Fitting phenological curves with GLMMs

Abstract

Estimating population abundance is central to population ecology. With increasing concern over declining insect populations, estimating trends in abundance has become even more urgent. At the same time, there is an emerging in interest in quantifying phenological patterns, in part because phenological shifts are one of the most conspicuous signs of climate change. Existing techniques to fit activity curves (and thus both abundance and phenology) to repeated transect counts of insects (a common form of data for these taxa) frequently fail for sparse data, and often require advanced knowledge of statistical computing. These limitations prevent us from understanding both population trends and phenological shifts, especially in the at-risk species for which this understanding is most vital. Here we present a method to fit repeated transect count data with Gaussian curves using linear models, and show how robust abundance and phenological metrics can be obtained using standard regression tools. We then apply this method to eight years of Baltimore checkerspot data using generalized linear models (GLMs). This case study illustrates the ability of our method to fit even years with only a few non-zero survey counts, and identifies a significant negative relationship between population size and annual variation in thermal environment (in growing degree days). We believe our new method provides a key tool to unlock previously-unusable sparse data sets, and may provide a useful middle ground between ad hoc metrics of abundance and phenology and custom-coded mechanistic models.