A Generalized Abundance Index for Seasonal Invertebrates

At a time of climate change and major loss of biodiversity, it is important to have efficient tools for monitoring populations. In this context, animal abundance indices play an important role. In producing indices for invertebrates, it is important to account for variation in counts within seasons. Two new methods for describing seasonal variation in invertebrate counts have recently been proposed; one is nonparametric, using generalized additive models, and the other is parametric, based on stopover models. We present a novel generalized abundance index which encompasses both parametric and nonparametric approaches. It is extremely efficient to compute this index due to the use of concentrated likelihood techniques. This has particular relevance for the analysis of data from long-term extensive monitoring schemes with records for many species and sites, for which existing modeling techniques can be prohibitively time consuming. Performance of the index is demonstrated by several applications to UK Butterfly Monitoring Scheme data. We demonstrate the potential for new insights into both phenology and spatial variation in seasonal patterns from parametric modeling and the incorporation of covariate dependence, which is relevant for both monitoring and conservation. Associated R code is available on the journal website.