Transmission biases: the copying rules behind cultural change

Imagine a valley of 100 farming households in which 60 grow a new bean variety and 40 keep the old one. Each spring a young household sets up and decides what to plant by watching others. If newcomers simply copy one household chosen at random, the expected share next year is still 60 percent, and nothing changes except by luck. Real people rarely copy like that. They count heads, they watch the family with the fullest granary, and they notice that one bean cooks faster. Each of those habits is a transmission bias, and each pushes the 60 percent in its own direction.

Robert Boyd and Peter Richerson set out the main types in Culture and the Evolutionary Process (1985), and their scheme is still where most models in cultural evolution begin.

The baseline: copying without bias

Call the two variants A and B, and let p be the share of the population that has A. A learner who picks one model at random adopts A with probability p, so the share in the next generation, p', is simply

p' = p

This is unbiased transmission. Frequencies still wander by luck (drift), but nothing pushes them. Any rule that makes p' differ from p in a predictable way is a bias.

Who counts as a model matters as well. In kin-type shorthand (F father, M mother, B brother, Z sister, so MB is mother's brother), a learner might copy F or M (vertical transmission), an MB or an unrelated elder (oblique), or age-mates (horizontal). The biases below can act along any of these routes.

Three ways to tilt the odds

Boyd and Richerson called these direct bias, indirect bias and frequency-dependent bias; "content", "prestige" or "payoff", and "conformist" are the everyday labels now. The recursions are the teaching forms in Alex Mesoudi's open tutorial on simulation models of cultural evolution. In each, s or D sets the strength of the bias, and setting it to 0 gives back p' = p.

Conformity, worked by hand

A conformist has to see more than one model, and three is the smallest number that can produce a majority. So let each learner meet three models drawn at random. With p = 0.6, the binomial rule gives the chance of each possible mix:

The last column is the heart of it. An unbiased learner who sees two A's and a B adopts A two times in three, exactly the share in the sample. A conformist adds a little extra, D/3, toward the majority, and takes the same amount away when A is in the minority. D runs from 0 (no conformity) to 1 (always follow the majority of three).

Take D = 0.5, so 2/3 + D/3 = 5/6 and 1/3 - D/3 = 1/6. Multiply each probability by its adoption chance and add:

p' = 0.216 × 1 + 0.432 × 5/6 + 0.288 × 1/6 + 0.064 × 0 = 0.216 + 0.360 + 0.048 = 0.624

Do the same algebra with a general p (a good exercise: expand, then collect the terms that carry D) and everything collapses to the formula in the table above:

p' = p + D p(1 - p)(2p - 1)

Check: 0.6 + 0.5 × 0.6 × 0.4 × 0.2 = 0.6 + 0.024 = 0.624. Same answer.

Now iterate. Each row uses the p from the row before, rounded to three places:

The majority grows, slowly at first and then faster, because 2p - 1 keeps rising. Start at 0.4 instead and every change flips sign, so the share falls to 0.376, 0.347, 0.312 and on toward zero (the formula is symmetric around one half, so the table simply mirrors). Start at exactly 0.5 and 2p - 1 = 0, so nothing moves; but any nudge grows, which makes one half an unstable balance point between two stable endpoints at 0 and 1.

Why conformity can keep neighbors different

That knife edge matters to anthropologists. Suppose village X has 90 percent A and the next village, Y, has 10 percent. Each generation, one learner in ten in X draws models from Y, through marriage, trade or moving in with in-laws. The pool X's learners see is then

0.9 × 0.9 + 0.1 × 0.1 = 0.81 + 0.01 = 0.82

Under unbiased copying the share stays at 0.82, and with this mixing repeated every generation the two villages slide toward each other. With strong conformity (D = 1):

p' = 0.82 + 1 × 0.82 × 0.18 × 0.64 = 0.82 + 0.094 = 0.914

The majority wins back everything migration took, and a little more. Boyd and Richerson, and later Joseph Henrich and Boyd (1998), used this logic to argue that conformist transmission can keep neighboring groups culturally distinct even when people move between them. Whether it does so in any real case is a separate, empirical question.

Copying the person: prestige and success

Model-based biases skip the comparison of variants and look at the people who carry them. If the most successful farmers plant A, copy a successful farmer. In Mesoudi's payoff version, carriers of A earn 1 + s, carriers of B earn 1, and each model is copied in proportion to what it earns, which gives the recursion in the table.

Henrich and Francisco Gil-White (2001) gave prestige its own evolutionary account. They separated dominance, deference extracted by force or threat, from prestige, deference freely given to people who know things. On their view, learners grant respect and attention to skilled individuals in return for access to them as models, so prestige works partly as a market in information. One corollary: copying a whole person means copying more than the skill that made them successful, so arbitrary habits (a style of dress, a turn of phrase) can ride along with useful ones. Mesoudi's tutorial models this as a neutral trait hitchhiking on a useful one.

Content bias: when the idea itself is the draw

Content bias is the simplest to state: some variants are easier to learn, remember or like. In p' = p + s p(1 - p), s is the chance that a learner with B who meets an A abandons B for it.

Much of the evidence comes from transmission chains, where each participant passes material to the next, as in the children's game of telephone. Alex Mesoudi, Andrew Whiten and Robin Dunbar (2006, British Journal of Psychology) found that information about social relationships came through chains more accurately than matched non-social information. Joseph Stubbersfield, Jamshid Tehrani and Emma Flynn (2015, same journal) found that urban legends carrying social or survival content were recalled better than control stories, with social content doing best; when people instead chose which stories to read or pass on, the legend types did not differ.

One start, three outcomes

Here are the three rules side by side, starting with A as a minority (p = 0.2) and using s = 0.5 and D = 0.5:

First-step checks: content, 0.2 + 0.5 × 0.2 × 0.8 = 0.28; payoff, 0.2 × 1.5 / (1 + 0.5 × 0.2) = 0.3 / 1.1 = 0.273; conformist, 0.2 + 0.5 × 0.2 × 0.8 × (-0.6) = 0.2 - 0.048 = 0.152.

Content and payoff biases let a rare, better idea spread along the S-shaped path familiar from studies of how innovations diffuse. Conformity smothers the same idea, because a minority is a minority. Henrich (2001, American Anthropologist) used the shape of such curves as evidence: learning on one's own never produces the S-shaped adoption curves seen in diffusion studies, biased transmission always does, and a mixture produces them only when biased transmission is the main force. Notice what the table adds: conformity alone cannot start a take-off. Something else has to carry A past the halfway mark first.

What the evidence shows, and what is disputed

The experiments are messier than the curves.

• Charles Efferson and colleagues (2008) had players choose repeatedly between two "technologies" with uncertain payoffs. Some social learners behaved like the classic conformist model; the rest ignored frequency information altogether. The authors called them conformists and mavericks. A population average would hide that split.
• Thomas Morgan and colleagues (2012) ran a series of computer tasks and found that the number of demonstrators, their consensus, task difficulty and the learner's own confidence all shaped how much people used social information. The response to social information was conformist, most clearly when people were uncertain and saw many demonstrators, but final choices often were not, because people's own judgment pulled the other way.
• Nicolas Claidière and colleagues (2014) let zoo visitors choose whether to write or draw their answers on a display, and varied how many answers already on show were written. Visitors followed the majority, but almost in proportion: the effect was largely linear. Proportional following is what unbiased copying already predicts. The exaggerated majority preference that drives the recursion was weak.

Some of the disagreement is about words. In the models, conformity is not just a tendency to follow the majority but an exaggerated one, strong enough to make the majority grow, as Efferson and colleagues stress; in everyday speech, and in much social psychology, it means any going along with the group. Claidière and Andrew Whiten (2012, Psychological Bulletin) argued that the field should borrow social psychology's older distinction between informational conformity (following others because they probably know something) and normative conformity (following them to fit in). Researchers in the cultural attraction tradition associated with Dan Sperber go further, arguing that much cultural stability comes from people rebuilding ideas toward the same appealing forms rather than copying them faithfully; the Stanford Encyclopedia of Philosophy's entry on cultural evolution sets out that debate fairly.

The practical lesson for students is about identification. An S-curve, a stable majority or a difference between villages can each come from several copying rules, and the population pattern alone rarely tells you which. Separating them takes data on who learned from whom and what each learner saw, which is why network data matter (our first network measures explainer starts there) and why the statistics starter dwells on reading causes from correlations. The research overview places this work among the field's other lines.

A pencil exercise to finish: set D = 1 and start at p = 0.45. The first step gives 0.45 + 0.45 × 0.55 × (-0.1) = 0.425 (rounded). Keep going and count the generations until A drops below one in ten. (Answer: six generations, ending at 0.076.)

Sources and further reading

• Boyd, Robert, and Peter J. Richerson. 1985. Culture and the Evolutionary Process. Chicago: University of Chicago Press.
• Henrich, Joseph, and Robert Boyd. 1998. "The evolution of conformist transmission and the emergence of between-group differences." Evolution and Human Behavior 19 (4): 215-241. https://doi.org/10.1016/S1090-5138(98)00018-X
• Henrich, Joseph. 2001. "Cultural transmission and the diffusion of innovations: adoption dynamics indicate that biased cultural transmission is the predominate force in behavioral change." American Anthropologist 103 (4): 992-1013. https://henrich.fas.harvard.edu/sites/scholar.harvard.edu/files/henrich/files/henrich_2001.pdf
• Henrich, Joseph, and Francisco J. Gil-White. 2001. "The evolution of prestige: freely conferred deference as a mechanism for enhancing the benefits of cultural transmission." Evolution and Human Behavior 22 (3): 165-196.
• Efferson, Charles, Rafael Lalive, Peter J. Richerson, Richard McElreath, and Mark Lubell. 2008. "Conformists and mavericks: the empirics of frequency-dependent cultural transmission." Evolution and Human Behavior 29 (1): 56-64.
• Morgan, T. J. H., L. E. Rendell, M. Ehn, W. Hoppitt, and K. N. Laland. 2012. "The evolutionary basis of human social learning." Proceedings of the Royal Society B 279 (1729): 653-662. https://doi.org/10.1098/rspb.2011.1172
• Claidière, Nicolas, Mark Bowler, Sarah Brookes, Rebecca Brown, and Andrew Whiten. 2014. "Frequency of behavior witnessed and conformity in an everyday social context." PLOS ONE 9 (6): e99874. https://doi.org/10.1371/journal.pone.0099874
• Mesoudi, Alex. Simulation Models of Cultural Evolution in R (online tutorial), models 3 to 5 on direct, indirect and conformist bias. https://bookdown.org/amesoudi/ABMtutorial_bookdown/