Fish harvesting advice under climate change: A risk-equivalent empirical approach

for immediate planning related to CC, providing the same advantages that have been found with semi-empirical models in SLR research. In fisheries and marine community modelling, EMs have a fairly long history depending on how broadly this class of models is defined. Schaefer’s 1957 biomass surplus production model [13] might be seen as an EM model because it contains only two parameters which subsume many distinct production processes such as individual growth, recruitment and mortality. A variety of size-based empirical models have been used to investigate broad changes in the pro- ductivity process of entire communities and size dependence of processes such as predation, growth and mortality [14–19] forming what has become known as size spectrum theory. Size spectrum ideas have been used as macro-ecological methods, to predict community responses to fishing [20], to disentangle species effects while still employing broad parameters like preda- tor-prey size ratios [21,22], and as a basis for exploring balanced harvesting strategies [23]. Although these size based EMs are not usually seen as tactical fisheries models advice for indi- vidual species, they provide information as a basis for advice on the impacts of fishing on com- munity structure, more sustainable directions and magnitude for fisheries exploitation, and ecological imbalances that could develop in a marine fish community with continued fishing at different intensities. In the present context of CC effects on fisheries, we propose the EM

approach as a central tool in developing timely advice to manage risks associated with manage- ment decisions under plausible CC scenarios. Here we have developed an EM approach as a basis for quantifying the change in risk in fisheries advice and management owing to CC. This advice uses the estimated incremental risk [24] due to climate change to guide directional changes in the amount, location and/or timing of removals, or other aspects of management, which may mitigate that incremental risk, even in the absence of a full understanding of the mechanisms linking the environmental drivers to stock productivity. We detail a case study to illustrate how CC-informed, risk-based advice can be developed in data moderate situations commonly encountered in fisheries. The case involves a cold-water adapted groundfish stock facing increased warm water inflows at the southern limit of its distribution range. We develop and use an EM to provide information on the stock’s likely response to a plausible range of environmental change scenarios, and how these responses would affect the risk of not achieving a fishery management objective and quantify the incremental risk to the stock meeting its conservation objective owing to CC and how risk equivalent advice can be derived accordingly. 2 Methods 2.1 An EM of fish production dependence on climate We calculate the surplus production of the stock from the biomass and catch time series [25,26]. The surplus production is a rate of annual net production which is influenced by cli-

mate or any other external variable. Surplus production as used here is simply the difference in biomass between two successive years plus the fisheries removals in that year. If the stock grew from one year to the next, the surplus production is positive and if it declined then surplus pro- duction is negative. Surplus production can be turned into a specific rate by dividing its value by the biomass (e.g. in the middle of the year). This is equivalent to a population growth rate. We can infer that since these population growth rates remove the impact of fishing (by adding it to biomass difference) these population growth rates reflect changes in stock production owing to natural processes and will reflect changes in stock productivity owing to factors such as climate change and ecosystem changes. We therefore developed an empirical model where the time series of biomass specific surplus production rates are a function of an external PLOS ONE Climate-change conditioned risk-equivalent fisheries advice PLOS ONE | https://doi.org/10.1371/journal.pone.0239503 February 19, 2021 4 / 22