Expanding
windows
The alternative to the above computation differs by assessing change in
an expanding window via a composite metric consisting of multiple
indicators (Figure 2c). The same EWS indicators as above are available
to the expanding window approach (Table 2), but each indicator is
standardised by subtracting its expanding mean from its calculated value
at time t . This value is then normalised by division by its
expanding standard deviation (Drake and Griffin 2010) – at each time
point, the prediction is updated (Figure 2d). A composite metric can
then be constructed by summing all individual indicator values
calculated per t . The resulting indicator value or score is
hereafter referred to as ‘strength’. If the indicator strength exceeds a
threshold value, then a ‘signal’ has been identified. Typically, this
threshold value is 2σ which is approximately equivalent to a 95%
confidence interval and performs favourably compared to other threshold
levels (Clements and Ozgul 2016, Clements et al. 2017).
The expanding window approach also allows multiple information sources
to contribute to the assessment. For example, including body size
estimates improves assessment reliability by reducing false positive
rate whilst increasing the number of true positives (Clements and Ozgul
2016, Baruah et al. 2020). uniEWS consequently accepts a trait
argument where an additional trait time series can be combined with the
other ‘abundance-based’ EWSs as a composite metric.
Furthermore, the EWSs assessed using the expanding window approach can
be improved using a consecutive signal strategy (Clements et al. 2019,
Southall et al. 2022) where a ‘warning’ is only acknowledged when two or
more signals are identified in a row. Southall and colleagues (2022)
have recently showed that using this approach results in earlier and
more reliable warnings over the rolling window approach.