Indexing butterfly abundance whilst accounting for missing counts and variability in seasonal pattern

Volunteer-based 'citizen science' schemes now play a valuable role in deriving biodiversity indicators, both aiding the development of conservation policies and measuring the success of management. We provide a new method for analysing such data based on counts of invertebrate species characterised by highly variable numbers within a season combined with a substantial proportion of proposed survey visits not made. Using the UK Butterfly Monitoring Scheme (UKBMS) for illustration, we propose a two-stage model that makes more efficient use of the data than previous analyses, whilst accounting for missing values. Firstly, generalised additive models were applied separately to data from each year to estimate the annual seasonal flight patterns. The estimated daily values were then normalised to estimate a seasonal pattern that is the same across sites but differs between years. A model was then fitted to the full set of annual counts, with seasonal values as an offset, to estimate annual changes in abundance accounting for the varying seasonality. The method was tested and compared against the current approach and a simple linear interpolation using simulated data, parameterised with values estimated from UKBMS data for three example species. The simulation study demonstrated accurate estimation of linear time trends and improved power for detecting trends compared with the current model. Comparison of indices for species covered by the UKBMS under the various model approaches showed similar predicted trends over time, but confidence intervals were generally narrower for the two-stage model. In addition to creating more robust trend estimates, the new method allows all volunteer records to contribute to the indices and thus incorporates data from more populations within the geographical range of a species. On average, the current model only enables data from 60% of 10 km² grid squares with monitored sites to be included, whereas the two-stage model uses all available data and hence provides full coverage at least of the monitored area. As many invertebrate species exhibit similar patterns of emergence or voltinism, our two-stage method could be applied to other taxa.