Abstract
The accumulated copying error model (ACE) combines findings on the proportional nature of human visual perception error with cultural transmission theory. Previous studies have employed ACE to provide population-level expectations of the coefficient of variation (CV) of a continuous trait, such as the thickness of ceramic vessels. To date, empirical departures from expected CV values have been interpreted as evidence of biased cultural transmission or functional constraints without consideration for how population size might affect population-level cultural variation in the presence of proportional perception error. Here, I employ agent-based simulation experiments to investigate the ways in which population size affects the CV of a continuous cultural trait under different cultural transmission mechanisms. Results show that the CV of a continuous cultural trait is a function of its cultural equivalent N and effective population size (Ne) as well as the relative strength of cultural selection. The results also demonstrate that different combinations of N and cultural transmission yield identical CV values. The study highlights a new set of difficulties with inferring individual-level process—the mechanism(s) by which cultural information is transmitted among individuals—from population-level pattern—the CV of a continuous cultural trait. In light of these results, I identify and discuss one avenue through which we might improve our ability to infer past cultural transmission from archeological data.
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The source code and data associated with this research are available at https://www.comses.net/codebases/a6fa3560-3447-4e7c-9ba5-d6cabb802378/releases/1.0.0/.
Notes
To avoid confusion, note that Eerkens and Lipo (2005, p. 321) repeatedly use the term “unbiased transmission” to refer to what is actually vertical cultural transmission. Unbiased cultural transmission (or “random copying”) is different from vertical transmission in important ways. For example, the effective population size (Ne) of a trait passed via unbiased cultural transmission is approximately N, while the effective population size of a trait passed via vertical transmission (e.g., where each “parent” teaches just one “offspring”) is infinitely large. Perhaps this precedent explains why Hamilton and Buchanan (2009, p. 57) also use the terms “unbiased vertical transmission” and “unbiased transmission” interchangeably to refer to the condition where “technological knowledge is transmitted strictly from parent to offspring,” which is vertical cultural transmission, not unbiased transmission.
Although none of the equations presented in the studies reviewed above includes a term for census size or cultural equivalent N, Cavalli-Sforza and Feldman (1981, pp. 314–317) briefly consider two ways in which the variance of a continuous trait could be limited within a finite population. However, unlike the models reviewed above, their formal model (Eq. 5; Cavalli-Sforza and Feldman 1981, p. 314) does not include proportional copying error. Their model assumes the error introduced during each transmission event is independent of the target value. Because their formal model does not include proportional copying error, their findings concerning the variance of a continuous trait in a finite population apply to an additive (not a multiplicative) stochastic process.
The right panel of Fig. 5 presents results for median conformist biased transmission only, not mean conformist transmission. Because no member of the experienced generation displays the average attribute value, Vk (and thus Ne) cannot be calculated under mean conformist biased transmission. In Figs. 6 and 7, I use the Ne values obtained under median conformist biased transmission as an approximation of what they would be under mean conformist transmission. This is a serviceable but imperfect substitute. Because there is a touch of vertical transmission embedded in median conformist biased transmission that is not present in mean conformist biased transmission (one member of the experienced generation displays the median value but no member of the experienced generation displays the mean value), the Ne values obtained from the former overestimate the Ne of the latter, especially when p is low. This difference is made apparent by the separation (along the x-axis) between the two conformist biased transmission mechanisms in Figs. 6 and 7.
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Acknowledgments
Dr. Anne Kandler was kind enough to spend time discussing this project with me, and her suggestions were extremely helpful. I thank Prof. Jean-Jacques Hublin for supporting my sabbatical stay at the Max Planck Institute for Evolutionary Anthropology, where this work was conducted. I thank three anonymous reviewers for their helpful critiques.
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Premo, L.S. Population Size Limits the Coefficient of Variation in Continuous Traits Affected by Proportional Copying Error (and Why This Matters for Studying Cultural Transmission). J Archaeol Method Theory 28, 512–534 (2021). https://doi.org/10.1007/s10816-020-09464-9
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DOI: https://doi.org/10.1007/s10816-020-09464-9