A statistical estimator for determining the limits of contemporary and historic phenology

  • Nature Ecology & Evolutionvolume 1pages18761882 (2017)
  • doi:10.1038/s41559-017-0350-0
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Climate change affects not just where species are found, but also when species’ key life-history events occur—their phenology. Measuring such changes in timing is often hampered by a reliance on biased survey data: surveys identify that an event has taken place (for example, the flower is in bloom), but not when that event happened (for example, the flower bloomed yesterday). Here, we show that this problem can be circumvented using statistical estimators, which can provide accurate and unbiased estimates from sparsely sampled observations. We demonstrate that such methods can resolve an ongoing debate about the relative timings of the onset and cessation of flowering, and allow us to place modern observations reliably within the context of the vast wealth of historical data that reside in herbaria, museum collections, and written records. We also analyse large-scale citizen science data from the United States National Phenology Network and reveal not just earlier but also potentially more variable flowering in recent years. Evidence for greater variability through time is important because increases in variation are characteristic of systems approaching a state change.

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We thank the volunteers of the NPN for data collection. W.D.P. and T.J.D. were funded by Fonds de Recherche Nature et Technologies grant number 168004. The Colorado data collection was supported by National Science Foundation grants DEB 75-15422, DEB 78-07784, BSR 81-08387, DEB 94-08382, IBN 98-14509, DEB 02-38331 and DEB 09-22080 to D.W.I. We are grateful to D. Roberts and A. Solow for helping to calculate the s.e. of estimates of timing, and E. L. Wolkovich and B. G. Waring for comments on the paper. We also thank the photographers whose images we used in Fig. 3.

Author information


  1. Department of Biology, McGill University, Montréal, Québec, H3A 1B1, Canada

    • William D. Pearse
    •  & T. Jonathan Davies
  2. Department of Biological Sciences, Université du Québec à Montréal, Montréal, Québec, H2X 1Y4, Canada

    • William D. Pearse
  3. Department of Biology and Ecology Center, Utah State University, 5305 Old Main Hill, Logan, UT, 84322, USA

    • William D. Pearse
  4. Department of Organismic and Evolutionary Biology and Harvard University Herbaria, Harvard University, 22 Divinity Avenue, Cambridge, MA, 02138, USA

    • Charles C. Davis
  5. Department of Biology, University of Maryland, College Park, MD, 20742, USA

    • David W. Inouye
  6. Rocky Mountain Biological Laboratory, PO Box 519, Crested Butte, CO, 81224, USA

    • David W. Inouye
  7. Biology Department, Boston University, 5 Cummington Street, Boston, MA, 02215, USA

    • Richard B. Primack


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W.D.P., T.J.D. and C.C.D. conceived of the study. W.D.P. analysed the data. All authors wrote the manuscript and interpreted the results.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to William D. Pearse or T. Jonathan Davies.

Supplementary information

  1. Supplementary Information

    Supplementary Figures 1–4, Supplementary Tables 1–8, Supplementary Reference

  2. Life Sciences Reporting Summary

  3. R code

    R code to calculate limits. This file was missing when the Article was first published.