Featuring 10 phenological estimators using simulated data

1. Studies reporting phenological changes in response to climate change are numerous and concern all groups of living organisms. Phenological changes could cause mismatching in food chains, thus inducing important perturbations in ecosystem functioning. Nevertheless, the relevancy of the conclusions drawn from phenological studies strongly depends on the estimation accuracy of such phenological changes. Many different estimators exist and some have already raised major criticism, although they continue to be used. Therefore, there is a crucial need for an extensive study documenting the behaviour of phenological estimators. 2. Here, we compare the estimation efficiency of 10 phenological estimators: different first appearance dates, mean dates, different percentile dates and a smoothing method based on spline functions using simulated phenological data. Root mean-squared errors and bias of the phenological estimations are calculated in relation to different parameters of the simulated phenological data. 3. Results show that first appearance dates behave as a very inaccurate and biased estimator regarding any phenological data set. Mean dates and estimates calculated using the smoothing method provided in general the most accurate estimates of phenological shifts. They were also the most robust to variation in sample sizes and to imperfect detectability. 4. Our results allow us to warn against the use of first appearance dates in future phenological studies and to recommend using mean dates or smoothing techniques to estimate phenological change of entire distributions. We also provide advice concerning phenological monitoring effort. These recommendations should most importantly apply to studies aiming at comparing phenological variation among sites or among species.