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

variable, we call E: Pt Bt ¼ f Et ð Þ Eq 1 Where Bt is the biomass in year t and Pt is the surplus production (Bt+1-Bt) in year t (which is effectively a population growth rate), and Et is the value of an external (e.g. climate or ecosys- tem) variable hypothesised to influence surplus production rate. The surplus production rate is like a population growth rate and therefore given an estimate of Bt in a year and a surplus production rate one can determine the production of the stock in that year by multiplying the rate by the biomass and adding it to the previous year’s biomass. This is the simplest kind of surplus production model. A full derivation of our model is provided in S1 Appendix but the main point is that we derived a simple population growth rate from a time series of survey and catch data and this growth rate is not simply a function of stock characteristics but can be influenced by external variables. For the sake of completeness and testing sensitivity of our analysis we also developed a version with a density dependent term. Btþ1 ¼ Bt þ Pt Bt � Bt � Kt Ct Eq 2 Where Bt+1 is the biomass in year t+1, Bt is the biomass in year t, Pt is the surplus produc- tion in the year t, Kt is the density dependent term in year t which (Kt�1) where Kt = 1 in the density independent case and Ct is the fishery removals in year t. From Eq 1 we can see that the surplus production specific rate will be a function of the Et variable. 2.2 Gulf of St Lawrence Greenland halibut as a case study

Greenland halibut (Reinhardtius hippoglossoides) or Greenland halibut is a cold water adapted flatfish with a mean generation time of about seven years. Commercial sized Greenland halibut (>40 cm total length) live on the bottom and are concentrated at depths between 100m and 300m [27]. The Gulf of St Lawrence (Fig 1) is located at the southern extent of the species’ dis- tribution range. Recent warming of bottom water in this region [28] is expected to negatively impact Greenland halibut production and fishery sustainability. The mechanisms linking warming bottom water temperature and decreased Greenland halibut productivity are proba- bly varied and could operate directly through decreases in fecundity, larval and juvenile sur- vival, individual growth and increases in natural mortality of recruited ages, or indirectly through oxygen depletion in warming bottom waters and associated decreases in individual growth [29]. There is a 30-year time series of fishery independent survey catch and environmental data for the Greenland halibut stock in the Gulf of St-Lawrence (Fig 2), but no accepted or benchmarked stock assessment model to assess the impacts of fishing and/or climate on stock dynamics (though assessment models are being explored). Standard age-based modelling methods have not been used mainly due to age determination challenges with this species. The stock is assessed using biomass indicators primarily derived from fishery independent trawl surveys. Recent science advice for the stock indicated that considering

“stock status indicators and ecosystem conditions, a reduction in the exploitation rate may be necessary to promote stock recovery” [30], however no tools are currently in place to quantify how large the reduction should be to have a high likelihood of stock increase. PLOS ONE Climate-change conditioned risk-equivalent fisheries advice PLOS ONE | https://doi.org/10.1371/journal.pone.0239503 February 19, 2021 5 / 22