Abstract
Benford’s law (BL) specifies the expected digit distributions of data in social sciences, such as demographic or financial data. We focused on the first-digit distribution and hypothesized that it would apply to data on locations of animals freely moving in a natural habitat. We believe that animal movement in natural habitats may differ with respect to BL from movement in more restricted areas (e.g., game preserve). To verify the BL-hypothesis for natural habitats, during 2015–2018, we collected telemetry data of twenty individuals of wild red deer from an alpine region of Austria. For each animal, we recorded the distances between successive position records. Collecting these data for each animal in weekly logbooks resulted in 1132 samples of size 65 on average. The weekly logbook data displayed a BL-like distribution of the leading digits. However, the data did not follow BL perfectly; for 9% (99) of the 1132 weekly logbooks, the chi-square test refuted the BL-hypothesis. A Monte Carlo simulation confirmed that this deviation from BL could not be explained by spurious tests, where a deviation from BL occurred by chance.
Highlights
Benford’s law (BL) proposes that the first nonzero digits of certain data are distributed according to (1)
A Monte Carlo simulation confirmed that this deviation from BL could not be explained by spurious tests, where a deviation from BL occurred by chance
When the data of each animal were considered separately, for 13 of the 20 individuals, the chi-square test refuted the null hypothesis that the data fit BL
Summary
Benford’s law (BL) proposes that the first nonzero digits of certain data (in decimal notation) are distributed according to (1). 9, the probability Prob(d) that d is observed as the first nonzero digit is (log is decadic logarithm): Received: 4 October 2021. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The probabilities decrease from 30% for d = 1 to 5% for d = 9.
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