Dunbar’s number, first proposed by the anthropologist Robin Dunbar (1992), proposes to explain the size of human social groups in terms of brain size. A common rule of thumb is that stable human social groups, based on mutual interpersonal knowledge, have a maximum size of around 150 people. Dunbar’s number has been frequently invoked in popular culture, such as in Malcolm Gladwell’s Tipping Point Gladwell (2000) and Yuval Noah Harari’s Sapiens Harari (2011), though as we will see, the foundation for the number is shaky.
Dunbar’s Derivation
Dunbar brings two lines of evidence to argue for the maximum group size. In Dunbar (1992), he derives the brain size/group size relationship from a linear regression of 36 genera of primates. For the independent variable, Dunbar chooses the neocortex ratio, or the ratio between the volume of the neocortex and the volume of the rest of the brain, as this variable provides the best regression fit among several variables that are considered. Applying the regression to the genus Homo, the maximum group size is found to be about 148 people, typically rounded to 150 in popular discussions. The 95% confidence interval is a maximum size of roughly 100 to 231 (Dunbar (1993)).
Dunbar is concerned with the evolutionary function of large brains in humans, and to this end, he considers two possible ecological explanations for brain sizes in primates. The first is that fruit consumption, which requires greater mental processing power to monitor a dispersed and ephemeral food supply. The second is that larger grazing areas are a driver of larger brain sizes. Dunbar (1992) fails to find evidence for either of these hypotheses, and he concludes that social, rather than ecological, forces are drivers of human brain growth.
The second line of evidence, as discussed in Dunbar (1993), is the widespread presence of basic human communities of around 150 people. For this, Dunbar offers several examples. The first is a review of contemporary hunter-gatherer societies, for which Dunbar acknowledges the problem of extrapolating conclusions about Pleistocene societies. Modern hunter-gatherer societies show hierarchical patterns, with the smallest unit overnight camps, the largest unit the tribe, and intermediate units of bands or villages. Citing ethnographic reviews of modern hunter-gatherer societies, Dunbar (1993) finds that the mean band/village size is 148.4, close to his prediction, with reported values ranging from 53 to 250.
Citing Price and Beaver (1966), Dunbar (1993) finds that academic subdisciplines typically grow to around 200 researchers, and beyond that point, they tend to further subdivide. Finally, Dunbar (1993) considers the size of armies. The basic unit of the Roman Army was the maniple, of about 120-130 men, before the reforms of Marius in 104 BC; and after the reforms, the basic unit was the century of 100 men. Also, Dunbar cites figures that the basic unit of armies since the 16th century has a mean size of 179.6.
The Origins of Language
In a society based on interpersonal familiarity, a larger society increases the number of people that each person needs to know. Above, we discussed how Dunbar (1992) assesses the members’ cognitive capacity as the constraining factor on growth of a society. Dunbar (1993) examines the question in terms of time. Social grooming is a key mechanism that enforces cohesion, and since larger groups increase the number of members that each individual must groom, larger groups imply larger amounts of time spent grooming. Considering 22 genera of the catarrhine order of apes, a group that includes humans, Dunbar (1993) finds that the following regression on grooming time: G = -0.772 + 0.287 N, where G is the proportion of time spent grooming and N is the size of the group. A group size of N=148, the predicted human average, is well outside of range of data points used to construct the regression, and the resulting grooming time of 41.6% would be infeasibly high. A better solution is needed to support large groups.
It is this need, argues Dunbar (1993), that governed the development of language among humans. As a replacement for social grooming for bonding, language offers several major advantages. It is possible to speak and do other activities, such as foraging, at the same time, and it is possible to speak to more than one person at a time. The prevalence of ritualistic and formulaic conversion is evidence that they are substitutes for social grooming, and language has the value of conveying social information about third parties in the form of gossip. The transmission of ecological information, such as the location of food, is for Dunbar (1993) a secondary purpose of language. Data from observed conversations at a university refectory found that, on average, 3.4 people were involved in a conversation (1 speaker and 2.4 listeners), so that speaking is 2.4 times as efficient as social grooming. Dunbar finds that the maximum number of people who can comfortably participate in a conversation is 5.
Weaknesses with Dunbar’s Number
The purpose of a linear regression is to create a simple model that can be used to make predictions about new data points. Predictions can come in two forms. Interpolation is a prediction on a data point that lies within the range of the data points used to build the model, while extrapolation is a prediction on a data point that is out of the range of data points used to build the model. In the case of Dunbar (1992), the prediction is extrapolation, in that the neocortex ratio for humans is greater than that of any animal that is used to build the model. Perrin (1904) is among the many researchers that have warned that, even when a linear model is a good fit for the range of data on which it is built, the model might not necessarily fit well to data outside the range.
Hahn (1977) also warns about the risks of extrapolation, and in particular, he warns about the unreliability of extrapolation when the relationship between the independent and dependent variables is merely an observed correlation without an established physical basis. The reason that the neocortex ratio is chosen in Dunbar (1992) as the independent variable is that this variable offers the highest R² value of several variables considered, not because there is an obvious reason why the neocortex ratio and group size should be related.
Lindenfors, Wartel, and Lind (2021) critically examine Dunbar’s number with a series of differing statistical tests. The tests use two methods of regression: Bayesian analysis and generalized least squares. The tests use the neocortex ratio and other metrics of brain size, and they use somewhat different data sets of primate brains. The resulting regressions based on Bayesian analysis predict an average human group size of 69.2, 79.8, or 108.6 people, with 95% confidence intervals ranging from 3.8 to 520.0. The regressions based on generalized least squares predict an average human group size of 16.4, 23.6, or 42.0 people, with 95% confidence intervals ranging from 2.1 to 336.3. The wide ranges are not to argue for a different value of ideal group sizes, but rather to demonstrate that the kind of regression performed in Dunbar (1992) does not yield meaningful results.
Dunbar’s Number and Human Societies
The modern world consists of coherent human societies of millions or even billions of people, obviously far in excess of any reasonable estimate of an individual human’s capacity to maintain relationships. Structures such as written languages, formal governance institutions, legal systems, and many others allow for the functioning of human societies far beyond what is possible on the basis of personal knowledge. Dunbar’s number is not meant to posit a limit on the size of functioning human societies per se, but rather on social units that are based on personal knowledge. Which units in the modern world, then, are best described by Dunber’s number-like reasoning? Dekker (2020) argues that the groups that are selected for analysis in Dunbar (1993) are somewhat arbitrary, perhaps chosen specifically so as to provide evidence for Dunbar’s number.
As discussed in de Ruiter, Weston, and Lyon (2011), a major difficulty in extending Dunbar’s number–a concept developed in the context of non-human primates–to human societies is the great difference in “groups” among them. The groups that are analyzed in Dunbar (1993), such as academic subdisciplines and military units, are not of the same kind of groups as, for example, a troop of baboons, and thus it is dubious to extrapolate data on groups of non-human primates that live together to radically different kinds of human groups. Also radically different is the mechanism of group cohesion: social grooming for most non-human primates and language for humans. As Coward and Gamble (2008) demonstrate, human capacity to build social networks is deeply integrated with the material culture, which in turn is inextricably intertwined with human evolution. There is thus not a clear-cut distinction between human communities that are based in mutual interpersonal knowledge and communities that are extended through social innovations.
Beyond its diffusion into the popular culture, Dunbar’s number often takes on a normative stance, such as in a 2010 interview Krotoski (2010), in which Dunbar claims that large, dense networks detract from social integration. Such claims carry significant political implications, and thus it is necessary to be as aware of the limitations of Dunbar’s number as with the concept itself.
References
Dunbar, R.I. “Neocortex size as a constraint on group size in primates”. Journal of Human Evolution 22(6), pp. 468-493. June 1992.
Dunbar, R.I. “Coevolution of neocortical size, group size and language in humans”. Behavioral and brain sciences 16(4), pp. 681-694. December 1993.
Price, D. J., Beaver, D. “Collaboration in an invisible college”. American Psychologist 21(11), pp. 1011-1018. 1966.
Gladwell, M. The Tipping Point: How Little Things Can Make a Big Difference. Little Brown, ISBN 0-316-31696-2. March 2000.
Harari, Y. N. Sapiens: A Brief History of Humankind. Dvir Publishing House Ltd. ISBN 978-0062316097. 2011.
Perrin, E. “On some dangers of extrapolation”. Biometrika 3(1), pp. 99-103. January 1904.
Hahn, G.J. “The hazards of extrapolation in regression analysis”. Journal of Quality Technology 9(4), pp. 159-165. October 1977.
Lindenfors, P., Wartel, A., Lind, J. “‘Dunbar’s number’ deconstructed”. Biology Letters 17(5): 20210158. May 2021.
Dekker, J. “Do we have a ‘natural’ friend limit? Taking a closer look at Dunbar’s Number”. Leiden Archaeology Blog. March 2020.
De Ruiter, J., Weston, G., Lyon, S.M. “Dunbar’s number: Group size and brain physiology in humans reexamined”. American Anthropologist 113(4), pp. 557-569. December 2011.
Coward, F., Gamble, C. “Big brains, small worlds: material culture and the evolution of the mind”. Philosophical Transactions of the Royal Society B: Biological Sciences 363(1499), pp. 1969-1979. June 2008.
Krotoski, A. “Robin Dunbar: we can only ever have 150 friends at most…”. The Observer. March 2010.