First Digit Distribution in Some Biological Data Sets. Possible Explanations for Departures from Benford's Law

Aim: To explore whether the first digit law (FDL) is abided by data sets from biological origin. Materials and Methods: Data were collected from different sources, including gene data length for bacteria, pre-vaccination measles incidence data and absolute values from human MEG recordings. First digit frequencies were computed and compared to predictions from FDL. Simulations included a simple model for two-dimensional epidemics spread and a randomly set upper bound model aimed to explain the behaviour of MEG data. Results: We observed that FDL is obeyed in a case of epidemic data reported at a putative focus of spread (pre-vaccination measles incidence for Preston, England). However, peculiar departures were observed for gene length distribution in microorganisms, magneto-encephalograms (MEG), and epidemic data pooled from large geographical regions. Conclusions: Simulation studies revealed that averaging data on a scenario of propagating waves can explain some of the observed distortions from FDL. This could help to understand the behaviour of epidemics data. A randomly set upper bound model (RUBM) can likely explain the observed behaviour of MEG data. Explanation for gene length data behaviour requires further theoretical work.