.

Precisely how close is this parallel? The answer depends on which version of the bookkeeping objection we are dealing with. In Chapter 5 we contrasted the original version, which focused on heterosis, with the 'correct' version, which focuses on meiotic drive. The key point, to recall, is that heterosis has no bearing on which level selection is occurring at, while meiotic drive does. The fact that the overall genic fitness values can be the same whether or not there is meiotic drive is thus the relevant consideration.

There is a perfect parallel between the averaging fallacy as described by Sober and Wilson and the 'correct' version, though not the original version, of the bookkeeping argument. Indeed, both arguments are instances of a point noted in Chapter 2. In an abstract multi-level scenario, consisting of particles nested within collectives, the change in average particle character can be expressed in terms of the global character-fitness covariance among the particles; alternatively, it can be partitioned into two components a la Price. The global covariance predicts the evolutionary change, but is silent on whether particle or collective-level selection, or both, are responsible. Those who commit the averaging fallacy in relation to group selection, and those gene's-eye theorists who attribute all evolutionary change to 'genic selection', are both taking the global character-fitness covariance to define particle-level selection. But this is a mistake, for it is tantamount to defining collective-level selection out of existence. This point is the essence of Sober and Wilson's (1998) discussion; it is also the essence of the 'correct' version of the bookkeeping objection.

Sober and Wilson are surely right that the averaging fallacy is a fallacy. The only circumstance in which this might be disputed is if there is indeterminacy of hierarchical structure; for then it becomes moot whether a multi-level or single-level description of the overall change is preferable. If one did not accept that a given population is hierarchically structured, that is, subdivided into genuine groups, one would see nothing wrong with averaging; indeed, one would regard the multi-level description as a statistical artefact. So for example, in the Prisoner's Dilemma game discussed above, where the 'groups' have a fleeting existence, someone might well argue that computing the overall fitness of each type is not just a computational convenience, but provides a better reflection of the underlying dynamics than the multilevel description. However, if the existence of hierarchical structure is not in dispute, then averaging fitnesses across groups and attributing all the change to 'individual selection' is indeed fallacious, for it obscures the role of group selection.

Importantly, the averaging fallacy can only be used to obscure group selection of the MLS1 type, not the MLS2 type. For in MLS2, group selection affects the evolution of a group character, not an individual character; so there is no way that an 'individualist' re-description is possible. This ties in with the point that pluralism is only a theoretical option in relation to MLS1, for only there is it possible to describe the overall change in both multi-level and single-level terms.

How common is the averaging fallacy? Sober and Wilson admit that in its 'general form' it has rarely been committed, but argue that particular instances are common (1998 p. 34). I agree with this assessment. Perhaps the most salient instance is the frequent suggestion that altruism in nature is 'only apparent'. Ghiselin (1974b) argued this way when he described altruism as a 'metaphysical delusion', as did Trivers (1971) and, arguably, Dawkins (1976). This idea arises naturally from averaging individual fitnesses across groups. For given that the individual-type, or genotype, with the highest overall fitness will spread, surely the behaviour of that type ultimately benefits it, hence is selfish? But this is a bad argument, as Sober and Wilson note, for it is tantamount to defining selfishness as 'whatever evolves'. Just as averaging threatens to define group selection out of existence, so it threatens to make 'the evolution of altruism' a contradiction in terms.16

To this point, our discussion of the averaging fallacy has largely agreed with Sober and Wilson. I turn now to an important challenge to Sober and Wilson due to L. Nunney (1985a, b, 2002). Like Sober and Wilson, Nunney agrees that 'individual selection' should not be defined in terms of differences in overall individual fitness, averaged across groups. However, he argues that Sober and Wilson's account of how individual selection should be defined, that is, in terms of fitness differences within groups, is flawed. Nunney's argument also brings out

16 Uyenoyama and Feldman (1980) write: 'several authors have maintained that ''evolution of altruism'' is a contradiction in terms since it implies ultimately ''selfish'' promotion of the altruistic genotype by some means' (p. 381). The authors they cite include Haldane (1932), Trivers (1971), West-Eberhard (1975), and Dawkins (1976), but the list could easily be extended.

an ambiguity in the concept of biological altruism, and ties in with the discussion of contextual analysis from Chapter 3.


Before Nunney's argument can be addressed, some preliminaries are necessary. On the standard definition in biology, a behaviour counts as altruistic if it reduces an individual's fitness but increases the fitness of others. 'Fitness' here is usually interpreted as absolute fitness; so altruism entails a reduction in the donor's absolute fitness. This is the basis of Nunney's 'mutation test' for classifying behaviours. The mutation test compares the fitness of an individual that performs a given behaviour with what its fitness would be ifit 'mutated' and stopped doing so. Only if its fitness would increase does the behaviour count as altruistic.

Sober and Wilson's concept of altruism is subtly different. They argue that a behaviour counts as altruistic if two conditions are met. First, within any group, individuals that perform the behaviour are less fit than those that don't; secondly, the greater the proportion of individuals that perform the behaviour, the greater the group's fitness.17 These conditions do not imply that altruism reduces the donor's absolute fitness. For consider a behaviour that increases an individual's fitness by x, but increases the fitness of every other group member by y, where y > x > 0. The behaviour counts as altruistic by Sober and Wilson's lights, but fails the mutation test. If an individual who performs the behaviour ceased to do so, his fitness would be reduced, not enhanced. Behaviours of this sort, which boost an individual's fitness but boost that of others by even more, were termed 'weakly altruistic' by Wilson (1980). They contrast with 'strongly altruistic' behaviours that reduce absolute fitness, hence pass the mutation test.

The weak/strong altruism distinction can be expressed more precisely. Suppose individuals of two types, A and B, live in groups of size n; see Figure 6.1. Let Wa(x) denote the absolute fitness of an A individual in a group containing x A types and (n-x) B types; similarly for Wb(x). Let G(x) denote the fitness of such a group, that is, its average individual fitness, so G(x) = 1/n (x WA(x) + (n-x) WB(x)).

To capture the idea that type A is altruistic, consider the following conditions:

17 'Group fitness' here means group fitnessi, i.e. average individual fitness.

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