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.