Estimating butterfly population trends from sparse monitoring data using Generalized Additive Models

Concerns of declines in insects and population level responses to climate change have highlighted the importance of estimating trends in abundance and phenology from existing monitoring data. As the taxa with the most systematic monitoring data, butterflies are a frequent focus for understanding trends in insects. Even so, ecologists often have only sparse monitoring data for at-risk butterfly populations. As existing statistical techniques are typically poorly suited to such data, these at-risk populations are frequently excluded from analyses of butterfly trends. Here we present guidelines for estimating population trends from sparse butterfly monitoring data using generalized additive models (GAMs), based on extensive simulations and our experiences fitting hundreds of butterfly species. These recommendations include pre-processing steps, model structure choices, and post-hoc analysis decisions that reduce bias and prevent or mitigate biologically implausible model fits. We also present the ButterflyGamSim package for the programming language R, available at https://github.com/cbedwards/butterflyGamSims. This open source software provides tools for ecologists and applied statisticians to simulate realistic butterfly monitoring data and test the efficacy of different GAM model choices or monitoring schemes.