What is it about?
While nature may seem chaotic, hidden patterns emerge across biological and physical systems, revealing an underlying mathematical order. This research examines how the Newcomb-Benford number law, a simple mathematical principle predicting the frequency of leading digits (1 to 9) in datasets, can be used to monitor ecological processes associated with system attributes of stability and complexity. By analyzing real-world measurements against Benford’s expected patterns, the research explores whether ecological processes follow hidden statistical trends with real-world applications. Multiple analytical methods, including multidimensional Euclidean distance, Kossovsky sum of square deviations (SSD), Cohen-W effect size, Pearson residuals, and Kullback-Leibler relative entropy, were utilized to enhance understanding of natural variation within datasets spanning multiples levels of scale and organization.
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Why is it important?
Ecological systems are dynamic, influenced by both randomness and natural selection. Yet detecting early warning signals of instability has long been a challenge. Research findings suggest that deviations from the Benford’s law pattern of expected first digit probabilities can help quantify anomalies and disruptions of ecological processes related to relative entropy, a measure of disorder, from an expected probability distribution. The measurement of Kullback-Leibler relative entropy, a metric derived from information theory, allows researchers to track temporal and spatial variations of ecological information in response to constantly changing environmental conditions. Beyond ecology, the findings of the research hold relevance across multiple disciplines. The real-time Benford Online Bibliography showcases 2200+ applications from the physical and social sciences, including financial fraud detection: [https://www.benfordonline.net; date accessed 09/24/2024].
Perspectives
Ecological systems are shaped by both randomness and natural selection, yet identifying universal patterns across different scales has remained a challenge. By applying the Newcomb-Benford number law, researchers can uncover hidden self-organizing statistical patterns and anomalies in naturally occurring systems to help quantify their stability and complexity. The proposed analytical methods I suggest invite researchers to reexamine empirical datasets with fresh eyes to address the question of how best to simplify and extract information from the complex adapted systems of nature. It is the author’s hope that this research will trigger future research to better understand the correspondence of the Newcomb-Benford number law with ecological processes. Caption to attached Fig. 6 from the paper: Fig 6. Canonical representation of the Benford probability distribution for naturally occurring multi-scale ecological systems with minimal anthropogenic disturbance in states of balanced dynamic equilibrium (case comparisons left to right: 1A, 1B, 3A, 4; Table 7). https://doi.org/10.1371/journal.pone.0310205.g006 For questions and/or comments, contact the author at: r_davic@yahoo.com
Robert Davic
State of Ohio Environmental Protection Agency, Retired
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This page is a summary of: Newcomb-Benford number law and ecological processes, PLOS One, March 2025, PLOS,
DOI: 10.1371/journal.pone.0310205.
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