1. 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.
2. 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.
3. 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.
4. 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.

中文翻译：

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稀疏采样仅存在观测值的物候估计量的准确性

1. 物候学是对全球气候变化最直接的反应之一，但是数据限制使得在更大的分类学，空间和时间尺度上检查物候学模式具有挑战性。一个重要的机会是利用来自数字化博物馆标本和社区科学平台的快速增长的数据资源，但这假设可以使用可靠的统计方法来使用仅存在数据来估计物候。对于偶然数据，估计关键事件的发生或偏移特别困难，因为较低的数据密度朝着丰度分布的尾部出现。
2. Weibull分布已被认为是一种基于仅在场数据来估计物候的合适分布，但是Weibull通知的估计量仅适用于发作和偏移。我们描述了适用于分布的任何百分位数的新的Weibull参数化物候估计器的数学框架，并将其提供给r组合phenesse。我们使用有关开花时间和帝王蝶首次到达的模拟和经验数据来量化我们的估计量和其他常用的物候估计量的准确性，用于10个物候指标：发病日期，均值和偏移日期，以及1、5、10 ，第50、90、95和99个百分位数日期。针对丰度和观察过程的不同模式，计算了物候估计量的均方根误差和均值偏差。
3. 结果表明，当从均值估计值向季节性丰度曲线的尾部移动时，估计值的性能通常会下降，这表明开始和偏移仍然是最难以估计的物候计量学。但是，凭借简单的物候学和足够的观察力，我们新开发的估算器可以提供有用的起始和偏移估算。对于本赛季初，尤其是偶然观察到的情况，尤其如此。
4. 我们的模拟展示了从仅在场数据中生成准确的物候估计的潜力，并指导最佳使用估计器。我们开发的估计量phenesse在所考察的大多数模拟和经验条件下，对于初始估计而言偏差最小，估计误差最小，从而提高了这些估计用于物候研究的稳健性。