Estimating phenology and phenological shifts with hierarchical modeling

Climate‐driven changes to phenology are some of the most prevalent climate change impacts, yet there is no commonly accepted approach to modeling phenological shifts. Here, we present a hierarchical modeling framework for estimating intra‐annual patterns in phenology (e.g., peak phenological expression) and analyzing interannual rates of change in peak phenology. Our approach allows for the estimation of multiple sources of uncertainty, including observation error (e.g., imperfect observations of intra‐annual patterns in phenology like peak flowering date) and variation in phenological processes (e.g., uncertainty in the rate of change in annual peak phenological expression). Covariates may be included as predictors of annual peaks or interannual variability in phenological responses. We demonstrate the use of our hierarchical modeling framework in two migratory species—juvenile chum salmon and Swainson's thrush. We acknowledge that the complexity of hierarchical models can be difficult to implement from scratch and present an R package that can be used to model peak dates and range (number of days between 25th‐ and 75th‐quartile dates), as well as a rate of change in peak phenology. Increasing precision, calculating uncertainty, and allowing for imperfect data sets when estimating phenological shifts should help ecologists understand how organisms respond to climate change.