A New Approach to Modelling the Relationship Between Annual Population Abundance Indices and Weather Data

  • D. A. Elston
  • M. J. Brewer
  • B. Martay
  • A. Johnston
  • P. A. Henrys
  • J. R. Bell
  • R. Harrington
  • D. Monteith
  • T. M. Brereton
  • K. L. Boughey
  • J. W. Pearce-Higgins
Article

Abstract

Weather has often been associated with fluctuations in population sizes of species; however, it can be difficult to estimate the effects satisfactorily because population size is naturally measured by annual abundance indices whilst weather varies on much shorter timescales. We describe a novel method for estimating the effects of a temporal sequence of a weather variable (such as mean temperatures from successive months) on annual species abundance indices. The model we use has a separate regression coefficient for each covariate in the temporal sequence, and over-fitting is avoided by constraining the regression coefficients to lie on a curve defined by a small number of parameters. The constrained curve is the product of a periodic function, reflecting assumptions that associations with weather will vary smoothly throughout the year and tend to be repetitive across years, and an exponentially decaying term, reflecting an assumption that the weather from the most recent year will tend to have the greatest effect on the current population and that the effect of weather in previous years tends to diminish as the time lag increases. We have used this approach to model 501 species abundance indices from Great Britain and present detailed results for two contrasting species alongside an overall impression of the results across all species. We believe this approach provides an important advance to the challenge of robustly modelling relationships between weather and species population size.

Supplementary materials accompanying this paper appear online.

Keywords

Abundance index Climate change impacts Distributed lag models Population abundance models Population change Weather variables 

Supplementary material

13253_2017_287_MOESM1_ESM.docx (32 kb)
Supplementary material 1 (docx 31 KB)
13253_2017_287_MOESM2_ESM.docx (21 kb)
Supplementary material 2 (docx 20 KB)
13253_2017_287_MOESM3_ESM.txt (112 kb)
Supplementary material 3 (txt 112 KB)
13253_2017_287_MOESM4_ESM.rsave (182 kb)
Supplementary material 4 (Rsave 181 KB)
13253_2017_287_MOESM5_ESM.rsave (52 kb)
Supplementary material 5 (Rsave 52 KB)

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Copyright information

© International Biometric Society 2017

Authors and Affiliations

  • D. A. Elston
    • 1
  • M. J. Brewer
    • 1
  • B. Martay
    • 2
  • A. Johnston
    • 2
  • P. A. Henrys
    • 3
  • J. R. Bell
    • 4
  • R. Harrington
    • 4
  • D. Monteith
    • 3
  • T. M. Brereton
    • 5
  • K. L. Boughey
    • 6
  • J. W. Pearce-Higgins
    • 2
  1. 1.Biomathematics and Statistics ScotlandAberdeenUK
  2. 2.British Trust for OrnithologyThetfordUK
  3. 3.Centre for Ecology and HydrologyLancasterUK
  4. 4.Rothamsted ResearchHarpendenUK
  5. 5.Butterfly ConservationWarehamUK
  6. 6.Bat Conservation TrustLondonUK

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