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What the evidence says about Dunbar's number

Where the 150 in Dunbar's number comes from, the arithmetic behind it, what network studies find, and why a 2021 reanalysis and Dunbar's reply disagree.

Portrait of Tomasz WierzbaTomasz Wierzba · · 9 min read
What the evidence says about Dunbar's number

"Dunbar's number" is usually stated as a fact about brains: a person can keep up about 150 stable relationships, and no more. It is quoted far outside anthropology, often with more confidence than its author shows. Robin Dunbar, the Oxford evolutionary psychologist whose name it carries, put the scope plainly in a 2021 defense of the idea: "Dunbar's number applies to quality relationships, not to acquaintances." This piece goes through where the number comes from, does the arithmetic, and sets the main critique beside his reply. The short version is that 150 is an estimate with a wide margin, and the margin is the interesting part.

Where 150 comes from

The idea began with monkeys and apes. In a 1992 paper in the Journal of Human Evolution, Dunbar related the average group size of primate species to their neocortex ratio, the volume of the neocortex divided by the volume of the rest of the brain. Species with relatively more neocortex tend to live in larger groups. The proposal, now called the social brain hypothesis, is that the neocortex limits how many relationships an animal can track.

In a 1993 paper in Behavioral and Brain Sciences he carried the line on to humans. The regression fitted to the primates was

log N = 0.093 + 3.389 × log CR

with N the mean group size, CR the neocortex ratio, and logarithms to base 10. For humans he used a neocortex volume of 1006.5 cc and a total brain volume of 1251.8 cc. Work it through:

  1. Rest of the brain: 1251.8 - 1006.5 = 245.3 cc.
  2. Neocortex ratio: CR = 1006.5 / 245.3 ≈ 4.10.
  3. log 4.1 ≈ 0.6128.
  4. 3.389 × 0.6128 ≈ 2.0767, and adding 0.093 gives 2.1697.
  5. N = 10^2.1697 ≈ 147.8.

Round 147.8 and you have 150. Dunbar reported 95% confidence limits around the prediction of 100.2 to 231.1.

The exponent explains why the limits are wide. The fitted line is a power law, N proportional to CR^3.389, so a neocortex ratio 10% larger predicts a group 1.1^3.389 ≈ 1.38 times larger. Small uncertainty in the brain measure turns into large uncertainty about the group:

neocortex ratio predicted N
3.7 104
3.9 125
4.1 148
4.3 174
4.5 203

There is a second reason for caution. Dunbar noted that the human ratio is about 50% larger than the highest value for any other primate, so the human figure is an extrapolation beyond the data, which is where any fitted line is least reliable.

He then looked for groups of about that size in the ethnographic record. Among hunter-gatherers he distinguished overnight camps (mean about 38 people), larger intermediate groupings such as clans or villages (mean 148.4 in societies with census data) and tribes (mean about 1,155). The middle level matched the prediction. He also pointed to Hutterite farming communities, which averaged 106.9 people across the 51 communities in his data and which treat 150 as the size at which a community should divide, and to army companies of roughly 100 to 200. The same paper proposed that language evolved partly as a cheaper substitute for grooming, the way other primates service relationships; by his calculation, grooming alone would have taken about 42% of the day at human group sizes.

Circles inside circles

Later work by Dunbar and colleagues treats 150 as one layer in a series. In his 2021 summary the layers run from about 5 intimate relationships to 15 close friends, 50 good friends and 150 meaningful relationships, then roughly 500 acquaintances and 1,500 people whose names one knows, each layer about three times the size of the one inside it. A 2005 study by Zhou, Sornette, Hill and Dunbar, pooling data on human group sizes, reported a preferred scaling ratio close to 3.

The layers are worth some arithmetic, because they show how fast the relationships among other people multiply. A group of n people contains n(n - 1) / 2 pairs:

layer people pairs among them
intimate 5 10
close 15 105
good friends 50 1,225
meaningful 150 11,175

Your own ties grow in step with the layer, one per person. The ties among the people you know grow roughly with the square: tripling the group from 50 to 150 multiplies the pairs by about 9 (11,175 / 1,225 ≈ 9.1). If knowing a community means knowing who gets on with whom, the load rises much faster than the headcount. In a 150-person community where each member keeps up closely with 15 others, the density of that close-tie network is 15/149 ≈ 0.10, a calculation explained in network density and centrality.

What studies of real networks find

Tests on living people depend heavily on what counts as a relationship.

Hill and Dunbar (2003) used Christmas cards in Britain. Forty-three respondents filled in questionnaires while sending their cards, 2,984 cards in all. Counting everyone in the households that received a card gave a mean network of 153.5 people, with a standard deviation of 84.5; counting only the people respondents said they actively contacted gave a mean of 124.9, from the 22 questionnaires that made the distinction. The mean sits close to 150. The spread matters as much: with a standard deviation of 84.5, many individual networks were far from the mean.

McCarty, Killworth, Bernard, Johnsen and Shelley (2001) asked nationally representative US samples how many people they knew in particular subpopulations and relationship categories, then scaled up. Two estimation methods agreed on an average personal network of about 291. That is a different quantity, people one knows rather than people one keeps up with, and most of the gap between 150 and 291 is a gap between definitions.

The network evidence fits a layered picture reasonably well. It cannot, by itself, confirm a ceiling set by the brain: the numbers move with the question asked, and individuals differ widely.

The 2021 reanalysis

In 2021 Patrik Lindenfors, Andreas Wartel and Johan Lind of Stockholm University reran the primate analysis in Biology Letters, with updated brain data and phylogenetic methods that allow for related species not being independent data points. Their Bayesian analyses gave mean human group sizes of 69 to 109, and their generalized least squares analyses gave 16 to 42. The 95% intervals ran from 4 to 520 and from 2 to 336. They concluded that specifying any one number is futile and that a cognitive limit on human group size cannot be derived this way. In the accompanying university release they added that primate social life depends heavily on diet and predators, that human network sizes vary a great deal, and that culture lets people learn to handle more contacts.

Dunbar's reply, and theirs

Dunbar answered in The Conversation in May 2021. His main objection was statistical. Ordinary least squares regression, he argued, underestimates the slope when the variables cannot be measured or controlled precisely, as with brain volumes; reduced major axis regression, which he favored, avoids that. On the same dataset, he wrote, least squares predicts a group of 71 and reduced major axis 158. He added that the primate data fall into four grades, separate bands that a single line handles badly.

Why should the choice of line matter so much? Least squares finds the line that best predicts y from x. Reduced major axis treats the two variables symmetrically, and its slope equals the least squares slope divided by the correlation coefficient r. A hypothetical example (the statistics starter covers the basics) shows the effect. Suppose the primate data center on log CR = 0.35 and log N = 1.2, invented values for illustration only, with a least squares slope of 2.7 and r = 0.8. The reduced major axis slope is then 2.7 / 0.8 = 3.375. Humans sit at log CR = 0.613, which is 0.263 beyond the center.

  • Least squares: 1.2 + 2.7 × 0.263 = 1.910, about 81 people.
  • Reduced major axis: 1.2 + 3.375 × 0.263 = 2.088, about 122 people.

Same data, same center, a difference of about 50%, and the gap widens the further out you extrapolate. Humans are far out.

Lind and Lindenfors replied in June 2021 that reduced major axis overcorrects. Run Dunbar's preferred method on their data anyway, they wrote, and the estimate is 289.8 (interval 226.0 to 371.6); for monkeys and apes alone it is 404.1 (300.6 to 543.3). Neither is 150. They also reported that the correlation between brain and group size disappears when further variables enter the models, and that diet may predict primate brain size better than sociality does.

analysis central estimate 95% interval
Dunbar 1993 147.8 100.2 to 231.1
Lindenfors et al. 2021, Bayesian 69 to 109 4 to 520
Lindenfors et al. 2021, least squares 16 to 42 2 to 336
Dunbar 2021, least squares vs reduced major axis 71 vs 158 not given
Lind and Lindenfors 2021, reduced major axis 289.8 226.0 to 371.6

The anthropologists' objection

An older line of criticism does not depend on regression at all. Jan de Ruiter, Gavin Weston and Stephen Lyon argued in American Anthropologist in 2011 that the way humans form and manage groups cannot be understood as a simple product of brain physiology, and drew on cross-cultural evidence about group organization and kinship to make the case. One way to see their point: people run large groups with tools other primates lack, such as named categories of kin, rules of descent and marriage, and offices. A classificatory kinship terminology gives a person a known relationship to anyone placed in a category, met or not. Whatever the brain's limit, culture changes how much has to be remembered one person at a time.

Questions worth asking

Is 150 a hard limit?

Nothing above shows one. The original prediction carried an interval from about 100 to 231, and the reanalyses give intervals far wider.

Is the idea useless, then?

Not quite. The layered pattern, each circle about three times the last, appears in several datasets, and community-level groups of around 150 recur in Dunbar's ethnographic comparisons. Those regularities are worth explaining even if the brain explanation is disputed.

What should a student report?

The definition of a relationship, the method used to count it, and the spread as well as the mean. "Mean 153.5, standard deviation 84.5" says more than "about 150".

The whole calculation fits on an index card: divide 1006.5 by 245.3, take the logarithm, multiply by 3.389, add 0.093, and raise 10 to the result. Shift the neocortex ratio by 0.2 either way and the answer runs from 125 to 174.

Sources and further reading

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