Self-starting cumulative sum harvest control rule (SS-CUSUM-HCR) for status-quo management of data-limited fisheries

Abstract

We demonstrate a harvest control rule based on the self-starting cumulative sum (SS-CUSUM) control chart that can maintain a fish stock at its starting (status-quo) level. The SS-CUSUM is an indicator monitoring tool commonly used in quality control engineering and does not require a long time series or predefined reference point for detecting temporal trends. The reference points in SS-CUSUM are calibrated in the form of running means that are updated on an ongoing basis when new observations become available. The SS-CUSUM can be initiated with as few as two observations in the time series and can be applied long before many other methods, soon after initial data become available. A wide range of stock indicators can be monitored, but in this study, we demonstrate the method using an equally weighted sum of two indicators: a recruitment indicator and a large fish indicator from a simulated fishery. We assume that no life history data are available other than 2 years of both indicator data and current harvest levels when the SS-CUSUM initiates. The signals generated from SS-CUSUM trigger a harvest control rule (SS-CUSUM-HCR), where the shift that occurs in the indicator time series is computed and is used as an adjustment factor for updating the total allowable catch. Our study shows that the SS-CUSUM-HCR can maintain the fish stock at its starting status-quo level (even for overfished initial states) but has limited scope if the fishery is already in an undesirable state such as a stock collapse. We discuss how the SS-CUSUM approach could be adapted to move beyond a status-quo management strategy, if additional information on the desirable state of the fishery is available.