Data from: A user-friendly guide to using distance measures to compare time series in ecology

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 (e.g.
assigning species to individual bird calls); clustering (e.g. clustering
similar responses in population dynamics to abrupt changes in the
environment or management interventions); prediction (e.g. accuracy of
model predictions to original time series data); and anomaly detection
(e.g. detecting possible catastrophic events from population time series).
These common tasks in ecological research rely on the notion of (dis-)
similarity, which can be determined using distance measures. A plethora of
distance measures have been described, predominantly in the computer and
information sciences, but many have not been introduced to ecologists.
Furthermore, little is known about how to select appropriate distance
measures for time-series-related tasks. Therefore, many potential
applications remain unexplored. Here we describe 16 properties of distance
measures that are likely to be of importance to a variety of ecological
questions involving time series. We then test 42 distance measures for
each property and use the results to develop an objective method to select
appropriate distance measures for any task and ecological dataset. We
demonstrate our selection method by applying it to a set of real-world
data on breeding bird populations in the UK and discuss other potential
applications for distance measures, along with associated technical issues
common in ecology. Our real-world population trends exhibit a common
challenge for time series comparisons: 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
ecological time series, and help us answer new ecological questions.