Fitting phenological curves with Generalized Linear Mixed Models (GLMMs)

Understanding organismal phenology has been an emerging interest in ecology, in part because phenological shifts are one of the most conspicuous signs of climate change. While we are seeing increased collection of phenological data and creative use of historical data sets, existing statistical tools to measure phenology are generally either limited (e.g., first day of observation, which has problematic biases) or are challenging to implement (often requiring custom coding, or enough data to fit many parameters). We present a method to fit phenological data with Gaussian curves using linear models, and show how robust phenological metrics can be obtained using standard linear regression tools. We then apply this method to eight years of Baltimore checkerspot data using generalized linear mixed models (GLMMs). This case study illustrates the ability of years with extensive data to inform years with less data and shows that butterfly flight activity is somewhat earlier in warmer years. We believe our new method fills a convenient midpoint between ad hoc measures and custom-coded models.