Multivariate forms of EWSs (Weinans et al. 2019, Lever et al. 2020,
Medeiros et al. 2022) and deep learning models are of particular
interest as they appear superior tools to the univariate signals
described above. Multivariate approaches exploit information from
multiple measurements of a shared system (e.g. multiple species in an
ecosystem or
multiple
sensors in a combustion engine) to provide an overall signal of system
resilience. Pooling information in this way buffers against the
uncertainty of choosing which data source should be assessed. For
example, the trophic level of EWS assessment influences the strength of
signal observed in simulated communities (Patterson et al. 2021), and
whilst the authors provide guidance on the optimum species/time series
to monitor, the required information to identify those time series may
not be available to empirical users. Multivariate EWSs can therefore
provide a naïve yet robust assessment for multivariate data in the
absence of complete information.
Similarly, CSD may not be the only signature of systems close to a
tipping point. Our identification of the phenomenon stems from linear
stability analysis (LSA) of mathematical models (Ludwig et al. 1978,
Scheffer et al. 2009), but machine learning tools can identify other
phenomenological features not detected from LSA. For example, machine
learning models trained upon transitioning data outperform equivalent
models trained upon the EWSs of the same transitioning data (Deb et al.
2022). This is indicative of alternative features being more informative
than CSD to warrant general usage, although the ‘black-box’ nature of
the approach limits its accountability (Enni and Herrie 2021). This
being said, multiple machine learning models are now available for
transitioning systems that improve the transparency of predictions by
training on simple mathematical models associated with LSA (Bury et al.
2021, Deb et al. 2022). These models can consequently build upon our
foundational knowledge of tipping points by taking advantage of the
biases inherent in their training.
Currently, neither multivariate nor machine learning approaches have
functionality for R users and resultingly there is a need for simple
tools to interact with the variety of EWS approaches available to
researchers. Certain EWS functionality has previously been provided by
the earlywarnings R package , however the package is limited to
one form of EWS calculation (rolling windows) in univariate data only.
There have also been advances using alternative methodologies such as
expanding window and composite EWSs, which introduce data in an
add-one-in fashion to provide a standardised time series of EWS strength
. This second approach improves the reliability of EWS predictions in
univariate data but is not currently available in an easy-to-use form.
Unfortunately, many of the custom functions written to facilitate this
research are limited to the subscription MATLAB product or hidden in
publications’ supplementary information . In combination, this has
limited the accessibility of EWS development to the wider community.
Compiling these various functions in to a single and comprehensive R
package whilst rectifying computational errors is required to increase
reproducibility of empirical ecological tipping point research and
improve the interpretation and visualisation of results. We therefore
designed the EWSmethods R package to provide a suite of
‘user-friendly’ functions to predict critical transitions across both
univariate and multivariate data sources and provide interpretable
graphics. For univariate data, such as local fisheries or country level
disease cases, EWSs can be estimated using either the rolling window
approach of earlywarnings or the expanding window approach of
Drake and Griffen (2010). The package also provides the user the
capability to query the Python based EWSNet deep learning model in the R
environment and generate predictions on the time series’ future. And
finally, if multiple measurements have been made of a single system –
such as when monitoring multiple species in the same community –
multivariate EWSs can be estimated using either rolling or expanding
window approaches. EWSmethods therefore represents a compilation
of new and existing tools to support this expanding field in an easy to
use and interpret form. A comparison of the features EWSmethodsprovides versus the currently available earlywarnings package is
provided in Table 1.