A New Approach to Modelling the Relationship Between Annual Population Abundance Indices and Weather Data
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.
KeywordsAbundance index Climate change impacts Distributed lag models Population abundance models Population change Weather variables
This work was undertaken for a project funded jointly by Defra, Natural Resources Wales (NRW), Natural England (NE), Scottish Natural Heritage (SNH) and the Joint Nature Conservation Committee (JNCC). Subsequent methodological development was funded by the Scottish Government Rural and Environment Science and Analytical Services Division. We thank members of the project Steering Group, colleagues (particularly Nick Isaac, CEH) two external reviewers and the Associate Editor for constructive comments. We are grateful to all volunteers and organisations contributing to the data sets used in this work, namely: the National Bat Monitoring Programme (Bat Conservation Trust, in partnership with JNCC and supported and steered by NE, NRW, Northern Ireland Environment Agency and SNH); the former CBC and current BBS (a partnership between the BTO, JNCC (on behalf of NRW, NE, Council for Nature Conservation and Countryside and SNH) and Royal Society for Protection of Birds); and the UK Butterfly Monitoring Scheme operated by CEH, Butterfly Conservation and funded by a consortium of government agencies.
- Greenwood, J.D. & Baillie, S.R. (1991) Effects of density-dependence and weather on population changes of English passerines using a non-experimental paradigm. Ibis 133 S1:121-133Google Scholar
- Huntley, B., Green, R.E., Collingham, Y.C. & Willis, S.G. (2007) A climatic atlas of European breeding birds. Lynx Edicions, Barcelona.Google Scholar
- Johnston, A., Ausden, M., Dodd, A. M., Bradbury, R. B., Chamberlain, D. E., Jiguet, F., Thomas, C.D., Cook, A.S.C.P., Newson, S.E., Ockendon, N., Rehfisch, M.M., Roos, S., Thaxter, C.B., Brown, A., Crick, H.Q.P., Douse, A., McCall, R.A., Pontier, H., Stroud, D.A., Cadiou, B., Crowe, O., Deceuninck, B., Hornman, M. & Pearce-Higgins, J.W. (2013) Observed and predicted effects of climate change on species abundance in protected areas. Nature Climate Change 3:1055–1061CrossRefGoogle Scholar
- Long, O.M., Warren, R., Price, J., Brereton, T., Botham, M.S. & Franco, A.M.A. (2017) Sensitivity of UK butterflies to local climatic extremes: which life stages are most at risk? Journal of Animal Ecology 85:1636-1646Google Scholar
- Martay, B., Brewer, M. J., Elston, D. A., Bell, J. R., Harrington, R., Brereton, T. M., Barlow, K. E., Botham, M. S. & Pearce-Higgins, J. W. (2016). Impacts of climate change on national biodiversity population trends. Ecography. doi: 10.1111/ecog.02411.
- Morrison, C.A., Robinson, R.A. & Pearce-Higgins, J.W. (2016) Winter wren populations show adaptation to local climate. Open Science 3:160250Google Scholar
- Ockendon, N., Baker, D.J., Carr, J.A., Almond, R.E.A., Amano, T., Bertram, E., Bradbury, R.B., Bradley, C., Butchart, S.H.M., Doswald, N., Foden, W., Gill, D.J.C., Green, R.E.,Sutherland, W.J., Tanner, E.V.J. & Pearce-Higgins, J.W. (2014) Mechanisms underpinning climatic impacts on natural populations: altered species interactions are more important than direct effects. Global Change Biology 20:2221-2229CrossRefGoogle Scholar
- Pinheiro J., Bates D., DebRoy S., Sarkar D. & R Core Team (2014) nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1-118, URL: http://CRAN.R-project.org/package=nlme.
- R Core Team (2015) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, URL https://www.R-project.org/.
- Waring, P. & Townsend, M. (2009) Field Guide to the Moths of Great Britain and Ireland 2nd edn. British Wildlife Publishing, Gillingham.Google Scholar
- Warren, R., VanDerWal, J., Price, J., Welbergen, J.A., Atkinson, I., Ramirez-Villegas, J., Osborn, T.J., Jarvis, A., Shoo, L.P., Williams, S.E. & Lowe, J. (2013) Quantifying the benefit of early climate change mitigation in avoiding biodiversity loss. Nature Climate Change 3:678–682CrossRefGoogle Scholar