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Articles · Anthropology · Galton’s problemIssue 87 · Sunday, 8 November 2026

Galton’s Problem Waited Ninety-Six Years for Its Fix

The fix came from biology, and it does not travel as easily as it looks

Abstract. In 1889 Francis Galton told anthropologists that their cross-cultural correlations proved nothing, because societies sharing an origin or a neighbour are not independent cases. In 1985 the population geneticist Joseph Felsenstein showed that species have exactly the same defect, and built a fix from a phylogenetic tree. Anthropology held the problem alone for ninety-six years before biology’s answer existed to borrow, and when it was finally borrowed, the tree anthropology could supply was not quite the tree the fix had assumed it would get.

In May 1889, after Edward Tylor read a paper to the Anthropological Institute correlating marriage and descent customs across 350 societies, Francis Galton rose to say that the correlations proved almost nothing. Tylor had found that matrilineal descent tended to travel together with particular rules about where a married couple should live, and had treated each of his 350 societies as an independent test of that association, the way a pollster treats each respondent as a separate data point. Galton’s objection, recorded in the discussion that followed at page 270 of the same volume, was that the societies were not 350 independent cases. Many of them had borrowed the custom from a common neighbour or inherited it from a common ancestor, so the sample might contain only a handful of genuinely separate inventions wearing hundreds of coats. The correlation Tylor reported could be one true pattern copied widely across a region, or it could be three or four unrelated accidents that happened to resemble each other, and the raw count of societies gave no way to tell the two apart.

The anthropologists who inherited this difficulty gave it Galton’s name and spent most of the twentieth century trying to patch it from outside the data rather than from within it. Raoul Naroll’s 1961 paper proposed sorting cases into those connected by a known route of diffusion, trade or conquest and those that were not, and then testing whether the correlation held up separately within each group (Naroll 1961). George Murdock and Douglas White built the Standard Cross-Cultural Sample in 1969 by deliberately choosing cultures spaced apart within sampling provinces, so that neighbouring cases would not simply be copies of each other, and wrote historical controls for non-independence directly into the sample’s design before a single correlation was ever run on it (Murdock & White 1969). Both are real fixes, still in use today through archives such as D-PLACE, and both work by managing the sample rather than modelling the history that produced it: you choose your cases carefully in advance, or you sort them into groups after the fact, because you do not have, and are not expected to have, a family tree of cultures to compute with directly.

Ninety-six years after Galton’s objection, a population geneticist working on an entirely different problem wrote down the tree. Joseph Felsenstein’s 1985 paper showed that comparing traits across species faces exactly Galton’s difficulty: if ten species all inherited long legs from one ancestor, that is one evolutionary event dressed up as ten confirmations that long legs and some other trait travel together (Felsenstein 1985). His fix, phylogenetically independent contrasts, does not sort cases into buckets or resample them. It takes a phylogeny with branch lengths, assumes a model of how a trait drifts along those branches over time, and computes, from the shape of the tree itself, which comparisons across the tips are actually independent and by how much weight each one deserves. Where Naroll and Murdock manage the sampling problem from outside, Felsenstein dissolves it from inside, because a sufficiently resolved tree tells you exactly how much of an apparent correlation to discount before you ever look at the trait values.

The two fields had been describing one statistical structure for ninety-six years without citing one another, which is a pointed fact about the shape of disciplinary boundaries but not yet an argument. The interesting question is why anthropology did not simply adopt Felsenstein’s answer once it existed, and the honest reason is not neglect. Ruth Mace and Mark Pagel’s 1994 paper did import the comparative method into anthropology directly, applying tree-based contrasts to questions of cultural co-evolution and naming Galton’s problem as the target the method was built to hit (Mace & Pagel 1994). Three decades on, this remains closer to the exception than the default tool in cross-cultural research, and the reason is the one thing the method needs and simply assumes it will be given: the tree.

Felsenstein’s contrasts are only ever as good as the phylogeny feeding them. A biological phylogeny, built from DNA sequence divergence under a reasonably well-behaved mutation process, is routinely resolved enough to support the method’s assumptions, because a gene mostly only descends. A tree of cultures is a far less cooperative object, because culture does not only descend, it also borrows sideways between neighbours who share no ancestor at all, and borrowing was precisely the phenomenon Galton rose to name in 1889. Where language itself is the trait under study, the tree can sometimes be built well enough to use: Russell Gray and Quentin Atkinson’s 2003 Bayesian phylogeny of eighty-seven Indo-European languages, built from lexical cognate data, returned a divergence date supporting the Anatolian farming theory of Indo-European origins and held up under extensive checks for robustness to coding, calibration and rooting (Gray & Atkinson 2003), which shows that the tree-building machinery anthropology needs is not in principle beyond reach. That paper is itself a limiting case, though, because it concerns one well-documented family descended overwhelmingly through inheritance rather than assembled by borrowing between unrelated neighbours. Most of what the Standard Cross-Cultural Sample exists to study, marriage rules, political complexity, subsistence strategy, moves sideways between societies in contact far more freely than a word’s sound changes, the way two highland and lowland groups can converge on a shared descent rule through trade and intermarriage without either inheriting it from the other. A method that assumes a tree has nothing useful to say about an edge that was in truth a loan and was fed into the model as an inheritance.

So the claim that the two fields solved the same problem understates what still divides them. They had the same problem, and biology got the better instrument first because its traits travel down one structure, descent, while anthropology’s traits travel down two, descent and borrowing, and only the first of those is reliably tree-shaped. Naroll and Murdock were not working around a problem that anthropology had simply failed to see through to Felsenstein’s solution; they were working around a problem that genuinely resists the solution biology happened to find, because the object biology’s fix requires, a tree whose branches carry all of the relevant history, is harder to obtain for culture than for species, and for culture in general does not exist as a single tree at all.

The strongest reply is that this makes the gap sound larger and more permanent than it is. Phylogenetic methods in historical linguistics and cultural evolution have grown considerably since 1994, and researchers working on well-bounded language families or on recent, richly documented lineages now build and use trees routinely, with explicit statistical models for detecting and down-weighting likely borrowings rather than simply assuming their absence. The objection is fair, and it narrows the claim rather than refuting it. Where the unit under study has one dominant line of descent and borrowing is the exception that a model can flag and discount, anthropology has substantially closed the gap with biology. Where it does not, where diffusion is not noise scattered around a tree but a force roughly as strong as inheritance itself, Galton’s 1889 objection still has no tree-shaped answer on offer, and the discipline is still doing by careful sampling and after-the-fact sorting what biology does by computing directly from a tree. The problem was never anthropology’s alone to have solved badly. It was anthropology’s bad luck to have drawn the harder version of it first, a century before biology drew the easier one and handed back a tool that only partly fits the case it came from.

References

Felsenstein, J. (1985). Phylogenies and the comparative method. The American Naturalist, 125(1), 1–15. https://doi.org/10.1086/284325

Gray, R. D., & Atkinson, Q. D. (2003). Language-tree divergence times support the Anatolian theory of Indo-European origin. Nature, 426(6965), 435–439. https://doi.org/10.1038/nature02029

Mace, R., & Pagel, M. (1994). The comparative method in anthropology. Current Anthropology, 35(5), 549–564. https://doi.org/10.1086/204317

Murdock, G. P., & White, D. R. (1969). Standard cross-cultural sample. Ethnology, 8(4), 329–369. https://doi.org/10.2307/3772907

Naroll, R. (1961). Two solutions to Galton’s problem. Philosophy of Science, 28(1), 15–39. https://www.cambridge.org/core/journals/philosophy-of-science/article/two-solutions-to-galtons-problem/19369CED66002106B4DF0F4B823C19AD

Tylor, E. B. (1889). On a method of investigating the development of institutions; applied to laws of marriage and descent. Journal of the Anthropological Institute of Great Britain and Ireland, 18, 245–272. https://doi.org/10.2307/2842423