A core issue in temporal ecology is the concept of trajectory—that is, when can ecologists have reasonable assurance that they know where a system is going? In this paper, we describe a non-random resampling method to directly address the temporal aspects of scaling ecological observations by leveraging existing data. Findings from long-term research sites have been hugely influential in ecology because of their unprecedented longitudinal perspective, yet short-term studies more consistent with typical grant cycles and graduate programs are still the norm. We use long-term insights to create ‘broken windows,’ that is, reanalyze long-term studies from short-term observational perspectives to examine discontinuities in trends at differing temporal scales.

The broken window algorithm connects our observations between the short-term and the long-term with an automated, systematic resampling approach: in short, we repeatedly ‘sample’ moving windows of data from existing long-term time series, and analyze these sampled data as if they represented the entire dataset. We then compile typical statistics used to describe the relationship in the sampled data, through repeated samplings, and then use these derived data to gain insights to the questions: 1) how often are the trends observed in short-term data misleading, and 2) can characteristics of these trends be used to predict our likelihood of being misled? We develop a systematic resampling approach, the ‘broken_window algorithm, and illustrate its utility with a case study of firefly observations produced at the Kellogg Biological Station Long-Term Ecological Research Site (KBS LTER). Through a variety of visualizations, summary statistics, and downstream analyses, we provide a standardized approach to evaluating the trajectory of a system, the amount of observation required to find a meaningful trajectory in similar systems, and a means of evaluating our confidence in our conclusions.

时间生态学的一个核心问题是轨迹的概念——也就是说，生态学家什么时候可以合理地保证他们知道系统的去向？在本文中，我们描述了一种非随机重采样方法，通过利用现有数据直接解决缩放生态观测的时间问题。长期研究站点的发现因其前所未有的纵向视角而对生态学产生了巨大影响，但与典型的资助周期和研究生课程更一致的短期研究仍然是常态。我们使用长期洞察力来创造“破窗”，即从短期观察的角度重新分析长期研究，以检查不同时间尺度上趋势的不连续性。

破窗算法通过自动、系统的重采样方法将短期和长期之间的观察联系起来：简而言之，我们从现有的长期时间序列中重复“采样”移动数据窗口，并分析这些采样数据好像它们代表了整个数据集。然后，我们通过重复抽样编制用于描述抽样数据中关系的典型统计数据，然后使用这些派生数据来深入了解以下问题：1)在短期数据中观察到的趋势具有误导性的频率，以及 2)这些趋势的特征可以用来预测我们被误导的可能性吗？我们开发了一种系统的重采样方法，即“broken_window 算法”，并通过在凯洛格生物站长期生态研究站点 (KBS LTER) 进行的萤火虫观测案例研究来说明其效用。通过各种可视化、汇总统计和下游分析，我们提供了一种标准化的方法来评估系统的轨迹、在类似系统中找到有意义的轨迹所需的观察量，以及一种评估我们对结论的信心的方法.