Attributing changes in the distribution of species abundance to weather variables using the example of British breeding birds

1. Modelling spatio-temporal changes in species abundance and attributing those changes to potential drivers such as climate, is an important but difficult problem. The standard approach for incorporating climatic variables into such models is to include each weather variable as a single covariate whose effect is expressed through a low-order polynomial or smoother in an additive model. This, however, confounds the spatial and temporal effects of the covariates.
2. We developed a novel approach to distinguish between three types of change in any particular weather covariate. We decomposed the weather covariate into three new covariates by separating out temporal variation in weather (averaging over space), spatial variation in weather (averaging over years) and a space-time anomaly term (residual variation). These three covariates were each fitted separately in the models. We illustrate the approach using generalized additive models applied to count data for a selection of species from the UK’s Breeding Bird Survey, 1994-2013. The weather covariates considered were the mean temperatures during the preceding winter and temperatures and rainfall during the preceding breeding season. We compare models that include these covariates directly with models including decomposed components of the same covariates, considering both linear and smooth relationships.
3. The lowest QAIC values were always associated with a decomposed weather covariate model. Different relationships between counts and the three new covariates provided strong evidence that the effects of changes in covariate values depended on whether changes took place in space, in time, or in the space-time anomaly. These results promote caution in predicting species distribution and abundance in future climate, based on relationships that are largely determined by environmental variation over space.
4. Our methods estimate the effect of temporal changes in weather, while accounting for spatial effects of long-term climate, improving inference on overall and/or localized effects of climate change. With increasing availability of large-scale data sets, need is growing for appropriate analytical tools. The proposed decomposition of the weather variables represents an important advance by eliminating the confounding issue often inherent in analyses of large-scale data sets.