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

1. 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.

2. Using the UK Butterfly Monitoring Scheme (UKBMS) for illustration, we propose a two-stage model that

makesmore 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.

3. 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.

4. 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.

5. 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.