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Dynamics of North American breeding bird populations

Author

Listed:
  • Timothy H. Keitt

    (Santa Fe Institute
    National Center for Ecological Analysis and Synthesis, University of California Santa Barbara)

  • H. Eugene Stanley

    (Boston University)

Abstract

Population biologists have long been interested in the variability of natural populations1,2,3,4,5,6. One approach to dealing with ecological complexity is to reduce the system to one or a few species, for which meaningful equations can be solved. Here we explore an alternative approach7,8 by studying the statistical properties of a data set containing over 600 species, namely the North American breeding bird survey9. The survey has recorded annual species abundances over a 31-year period along more than 3,000 observation routes10. We now analyse the dynamics of population variability using this data set, and find scaling features in common with inanimate systems composed of strongly interacting subunits11. Specifically, we find that the distribution of changes in population abundance over a one-year interval is remarkably symmetrical, with long tails extending over six orders of magnitude. The variance of the population over a time series increases as a power-law with increasing time lag, indicating long-range correlation in population size fluctuations12. We also find that the distribution of species lifetimes (the time between colonization and local extinction) within local patches is a power-law with an exponential cutoff imposed by the finite length of the time series. Our results provide a quantitative basis for modelling the dynamics of large species assemblages.

Suggested Citation

  • Timothy H. Keitt & H. Eugene Stanley, 1998. "Dynamics of North American breeding bird populations," Nature, Nature, vol. 393(6682), pages 257-260, May.
    • Handle: RePEc:nat:nature:v:393:y:1998:i:6682:d:10.1038_30478
    DOI: 10.1038/30478
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    Citations

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    Cited by:

    1. Stanley, H.E. & Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki, 2007. "Economic fluctuations and statistical physics: Quantifying extremely rare and less rare events in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 286-301.
    2. R. Ferriere & B. Cazelles, 1998. "Universal Power Laws Govern Intermittent Rarity in Communities of Interacting Species," Working Papers ir98095, International Institute for Applied Systems Analysis.
    3. Misako Takayasu & Hayafumi Watanabe & Hideki Takayasu, 2013. "Generalised central limit theorems for growth rate distribution of complex systems," Papers 1301.2728, arXiv.org, revised Jan 2014.
    4. Stanley, H.Eugene, 2000. "Exotic statistical physics: Applications to biology, medicine, and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(1), pages 1-17.
    5. Stanley, H.Eugene, 2003. "Statistical physics and economic fluctuations: do outliers exist?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(1), pages 279-292.
    6. Stanley, H.E & Amaral, L.A.N & Gopikrishnan, P & Ivanov, P.Ch & Keitt, T.H & Plerou, V, 2000. "Scale invariance and universality: organizing principles in complex systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 60-68.
    7. Watanabe, Hayafumi & Takayasu, Hideki & Takayasu, Misako, 2013. "Relations between allometric scalings and fluctuations in complex systems: The case of Japanese firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 741-756.
    8. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
    9. de Oliveira Santos, Maíra & Stosic, Tatijana & Stosic, Borko D., 2012. "Long-term correlations in hourly wind speed records in Pernambuco, Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1546-1552.
    10. Stanley, H.E & Amaral, L.A.N & Gopikrishnan, P & Plerou, V, 2000. "Scale invariance and universality of economic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(1), pages 31-41.
    11. Krysiak, Frank C. & Krysiak, Daniela, 2002. "Aggregation of Dynamic Systems and the Existence of a Regeneration Function," Journal of Environmental Economics and Management, Elsevier, vol. 44(3), pages 517-539, November.
    12. Stanley, H.E. & Gopikrishnan, P. & Plerou, V. & Amaral, L.A.N., 2000. "Quantifying fluctuations in economic systems by adapting methods of statistical physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 339-361.
    13. Samuel R Bray & Bo Wang, 2020. "Forecasting unprecedented ecological fluctuations," PLOS Computational Biology, Public Library of Science, vol. 16(6), pages 1-17, June.
    14. Xie, Wen-Jie & Gu, Gao-Feng & Zhou, Wei-Xing, 2010. "On the growth of primary industry and population of China’s counties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3876-3882.
    15. Stanley, H.E. & Amaral, L.A.N. & Gabaix, X. & Gopikrishnan, P. & Plerou, V., 2001. "Similarities and differences between physics and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 1-15.
    16. Rudy Calif & François G. Schmitt, 2015. "Taylor Law in Wind Energy Data," Resources, MDPI, vol. 4(4), pages 1-9, October.
    17. Behzod B. Ahundjanov & Sherzod B. Akhundjanov & Botir B. Okhunjanov, 2022. "Power law in COVID‐19 cases in China," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(2), pages 699-719, April.

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