The accuracy of phenology estimators for use with sparsely sampled presence‐only observations

Abstract Phenology is one of the most immediate responses to global climate change, but data limitations have made examining phenology patterns across greater taxonomic, spatial and temporal scales challenging. One significant opportunity is leveraging rapidly increasing data resources from digitized museum specimens and community science platforms, but this assumes reliable statistical methods are available to estimate phenology using presence‐only data. Estimating the onset or offset of key events is especially difficult with incidental data, as lower data densities occur towards the tails of an abundance distribution. The Weibull distribution has been recognized as an appropriate distribution to estimate phenology based on presence‐only data, but Weibull‐informed estimators are only available for onset and offset. We describe the mathematical framework for a new Weibull‐parameterized estimator of phenology appropriate for any percentile of a distribution and make it available in an r package, phenesse . We use simulations and empirical data on open flower timing and first arrival of monarch butterflies to quantify the accuracy of our estimator and other commonly used phenological estimators for 10 phenological metrics: onset, mean and offset dates, as well as the 1st, 5th, 10th, 50th, 90th, 95th and 99th percentile dates. Root mean squared errors and mean bias of the phenological estimators were calculated for different patterns of abundance and observation processes. Results show a general pattern of decay in performance of estimates when moving from mean estimates towards the tails of the seasonal abundance curve, suggesting that onset and offset continue to be the most difficult phenometrics to estimate. However, with simple phenologies and enough observations, our newly developed estimator can provide useful onset and offset estimates. This is especially true for the start of the season, when incidental observations may be more common. Our simulation demonstrates the potential of generating accurate phenological estimates from presence‐only data and guides the best use of estimators. The estimator that we developed, phenesse, is the least biased and has the lowest estimation error for onset estimates under most simulated and empirical conditions examined, improving the robustness of these estimates for phenological research.