IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v4y2021i4p55-949d683761.html
   My bibliography  Save this article

Benford’s Law for Telemetry Data of Wildlife

Author

Listed:
  • Lasse Pröger

    (Department of Integrative Biology and Biodiversity Research, Institute of Wildlife Biology and Game Management, University of Natural Resources and Life Sciences, Vienna (BOKU), 1180 Vienna, Austria)

  • Paul Griesberger

    (Department of Integrative Biology and Biodiversity Research, Institute of Wildlife Biology and Game Management, University of Natural Resources and Life Sciences, Vienna (BOKU), 1180 Vienna, Austria)

  • Klaus Hackländer

    (Department of Integrative Biology and Biodiversity Research, Institute of Wildlife Biology and Game Management, University of Natural Resources and Life Sciences, Vienna (BOKU), 1180 Vienna, Austria)

  • Norbert Brunner

    (Department of Integrative Biology and Biodiversity Research, Institute of Mathematics, University of Natural Resources and Life Sciences, Vienna (BOKU), 1180 Vienna, Austria)

  • Manfred Kühleitner

    (Department of Integrative Biology and Biodiversity Research, Institute of Mathematics, University of Natural Resources and Life Sciences, Vienna (BOKU), 1180 Vienna, Austria)

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.

Suggested Citation

  • Lasse Pröger & Paul Griesberger & Klaus Hackländer & Norbert Brunner & Manfred Kühleitner, 2021. "Benford’s Law for Telemetry Data of Wildlife," Stats, MDPI, vol. 4(4), pages 1-7, November.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:4:p:55-949:d:683761
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/4/4/55/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/4/4/55/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Pietronero, L. & Tosatti, E. & Tosatti, V. & Vespignani, A., 2001. "Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 297-304.
    2. Roy Cerqueti & Claudio Lupi, 2021. "Some New Tests of Conformity with Benford’s Law," Stats, MDPI, vol. 4(3), pages 1-17, September.
    3. Juan Miguel Campanario & María Angeles Coslado, 2011. "Benford’s law and citations, articles and impact factors of scientific journals," Scientometrics, Springer;Akadémiai Kiadó, vol. 88(2), pages 421-432, August.
    4. G. M. Viswanathan & Sergey V. Buldyrev & Shlomo Havlin & M. G. E. da Luz & E. P. Raposo & H. Eugene Stanley, 1999. "Optimizing the success of random searches," Nature, Nature, vol. 401(6756), pages 911-914, October.
    5. Engel, Hans-Andreas & Leuenberger, Christoph, 2003. "Benford's law for exponential random variables," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 361-365, July.
    6. Beber, Bernd & Scacco, Alexandra, 2012. "What the Numbers Say: A Digit-Based Test for Election Fraud," Political Analysis, Cambridge University Press, vol. 20(2), pages 211-234, April.
    7. Druică, Elena & Oancea, Bogdan & Vâlsan, Călin, 2018. "Benford's law and the limits of digit analysis," International Journal of Accounting Information Systems, Elsevier, vol. 31(C), pages 75-82.
    8. Malcolm Sambridge & Andrew Jackson, 2020. "National COVID numbers — Benford’s law looks for errors," Nature, Nature, vol. 581(7809), pages 384-384, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Roy Cerqueti & Claudio Lupi, 2023. "Severe testing of Benford’s law," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 677-694, June.
    2. Bormashenko, Ed. & Shulzinger, E. & Whyman, G. & Bormashenko, Ye., 2016. "Benford’s law, its applicability and breakdown in the IR spectra of polymers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 524-529.
    3. Whyman, G. & Ohtori, N. & Shulzinger, E. & Bormashenko, Ed., 2016. "Revisiting the Benford law: When the Benford-like distribution of leading digits in sets of numerical data is expectable?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 595-601.
    4. Hsiang-chi Tseng & Wei-neng Huang & Ding-wei Huang, 2017. "Modified Benford’s law for two-exponent distributions," Scientometrics, Springer;Akadémiai Kiadó, vol. 110(3), pages 1403-1413, March.
    5. Alexandre Donizeti Alves & Horacio Hideki Yanasse & Nei Yoshihiro Soma, 2014. "Benford’s Law and articles of scientific journals: comparison of JCR® and Scopus data," Scientometrics, Springer;Akadémiai Kiadó, vol. 98(1), pages 173-184, January.
    6. Ferreira, A.S. & Raposo, E.P. & Viswanathan, G.M. & da Luz, M.G.E., 2012. "The influence of the environment on Lévy random search efficiency: Fractality and memory effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3234-3246.
    7. Priscila C A da Silva & Tiago V Rosembach & Anésia A Santos & Márcio S Rocha & Marcelo L Martins, 2014. "Normal and Tumoral Melanocytes Exhibit q-Gaussian Random Search Patterns," PLOS ONE, Public Library of Science, vol. 9(9), pages 1-13, September.
    8. Shao, Zhi-Gang & Jian-Ping Sang, & Zou, Xian-Wu & Tan, Zhi-Jie & Jin, Zhun-Zhi, 2005. "Blackmail propagation on small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 662-670.
    9. Villas-Boas, Sofia B. & Fu, Qiuzi & Judge, George, 2017. "Benford’s law and the FSD distribution of economic behavioral micro data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 711-719.
    10. Christopher Blattman & Horacio Larreguy & Benjamin Marx & Otis Reid, 2019. "Eat Widely, Vote Wisely ? Lessons from a Campaign Against Vote Buying in Uganda," SciencePo Working papers Main hal-03608420, HAL.
    11. Ma, Brian O. & Davis, Brad H. & Gillespie, David R. & VanLaerhoven, Sherah L., 2009. "Incorporating behaviour into simple models of dispersal using the biological control agent Dicyphus hesperus," Ecological Modelling, Elsevier, vol. 220(23), pages 3271-3279.
    12. George Judge & Laura Schechter, 2009. "Detecting Problems in Survey Data Using Benford’s Law," Journal of Human Resources, University of Wisconsin Press, vol. 44(1).
    13. Eric Zitzewitz, 2012. "Forensic Economics," Journal of Economic Literature, American Economic Association, vol. 50(3), pages 731-769, September.
    14. Marina E Wosniack & Marcos C Santos & Ernesto P Raposo & Gandhi M Viswanathan & Marcos G E da Luz, 2017. "The evolutionary origins of Lévy walk foraging," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-31, October.
    15. Poulsen, Jonas, 2013. "After Apartheid: The Effects of ANC Power," Working Paper Series, Center for Fiscal Studies 2013:10, Uppsala University, Department of Economics.
    16. Costa-Font, Joan & Vilaplana-Prieto, Cristina, 2023. "Health System Trust and Compliance with COVID-19 Restrictions," IZA Discussion Papers 15961, Institute of Labor Economics (IZA).
    17. Yang Qi & Pulin Gong, 2022. "Fractional neural sampling as a theory of spatiotemporal probabilistic computations in neural circuits," Nature Communications, Nature, vol. 13(1), pages 1-19, December.
    18. Cody T Ross & Bruce Winterhalder, 2018. "Evidence for encounter-conditional, area-restricted search in a preliminary study of Colombian blowgun hunters," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-13, December.
    19. Hürlimann, Werner, 2015. "On the uniform random upper bound family of first significant digit distributions," Journal of Informetrics, Elsevier, vol. 9(2), pages 349-358.
    20. Pascual López-López & José Benavent-Corai & Clara García-Ripollés & Vicente Urios, 2013. "Scavengers on the Move: Behavioural Changes in Foraging Search Patterns during the Annual Cycle," PLOS ONE, Public Library of Science, vol. 8(1), pages 1-9, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jstats:v:4:y:2021:i:4:p:55-949:d:683761. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.