Performance of length-based assessment in predicting small-scale multispecies fishery sustainability

Small-scale fisheries play a critical role in food security and contribute to nearly half of reported global fish catches. However, the status of most small-scale fisheries stocks is still poor. In data-limited situations, length-based methods have been widely applied to estimate reference points and to understand stock status. This study applied three different length-based assessment methods (length-based indicators—LBI, length-based spawning potential ratio—LBSPR, and the length-based Bayesian biomass approach—LBB) to predict fisheries stock sustainability in the Azores. Overall, the three methods showed robustness for 15 out of 18 stocks assessed and agreed on their exploitation status. The results showed that 45% of the Azorean stocks were classified as sustainable stocks, 33% possible rebuilding/overfished and 22% overfishing/overfished stock status. Sensitivity analysis showed that biases on the source of initial life-history parameters, especially the asymptotic length (L∞) and the ratio of natural mortality and growth coefficient (M/k), have a stronger influence on the reference points of conservation of mature individuals (LBI), spawning potential ratio and fishing mortality (LBSPR) and the biomass relative to the maximum sustainable yield (LBB). Furthermore, sensitivity analysis indicated that, among the three methods, LBI is more robust. Our findings provide some management recommendations such as (1) catches and effort should be reduced; (2) minimum landing size should be increased; (3) minimum hook size should be increased, to be applied mainly for those stocks classified as possible rebuilding/overfished and overfishing/overfished stock status.


Introduction
Small-scale fisheries are recognized as an economic and social driving force that provides global food and nutrition security and are responsible for twothirds of seafood consumption (FAO 2015). Furthermore, small-scale fisheries generate employment and other multiplier effects to local economies worldwide and contribute to nearly half of reported global fish catches (FAO 2015). Small-scale fisheries are highly productive and are characterised by a highly diverse catch composition, with hundreds of species being caught (Nadon and Ault 2016;Newman et al. 2018). However, these fisheries often lack important historical information including species-specific catch data and effort data, often leaving these stocks unassessed and undermanaged (Stobutziki et al. 2006;Hilborn et al. 2020). Given this importance, small-scale fisheries knowledge of stock status and of future harvest and exploitation potential of target species is essential for both users and managers of fishing resources (Herrón et al. 2018).
Stock assessment provides a comprehensive understanding of the historical and current harvested resources and predictions of future population dynamics, which contribute to rational management strategies (Hilborn and Walters 1992). Traditional stock assessment models rely on substantial data sets, such as time series of total catch, absolute or relative abundance indices, fishing effort and age structure (Quinn and Deriso 1999). However, some of these data are usually unavailable for most small-scale fisheries and prevent the application of traditional assessment models.
Fisheries are considered data-limited if the available data is insufficient or unreliable for performing a realistic quantitative, model-based stock assessment that estimates time-series of biomass relative to their limit, target and trigger biomass and fishing mortality reference points such as the level corresponding to maximum sustainable yield (MSY) (Dowling et al. 2019;ICES 2021aICES , 2021b. Nevertheless, even with limited data, some features of stock status can be inferred, and data-limited assessment approaches have been increasingly used for management purposes (Chrysafi and Kuparinen 2016;Dowling et al. 2019). Since it is cost-effective and usually easy to collect, length-frequency data from commercial catches are often the primary data type obtained in data-limited fisheries such as small-scale fisheries (Hordyk et al. 2015a;Mildenberger et al. 2017). Several length-based approaches have been developed and widely used to serve these data-limited fisheries where only length data are available, such as lengthbased indicators (LBI; Froese 2004), length-based spawning potential ratio (LBSPR; Hordyk et al. 2015b) and length-based Bayesian biomass approach (LBB; Froese et al. 2018a).
The LBI method is used to screen catch/landingslength composition and to classify the stocks according to conservation, yield optimization and MSY considerations (ICES 2018). The LBSPR method assesses the stock status by the spawning potential ratio defined as the proportion of spawning biomass per recruit (SBPR) in an exploited stock compared to SBPR in an unfished stock (Hordyk et al. 2015b(Hordyk et al. , 2016Prince et al. 2015). The LBB method is a newly developed method to estimate relative biomass level and other biological reference points relative to levels that can produce MSY, by Bayesian Monte Carlo Markov Chain estimation (Froese et al. 2018a).
The LBI, LBSPR and LBB are highly sensitive to values of the input life-history parameters (Hordyk et al. 2015b(Hordyk et al. , 2016, recruitment variability and domeshaped fishery selectivity (Pons et al. 2019;Hommik et al. 2020). For example, Hordyk et al. (2015b) showed that LBSPR was highly sensitive to the bias of the asymptotic length (L∞) and the ratio of natural mortality and the growth coefficient (M/k) parameters. Although sensitivity analysis studies of lengthbased methods using simulated data have already been carried out, only a few studies have been carried out using case studies with real data from exploited stocks (Sun et al. 2018;Cousido-Rocha et al. 2022;Pennino et al. 2022). Therefore, understanding the sensitivity of the methods to parameter inputs and selectivity pattern effects in more case studies such as Azorean fisheries remains necessary to understand and improve the robustness of the results (ICES 2018;Hordyk et al. 2015b).
In the Azores, a Portuguese archipelago located in the North Atlantic along the Mid-Atlantic Ridge, fishing is a significant activity representing 2% of the economy's gross value in the region (Carvalho et al. 2011;ICES 2020). Azorean fisheries are primarily small-scale and artisanal (Carvalho et al. 2011), most of these fisheries are developed by small-scale vessels (< 12 m in length) that target several different species (multispecies fisheries) and the remaining fleet is composed of larger vessels (12-31 m) that operate mostly between 3 and 200 nautical miles from shore (Pinho and Menezes 2009;ICES 2020). Handlines and bottom longline are the main fishing gears used by these fisheries, targeting, and capturing many of the same species, although some species are more characteristic than others (Carvalho et al. 2011;Santos et al. 2020a).
A total of 138 species of algae, molluscs, crustaceans, echinoderms, and fishes (teleost and elasmobranch species) have been landed in the Azores in the last decade. Of this total, 22 species (18 fishes, 2 crustaceans and 2 molluscs) were identified as priority stocks for local assessment and monitoring under the European Union Marine Strategy Framework Descriptor 3 and United Nations Sustainable Development Goal 14 (Santos et al. 2020a) and are presented in Table 1. These stocks were classified as data-limited under the International Council for Exploration of the Sea (ICES) MSY framework (Medeiros-Leal et al. 2021a). According to their preferred habitat, the Azorean priority stocks can be divided into: (1) coastal species (rough limpet, common spiny lobster and mediterranean slipper lobster) which are limpet and lobster species that live on the island's shelves (Torres et al. 2022); (2) Pelagic fish and squid species (veneid squid, blue jack mackerel, atlantic chub mackerel and amberjacks nei) which are typically found in the midwater and upper layers of the oceans (Stephenson and Smedbol 2019); (3) Demersal fish species which are typically found near the seafloor at least some of the time (benthic or benthopelagic; Pinho and Menezes 2009). The demersal fish species can be further divided into three subgroups according to their bathymetric distribution  Fig. 1). In general, species' landings increased from the 1980s to the late 1990s, peaking at over 7000 tonnes. From the 2000s to the early 2010s, landing averages were stable and have since decreased to close to 3000 tonnes in the last ten years (Fig. 1). The past two decades have seen fishing area restrictions to reduce fishing impacts on these stocks and the subsequent spatial expansion of fishing efforts to deep offshore areas . As a result, commercial landings of deep-water species increased from approximately 70 tonnes in the early 2000s to over 150 tonnes in recent years (Fig. 1;ICES 2021aICES , 2021b. Most of the Azorean fishery stocks are considered intensively exploited and their current stock statuses are unknown (ICES 2018).
The present study's main goal is to assess the performance of length-based methods (LBI, LBSPR and LBB) in predicting small-scale multispecies fishery sustainability using the 22 Azorean priority stocks as a case study. The aspects to be studied also included: (1) analysing the methods' applicability towards the case study stocks and (2) the methods' robustness to initial life-history input parameters.

Species length composition
Length-frequency data for the 22 priority stocks were obtained from the database of the Department of Oceanography and Fisheries, University of  L 95% = 1.1*L mat Prince et al. (2015a) the Azores (DOP/UAz) and collected as part of the European Commission's Data Collection Framework (DCF; EU, 2008). The length-frequency data analysed in the present study focuses on the period between 1990 and 2017. However, for species such as parrotfish, thornback ray, silver scabbardfish and common mora, sampling data only exist from the 2000s onward. Due to the scarcity or non-existence of length composition data for the invertebrate species, rough limpet, common spiny lobster and mediterranean slipper lobster, these species were removed from the analysis, because they were not sampled by the DCF during the study period. Length-composition and selectivity pattern was analysed for each métier. According to the DCF (EU, 2008) métiers is defined as a group of fishing operations targeting a specific assemblage of species, using a specific gear, during a precise period of the year and/or within the specific area. The DCF defines métiers according to a hierarchical structure using six nested levels: (1) activity (fishing/non-fishing); (2) gear class (e.g., trawls and hook and lines); (3) gear group (e.g., bottom trawls and longlines); (4) gear type [e.g., bottom otter trawl (OTB) and set longlines (LLS)]; (5) target assemblage based on the main species group (demersal fish vs. crustaceans); (6) selectivity devices. In the end, for convenience, we also define here a further disaggregation level distinguishing targets at the true species level (e.g., blue jack mackerel, red porgy, blackspot seabream, common mora) as level 7, as distinct from DCF level 5, which deals only with species group. This level 7 to describe the landing profile. The métiers included in the current study are presented and defined in Table 2 and those with a sampling frequency of 25% or more were designated as main fishing gear (Fig. 2).
Our study objective is to predict the sustainability of the stocks and, the following criteria for data aggregation (based on Pons et al. (2019)) were used: (1) for stocks that have the same selectivity pattern for the main métiers, aggregate data from these métiers for use in the length-based models; and (2) for those stocks with a different selectivity pattern for each métier, the data for the métier with the widest size range was used.

Life-history traits
Length-based models are sensitive to values of the input life-history parameters (Hordyk et al. 2015a(Hordyk et al. , 2016. Three sources are presented here: (1) Azores-based on an extensive literature review of local life-history parameters , in which the median values for each one of these lifehistory parameters were considered; (2) FishLife R package (Thorson et al. 2017)-this package can reliably estimate life-history parameters, either derived statistically from taxonomically-related species or derived from FishBase; (3) Empirical relationships-this approach only requires a local estimate of maximum length (L max ) to generate the missing life-history parameters (Table 3). Stocks in the Azores without these estimated parameters, such as amberjacks nei, parrotfish, red scorpionfish, European conger and black scabbardfish, had their growth parameters (asymptotic length-L ∞ and growth coefficient-k) estimated in this study through the von Bertalanffy growth function, using monthly lengthfrequency data derived from the DCF database for the period between 2010 and 2017. These growth parameters were calculated by length-frequency analysis using a genetic algorithm (ELEFAN_GA) within the TropFishR R package Taylor and Mildenberger et al. 2017). The natural mortality (M) was computed as the average value of natural mortality, estimated from several methods (Tanaka 1960;Taylor 1960;Pauly 1980;Gunderson and Dygert 1988;Pauly and Binohlan 1996;Cubillos et al. 1999;Hewitt and Hoenig 2005). The values used for the sensitivity analyses of the three sources presented here are summarised in Table A1 in Supplementary Material. The life-history parameters for SQF (a squid species) were not available, and the ELEFAN_GA result was unreliable; therefore, this species was removed from the analysis. Considering that blackspot seabream is a protandric hermaphrodite (i.e., individuals are at first male and then become female), this study considered length at maturity (L mat ) as the length at which individuals change sex.

Length-based indicators (LBI)
The LBI method requires data on catch length composition and life-history parameters (Fig. 3), and are based on ratios between several parameters, such as: length at first capture (L c ); length at maturity (L mat ); 25th percentile of length distribution (L 25% ); mean length of largest 5% of individuals in the catch (L max5% ); asymptotic length (L∞); the proportion of individuals above length optimal yield (L opt ) + 10%, where Lopt = L∞ 3/(3 + M⁄k); mean length of individuals (L mean ) > L c ; mean length-based proxy for MSY (L F=M = 0.75L c + 0.25 L∞; Jardim et al. 2015;ICES 2018). LBI indicators were calculated by year and the analyses were run using the R-script LBIindicators.R (ICES 2018).
Length-based spawning potential ratio (GTG -LBSPR) The LBSPR method uses life-history ratio M/k, which is believed to vary less across stocks and species than M (Prince et al. 2015). Additionally, the LBSPR applies the shape of the length composition data compared to the expected unfished length structure to estimate the ratio of fishing mortality and natural mortality (F/M). The selectivity parameters (SL 50 and SL 95 ) were adjusted (by minimising a multinomial negative log-likelihood function) to obtain the closest match between these two lengths distributions and derive the spawning potential ratio (SPR) (Hordyk et al. 2015a(Hordyk et al. , 2016ICES 2018). SPR is 100% in unexploited stocks (SPR = 1) and 0% in stocks with no spawning (SPR = 0, e.g., all mature fish have been removed or all female fish have been caught), therefore in these situations, years corresponding to such values were removed from the model. The analyses were run using the growth-type-group model available in LBSPR R-package (Hordyk and Mardones 2019).

Length-based Bayesian biomass (LBB)
The length-based Bayesian biomass estimator (LBB) method stands out from the two other length-based methods because it can be used in stock assessment to estimate the relative stock size and other reference points. Firstly, the LBB estimates L∞, L c , M/k, and F/k. If a reliable local estimate of L∞ from an independent source is available, this is the recommended value to use, thus decreasing uncertainty in LBB results (Froese et al. 2018a). With these parameters, the current stock size in the form of biomass depletion B/B 0 and L mean /L opt for size and age composition of health state can be calculated from standard equations. The version of the code used (LBB_33a; . Here, we have presented only the main equations, and referred to Froese et al. (2018a) for detailed information.
The LBB method assumes that fish grow according to the standard von Bertalanffy growth equation (von Bertalanffy 1938;Beverton and Holt 1959): where L t is the length at age t, L∞ is the asymptotic length, k is the growth coefficient and t 0 is theoretical age at zero length.
If the gear operates with full selectivity, the curvature of the catch samples in numbers-at-length is a function of Z/k, total mortality rate relative to k, and is described by the equation (Quinn and Deriso 1999): where N L is the number of survivors to length L, and N Lstart is the number at length L start , which indicates the starting size of full selection by gears.
The catch in numbers that is subject to partial selection is a function of gear selectivity (here assumed to be knife-edge), which could be used as a complement to Eq. 2 and is described below: where SL is the fraction of individuals that are retained by the gear at length L, L c is defined above, and α describes the steepness of the ogive (Froese et al. 2018a).
Adjusting and combining Eqs. 2 and 3 leads to Eq. 4 (Froese et al. 2018a), the parameters of the selection ogive are estimated simultaneously as L∞, L c , alpha, M/k, and F/k by fitting: where N L_i is the number of individuals in length i, N L_i-1 is the number at the previous length, C refers to the number of individuals vulnerable to the gear, and all other parameters are as described above (Froese et al. 2018a).
Finally, the following equation describes the framework to estimate the stock status from L∞, M/k, F/k, and L c (Froese et al. 2016). With the estimation of the parameters above, the value of L opt maximising the unexploited cohort biomass can be obtained from Eq. (6): Based on Eq. (6) and a given fishing pressure (F/M), the L C which maximises catch and biomass (L c_opt ) can be obtained from: (2) Estimates of L c_opt are used to calculate a proxy for the relative biomass that can produce the MSY (B MSY /B 0 ) (Froese et al. 2018a).

LBI
Froese (2004) proposed three simple and easily understood reference points, P mat , P opt and P mega , that were derived primarily from understanding the biology and exploitation of demersal teleost fish stocks. The principles were: (i) P mat -the proportion of fish in the catch that are larger than length at maturity (L mat ); (ii) P opt -the proportion of fish larger than optimal harvest length (L opt ); (iii) P mega -no fish larger than L mega should be caught and P mega in the population should be at least 30%. Each LBI comprises the ratio of a measured length statistic and corresponding exploitation or life-history threshold; thus, a traffic light approach (Caddy et al. 2005) is then used to compare LBI estimates to a reference point at which sustainable yield is achieved.

LBSPR
In fisheries without catch or abundance information, the SPR is typically used as an alternative reference point to the biomass at maximum sustainable yield (B MSY ). According to Brooks et al. (2010), SPR has been recommended for data-limited assessments because it can be estimated using only biological information and length data and could be proposed as thresholds for overfishing or F MSY proxy. In this study, a limit of 30% SPR was used, and stocks with SPR values below this value were considered unsustainable. This threshold value is a standard recommendation for lesser-known stocks (Restrepo et al. 1998;Nadon et al. 2015). Selectivity parameters were assumed to be equal to length at maturity (Hordyk et al. 2016) and a default value of F/M ratios = 1 was used for all species.
The reference points estimated from LBB could be proposed as thresholds for overfishing. Parameter F/M > 1 indicates that the assessed stocks are being overfished or overfishing (F > F MSY ). Besides, if the ratios (L mean /L opt and L c /L c_opt ) are below 1 the stocks are considered as suffering from growth overfishing. If the parameter of the 95th percentile length to L∞ (L 95th /L∞) is approximately one (> 0.9), this suggests there are at least some large fish in the region.  (Worm et al. 2009;Froese et al. 2018b). Based on this information, management can propose changes in Lc and fishing effort until relative biomass predicted by length-frequency data exceeds the approximate MSY level: (i) B/B 0 is smaller than B MSY /B 0 (B/B MSY < 1), the catches should be reduced; (ii) L c is smaller than L c_opt , then fishing can be started with a larger individual size.

Sensitivity analyses
For the sensitivity analyses, the most important stock (in landed weight) from each fish assemblage was selected: pelagic, Atlantic chub mackerel: shallow demersal, red porgy; intermediate demersal, blackspot seabream; and deep demersal, common mora. Length-composition data from 2017, selected based on the criteria described in the Species length composition section, were used as a baseline for comparing the potential biases introduced by life-history input data in the reference points' output estimations. To investigate the robustness of the length-based models, sensitivity analyses were performed to test the effects of source bias of initial parameters. To do this, in addition to the estimated data for the Azores, statistically derived life-history parameters of taxonomically related species found in the FishLife R package were used (Thorson et al. 2017), along with parameters estimated from empirical relationships based on the local estimate of maximum length (L max ). The three sources of input life-history parameters (i.e., Azores, FishLife and empirical equations) are summarised in Table A1 in Supplementary Material. The estimated values of L∞, L mat and M/k, from these three different sources, were used to check for uncertainty in LBI and LBSPR reference points' outputs, and whether these models are sensitive to the selection of input data parameters. In this study, we also conducted sensitivity analyses for the LBB method with prior information from those sources and estimates derived from the LBB method.

Species-length composition
Length-frequency data was unimodal for most of the 18 fish stocks assessed in this study, except for the pelagic species blue jack mackerel, atlantic chub mackerel and amberjacks nei, which were bimodal (Fig. 4). Fishing targeting the studied stocks used several fishing gears, with six main métiers: longlines for demersal fish (LLS_DEF), hand lines for demersal fish (LHP_FIF), han lines for pelagic fish (LHP_ MDP), drifting longlines (LLD), purse seine for small-pelagic fish (PS_SPF) and gillnets for coastal demersal and pelagic fish (GNS_FIF). Longlines for demersal fish (LLS_DEF) and hand lines for demersal fish (LHP_FIF) were used to capture 13 of the 18 stocks (Fig. 4). Larger individuals were mainly caught by longlines (LLS_DEF), while the smaller ones were mainly caught by handlines (LHP_FIF; Fig. 4).
Sixteen of eighteen study stocks (amberjacks nei, red porgy, forkbeard, parrotfish, red scorpionfish, blacktail comber, thornback ray, blackspot seabream, blackbelly rosefish, European conger, alfonsino, splendid alfonsino, silver scabbardfish, offshore rockfish, common mora and black scabbardfish) have the same selectivity patterns for the main métiers, thus, aggregate data were used to test the stock assessment models' performance. Just two pelagic stocks Jblue jack mackerel and Atlantic chub mackerel presented different selectivity patterns for the main métiers, and in this case, data from the métier purse seine for small pelagic fish (PS_SPF) was used in the length-based assessments.

Length-based indicators (LBI)
The LBI results for conservation (immature and larger individuals), optimum yield and MSY are shown in a traffic light table for the last three years 2015-2017 (Table 4) and are compared to the reference points recommended by ICES (2018). The L c / L mat and L 25% /L mat were below the reference points in 44% of the stocks assessed, indicating that immature individuals are being depleted, with lengths at first capture shorter than lengths at maturity. In 55% of the stocks, the indicators L max5% /L∞ and P mega were less than the reference points, suggesting that larger individuals and mega-spawners are uncommon in the population. The optimum yield (L mean /L opt ) and MSY (L mean /L F = M) indicators were above the reference points in 61% of the stocks, suggesting a sustainable fishery at levels close to optimum yield and with exploitation at the MSY level for these stocks. Only four stocks presented good biological limits for all indicators: red scorpionfish, European conger, common mora and black scabbardfish. The LBI findings revealed a similar pattern of changes in the conservation indicator (immature and larger individuals) after the 2000s, based on the study years . Table A2 in Supplementary Material contains traffic light tables including the LBI results for all stocks and time periods.
Length-based spawning potential ratio (GTG -LBSPR) The LBSPR results for the reference points SPR, F/M and selectivity parameters (SL 50 and SL 95 ) are presented in Fig. 5. SPR estimates over the entire period (1990-2017) resulted in low values (below 30%) for 44% of the stocks analysed, indicating that these stocks are below proxies that would be consistent with high long-term yields (Fig. 5). The F/M ratio was greater than 1 in 66% of the stocks, suggesting overfishing since current exploitation is above the fishing mortality at MSY (F MSY ; Fig. 5). The parameters SL 50 and SL 95 were lower than the length at maturity in 44% of the stocks, suggesting that the fishery targeted undersized individuals (Fig. 5). Only three stocks had all three reference points inside the safe biological limits: blacktail comber, forkbeard and common mora. Based on all study years , the LBSPR results showed a similar   (Fig. 5).

Length-based Bayesian biomass (LBB)
The values of reference points L mean /L opt , L c /L c_opt , L 95th /L∞, M/k, F/M, B/B 0 and B/B MSY for all 18 stocks assessed in this study are summarised in Table 5. The L mean /L opt and L c /L c_opt ratios were lower than 1 for 33% of the stocks, suggesting a truncated length structure and fishing of undersized individuals. The L 95th / L∞ ratio was close to one (> 0.9) in 65% of the stocks, suggesting that at least some larger fish were still present. Of the 18 stocks assessed, the atlantic chub mackerel and parrotfish had a stock status classified as Amberjacks nei, red porgy, forkbeard, blacktail comber, blackspot seabream, blackbelly rosefish, european conger, alfonsino, common mora and black scabbardfish were classified as healthy. The estimated values of B/ B MSY ranged from 1.5 to 2.8 and the estimated value of F/M was lower than 1. Most of the stocks assessed here showed high estimates of B/B MSY , low F/M and a good length structure, indicating that these stocks were inside of safe biological limits (Fig. 6).

Length-based indicators (LBI)
Biases in selected initial values of L∞ and the ratio M/k negatively affected the indicators of conservation to the proportion of larger individuals in the catches (L max5% /L∞ and P mega ) and optimum yield (OY; Fig. 7; Table A3 in Supplementary Material). The opposite was observed in L mat bias, which was not as sensitive and resulted only in minor changes in the indicators of conservation to the proportion of immature individuals in the catches (L c /L mat and L 25% /L mat ; Table A4 in Supplementary Material). In general, the MSY indicator was not strongly impacted by bias in selected initial values of L∞, L mat and M/k (Fig. 7). The most sensitive indicator to bias in the input parameters was P mega (Fig. 7). Although the choice of both the input parameters L∞ and M/k had an impact on the results of the LBI method, the parameter L∞ had the greatest impact. Furthermore, the conservation indicators of immature individuals were not affected by the L∞ or M/k biases. Changes in percentage for all indicators and absolute values of the LBI sensitivity analysis output can be found in Tables A3 and A4 in Supplementary Material, respectively.

Length-based spawning potential ratio (GTG -LBSPR)
The reference points SPR and F/M estimated by the LBSPR were sensitive to bias in the input parameters L∞ and M/k ratio (Fig. 8). Bias in initial values of L∞ and M/k ratio negatively affected SPR estimates while positively affecting F/M estimates (Fig. 8). The opposite was noted in L mat bias, which was not as sensitive and resulted only in minor changes mainly in SPR estimates (Fig. 8). In general, the selectivity parameters (SL 50 and SL 95 ) were not strongly impacted by bias in selected initial values of L∞, L mat and M/k (Fig. 8), and the most sensitive indicator to bias in the input parameters was F/M (Fig. 8).
Although the choice of both input parameters L∞ and M/k had an impact on the results in the LBSPR method, the ratio M/k had the greatest impact. Changes in percentage for all indicators and absolute values of the LBSPR sensitivity analysis output can be found in Tables A5 and A6 in Supplementary Material, respectively.

Length-based Bayesian biomass (LBB)
The reference points L 95th / L∞, F/M and B/B MSY estimated by the LBB method were strongly sensitive to source bias (FishLife, Empirical equations and LBB) of the input parameters (L∞, L mat and M/k; Fig. 9). Source bias in the initial life-history parameters showed a high, negative impact on the F/M ratio (Fig. 9). The relative biomass (B/B MSY ) also was sensitive to source bias in the initial parameters and being positively affected, could overestimate biomass  (Fig. 9). The ratios L 95th /L∞ were sensitive to source bias in the initial life-history parameters but not to the degree of F/M and B/B MSY (Fig. 9). Although the choice of source bias in the input parameters impacted the results of the LBB method, the sources Fish-Life and derived from LBB were the ones that most affected the reference points. Changes in percentage for all indicators and absolute values of the LBB sensitivity analysis output can be found in Tables A7 and A8 in Supplementary Material, respectively.

The stock status of Azores priority stocks
In this contribution, we applied the LBI, LBSPR and LBB methods to 18 fishery stocks distributed in the Azores region. The results showed that 45% of the evaluated stocks were sustainable stocks (FOR, SER, WSA, BRF, COE, BXD, RIB and BSF), 33% were possible rebuilding/overfished (AMX, RPG, PRR, SBR, BYS and POI) and 22% were overfishing/overfished (JAA, MAZ, RJC and SFS; Fig. 10). According  to the biological reference points estimated by these three methods, the stocks with possible rebuilding/ overfished or overfishing status presented high F/M rates, poor conservation of small or larger individuals, low relative biomass, and exploitation at or above MSY levels (Fig. 10).

Applicability of length-based methods
This study demonstrates that the length-based methods LBI, LBSPR and LBB offer a valuable tool for stock assessment of small-scale fisheries. These  2015a) as the most appropriate methods to achieve reliable assessments. Additionally, we also included the LBB method (Froese et al. 2018a) because it can be applied to the Azorean stocks by specifying priors for the known life-history parameters (i.e., L∞ or M/k),has been considered as a useful method by the International Commission for the Conservation of Atlantic Tunas (ICCAT) (Dimarchopoulou et al. 2021), and has been applied to Asian fisheries (Ju et al. 2020;Liang et al. 2020;Kindong et al. 2020).
Despite LBB's application elsewhere, our study represents the first comparison of LBB and other lengthbased methods (Pons et al. 2020;Dimarchopoulou et al. 2021).
The length-based assessment methods LBI, LBSPR and LBB assume that equilibrium conditions, i.e., mortality rates (Z, M and F) and recruitment have been constant for a period equal to the lifetime of the time series. According to Gedamke and Hoenig (2006) equilibrium assumptions are often violated, Fig. 10 Summary of the LBI, LBSPR and LBB results, current stock status and management measures recommendations for the Azorean priority stocks. CL: conservation of large individuals; CI: conservation of immature individuals; OY: optimal yield and MSY: maximum sustainable yield; * indicated that the indicator ratios of the corresponding property are above their expected values whereas; x indicates the opposite and ≈ indicates that the indicator ratios of the corre-sponding property are below, but very close to, their expected values. Recommendations: The vessel indicates fishing effort should be reduced; Decreasing trend indicates catches should be reduced; Stable trend indicates catches should be maintained; Hook with fish indicates minimum hook size should be applied; and the fish draw indicates minimum landing size should be applied or increased as recruitment is variable for most species because of the stochastic ocean conditions Szuwalski et al. 2015) and F changes due to markets and other socioeconomic factors (Thorson et al. 2013;. However, the violation of the equilibrium assumption may be difficult to detect, appearing valid when the mean length is constant over time (Gedamke and Hoenig 2006;Nadon et al. 2015;Rudd and Thorson 2018). Nevertheless, these assumptions seem to cancel each other out, i.e., if the recruitment is constant over time, increases in F will lead to decreases in mean length as larger/ mega-spawner individuals are harvested, and if F is constant with pulses of recruitment the same situation occurs, with more young individuals entering the population. Given both variable F and recruitment occurring in the population, as well as errors in the mean length measurement, a mean length time-series should appear constant when time-varying population processes are cancelling each other out (Rudd and Thorson 2018). The present study used length data collected by standardised methods and a robust sampling design, with mixed gear selectivity being properly accounted for and all fishing gear types sampled (métiers) in a time-series ~ 27 years , resulting in greater accuracy and precision of reference points' estimates from length-based assessment methods.
According to Chong et al. (2020), life histories have a clear impact on the performance of the lengthbased assessment methods, and notably, each method had difficulties in assessing short-lived species, especially when estimating F and F MSY , and consequently F/F MSY . The increased bias and decreased precision of F/F MSY stem from the decreased accuracy of calculating fishing mortality and F MSY . Hordyck et al. (2015b) also found biased estimates for shortlived species, as these methods often rely on detecting the signal of F on the upper tail of the length composition. On the other hand, for longer-lived species, spawning biomass is represented by older individuals and is reduced even with low fishing rates. Meanwhile medium-lived species are recruited at an early age, which allows for more accurate data to be collected about the population, and thus these species seem the easiest to assess as their cohorts can be tracked, and it is easier to sufficiently sample length classes (Chong et al. 2020;Pons et al. 2020). The eighteen stocks here assessed are considered medium (blue jack mackerel, atlantic chub mackerel, amberjacks nei, red porgy, forkbeard, parrotfish, blacktail comber, thornback ray, blackspot seabream, splendid alfonsino, silver scabbardfish, offshore rockfish and black scabbardfish) or long-lived (red scorpionfish, blackbelly rosefish, european conger, alfonsino and common mora) species thus reinforcing the greater accuracy and precision of our reference points' estimates from length-based methods..
The reliability of stock statuses estimated by length-based assessment methods relies on the assumption that fisheries display asymptotic selectivity (logistic size-selectivity; Hordyck et al. 2015a; Froese et al. 2018a;Rudd and Thorson 2018) and results are sensitive to dome-shaped selectivity. That is, the absence of larger fish in the catch entails a right truncated catch length distribution, with the logistic selectivity models subsequently assuming these individuals do not exist in the population, when in fact they simply were not caught by the fishing gear. The logistic selectivity assumption often is violated in size-selective fisheries (i.e., gillnets) and in multi-fleet fisheries, where stocks are caught in different proportions by multiple gears with different selectivity patterns (Pons et al. 2019). On the other hand, changes in availability in space (e.g., seasonal migration or fishing vessel operation area) also can result in a violation of the logistic selectivity assumption (O'Boyle et al. 2016).
Based on our results derived from the LBB method, the ratios L mean /L opt and L c /L c_opt were higher than 1 for most (67%) of the stocks assessed (forkbeard, parrotfish, red scorpionfish, blacktail comber, thornback ray, blackspot seabream, blackbelly rosefish, european conger, alfonsino, splendid alfonsino, common mora and black scabbardfish), suggesting that the right truncation of the catch length distribution was not observed (i.e., selectivity was asymptotic, as assumed). Just six (33%) stocks (blue jack mackerel, atlantic chub mackerel, red porgy, offshore rockfish, and silver scabbardfish) had a truncated length structure and undersized individuals were fished, although for three stocks (red porgy, offshore rockfish, and silver scabbardfish) it seems at least some larger fish are no longer present (L 95th /L∞ ratio < 1), which indicates selectivity is not domeshaped for these stocks and instead recruitment overfishing may be occurring. Lastly, asymptotic selectivity historically has been assumed for most Azorean stocks (Morais 1990;Sousa et al. 1999).
Dome-shaped selectivity and a multimodal length composition were observed in the three pelagic stocks blue jack mackerel, atlantic chub mackerel, amberjacks nei, and the models likely did not fit well, leading to unrealistic estimates in these cases. This occurred despite following the recommendations of Pons et al. (2019) for stocks that showed a different selectivity pattern, which state that length-based assessment methods should be applied to length data coming from the métier that targets the broadest range of sizes including adults, providing a lower bias in SPR estimates. For two of these three stocks, the broadest range of sizes came from the purse seine fishery which targets small fish. Therefore, it is possible that larger fish are underrepresented in our data for these stocks, and consequently, the model overestimates F/M ratios and underestimates SPR, and the effects of length data biased towards smaller fish have a greater impact (almost threefold) on SPR estimates than length data biased towards larger fish (Dai et al. 2021).
Estimates of P mega from LBI were less than 0.3 for most of the assessed stocks, which indicates a possible violation of the assumption of asymptotic selection or depletion of the mega spawners in the population. However, most of the stocks fulfilled the assumption of asymptotic fishing selectivity -except blue jack mackerel, atlantic chub mackerel, amberjacks nei, which showed dome-shaped selectivity, and ed porgy, offshore rockfish, and silver scabbardfish, in possible recruitment overfishing. In addition, Cope and Punt (2009) found that P mega showed a wide range of possible values depending on fishery selectivity and challenged the notion that P mega values between 0.3 and 0.4 indicate healthy stocks, which could encourage fake overfishing scenarios (Froese 2004). Thus, like Cousido-Rocha et al. (2022), our results showed that P mega should not be used because it may provide misleading conclusions. We also recommend that the reference point L max5% (LBI method) should be used to evaluate the presence of mega spawners (very large individuals) in the catch and help determine exploitation level. Thus, for those stocks with high M/k ratios (> 1), L max5% combined with the appropriate reference point can be used to provide a data-limited stock assessment (Miethe et al. 2019).
Lastly, the length-based assessment methods (LBI, LBSPR and LBB) used in the current study were robust, converged to the same stock status, and achieved the data-limited methods assumptions-the guidance proposed by Chong et al. (2020) was helpful in applying these methods within a small-scale multispecies fishery context. These three methods provide rapid assessments, support management measures, and help guarantee stock sustainability. The Azorean stocks analysed here represented a range of challenges for assessment, including differences in data quality among stocks and longevity of the species from medium to long-lived, yet assessments generally provided robust results. Our example is evidence that assessments of data-poor stocks in other regions of the world also would benefit from application of these length-based methods.

Sensitivity analysis
Sensitivity analysis was performed to investigate the effects of source biases (Azores, FishLife and Empirical equations) of initial life-history parameters (L∞, L mat and M/k) for the length-based methods (LBI and LBSPR). For both methods, biases in L∞ and M/k parameters respectively had a stronger influence on the reference points values than L mat values, especially for the P mega estimates (LBI method), SPR and F/M (both LBSPR method). The same pattern was found by Amorim et al. (2020) for snapper and grouper fisheries in Indonesia, Cousido-Rocha et al. (2022) for fishery resources in the Bay of Biscay and the Iberian Coast ecoregion, and Pennino et al. (2022) for the common sole on the Iberian coast. Fig. 11 Overview of the recommendations to be applied in small-scale fishery stock assessment using length-based methods Through our study, we conclude that the effects of the misspecification of L∞ and M/k can generate failures in current stock status classification and in management measure recommendations. These mistakes are observed when L∞ is underestimated or overestimated, negatively affecting the estimates of P mega and OY (LBI method), SPR (LBSPR method) and positively F/M (LBSPR method). According to Shephard et al. (2018), a highly unrealistic L∞ may lead to false negatives (indicating a poor status when in fact status is good), whereas a low L∞ may lead to false positives (indicating a good status when in fact the status is poor). Therefore, best practices for determining initial life-history values in length-based assessments would be to use estimates from stock-specific studies .
However, in data-limited small-scale fisheries, these studies are often not available. Thus, our practical recommendation is for life-history parameters to be estimated by ELEFAN routines, based on the length composition data, thereby reducing uncertainties in the assessments. The estimates generated from ELEFAN routines are robust to changes in size structure due to fishing pressure , whereas the estimates derived from empirical equations are potentially affected when using L max and are not sensitive to changes in mean length. For the blacktail comber stock, this effect may have led to an unrealistic stock status in previous studies in the Azores (Amorim et al. 2021) since it was classified as fished at unsustainable levels. The performance of our assessments was based on initial life history estimated from stock-specific studies, and the WSA is classified as a sustainable stock. Finally, in the absence of stockspecific studies or of a time series of length composition data (single year assessments) to estimate initial life-history parameters using ELEFAN routines, our recommendation is to carry out sensitivity analysis on these parameters. A diagram with the pathway of our recommendations is presented in Fig. 11.
The sensitivity analysis also shows that the L mat parameter is crucial for realistic estimates, more so than L c /L mat and L 25%/ L mat (conservation of immature individuals, LBI method) and SPR estimates (LBSPR method). No effects of the L mat bias were found on L max5% /L∞, P mega , OY and MSY (LBI method) and F/M (LBSPR method). Given these results, we can conclude that the most robust reference point was MSY (LBI method), the least suitable was P mega , and both LBI and LBSPR methods can be used together to obtain more precise stock status estimates. Nevertheless, if the results from both methods do not converge on the same stock status, if the life-history input parameters are uncertain, and both model assumptions are fulfilled, the LBI method seems to be more robust and reliable than LBSPR. Studies performed for fishery resources in the Bay of Biscay and Iberian Coast ecoregion also found similar results regarding these methods robustness Pennino et al. 2022).
In this study, we also analysed the sensitivity of the LBB method to prior information from the three sources (Azores, FishLife and Empirical equations) and estimates derived from the LBB method. The reference points F/M (underestimated), B/B 0 and B/ B MSY (both overestimated) were strongly affected by the choice in the source of input parameters; the sources FishLife and derived from LBB affected results the most. The same pattern was found by Dimarchopoulou et al. (2021) for the Indonesian deep demersal fishery. Indeed, based on method sensitivity, lower L∞ priors from the FishLife and LBB resulted in an overestimation of B/B 0 and B/B MSY . Biases in M values also impact the biomass index, since higher M for the same Z will correspond to lower F given the catch, and consequently higher biomass (Punt et al. 2021). Therefore, based on our results, we also encourage users of the LBB method to use life-history input parameters from stock-specific studies, and to replace the default setting of M/k to reduce bias and uncertainty and increase the reliability of the estimates of B/B 0 and B/B MSY .
Finally, these three length-based methods performed well across the Azorean stocks' life-history strategies (medium and long lived), while other methods such as length-based integrated mixed effects (LIME; Rudd and Thorson 2018) can underestimate SPR (Chong et al. 2020;Pons et al. 2019). The exception is the Azorean pelagic stocks, which did not present a good fit and the exploitation status seems unrealistic, due to the dome-shaped selectivity (Pons et al. 2019) and disproportionately high frequency of small fish sampled (Dai et al. 2021).
The stock status of Azores priority stocks Most of the fish stocks presented here have never been, or cannot be, comprehensively evaluated because of a lack of data. This is the first application of an extensive assessment based on data-limited methods and sensitivity analyses on eighteen priority stocks in the Azorean waters. For most of these fish stocks, the estimates of stock status presented were not comparable with previous knowledge resulting from assessments, such as those provided as advice to the European Commission by ICES in the Northeast Atlantic, except for blue jack mackerel, thornback ray, blackspot seabream, alfonsino, and splendid alfonsino.
In this study, four stocks (blue jack mackerel, atlantic chub mackerel, thornback ray and silver scabbardfish), had an overfishing/overfished status. Blue jack mackerel and atlantic chub mackerel, small-pelagic species, have been historically exploited in the Azores by purse seine fishing gear that target their young/small individuals, to be used as live bait in tuna fisheries (Santos et al. 2020a). This selective fishing activity reduces the number of older females, with negative implications for recruitment (Berkeley et al. 2004) and consequently population density (Jobling 1995). Overfishing of thornback ray, has also been detected in other parts of the Atlantic (Ryland and Ajayi 1984;Walker and Howlett 1997;Whittamore and McCarthy 2005) and Mediterranean (Aldebert 1997;KrstulovićŠifner et al. 2009). Recently Santos et al. (2021b) warned of this stock's sensitivity in Azorean waters and our study results reinforce the elasmobranchs' (sharks, skates, and rays) fragility to fishing pressure (Bonfil 1994). The silver scabbardfish, is caught mainly as commercial by-catch in several countries worldwide (Robertson 1980;Tuset et al. 2006;Figueiredo et al. 2015;Torre et al. 2019) and appears to be a cyclic resource, that forms schools and undertakes nocturnal vertical migration (Demestre et al. 1993). Peaks in the Azorean historical landings data may be associated with these factors and strong recruitment events (Falsone et al. 2021). The silver scabbardfish stock status was also reported as overfished in the Mediterranean Sea (Falsone et al. 2021) and the fast decline of the stock in the Azores has been due to the increase of fishing effort starting in the 1990s for target species, such as blackspot seabream.
Six stocks (amberjacks nei, red porgy, parrotfish, blackspot seabream, splendid alfonsino and offshore rockfish), had a possible rebuilding/overfished status. Some of these stocks, such as the amberjack nei, parrotfish and red porgy share similar behaviour patterns and habitats, e.g., inhabiting coastal areas at depth ranges down to 50-80 m (Guidetti and Boero 2002;Pinho et al. 2020), high site fidelity (Afonso et al. 2008;Pinho et al. 2020), and amberjack nei is found in small schools (Smith-Vaniz 1995). The blackspot seabream and splendid alfonsino are found deeper than stocks mentioned above-typically between 100 and 600 m -however, the life stages of these two species are segregated by age and length, with juveniles in shallow and coastal zones (nursery areas), pre-adults in intermediate zones, and adults in deeper and offshore zones, using these deeper areas for spawning (Pinho et al. 2014;Santos et al. 2019a. In turn, offshore rockfish are sedentary, usually found at depths like blackspot seabream and splendid alfonsino. However, for offshore rockfish depth distributions do not differ between juveniles and adults (Santos et al. 2019a;Pinho et al. 2020), although juveniles seem to be more abundant on seamounts while adults tend to occur more often on island slopes (Catarino et al. 2013).
Two strong reasons that may explain the possible rebuilding/overfished status of these five stocks. Firstly, stocks such as amberjack nei, red porgy and parrotfish inhabit coastal shallow areas; these areas have been historically exploited by Azorean fisheries that operate near the islands (Carvalho et al. 2011). These coastal stocks are also exposed to recreational fishing which likely negatively affects their populations (Diogo and Pereira 2013;. Secondly, commercial fishing close to the islands also puts pressure on blackspot seabream and splendid alfonsino nursery grounds, having negative impacts on the annual rebuilding of the adult population in offshore areas, and removing offshore rockfish mega-spawners and negatively impacting recruitment. However, since the 2000s, several management measures have been implemented by the regional government of the Azores, including area-gear restrictions (prohibition of the use of bottom longlines from 3 to 6 nautical miles from the shore; Ordinance N°101/2002), areavessel size restrictions (fishing effort reduction; Ordinance N°1102-C/2000 and N°43/2009) and selectivity restrictions (minimum hook size and prohibition of drifting pelagic longline; Ordinance N°101/2002 and N°116/2018), which have reduced fishing pressure on these stocks (Santos et al. 2019b).
These priority Azorean stocks do not have analytical assessments (i.e., F MSY , SSB, B lim and MSY B trigger estimates) and are currently managed according to a precautionary approach, meaning they are managed by default following limitations of the blackspot seabream fishery. Despite this, the structuring and zoning of Azorean fish assemblages (Menezes et al. 2006) seemingly allows most of the stocks assessed in the current study to benefit from management measures adopted in the last 20 years (e.g., fishing areas restriction, effort reduction and selectivity measures). In addition to the technical measures presented above, advice by ICES for total allowable catches (TACs) are provided for stocks such as blue jack mackerel, blackspot seabream, alfonsino, splendid alfonsino and thornback ray, which have been applied since the 2000s and recently were recommended by the regional government of the Azores for blackbelly rosefish, forkbeard, european conger, parrotfish, offshore rockfish, and common mora. A minimum landing size or weight was also implemented for some stocks (blackspot seabream, blackbelly rosefish, red porgy, european conger, alfonsino, splendid alfonsino, parrotfish, blacktail comber and thornback ray, which helps to avoid growth overfishing, as well as the creation of several marine protected areas (MPAs; Abecasis et al. 2015). Therefore, these eight stocks, considered as sustainable, could be candidates for a rebuilding effort, after the application of management measures in Azores' waters. These eight stocks appear responsive measures because all three lengthbased models used in the current study showed a similar pattern of reference point recovery after the 2000s.
The deep-water stocks common mora and black scabbardfish are mainly found at depths greater than 600 m , with black scabbardfish showing sporadic occurrences in the Azores (ICES 2020; Santos et al. 2019b). The commercial exploitation of both stocks in the Azores started just after the 2000s, following the spatial expansion of fishing efforts to deep offshore areas  because of the previously mentioned management measures, which could explain the sustainable stock status for both these stocks. However, attention needs to be paid to fishing pressure on the common mora stock, as it is considered vulnerable to overfishing .
Local management units are difficult to define for some stocks, such as alfonsino and black scabbardfish, which have spatial distributions that go far beyond the Azores' Exclusive Economic Zone (EEZ), and detailed data is only available for the Azorean sub-region. (ICES Subdivision 10.a.2). However, most of the stocks assessed in the present study are already considered local management units (MU) or formed by several local MUs, due to their population structure and life-history traits (Chevelot et al. 2006;Catarino et al. 2013;Vieira et al. 2016;Santos et al. 2019bSantos et al. , 2020bSantos et al. 2021a, b;Medeiros-Leal et al. 2021b;Santos et al. 2022) and high sedentarism (Afonso et al. 2016;Santos et al. 2020bSantos et al. , 2021bMedeiros-Leal et al. 2021b). Finally, it is important to highlight that Santos et al. (2020a) followed the guidelines suggested by FAO (FAO 2018) and ICES (ICES 2011) to select the 22 priority stocks for regional assessment. This stock selection was based on the ranking of landings by commercial value excluding stocks that migrate through, or occur in, more than one EEZ (i.e., straddling stocks).
According to ICES, most Azorean fishery resources are intensively exploited, with high historical fishing effort levels and decreased catches and landings (ICES 2018;Santos et al. 2019b). However, the present study's assessment, using the three length-based models, showed a more optimistic scenario and suggested the main objective of the European Union's (EU) Common Fisheries Policy (CFP; CFP, 2013)-of rebuilding all commercially used fish stocks above levels that can produce MSY-has been advanced in the Azores, where 50% of stocks comply with CFP goals. To fully achieve this goal two steps are recommended: (1) fishing pressure (U) should be reduced to the F MSY ; (2) rebuilding the stocks' biomass above the B MSY level requires further reduction of U., i.e., U should be smaller than F MSY (Froese et al. 2018b).
The rebuilding time of stocks depends on the adoption of one of the following four exploitation scenarios: (1) no fishing takes place in stocks where B < 0.5 B MSY (fastest); (2) an F of 0.6 F MSY is applied if stock size (B/B MSY ) is ≤ 0.5 B MSY (intermediate); (3) an F of 0.8 F MSY is applied if B/B MSY is ≤ 0.5 B MSY (intermediate); (4) an F of 0.95 F MSY is applied independently of B/B MSY (slowest) (Froese et al. 2018b). Froese et al. (2018b) also state that implementing one of these rebuilding scenarios would be straightforward for Northeast Atlantic stocks which are already managed mainly with TACs based on exploitation rates and harvest control rules for depleted stocks. The ICES have been discussing harvest control rules for management of data-limited fisheries (ICES 2012).

Conclusion
This study provides robust stock statuses based on length-based assessment methods for a small-scale multispecies fisheries context. Given the results, 45% of the stocks assessed here display a sustainable stock status, and the three methods adopted showed good fit and a general agreement on exploitation status for most of the stocks assessed, except for pelagic species (blue jack mackerel, atlantic chub mackerel and amberjacks nei), thus strengthening our conclusions.
The LBI method performed more consistently than LBSPR and LBB. LBI is more sensitive to changes in the population structure, caused by fishing impacts and to management action responses. LBI, therefore, has the potential to help managers to assess changes in the fish community (Kell et al. 2022). The LBSPR and LBB methods the Beverton-Holt life history ratios (L mat , L∞, k, M, etc.). If these parameters are uncertain, the ability to classify stocks will be less reliable. Given these conclusions, we recommend future studies focus on exploring the decision tree proposed by Cope and Punt (2009) to estimate stock status indicators, based on three simple metrics: P mat (which reflects exclusive take of mature individuals), P opt (which consists primarily of optimal size fish), and P mega , to compare the results with those provided by the classic LBI approach.
On the other hand, for pelagic stocks and stocks unassessed in the present study due to unavailability of length-frequency data, we recommend exploring other data-limited assessment methods such as: (1) the stock reduction analysis approach, which has been further extended to incorporate prior information regarding resilience and population abundance at the start of the catch time series (Catch-MSY; Martell and Froese, 2013;Froese et al. 2017); (2) integrated stock assessments such as Stock Synthesis (Methot and Wetzel 2013) in a simplified way; (3) and the process and decision-support tool (FishPath), to guide identification of suitable harvest strategy component option given often debilitating conditions (Dowling et al. 2022).
Lastly, Fig. 10 provides management measures that we strongly recommend should be adopted based on each corresponding stock status. It is crucial that these recommendations be adopted given that, according to Hilborn et al. (2020), fish stocks scientifically assessed and managed around the world are increasing, or already are at or above levels that can provide a sustainable long-term catch (B MSY ).

Data availability
The data underlying this article will be shared upon reasonable request to the corresponding author.

Conflict of interest
The authors declare that they have no known conflicts or competing interests that influenced the work reported in this article.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.