A User-Friendly Guide to Using Distance Measures to Compare Time Series in Ecology

Abstract

Time series are a critical component of ecological analysis, used to track changes in biotic and abiotic variables. Information can be extracted from the properties of time series for tasks such as classification, clustering, prediction, and anomaly detection. These common tasks in ecological research rely on the notion of (dis-) similarity which can be determined by using distance measures. A plethora of distance measures have been described in the scientific literature, but many of them have not been introduced to ecologists. Furthermore, little is known about how to select appropriate distance measures and the properties they focus on for time-series related tasks.Here we describe 16 potentially desirable properties of distance measures, test 42 distance measures for each property, and present an objective method to select appropriate distance measures for any task and ecological dataset. We then demonstrate our selection method by applying it to a set of real-world data on breeding bird populations in the UK. We also discuss ways to overcome some of the difficulties involved in using distance measures to compare time series.Our real-world population trends exhibit a common challenge for time series comparison: a high level of stochasticity. We demonstrate two different ways of overcoming this challenge, first by selecting distance measures with properties that make them well-suited to comparing noisy time series, and second by applying a smoothing algorithm before selecting appropriate distance measures. In both cases, the distance measures chosen through our selection method are not only fit-for-purpose but are consistent in their rankings of the population trends.The results of our study should lead to an improved understanding of, and greater scope for, the use of distance measures for comparing time series within ecology, and allow for the answering of new ecological questions.

Quantifying reliability and data deficiency in global vertebrate population trends using the Living Planet Index

“…We selected an appropriate distance measure to compare sampled trends with ‘true trends’ using the selection process described in Dove et al (2022). Of the distance measures deemed appropriate, we chose the Jaccard distance because it uses a 0–1 scale, making it easier to interpret.…”

“…The simulated datasets used for this study are openly available in Dryad at https://doi.org/10.5061/dryad.mpg4f4r52 (Dove et al, 2023). Some of the Living Planet Database time series used in this study are not available to the public, but a limited version is available at https://www.livingplanetindex.org/data_portal.…”

“…We degraded the samples by randomly removing observations and adding observation error to resemble regional taxonomic groups in the Living Planet Database (LPD, the database underlying the LPI). We then compared the trends calculated from the samples with those from the complete datasets using the Jaccard distance metric (chosen using the distance measure selection method described in Dove et al, 2022) and constructed a multiple regression model to understand how the distance values are influenced by variations in properties of the data. Here, distance metrics can be thought of as a measure of trend accuracy.…”