Conceptual and practical issues limit the utility of statistical estimators of phenological events

Widespread shifts in phenological events in response to climate change have inspired phenological monitoring programs and new methods for analyzing sparse phenological data. For example, the Weibull distribution is increasingly used to estimate the dates of hard-to-observe phenological events, such as first and last flowering dates, in sparsely or unsystematically sampled data sets. In contrast, recent application of the Weibull estimator to an intensely and systematically sampled flowering phenology data set unexpectedly found different results than a previous analysis of the observed dates; at issue is whether different aspects of phenological curves shift uniformly or disparately. We used this case study to (1) raise conceptual and technical issues around when and how to infer phenological events using Weibull (or other) estimates, and (2) re-analyze the data set in question with these considerations in mind. Our re-analysis using the Weibull estimator shows that first, peak, and last flowering dates shift disparately through time, supporting the original analysis of the observed dates. We show that off-the-shelf usage of statistical estimators to generalize about an unsampled population may be inappropriate without considering how well sampled the focal study population is and how biological features such as habitat heterogeneity influence the natural scope of the unsampled population.