Statistical signals of copying are robust to time- and space-averaging.

Cattle brands (ownership marks left on animals) are subject to forces influencing other graphic codes: the copying of constituent parts, pressure for distinctiveness and pressure for complexity. The historical record of cattle brands in some US states is complete owing to legal registration, providing a unique opportunity to assess how sampling processes leading to time- and space-averaging influence our ability to make inferences from limited datasets in fields like archaeology. In this preregistered study, we used a dataset of ~81,000 Kansas cattle brands (1990-2016) to explore two aspects: (1) the relative influence of copying, pressure for distinctiveness and pressure for complexity on the creation and diffusion of brand components; and (2) the effects of time- and space-averaging on statistical signals. By conducting generative inference with an agent-based model, we found that the patterns in our data are consistent with copying and pressure for intermediate complexity. In addition, by comparing mixed and structured datasets, we found that these statistical signals of copying are robust to, and possibly boosted by, time- and space-averaging.