The broken window: An algorithm for quantifying and characterizing misleading trajectories in ecological processes

Abstract

Abstract 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.