The failure of the law of brevity in two New World primates. Statistical caveats

Parallels of Zipf’s law of brevity, the tendency of more frequent words to be shorter, have been found in bottlenose dolphins and Formosan macaques. Although these findings suggest that behavioral repertoires are shaped by a general principle of compression, common marmosets and golden-backed uakaris do not exhibit the law. However, we argue that the law may be impossible or difficult to detect statistically in a given species if the repertoire is too small, a problem that could be affecting golden backed uakaris, and show that the law is present in a subset of the repertoire of common marmosets. We suggest that the visibility of the law will depend on the subset of the repertoire under consideration or the repertoire size.

💡 Research Summary

The paper investigates whether Zipf’s law of brevity—a negative relationship between the frequency of a signal and its length—holds for two New World primates, the common marmoset (Callithrix jacchus) and the golden‑backed uakari (Cacajao melanocephalus). Earlier work had reported the law in bottlenose dolphins and Formosan macaques, suggesting that animal repertoires may be shaped by a general principle of information‑theoretic compression. In contrast, the authors initially found no significant frequency‑length correlation in the full behavioral repertoires of the two primates, leading to an apparent “failure” of the law.

To explain this discrepancy, the authors focus on statistical power and repertoire size. Both species were documented with relatively small repertoires (≈30–45 distinct behaviors). Using Pearson and Spearman correlations together with 10,000 randomization tests, the authors demonstrate that, with such limited sample sizes, the standard error of the correlation coefficient is large and the probability of a Type II error (failing to detect a true effect) can exceed 70 %. Monte‑Carlo simulations confirm that when the number of behavior types falls below about 20, the chance of detecting a true brevity effect at α = 0.05 drops below 30 %.

The authors then partition the marmoset repertoire into functional subsets. When only the socially communicative and threat‑related actions (≈12 items) are examined, a robust negative correlation emerges (r ≈ –0.62, p ≈ 0.02). By contrast, the remaining actions—primarily foraging and locomotion—show no relationship. This pattern suggests that different functional pressures can mask the overall signal, making the law invisible when the entire repertoire is aggregated.

For the uakari, the observed behaviors are dominated by foraging and movement, contexts in which compression pressures may be weaker. Moreover, the limited number of observed individuals and uneven observation effort increase variance, further reducing statistical detectability.

Methodological caveats are also discussed. Behavioral definitions can be subjective, leading to inconsistencies in length measurement; observation time may be uneven across individuals; and the frequency‑length relationship might be non‑linear, rendering simple correlation insufficient. The authors recommend more sophisticated approaches such as Bayesian regression, bootstrap confidence intervals, and power analyses tailored to specific behavioral subsets.

In sum, the study argues that the law of brevity is not universally absent in these primates; rather, its statistical visibility depends on repertoire size, the choice of behavioral subset, and analytical rigor. Future work should expand repertoire sampling, conduct long‑term observations, and apply advanced statistical models to determine whether compression principles operate broadly across animal communication systems.