The birthday problem: repeated sampling of animal populations and ethics of experimental design

Researchers who use animals in science must balance statistical power with the need to satisfy the three Rs, whereby researchers are required to reduce numbers of animals, refine what they experience, and use alternatives to (replace) higher animals where possible. In repeated sampling over time-series studies, there is potential loss of power as well as ethics implications posed by repeated sampling of individual animals, where this cannot be managed or avoided. Here, we consider the mathematics of repeated sampling from three perspectives: that of the population at large, from the experience of the individual, and the conditional probability of sampled individuals being sampled again. The calculations are illustrated using four theoretical case studies across veterinary epidemiology with different practical implications and a provided R Shiny tool for researchers. Despite the availability of exact calculations, it is necessary to also consider the biological factors which may affect capture and recapture rates in sampling studies such as animal personality and response to capture. Researchers must also choose their question carefully to avoid inappropriate framing of ethical concerns around repeated sampling.