Benford’s Law for Telemetry Data of Wildlife

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.

Correspondence of Newcomb-Benford Number Law with Ecological Processes

“…Data presented here support a hypothesis that ecological systems progressing toward a threshold of stable dynamic equilibrium can be well represented by constancy in the sequence of first significant digits predicted by the Newcomb-Benford number law (Figure 1). The results concur with similar observations for multiple physical and social systems (Table 2), mathematical constants of nature [56], and anecdotal biotic observations [26–29,48–50].…”

“…The number/ha of Red-Listed indicator species from 2707 conservation forest plots in Sweden visually conformed with the Benford distribution [49]. Pröger et al [50] applied a Benford FSD analysis to telemetry data for wild red deer freely moving in natural habitats. Ninety one percent of 1132 weekly sets of data conformed with NBL predictions.…”

“…29,[48][49][50].A Benford FSD analysis of random measurement data presents a variety of theoretical and empirical lines of inquiry for future ecological research:(1) demonstration of sample size effects on NBL predictions in the range N>80<500 at 13 multiple levels of organization and spatial scale, (2) expansion of the list of measurement variables, (3) identification of alternative statistical methods for early identification of regime shifts, (4) experiments investigating data collection constraints associated with human perturbation of environmental conditions,(5) …”

Newcomb-Benford Law characterization of solar wind magnetic field and geomagnetic indices

“…Benford [1938] demonstrated it in a wide range of domains including physical constants and physical and societal data. It has been found to apply in a broad range of observations of physical systems [Sambridge et al, 2010] and in the social [Mir, 2012;Pietronero et al,, 2001], and biological [Pröger et al, 2021] sciences. In particular, it has been proposed…”