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

advice conditioning that reflects the overall directional trend in the fish production system forced by plausible CC rather than a strategy that encompasses the full range of possibilities (even implausible ones) or very specific hypotheses about the directional trend. We define risk here as the probability of not achieving a fishery management objective (tar- get) over a specified time period [5], given the level of fishing mortality, uncertainty in the assessment, and we have explicitly highlighted additional uncertainty contributed by CC. Risk equivalency is the process of adjusting the fishing mortality (or any other managed aspects of the fishery) in order to maintain a level of risk considered acceptable to achieve the manage- ment objectives considering additional sources of uncertainty. Therefore, risk equivalent advice will ensure comparable probabilities of not achieving a fishery management objective, given additional uncertainty contributed by CC. A full exploration of risk concepts is a field of research in itself and is beyond the scope of this paper. Suffice it to say here, fisheries science generally operates within the scope of the well established PA risk framework within which the main component of risk is the probability of (or not) achieving objectives (such as maintaining stock status above levels below which recruitment may be impaired) and risk equivalency is the expectation that such probability will deliver comparable management outcomes despite external factors acting on the stock. 1.1 Fishery modelling approaches that include climate variables

One statistical approach for accounting for CC effects in fisheries assessments is by allowing a particular model parameter to be fitted by a random walk [6] or random effects. A random effect in fisheries models is usually a time-varying autocorrelated process like natural mortal- ity, which does not require a driving mechanistic relationship [7]. However, projecting such models into the future necessarily widens the variance, owing to the lack of an underlying mechanism so the randomness of the parameter “walk” continues multiplicatively into the future. This approach can provide a relatively complete and unbiased accounting of variance because directional processes like CC are subsumed under the aggregation of all possible future environmental combinations underlying the processes in the random walk. However, this can result in the variance window being so large as to make almost all future outcomes plausible. This can result in low power to differentiate outcomes of alternative strategies. An alternative class of models that can be useful is empirical or phenomenological models (EMs). EMs operate at an amalgamated process level, i.e. models which recognise broad amal- gamated mechanisms driving a population or biological process, even if the forcing driver may consist of multiple distinct mechanisms with different levels of covariance, non-linearities and threshold effects. EMs recognise past relationships as an indication of future possibilities in an informative but not strictly defining way. Consequently, EMs can provide general predictions

rather than the specific predictions of detailed modelling approaches [8]. These modelling approaches should not be viewed in opposition, however, and it is useful to have both. A good example of EMs in CC is that detailed mechanistic global climate models (GCM) driven mostly by physical processes have under-predicted observed sea level rise (SLR) [9–11]. Broader phenomenological models for SLR, called “semi-empirical” models in the CC science commu- nity, have made better predictions for SLR than GCM by statistically relating global surface temperature to sea level [12]. These models do not, however, predict SLR at finer regional scales and it is not obvious how to scale them down or if that should even be attempted. EMs are therefore complementary to detailed mechanistic models and use of one approach does not prevent the use of the other. EMs allow rapid development of a broad predictive capacity that may provide the basis for risk mitigation and management planning such as for coastal infrastructure in the case of SLR. Similarly, EMs could be used for providing fisheries advice PLOS ONE Climate-change conditioned risk-equivalent fisheries advice PLOS ONE | https://doi.org/10.1371/journal.pone.0239503 February 19, 2021 3 / 22