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.