Hierarchical surplus production stock assessment models improve management performance in multi-species, spatially-replicated fisheries
Introduction
Managers of multi-species fisheries aim to balance harvest of multiple interacting target and non-target species that vary in abundance and productivity. Among-species variation in productivity implies variation in single-species optimal harvest rates, and, therefore, differential responses to exploitation. Single-species optimal harvest rates (e.g., the harvest rate associated with maximum sustainable yield) typically ignore both multi-species trophic interactions that influence species’ demographic rates (Gislason, 1999, Collie and Gislason, 2001), and technical interactions that make it virtually impossible to simultaneously achieve the optimal harvest rates for all species (Pikitch, 1987).
Technical interactions among species that co-occur in non-selective fishing gear are a defining characteristic of multi-species fisheries (Pikitch, 1987, Punt et al., 2002) and, therefore, play a central role in multi-species fisheries management outcomes for individual species (Ono et al., 2017, Kempf et al., 2016). Catch limits set for individual species without considering technical interactions subsequently lead to sub-optimal fishery outcomes (Ono et al., 2017, Punt et al., 2011a, Punt et al., 2020). For example, under-utilization of catch limits could occur when technically interacting quota species are caught at different rates (i.e., catchability) by a common gear, leading to a choke constraint in which one species quota is filled before the others (Baudron and Fernandes, 2015). Choke constraints are considered negative outcomes for multi-species fishery performance, because they reduce harvester profitability as increasingly rare quota for choke species may limit access to fishing grounds, as well as driving quota costs above the landed value of the choke species (Mortensen et al., 2018).
Setting catch limits for individual species in any fishery usually requires an estimate of species abundance, which continues to be a central challenge of fisheries stock assessment (Hilborn and Walters, 1992, Quinn, 2003, Maunder and Piner, 2015), especially when species data are of low statistical power, such as short noisy time series of observations, or uninformative catch series (Johnson and Cox, 2018). Where such low power data exists, data pooling is sometimes used to extend stock assessments to complexes of similar, interacting stocks of fish (Appeldoorn, 1996). Examples include pooling data for a single species across multiple spatial strata when finer scale data are unavailable or when fish are believed to move between areas at a sufficiently high rate (Benson et al., 2015, Punt et al., 2018), and pooling data for multiple species of the same taxonomic group within an area when data are insufficient for individual species or during development of new fisheries (DeMartini, 2019). Data-pooled estimates of productivity represent means across the species complex, implying that resulting catch limits will tend to overfish unproductive species and underfish productive ones (Gaichas et al., 2012).
In multi-species and/or multi-area contexts, hierarchical stock assessment models, which treat each area/species combination as a discrete yet exchangeable replicate, may represent a compromise between single-species and data-pooling approaches. For this paper, we define a hierarchical stock assessment model as a model fit to multiple replicates (e.g. areas/species) simultaneously, using hierarchical hyper-priors on selected parameters to share information between replicates (Thorson et al., 2015). Hierarchical priors induce shrinkage effects in which parameter values are drawn towards an estimated overall mean value, thus improving model convergence for replicates with low statistical power data while still estimating replicate-specific parameters based on that data. Hierarchical methods based on data and hyper-priors stand in contrast to data-pooled methods that estimate a mean value only, or single-stock methods that usually rely on strong a priori assumptions about replicate specific parameters, forcing parameters to be identical among replicates, or using strongly informative priors, all of which will almost certainly increase assessment bias (Jiao et al., 2009, Jiao et al., 2011, Punt et al., 2011b).
Although hierarchical stock assessments are expected to produce better estimates of species biomass and productivity than single-species methods in data-limited contexts, it remains unclear whether such improved statistical performance translates into better management outcomes (Johnson and Cox, 2018). Aside from some related simulations determining the benefits of manually sharing information gained when actively adaptively managing spatially replicated groundfish stocks (Collie and Walters, 1991), to our knowledge there are no evaluations of the management performance of hierarchical stock assessment models. Further, low assessment model bias and/or high precision, which are often unattainable outside of simulations, are not necessary conditions for superior management performance, because biases can, in practice, sometimes compensate for each other (e.g., negative correlation in stock size and productivity), or be offset by other parts of the management system, such as a reduction in harvest rate. A modern fisheries management oriented paradigm is more concerned with the expected performance of a fisheries management system – made up of data, assessments, and harvest rules – despite the inherent, and at some point irreducible, uncertainties in the system (de la Mare, 1998).
In this paper, we investigated whether hierarchical stock assessment models improved management performance in a simulated multi-species, spatially replicated fishery. The simulated fishery was modeled on a spatially heterogeneous complex of Dover sole (Microstomus pacificus), English sole (Parophrys vetulus), and southern Rock sole (Lepidopsetta bilineata) off the coast of British Columbia, Canada, fished in three spatial management areas. Closed-loop feedback simulation was used to estimate fishery outcomes when catch limits were set based on estimates of biomass from single-species, data-pooling, and hierarchical state-space surplus production models under high, moderate, and low data quantity scenarios. Assessment models were either fit to species-specific data as single-species or hierarchical multi-species models, or fit to data pooled spatially across management units, pooled across species within a spatial management unit, or totally aggregated across both species and spatial management units. Management performance of each assessment approach was measured by both the risk of overfishing, and by cumulative absolute loss in catch, defined as deviation from optimal catch trajectories generated by an omniscient manager, who could set annual effort to maximize total multi-species/multi-stock complex yield given perfect knowledge of all future recruitments (Walters, 1998, Martell et al., 2008).
Section snippets
British Columbia's flatfish fishery
The multi-species complex of right-eyed flounders in British Columbia (BC) is a technically interacting group of flatfishes managed over the BC coast (Fig. 1). Although there are several right-eyed flounders in BC waters, we focus on the three species, indexed by , Dover sole (), English sole (), and southern Rock sole (), which we hereafter refer to as Rock sole. Taken together, these species comprise a multi-stock complex (DER complex), managed as part of the BC multi-species
Omniscient manager performance
As expected, the omniscient manager was able to achieve the theoretical multi-species optimal yield in the presence of technical interactions during the middle of the projection period (Fig. 4, blue closed circle). Median biomass, catch, and fishing mortality reach the equilibrium after a transition period of about 20 years. During the transitionary period, effort is slowly ramped up in each area from the end of the historical period, stabilising around area-specific after about 12 years (
Discussion
In this paper, we demonstrated that hierarchical stock assessment models may improve management performance in a spatially-replicated multi-species flatfish fishery. When available data quantity was moderate or low (indicated here by time-series length), biomass and harvest rate estimates from hierarchical stock assessment models resulted in catches that were closer to an omniscient manager's optimal reference series compared to catch limits derived from single-stock and data-pooling assessment
Conflict of interest
The authors declare no conflict of interest.
CRediT authorship contribution statement
Samuel D.N. Johnson: Conceptualization, Methodology, Software, Formal analysis, Writing - original draft, Visualization. Sean P. Cox: Conceptualization, Resources, Writing - review & editing, Supervision, Funding acquisition.
Declaration of Competing Interest
The authors report no declarations of interest.
Acknowledgements
Funding for this research was provided by a Mitacs Cluster Grantto S.P. Cox in collaboration with the Canadian Groundfish Research and Conservation Society, Wild Canadian Sablefish, and the Pacific Halibut Management Association. We thank S. Anderson and M. Surry at the Fisheries and Oceans, Canada Pacific Biological Station for fulfilling data requests. Further support for S.P.C. and S.D.N.J. was provided by an NSERC Discovery Grantto S.P. Cox. We finally thank A. E. Punt and one anonymous
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