Population trends
We calculated the population trends from their collated annual abundance indices. This was done separately for butterflies and moths.
For the butterflies, at each site, annual indices were computed from the weekly counts, following the method described in Dennis et al.(2013, 2016) and implemented in the rbms R package (Schmucki et al. 2020). Missing week counts were derived from a Poisson generalized linear model (GLM) that included the regional flight curve as an offset (Schmucki et al. 2016). Collated annual abundance indices were then estimated with a weighted Poisson regression, accounting for site, transect length and using the proportion of the flight curve monitored as weight. Thereby, sites with many missing counts during the flight period had lower weight than well monitored sites. For each species, we calculated the long-term trends with a linear model that we fitted on the log10 transformed collated annual indices, starting with the year the species was first recorded until the last within the 1999-2017 period.
For the moth species, population trends were estimated using the TRIM software (Pannekoek & Van Strien 2005), as implemented in the rtrim R package (Boogart et al. 2020). TRIM uses Poisson regression to estimate annual abundance indices, while accounting for missing observations, site differences, overdispersion and temporal autocorrelation. As a long-term trend estimate, TRIM calculates a regression through the annual indices, and this linear trend slope (on the log scale; the “additive” slope in TRIM) was used as a measure of population trend for the moth species over 1993-2016. Four species appeared in the dataset after 1993, with the first year of occurrence marking the start of the timeframe for trend calculation.