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The aim of this paper is to develop a methodology to estimate recovery times using a wide range of published Ecopath modeled overfished data-rich fisheries that had not recovered in the North Sea, Mediterranean, and South America shelves. Recovery times were estimated by biomass increase according to the Verhulst logistic equation mathematical solution, requiring the intrinsic rate of natural increase, r, and the carrying capacity for a fishery, KE, both derived from documented fishery biological process principles. The mathematical solution indicated recovery from <0.2KE may be possible, initially to the minimum overfished level, BOF, of 0.25, then recovered, BREC, 0.4 of the fishery carrying capacity. It was estimated recovery in about 5 to ≤10 years could be obtained with fishing mortalities at half the intrinsic rate of natural increase. Recovery may require fishery stakeholders to select various strategies for recovery, including potential limitations by phytoplankton production in the fishery area. The documented recoveries for fishery areas of the sardine Namibian shelf fishery and climate-related temperature changes and upwelling effects on biomass of the hake fishery in the northern North Sea and West of Scotland shelves are used as examples. The potential recovery of a data-limited fishery is also shown using the relationships derived from the biological processes of data-rich fisheries. Further research is suggested on how to estimate the biomass of data-limited fisheries for recovery from overfishing.

Introduction

Estimation of the time for recovery from overfishing is an important part of fisheries management (Garciaet al., 2018) because a timely recovery using sustainable fishing mortality means a potential increase in fishery biomass and increased catches with less effort (Murawski, 2010; Brittenet al., 2021). In that regard, the literature indicates estimating the time for recovery is poorly defined or unknown, requiring intensive management of fishing mortalities and continuous monitoring of the fishery biomass to reach target reference points within ten years (Melnychuket al., 2020). For example, ICES (2020a) suggested rebuilding from overfishing requires adaptive management of newly obtained data to determine if the fishery biomass has approached the rebuilding target in the time required. The importance of the recovery of overfished fisheries was emphasized by the FAO in 2020 because of the global trend of overfishing, and it called for new mechanisms to support sustainable fisheries and ecosystems (see Melnychuket al., 2020). Therefore, the aim of this paper is to develop a methodology to estimated time for recovery of fisheries using sustainable fishing mortalities. Recovery times were estimated using the innovative approach of a wide range of published Ecopath modeled overfished data-rich fisheries that had not recovered in the European fisheries of the North Sea, Bay of Biscay and the Celtic Sea, and Northern and Central Adriatic Sea, and at the South America shelves of Central Peru and Central Chile. The recovery process findings from those fisheries were applied to reported recoveries of a Sardine (Sardinops sagax) fishery on the African Shelf and the European Hake (Merluccius merluccius) fishery, both subject to shelf environmental changes. As Melnychuket al. (2020) found, over half of the fisheries they examined were data-limited fisheries, and most were overfished. The methodology was also applied to the overfished Herring (Clupea harengus) fishery in the Bay of Biscay, and the Celtic Sea and the Indo-Pacific King Mackerel fished at the Goa fishery on the southwest coast of India. The King Mackerel recovery was estimated using the Ecopath Model results for a related King Mackerel species at the Gulf of Mexico, Yucatan shelf.

Although the literature shows biomass recovery improves for data-rich fisheries after stock status assessment (Costelloet al., 2012), it may not always be successful (Brittenet al., 2021), apparently due to additional mortality due to discards (Benakaet al., 2016). In addition, Ricker (1975) suggested the surplus production model may include an overestimate of recruitment, and Edgaret al. (2024), see their Fig. 5, which suggested stock assessment models could have an overstated bias related to natural mortality and recruitment and suggested stock assessments for overfished fisheries are adjusted for known biases as part of a precautionary approach for fishery catches for recovery from overfishing. Hence, recruitment was adjusted for the literature-documented precautionary factors in the Methods and Results Sections. Furthermore, Murawski (2010) showed that, in most cases, relatively high fishing mortalities are allowed to increase as the biomass increases during the recovery period, thereby slowing or preventing overall recovery. Hence, Murawski (2010) suggested an ecosystem-based approach to fishing mortalities is required for stock recovery, and Hodgson (2022) suggested overfishing could be reduced by using EBFM for small pelagic and pelagic finfish, as currently used for European fisheries (ICES, 2020b).

Fishery Fishery biomass Bt P/B Intrinsic r Net biological production P K E Fishing mortality reported, FMSY, FE [(ICES, 2020)]a Overfishing and recovered limits BOF = 0.25×K BREC = 0.40K Recovery times Bt to BOF, Bt to BRECb Fish catch at Bt, BOF, BRECC Ecopth model source
Sardine (Sardinops sagax) 7.909 1.4 0.8755 11.073 40.35 0.421, 0.754, 0.438 10.09, 16.14 0.8337, 2.9139 3.33, 4.25, 6.80 Tamet al. (2008)
Other large pelagics (eg., Sarda chiliensis, Thunnus albacares) 1.757 0.4 0.3365 0.703 11.47 0.199, 0.300, 0.168 2.868, 4.588 3.9588, 10.103 0.35, 0.57, 0.91 Tamet al. (2008)
Herring (Clupea harengus) 0.893 0.59 0.4637 0.527 5.17 0.073, 0.407, 0.232 1.2925, 2.068 1.15155, 3.284 0.065, 0.094, 0.151 Bentorchaet al. (2017)
Mackerel ^^ (Scomber scombrus) 0.40 0.4 0.3365 0.16 2.611 0.210, (applied 0.335), 0.300, 0.168 0.6528, 1.044 2.905, 9.8767 0.134, 0.219, 0.350 Bentorchaet al. (2017)
Horse mackerel (Trachurus symmetricus murphyi) 13.79 0.823 0.600 11.34 71.44 0.470, 0.518, 0.300 17.86, 28.58 1.03423, 4.86871 6.48, 8.39, 13.43 Neiraet al. (2004)
Hake (Merluccius merluccius) (<40 cm) 0.12 1.0 0.693 0.12 0.613 0.942, 0.597, 0.347 0.153, 0.245 1.6893, 3.9877 0.113, 0.144, 0.231 Collet al. (2007)
Large pelagic fishes (Thunnus thynnus, Xiphias gladius) 0.138 0.37 0.3148 0.051 0.938 0.187, 0.282, 0.157 0.2345, 0.3752 2.9278, 9.9863 0.026, 0.044, 0.070 Collet al. (2007)
Saithe (Pollachius virens) 1.213 0.685 0.5218 0.831 6.513 0.408, 0.453, 0.261, {0.363} 1.628, 2.605 1.7847, 5.8711 [BOF = 2.9595] 0.495, 0.664, 1.063 Hillet al. (2021) {(ICES (2020b)}
Plaice (Pleuronectes platessa) 0.140 0.601 0.4706 0.084 0.779 0.471, 0.459 0.4107a, 0.235, {0.250} 0.179, 0.286 1.76535, 5.9597 [6.962] 0.066, 0.042, 0.067 Hillet al. (2021) {(ICES (2020b)}
Cod (Gadus morhua) 0.160 0.776 0.5744 0.124 0.841 0.544, 0.497, 0.287, {0.162} 0.210, 0.336 1.728, 4.948 [2.846] 0.087, 0.114, 0.183 Hillet al. (2021) {(ICES (2020b)}
Table I. Theoretical Recovery Times (years) from Initial Biomass (Bt, tww/km2) to Overfishing and Recovered Reference Points (BOF, BREC, tww/km2)

As an alternative to EBFM, Ricker (1975) noted half the intrinsic rate of natural increase is the rate of fishing under equilibrium conditions at maximum sustainable yield, and Walterset al. (2008) suggest using r/2 as an acceptable target for sustainable fishing mortality. That approach is used here, and r/2 is called the equilibrium fishing mortality, FE. However, Cortés (2016) indicated that the estimation of r values is complex, so they are estimated here by applying the basic fishery population principles outlined by Ricker (1975), described in the Methods Section below. That shows the estimation of r depends on knowing the P/B ratio, the rate of biomass regeneration, which is provided in Ecopath Models by references by Colléteret al. (2013) for fish species, along with the fishery biomass, FMSY values, applied fishing mortalities and catch or landings. The Ecopath Models are also available in EcoBase–Ecopath with Ecosim ( https://ecobase.ecopath.org/) and provide fishery environmental drivers of phytoplankton production, which is important to support fishery production (Tweddleet al., 2018; Link & Watson, 2019), and may limit recovery of some fisheries.

To aid the recovery process, Melnychuket al. (2020) suggest reductions in fishing mortality for recovery when the biomass is less than 25% of the Schaefer surplus production carrying capacity, K, and the catch rate could be increased after reaching the recovered level of 40% of K. Note that Clearyet al. (2010) suggested the same overfished and recovery reference points for Pacific herring and Froeseet al. (2018) used the same for European fisheries and included severely depleted stocks as <0.2 BMSY (0.1 K). However, as mentioned above, the Schaefer K value may be an overestimate of the carrying capacity due to including too much recruitment in the surplus production model. Therefore, a literature-based lower equilibrium carrying capacity for a fishery, KE, was used to estimate the depleted biomass limit of BOF 0.2KE and the recovered BREC 0.4KE reference points.

Methods

To develop a methodology for the estimation of time for recovery, ten data-rich fisheries were used for a range of fisheries covering a wide geographic area with data from published Ecopath Models. The fisheries are from the following areas: Northern Humboldt Current of Central Peru (Tamet al., 2008), Bay of Biscay and the Celtic Sea (Bentorchaet al., 2017), Humboldt Current system of Central Chile (Neiraet al., 2004), Northern and Central Adriatic Sea (Collet al., 2007) and northern North Sea (Hillet al., 2021). Various species were chosen because they were all indicated as overfished. They cover a 10-fold range of biomass and catch and 5-fold range of fishing mortalities from sardines to large pelagic fish. Although the fisheries had not recovered from overfishing at the time of modeling, it was assumed potential for biomass recovery in ≤10 years to 0.4K by applying the FE sustainable fishing mortalities with no additional mortality due to by-catch, which could limit recovery (Shelton & Morgan, 2005). The results showed some fisheries did not recover due to limitations in phytoplankton production in the fishery area, so further research is suggested in the Discussion Section to investigate limits to recovery for some fisheries.

Theoretical Basis for Estimating Fishery Recovery

The theoretical basis for fishery recovery is the rate of change in population by the Verhulst equation, dB/dt = r × B (1 – B/K), examined by Tsoularis (2001), who showed the mathematical solution for logistic growth. The model allows estimation of the annual rate of biomass increase by applying the r and K values to the remaining biomass each year for a fished species, with the biomass change reduced by the applied fishing mortality catch rate. Hence, the methodology described is aimed at assisting fishery managers in recovering the biomass of an overfished fishery using basic fishery characteristics as input to the logistic equation solution. The following relationships were investigated to estimate recovery: (i) net biological production of a fishery, (ii) the intrinsic rate of natural increase, r, (iii) carrying capacity, KE, of a fishery, (iv) time for recovery by the mathematical solution of the Verhulst logistic equation with applied fishing mortality, (v) sustainable fishing mortality using r/2.

The methodology was tested by applying to reported recoveries for the Sardine (Sardinops sagax) fishery in the Northern Benguela Current of Namibia and the Hake (Merluccius merluccius) fishery in the combined areas of North Sea, Scotland, Bay of Biscay and Celtic Sea. The relationships were also investigated to see if they could be used by data-limited fishery managers to recover overfish fisheries using sustainable fishing mortalities that maintain the expected long-term catch. Although further research is required to determine the data-limited biomass, a notional biomass was derived and used as an example of potential recovery for a data-limited fishery. Hence, the following sections represent the development of the recovery methodology for data-rich and data-limited fisheries.

Estimation of the Intrinsic Rate of Natural Biomass Increase

Estimation of the intrinsic rate of natural increase is complex, requiring detailed knowledge of the fishery characteristics (Cortés, 2016) and/or unknowns such as the Maximum Sustainable Yield, MSY or FMSY, defined as MSY divided by the fishery biomass, both related to r (Winkeret al., 2020). To minimize complexity, the intrinsic rate of natural increase is estimated in this paper using the aquatic ecosystem theory that P/B is the rate of biomass renewal (Gascuelet al., 2008). To estimate the biological production, P, for a fishery, the production to biomass ratio, P/B, is required, but it is unlikely to be known. However, the ratio could be obtained from published ratios for the species being fished (as suggested by Randall and Minns (2000) for freshwater fish), and for marine fish from published Ecopath Models for the species of interest (see the list of Ecopath Models in Colléteret al., 2013). The biological production is estimated by multiplying the biomass by P/B, P = (B × (P/B), which gives production transfers between trophic levels for a fished species from prey to predators by mass balance of steady-state ecosystems (Christensen & Pauly, 1992).

The P/B ratio from published Ecopath Model results are based upon estimates of the rate of biomass accumulation, less the natural mortalities for M0 and M2 (M0 due to disease, etc. and M2 predation), and fish catch (Christensenet al., 2005), (1). It is important that the published P/B for each species fished has been undertaken reliably because the value of r is the key to the estimation of MSY, FMSY, and unfished K in the Schaefer (1954) logistic equation. The r value is also used to estimate the biomass increase over time, the biological production of a fishery, the carrying capacity of a fishery, KE, and the time for recovery.

Although the intrinsic rate of natural increase applies to the fish biomass with no fishing, the literature indicates that r values are often estimated by changes in biomass over time for fisheries subject to various levels of fishing mortality using the instantaneous rate of biomass growth G = ln Wt+1 – ln Wt, described by Ricker (1975), or by some variation of that method. As that does not give the intrinsic rate of natural increase, the actual intrinsic r value is derived here using basic principles. The surplus production model assumes exponential growth when <1/2K (Ricker, 1975; Tsoularis, 2001). They show the total biological production of a fish community biomass (PTOT), by exponential growth for a short period of one year, is PTOT = B × ert giving the production, or total growth in weight of fish during the year, where B is the average biomass (tww/km2). Then the net fishery biomass production (P, tww/km2/year) is the exponential growth to Bt+1 less the initial biomass, Bt+1 − Bt:

P = B t x e r t B t

The net biomass production by (1) gives the same result as using P = B × (P/B) in the Ecopath Model because, as shown below in the derivation of (2), P/B = ert −1, and (Christensen & Pauly, 1992) showed the P/B ratio takes natural mortality into account during calculation by the Ecopath Model. Note the biomass production (tww/km2/year) by (1) is not the same as the rate of increase (dB/dt, per year) of biomass along the resource limited Verhulst logistic equation.

Hence, the equation for calculating the r value is derived by dividing P by B in (1), giving P/B = ert − 1 and rearranging gives ert = (P/B) + 1, then take natural logarithms, giving r by:

r = l n ( ( P / B ) + 1 )

Equation (2) is the intrinsic rate of natural increase (per year) of biomass increase and is understandably related to P/B. Note that r is not the maximum rate because it is based on the typical biological production to biomass ratio obtained for a fished species, which can vary with environmental conditions. The reliability of (2) is shown in the Results Section with significant relationships of P/B and r/2 with the FMSY values for the ten fisheries. That follows from the coefficient of variation (standard deviation/mean) of P/B for pelagic and bottom-dwelling fish, being typically 0.05 to 0.15 (Koehnet al., 2016).

The practicality of the estimated r values by (2) is shown by comparing those estimated for the wide range for 10 reference fisheries in the Results Section, with the ranges in Martell and Froese (2012, Table II). For highly productive small pelagic fish such as herrings and sardines, r is typically in high resilience and ranges from 0.6 to 1.5. The Sardine (Sardinops sagax) in the Northern Humboldt Current of Peru Ecopath Model data from Tamet al. (2008) (Table I) has P/B 1.4, giving r = 0.8755 (ln (1.4 + 1)). Using their fishery biomass of 7.909 tww/km2, (1) gives net biomass production, P = 11.073 (7.909 × e0.8755 − 7.909) tww/km2/year, the same by the Ecopath Model method of B × (P/B) = 11.0726 (7.909 × 1.4) tww/km2/year, being the net of biomass accumulation after loss to natural mortality. Further support of the estimated r values is shown by the large pelagic fish, such as tuna in trophic level 4, having estimated low r values of 0.3148 and 0.3365 in the low resilience range 0.05 to 0.5, while the other fisheries have r in range from 0.3365 to 0.693, including the overfished Herring (Clupea harengus) at 0.46, in the medium resilience range of 0.2 to 1.0 in Martell and Froese (2012).

Species PP Biomass K BREC 0.4K KE BREC 0.4KE Expected B at PP
Sardine 6739 7.909 56.99 22.8 40.35 16.14 6.739
Herring 2700 0.893 7.27 2.91 5.15 2.06 2.7
Mackerel 2700 0.4 3.69 1.476 2.611 1.0444 2.7
Horse mackerel 13453 13.79 100.9 40.36 71.44 28.576 13.453
Hake 1150 0.12 0.87 0.348 0.613 0.2452 1.15
Saithe 2010 1.213 9.20 3.68 6.513 2.6052 2.01
Plaice 2010 0.14 1.10 0.44 0.779 0.3116 2.01
Cod 2010 0.16 1.19 0.476 0.841 0.3364 2.01
Average 4097 3.08 22.65 9.06 16.04 6.416 4.10
Table II. Phytoplankton Production (tww/km2/year) and Fishery Biomass (tww/km2) Compared with the Schaefer Surplus Production K, Schaefer Reference Recovery Points 0.4K, Fishery KE, Recovery BREC 0.4KE (t/km2), and Expected Biomass at Fishery Area Phytoplankton Production by Regression 0.001 × PP in Fig. 8

Estimation of Carrying Capacity for a Fishery

To estimate recovery reference points for an overfished fishery, the equation for the carrying capacity of a fishery is derived using the traditional Schaefer (1954) surplus production model, under equilibrium conditions, applied to the overfished biomass, B ≤ 1/2K is related to FMSY and r with time of one year by FMSY = r × (1 − Bt /K). Rearranging to obtain K gave:

K = B / ( 1 ( F M S Y / r ) )

Table I shows the average for the ten fisheries, FMSY of 0.4567, r value 0.5187, and biomass 2.652 t/km2, giving K of 22.19 by Equation (3) and K/B 8.37. However, it is well known that recruitment is part of the surplus production model, and Ricker (1975) stated: “Maximum equilibrium yield (MSY) must be interpreted with caution because surplus production is the sum of individual growth increments plus recruitment less natural mortality.” That suggests K in (3) is lower than expected, and from Edgaret al. (2024), a precautionary factor, Pa, was applied to FMSY, equivalent to reducing K by the same value. The typical Pa of 2/3 by FAO (1996) and Duplisea (2013) to adjust the FMSY could be used, but many fisheries adjust the FMSY by 0.75 (Restrepo & Powers, 1999 and Newmanet al., 2015), which gives an average Pa 0.708 ([0.6667 + 0.75]/2). The adjustment is about 30% lower than by the surplus production model but in the range of using the MSY at 30 to 40% of the carrying capacity suggested by Melnychuket al. (2020) and similar to the 0.368 factor used by Fox (1970) to optimize catch rates for a fishery. Therefore, the carrying capacity of a fishery with a precautionary factor called KE, under equilibrium conditions was estimated as follows:

K E = 0.708 × B t t / ( 1 ( F M S Y / r )

The average KE /Bt obtained for the ten fisheries was 5.31/year (see summary of averages in Results 3.0), similar to the average by Walterset al. (2008, Table I), who showed that for productive species with F/r (their U/ro from 0.95 to 0.43) gave B0 /B of 5.45. Hence, the KE based recovery reference points for BOF and BREC are considered acceptable to estimate recovery times. However, in nature, the carrying capacity is not constant but varies with environmental conditions (Allen & Hightower, 2010; Chapman & Byron, 2018). To allow for those changes, the fishery biomass and recovery times are estimated using the processes derived in the next sections.

Estimation of Recovery Times

The recovery times shown in Table I are time from the depleted biomass, Bt from Ecopath Models, to estimate BOF and from BOF to BREC. As an overfished fishery has the biomass <1/2K and probably less than BOF of 0.25 KE, the biomass increase is expected to be in the exponential growth section of the logistic growth curve. Then, the time for recovery with F = 0, Texp , is estimated by modification of (1):

T E X P = l n ( B R E C / B O F ) / r

However, as the biomass increases to 1/2K, the consensus of the literature is the biomass increase follows the Schaefer (1954) logistic growth curve (Ricker, 1975). In addition, Tsoularis (2001) noted that the Schaefer (1954) model includes the resource limiting factor 1 − B/K, which moderates exponential biomass growth to a sigmoid-shaped curve, with the maximum rate at 1/2K and slower increase up to the carrying capacity. The resource factor does that by adjusting for an increased lack of prey food and increased predation as the biomass increases.

Using the Verhulst logistic equation, Tsoularis (2001) showed the mathematical solution of the logistic growth curve is:

B t + 1 = K × B t / ( ( K B t ) e r t + B t )

The logistic equation solution is based on year time steps, but the initial approximate time to reach BOF and BREC by TEXP could be used as a guide. It is assumed (6) applies to the recovery of an overfished species under the following conditions. The r value is the intrinsic rate of natural increase in one year, estimated by (2), and the initial biomass is Bt . Then, biomass increase from Bt to BOF or BOF to BREC could be estimated using (6), using KE for a fishery, and (4). When a fishing mortality is applied, the recovery rate is reduced, and recovery time is increased, as shown in the next section.

Effect of Fishing Mortality on Recovery Time

The Schaefer (1954) surplus production model in (3) applies for F = 0, but when fishing mortality is applied, yearly biomass changes with the annual fish catches. The effect of fishing on the biomass recovery is estimated by modification of the logistic equation solution in (6) by subtracting the fish catch:

B t = ( K E × B t 1 / ( ( K E B t 1 ) e r t + B t 1 ) ) F × B t 1

Note that the overfished fishery biomass is the biomass at the end of fishing in the previous year, Bt−1. At the beginning of the recovery sequence in years 1, 2, etc., a fishing mortality is applied to the previous year Bt−1 to give a new Bt at the end of fishing in the current year. As an overfished fishery, by definition, is <1/2 KE , the biomass recovers along the lower half of the logistic curve, provided it continues to increase with the applied F. In addition, (7) provides flexibility because the fishery manager could adjust the fishing mortality each year to agree with stakeholder requirements or changes in the rate of biomass increase due to environmental changes to reach the recovery biomass in the desired time to BOF and then to BREC in ≤10 years. For example, the EBFM fishing mortality of 0.084 ± 0.011 for a severely depleted fishery was suggested by Hodgson (2022) for recovery. That is likely to give a quicker recovery time and higher catch after recovery to BOF when the catch rate could be increased to r/2 to take advantage of the potentially increased biomass.

To find new knowledge and insights, the estimated recovery times by (7) were compared with recovery times for published examples of fish recoveries, where the biomass recovery was affected by environmental changes and stakeholders determined the reduced fishing mortalities to increase the fishery biomass after depletion by unintended overfishing. Comparisons for biomass recovery times with actual fisheries are shown in Section “Fishery examples to test biomass recovery time theory” below.

Estimation of Sustainable Fishing Mortality

Fishery managers need to know what fishing mortality gives an acceptable catch that also allows the fishery biomass to increase to BOF and then to BREC within a reasonable time. Ricker (1975) showed FMSY = r/2, and Wormet al. (2009) suggested a sustainable fishing mortality of 0.25 for the recovery of overfished fisheries. Using r/2 as sustainable fishing mortality, the average r/2 of the ten reference fisheries in Table I was similar to Wormet al. (2009) at 0.26 for a range of pelagic and bottom-dwelling fish. Hence, from (2), the fishing mortality under equilibrium conditions, FE , is assumed to be related to P/B by:

F E = I n ( P B + 1 ) 2

The fishing mortality in (8) makes the fishing mortality theoretically consistent with the rate of biomass production, P/B, and agrees with the suggested F = r/2 by Walterset al. (2008) as a “good” target rate. Equation (8) was tested in the Results Section by regression of the relationship of fishing mortalities for FMSY values with r/2 from the Ecopath Model results in Table I.

Results

The ten fishery examples to investigate potential recovery times for data-rich but overfished fisheries from published Ecopath models are shown in Table I. As the fisheries are data-rich but remained overfished at the time of running the Ecopath Model by the authors, possible strategies for the management of recovery were investigated. Note the Estimated recovery times are theoretical estimates and not by comparison with the actual recovery of the ten fisheries.

As shown in Table I, the ten reference fisheries had the following average characteristics: Bt 2.65 t/km2, r value 0.5187/year, FMSY 0.4567/year, catch at Bt 1.15 t/km2/year, KE 14.07 t/km2, KE relative to the average biomass, KE/Bt 5.31. The fisheries in Table I had potential recovery times to BREC in less than 10 years using FE r/2. The exceptions were: “Other large pelagics” (Tamet al., 2008), about one month longer, and Mackerel (Scomber scombrus) from Bentorchaet al. (2017). Due to the low Mackerel biomass, the EBFM fishing mortality of 0.084 was used to increase the biomass to BOF, thereby allowing the time to reach BREC with the higher FE r/2 in <10 years. Likewise, the “Large pelagic fishes” (Collet al., 2007) with a low biomass required initial F 0.084 and then reached BREC in <10 years.

When comparing the results of the ten Ecopath Models, the relative errors need to be known, so the coefficient of variation, CV, defined as the ratio of standard deviation to mean, for biomass and P/B given in Koehnet al. (2016) for typical fish species or groups were used. The CVs for Sardines B 0.15 and P/B 0.05, Herring B 0.35 P/B 0.15, Mackerel B 0.15 P/B 0.05, Hake B 0.15 P/B 0.05, Flatfish used for Plaice B 0.20 P/B 0.15 Lingcod used for Cod and Saithe B 0.15 P/B 0.10, Albacore B 0.20 P/B 0.15 was used for the large pelagic fish. The relatively low CV values are considered acceptable for comparison of the ten Ecopath Model results and are consistent with the significant regressions obtained in Section 3.1.

Relationships of Fish Catch with Biomass, Fishery Biological Production, and Fishing Mortality with P/B and r/2 for Sustainable Catch

The following relationships were investigated to indicate which fishery characteristics could be used to understand the important process for recovery of overfished fisheries: (i) catch with biomass, (ii) catch fishery biological production, (iii) FMSY with P/B and r/2.

Fish Catch Relationship with Biomass and Fishery Biological Production

The fish catch, FC, is expected to be related to biomass due to the standard equation FC = F × B and related to the biological production of the fishery for the 10 reference fisheries in Table I. The importance of the biological production of a fishery was first suggested by Jul-Larsenet al. (2003), who showed fish catch is a proportion of the fishery biomass and the biological production, followed by Skern-Mauritzenet al. (2015) that fishery production is the main ecosystem driver for catch. Accordingly, relationships between catch with biomass and fishery biological production for the ten fisheries in Table I are shown in Fig. 1.

Fig. 1. Relationships of fish catch with (A) biomass and (B) fishery biological production by intercept 0.0 for data from Table I. The Herring (Clupea harengus) catch was estimated at 0.363 tww/km2/year using FMSY 0.407 in Table I (rather than the reduced fishing mortality 0.073 for recovery that had not occurred at the time of Ecopath modelling) for both biomass and biological production (open blue diamonds) in (A) and (B). The Sardine (Sardinops sagax) catch of 3.33 tww/km2 was related to biomass of 7.909 tww/km2 in (A), but was not related to the fishery production of 11.073 tww/km2/year in (B). The catch relative to fishery production using the FMSY of 0.754 gives a likely catch of 5.96 tww/km2/year (3.33 × 0.754/0.421) shown as the red open diamond not included in the regression.

Fig. 1A gave the following regression of catch with biomass:

F C ( t w w k m 2 y e a r ) = 0.4542 × B i o m a s s ( t w w k m 2 )

where R2 is 0.9919, n is 10, p > 0.001.

Although Fig. 1B does not have biological production in the center of the regression, it gave a high correlation for nine of the observations in Table I:

F C ( t w w / k m 2 / y e a r ) = 0.5716 × B i o l o g i c a l P r o d u c t i o n ( t w w / k m 2 / y e a r )

where R2 is 0.9997, n is 9 and p > 0.001.

The overfished species indicated possible reasons for overfishing: (i) Fig. 1A and 1B showed the Herring (Clupea harengus) estimated catch of 0.363 tww/km2/year was consistent with the applied fishing mortality 0.407 but was significantly overfished with the biomass of 0.893 tww/km2 about 1/10th that of the Sardine (Sardinops sagax) fishery biomass 7.909 tww/km2 for the small pelagic trophic level TL3, (ii) the overfished Hake (Merluccius merluccius) (<40 cm), with a low catch of 0.113 tww/km2/year agreed with the low biomass of 0.12 tww/km2 and fishery production 0.12 tww/km2/year, but the biomass of 0.12 tww/km2 was an order of magnitude lower than Saithe at 1.213 tww/km2 for the same predatory pelagic finfish TL4, (iii) Fig. 1A shows the Large Pelagic TL4 catch of 0.35 tww/Km2/year; in the Northern Humboldt Current of Peru by (Tamet al., 2008) agreed with the low applied F of 0.199 for a biomass of 1.757 tww/km2 and in (B) catch was consistent with the fishery production of 0.703 tww/km2/year. However, the biomass was 10-fold higher than the Large Pelagic biomass in the Northern and Central Adriatic Sea in Collet al. (2007) due to the higher phytoplankton production of 6739 for Peru compared to 1150 tww/km2/year for the Adriatic (see footnotes in Table I).

Relationship of r/2 for Sustainable Catch Rates with FMSY

As FMSY is related to r/2, the proposed FE of r/2 sustainable fishing mortality by (8) in Table I is compared with the FMSY fishing mortalities in Fig. 2.

Fig. 2. Relationships of sustainable fishing mortality FE of r/2 with FMSY fishing mortalities in Table I.

The equation obtained was:

S u s t a i n a b l e f i s h i n g m o r t a l i t y , F E ( / y e a r ) r / 2 = 0.5729 × F M S Y ( / y e a r )

where R2 is 0.983, n is 10, p > 0.001. The coefficient 0.5729 is about 15% of the expected 1/2 KE 0.1458 ([0.5729 – 0.5]/0.5).

Relationship of FMSY with P/B

Due to Bt+1Bt in (3) is equivalent to the fishery biological production, P, and dividing both by B makes FMSY theoretically related to P/B, as well as the r value related to the P/B ratio in (2) and r/2 in (8) and with FMSY, Fig. 3 shows the relationship of FMSY with P/B.

Fig. 3. Relationships of FMSY with production to biomass ratio, P/B, for the 10 fisheries in Table I.

The regression of production to biomass ratio with fishing mortality obtained was:

F M S Y ( / y e a r ) = 0.4582 × P / B R a t i o ( / y e a r ) + 0.1339

where R2 is 0.9788, n is 10, p > 0.001. The relationship of FMSY with P/B indicates the fishing mortality catch rate, estimated by the Schaefer (1954) population dynamic model, may be controlled by the rate of the fishery biomass production.

The relationships in (11) and (12) indicated FMSY could be estimated from either the P/B ratio or r/2. Consequently, the biomass recovery and times indicated r/2 is a reasonably acceptable level of sustainable fishing mortality and was used to estimate recovery times by (7) in the next section.

Estimated Potential Recovery Times for Data-Rich but Overfished Fisheries

The estimated biomass and recovery times to BREC for six of the fisheries in Table I are shown in Fig. 4 using (7) with a constant FE as the biomass increased, except for Herring (Clupea harengus), which was set at F = 0.073 as suggested by for recovery by Bentorchaet al. (2017). The fisheries are Sardine (Sardinops sagax) and Mackerel (Scomber scombrus) are compared with Horse mackerel (Trachurus symmetricus murphyi), Herring (Clupea harengus), the bottom-dwelling Saithe (Pollachius virens) and Cod (Gadus morhua). As mentioned above, Mackerel had the initial fishing mortality reduced to EBFM level, and then, with r/2, it reached BREC in about 9 years and 10 months.

Fig. 4. Estimated biomass recovery and times from initial Bt to the year including BREC with constant sustainable FE = r/2 fishing mortalities for five fisheries and Herring (Clupea harengus) with F = 0.073 as the biomass recovers. Recovery times varied from about three years for the Sardine (Sardinops sagax) to just under 10 years for Mackerel (Scomber scombrus). The fishing mortalities and estimated biomass at BOF and BREC and potential catches are shown in Table I.

Fig. 5. Estimated biomass and recovery times for Sardine (Sardinops sagax), using for the same Sardine species r and KE values in Table I. Following the high fishing mortality in 1995, the catch rate was necessarily reduced to <0.1 and slowly increased to the set limit of 0.2 until environmental changes on the Namibian shelf added to the recruitment failure in 1998/99 when the F values were reduced to ≤0.1. Predicted recovery was undertaken for the following conditions: (i) recovery for reported biomass (squares) from effects of overfishing with F 0.778 in 1995 giving reduced biomass of 1.77 tww/km2 and recovery range 6.0 to 6.3 tww/km2 in 1997/98 by reported variable F ≤ 0.2. That was followed by recruitment collapse due to environment changes on the Namibian shelf, (ii) predicted recovery by (7) using reported variable F and no recruitment collapse (diamonds), (iii) predicted recovery using a higher constant FE = r/2 of 0.438, from 1.77 tww/km2 in 1995 to 2001 (triangles).

The highly productive small pelagic Sardine with the highest r value of 0.8755 had the shortest estimated recovery time of about three years to BREC 16.14 t/km2. In contrast, Mackerel in Bay of Biscay and Celtic Sea (Bentorchaet al., 2017) was estimated to take the longest to recover due to a low initial biomass of 0.4 tww/km2 and low r value 0.3365.

The Herring (Clupea harengus) fishery modelled by Bentorchaet al. (2017) with the suggested F 0.073 recovered in about three years and 4 months to BREC. The fishery was also used as an example of recovery from overfishing in Section 3.4.1, “Examples of how a data-limited fishery could be recovered from overfishing” in Fig. 7. It had an estimated recovery of about six years using constant fishing at the FE r/2 of 0.232, which had the potential benefit of a higher catch at the BREC of 2.068 t/km2; up from 0.893 t/km2 within a reasonable recovery time.

Fig. 6. Estimated biomass and recovery for Hake (Merluccius merluccius) (squares) for the following conditions: (i) initial slow recovery from 1998 to 2005 from reported biomass from 0.047 tww/km2 in 1998 (diamonds) due to overfishing with high fishing mortalities of 0.696 to 0.910, (ii) recovery from 2006 to 2010 with F reductions to 0.393 (yellow circles), (iii) predicted increase from 1998 to 2006 with an increased rate of production by increasing P/B of 1.0 for Hake in Table I to that from the literature of 1.17 and resulting r value increase from 0.693 to 0.785. The increase in P/B and r was applied for assumed nutrient upwelling effects onto northern shelves until 2006. (iv) Due to the high F values and shelf environmental effects, the KE was adjusted for the increase in reported biomass each year, giving the predicted recovery from 1998 to 2010 that followed the rapid measured biomass increase. The predicted recovery using constant FE of r/2 0.347 from 1998 (triangles), assuming no upwelling effects, is shown for comparison.

Fig. 7. Estimated Herring based notional data-limited biomass recovery from overfished biomass at year 0 to BOF 0.9275 tww/km2 in year two and then to BREC 1.484 tww/km2 in year 10 (triangle). The recovery is compared with the Herring (Clupea harengus) recovery in about 6 years (using a fishing mortality of r/2 0.232, open circle) and the notional biomass with constant fishing mortality of 0.438 to maintain a long-term steady biomass and catch (closed circle. For comparison, the predicted recovery of King Mackerel (Scomberomorus cavalla) is used as an example of applying a similar strategy for the recovery of a pelagic finfish TL4 predator in about 10 years.

The Central Chile fisheries for Horse mackerel (Trachurus symmetricus murphyi) by Neiraet al. (2004) in the 1990s were included as an example of using FE for fishery management when overfishing begins to occur. At the time of investigation, Horse mackerel had the highest biomass of 13.79 tww/km2 and r of 0.60 in the low range of high resilience (Martell & Froese, 2012). The fishing mortality for the fishery was estimated by Neiraet al. (2004) as 0.47 in 1992. However, using (7) with the initial applied F of 0.47 indicated BREC may not be reached in 10 years, which is consistent with the reduction of F to 0.15 six years later in 1998 due to overfishing. The alternate approach of using the Table II r/2 = 0.30 for the 1992 biomass indicates BREC may have been reached in four years eleven months (Fig. 4), with an estimated potential catch 9.07 tww/km2/year, compared to the initial yield of 6.48 tww/km2/year in 1992 (Table I), reduced to 2.9 tww/km2/year in 1998 by overfishing.

The recovery time for Saithe (Pollachius virens) of about five years and ten months was estimated using FE of 0.261. However, ICES (2020b) suggested using F of 0.363, but the expected recovery to BREC in <10 years was not evident, indicating 0.363 may be an upper limit for pelagic predators (see Thorpeet al., 2017) such as Saithe with a trophic level of 4.3. The r/2 of 0.2872 for Cod (Gadus morhua) was used even though it had one of the lowest biomass at 0.16 t/km2, but the relatively high r value of 0.5744 gave potential recovery in about five years.

Although the estimated recovery times are theoretical, the methodology developed using FE of r/2 is tested in the next section for two documented recoveries.

Examples of Fishery Recovery with Environmental Changes by the Logistic Equation Solution

The recovery times using r/2 are compared with two published fishery recovery examples. The first recovery is by the Sardine (Sardinops sagax) fishery in the Northern Benguela Current of Namibia, in southern Africa on the Atlantic coast by Boyeret al. (2001), using data from their Fig. 4 and estimated fishing mortalities from the text. The other recovery is the Hake (Merluccius merluccius) fishery in the combined areas of the North Sea, Scotland, the Bay of Biscay, and the Celtic Sea by Baudron and Fernandes (2014). The biomass recovery times were estimated using logistic growth by (7). As both fisheries were subject to environmental changes on their respective shelves, reductions in fishing mortalities by the fishery managers to adjust for the effects of the changes were compared with the r/2 recovery estimates.

Recovery for the Sardine (Sardinops sagax) Fishery on the Namibian Shelf

The Sardine (Sardinops sagax) fishery has a Namibian shelf area of about 84,000 km2. The initial overfished biomass in 1995 was about 1.77 t/km2/year when the fishing mortality was at FMSY of 0.778. Assuming the same P/B and equivalent r value for the same Sardine species in Table I, the carrying capacity, KE, was estimated by (4) at 11.25 (0.708 × 1.77/[1 – 0.778/0.8755]) t/km2. The biomass recovery with reductions in fishing mortality, followed by a response to recruitment collapse by environmental changes on the Namibian shelf, is shown in Fig. 5.

Due to using high fishing mortalities, the biomass fell to a low value in 1995, so the F values decreased in 1996, mostly determined by the inability of the fishery to catch fish rather than set by the fishery manager. As a result, the biomass increased in 1997 and stabilized in 1998 and 1999, with the F values increasing from <0.1 to the suggested limit of 0.2. The estimated recovery by (7) using the fishery applied variable F values gave a similar increase and recovery times as reported until the fishery declined due to the effects of environmental changes on the Namibian shelf on spawning stock recruitment, SSR, from 1999 (Boyeret al., 2001). However, if the excessive fishing mortality in 1995 of 0.778 had not been used and instead the sustainable r/2 of 0.438, the biomass potentially could have increased from 1.77 to 5.2 tww/km2, compared with 3.28 tww/km2 by 2001, as shown in Fig. 7.

Recovery for the Hake (Merluccius merluccius) Fishery in the Northern North Sea and West of Scotland

The findings for the Sardine fishery show the utility of predicting recovery times for an actual fishery using the logistic equation solution. That is further investigated for the Hake (Merluccius merluccius) fishery, as reported by Baudron and Fernandes (2014). The fishery biomass is converted from total stock biomass using the estimated expanded fishery area of about 898,900 km2 in 2011 (total biomass and average F data from Fig. 1, area from Fig. 2 in Baudron and Fernandes (2014). They found the hake biomass was at its lowest level in 1998 of 0.047 t/km2 due to high fishing mortalities of about 0.910, causing a low spawning stock biomass (SSB). Consequently, the fishing mortalities were reduced, and together with environmental changes on the shelves, the biomass showed a large increase in 2010.

Fig. 6 shows the changes in reported hake biomass compared with the estimated increase due to fishing mortality reductions and environmental changes on the shelf areas. The predicted biomass increase using the initial KE of 0.262 t/km2 and constant fishing mortality at r/2 is also shown.

The biomass increase with constant sustainable fishing mortality of r 0.347 (0.693/2) and no environmental changes was predicted to increase faster from 1998 and reach biomass of 0.126 in 2008, similar to that reported shortly after 2008 (Fig. 6). However, by using high fishing mortalities, the catch was always higher than 0.046 t/km2/year with the F value reduced to r/2, but with r/2, it is unlikely the SSB would have been reduced, forcing the reduction in F values. Fortunately, the combined effects of environmental changes, with the fishing mortality reductions, increased the biomass to 0.203 t/km2 and catch to 0.08 (0.203 × F 0.393) t/km2/year in 2010.

Baudron and Fernandes (2014) suggested the initial biomass increase from 1998 to 2005 was due to increased water temperatures of about 1°C by climate effects, causing the biomass to expand into the northern areas of the North Sea and West of Scotland. However, the biomass increase from the very low biomass of 0.047 t/km2 in 1998 was likely aided by the well-known upwelling of nutrient-rich waters onto the northern shelves, including the Celtic Sea and Bay of Biscay (see northern hake distribution by Baudron and Fernandes (2014)). Upwelling is known to mostly occur by wind forcing and internal waves adding nutrients and promoting phytoplankton production on the shelf areas (Huthnanceet al., 2009). The process of nitrogen input by upwelling, maintaining a sustainable fish harvest by increased phytoplankton production, is well-known (Lalli & Parsons, 1997).

Due to the likely nutrient inputs, the P/B was temporarily increased to 1.17 by Sayguet al. (2023), (Table I) for the Hake (Merluccius merluccius) fishery, which has a higher nutrient input than in the adjacent Aegean Sea where Collet al. (2007) reported a P/B of 1.0 for the same species. Hence, the r-value of 0.785 (ln [1.17 + 1]) by (2) was applied to the logistic (7) solution to estimate recovery for the northern areas of the North Sea and the West of Scotland. However, as shown in Fig. 6, the fishing mortality was reduced in 2005 to near the FMSY in 2006 and below it from 2005, so the original r value of 0.693 for a P/B of 1.0 for the same Hake species in Table I was used from 2006 to 2010 in (7). The FMSY was estimated by equation (12) using P/B in Table I because it was not provided, then the carrying capacity, KE, by (4) was 0.262 t/km2.

In contrast with the the Sardine fishery, the applied fishing mortalities during the initial recovery were higher than the FMSY until 2007, when the applied F was reduced to 0.580/year. Therefore, it was necessary to adjust the initial KE of 0.262 t/km2 using (7) as the biomass increased. However, Fig. 6 shows the biomass began a rapid increase from 2007 to 2010 due to the continued decrease in fishing mortalities to 0.400 and 0.393 in 2009 and 2010, apparently aided by the environmental changes. Hence, the KE applied to (7) had to be adjusted each year up to 1.132 in 2010 to give a reliable comparison with the reported biomass increase to 0.203 t/km2.

The findings for data-rich fisheries and recovery from shelf environmental changes provide valuable knowledge and insights that could be applied to the recovery of data-limited fisheries. Although the data-limited fisheries require further research, the approach used is expected to be of assistance to data-limited managers to maintain catches and potential recovery from overfishing.

Estimated Recovery Times for Data-Limited Overfished Fisheries

The concerns with estimating recovery of data-limited fisheries are as follows: the catch is typically a multispecies one, but the biomass and catch for each species are poorly known (Gillett, 2002). However, Fujita (2021) suggested some data collection could be undertaken by fishery management to assist in estimating the recovery. It is also likely data-limited fishery managers have some idea of overfishing due to a reduction in the number caught, changes to smaller fish, or the necessity to take species not previously targeted, as well as a reduction in average TL due to catching less prized TL4 fish, such as King Mackerel (Pauly & Palomares, 2005). For example, Sreekanthet al. (2020) found the Goa fishery on the southwest coast of India had a mixed fishery with an open sea average small pelagic TL of 3.61, and catch mostly by TL3 Clupieds (shads and Indian oil sardine), anchovies, mackerels, and Indian mackerel, with some TL4 trevallies, large pelagics (e.g., barracudas and Indo-Pacific king mackerel, Scomberomorus guttatus) and large benthic carnivores (groupers, snappers, seabass and threadfins). Therefore, following Fujita (2021), the catch of fish species preferred by consumers but significantly overfished could have been measured and targeted for recovery aided by the above fishery processes and characteristics in Table I and for the two recovery examples.

The other possibility is that a data-limited fishery is fishing at a rate equivalent to the biological production of the fishery to give a relatively consistent catch, providing no significant environmental changes in the fishery area. That assumption is considered reasonable because a data-limited manager may have estimated by trial-and-error the catch required to maintain a steady fish population for current and future catches. The assumption is supported by Jul-Larsenet al. (2003) that the catch is expected to be related to the biological production of a fishery.

Examples of how a Data-Limited Fishery could be Recovered from Overfishing

An example of estimating the catch rate from the biological production of a data-limited fishery is shown by applying the above ten fishery processes. The Herring (Clupea harengus) biomass was low at 0.893 t/km2 and nearly an order of magnitude below that of the Sardine (Sardinops sagax) fishery in Table I. For that reason, Herring was used as the basis to estimate the fishing mortality of a data-limited depleted fishery. Assuming a data-limited catch rate was related to the biological production, P, it was estimated using (1) for the Herring r value of 0.4637, so P = 0.527 (0.893 × e0.4637 − 0.893) t/km2/year. The data-limited biomass was estimated using relationships found by the ten reference fisheries. Equation (10) shows the fish catch could be estimated by FC = 0.5726 × P, giving FC 0.302 t/km2/year and convert to biomass using (9), B = FC/0.4542, so the estimated B = 0.664 t/km2, called the notional biomass. Assuming the Herring P/B and r values apply to the notional biomass, the FMSY was estimated from (12) as 0.405 and KE by (4) as 3.71 t/km2. Equation (7) estimated the fishing mortality as 0.438, about 8% higher than FMSY, to maintain constant notional biomass, as shown in Fig. 7. However, that level of fishing does not allow recovery, so the following strategy was used for recovery. The F values applied to (7) varied from 0.232 to reach BOF, then increased to 0.314 for two years to recover the forgone catch, and gradually reduced to 0.24 to reach BREC within ten years.

As mentioned above, the Goa fishery includes the prized Indo-Pacific King Mackerel, called King Fish, so it was used as an example of applying a similar strategy for recovery of a pelagic finfish TL4 predator in about 10 years. The Ecopath Model, also in tropical waters, by Arreguín-Sánchezet al. (1993), has a different species (Scomberomorus cavalla) but was used to show recovery from overfishing. The model gives the P/B of 0.65, biomass of 0.5 tww/km2, and catch 0.015 tww/km2/year (converted from t dry weight to wet weight by × 5). The r value was estimated by (2) as 0.5 (ln[0.65 + 1])/year, relating to medium resilience of 0.2 to 1.0 in Martell and Froese (2012), which includes the predatory fish. If King Mackerel were targeted for recovery in a data-limited fishery, it might be fished at a rate related to biological production, P = 0.324 (0.5 × (e0.5 − 0.5)) tww/km2/year, similar to the average P of 0.377 for the Large Pelagics in Table I. The FMSY was estimated by Equation (12) as 0.4364 and KE by (4) as 2.783. Accordingly, logistic (7) estimated the F value to maintain a constant biomass of 0.5 tww/km2 as F = 0.476, about 9% higher than the 0.438 for the Herring notional biomass. The catch at Bt when fishing at the rate equivalent to P was 0.238 (FC = B 0.5 × F 0.476) t/km2/year. Therefore, a similar recovery strategy as used for the Herring notional biomass for recovery was used for King Mackerel using the initial F of r/2 = 0.25 for two years, increased to the F of 0.342 for two years to replace forgone catch, followed by a reduction in F in year 5 to 0.300 in year 6 and steadily to 0.275 to reach BREC of 1.1132 in <10 years. The BREC catch 0.306 (1.1132 × 0.275) was about 29% higher than 0.238 t/km2/year when fished at the level of fishery production.

It was found both the Herring-based nominal biomass and the pelagic finfish predator King Mackerel reached their ecosystem-based fishing mortalities within ten years with a final F of 0.24 and 0.275/year, respectively, as suggested by Murawski (2010) for stock recovery. The final fishing mortalities were in the EBFM FMSY range suggested by Hodgson (2022) as 0.23 ± 0.03 for trophic level TL3 small pelagic fish such as Herring and 0.27 ± 0.03 for their TL4 pelagic finfish predators.

The Herring and King Mackerel examples indicate a similar strategy could be applied to the whole data-limited fishery area for the recovery of the most important and prized fish species. However, the application of those processes to provide a framework for data-limited fishery management requires further research, particularly on how to estimate the biomass of the targeted species. The other factor to consider is the effect of phytoplankton production in the fishery area to support recovery. That is examined in Section 4.

The Effect of Phytoplankton Production on Fishery Recovery from Overfishing

The effect of phytoplankton production, PP, was shown by Hodgson (2022) to support fish caught in tropical areas by small pelagic fish, SP, such as Herring by FCSP = 0.001 × PP (R2 = 0.8433, n = 6, p < 0.01) and pelagic finfish predators, PF, such as Mackerel by FCPF = 0.0003 × PP (R2 = 0.7304, n = 6, p < 0.05) with intercepts set to 0,0. As the interest here is the effect of PP on the fishery biomass, Fig. 8 shows the fishery biomass in the above Table I fisheries, other than the large pelagic fisheries, compared with phytoplankton production in each area listed in footnotes to Table I(c). It was assumed the expected biomass was similar to that for catch by 0.001 of the phytoplankton production suggested by Link and Marshak (2018).

Fig. 8. Fishery overfished biomass in Table I, except the large pelagic group, compared with phytoplankton production from the Ecopath Models, shown in footnotes to Table I(c), compared with the expected biomass by regression B = 0.001 × PP (R2 = 0.8978, n = 8, p < 0.001) for intercept 0,0. The regression line shows Herring, Mackerel, Hake, Saithe, Plaice, and Cod all had biomass lower than potentially supported by phytoplankton production, while the Horse mackerel and Sardine fisheries had biomass similar to that expected by phytoplankton production in their areas.

Fig. 8 indicates the Herring, Mackerel, Hake, Saithe, Plaice, and Cod were overfished relative to the phytoplankton production, consistent with the suggestion of Hodgson (2022) that phytoplankton production could be considered as part of fishery assessments when estimating fishing mortalities. The role of phytoplankton production is further investigated in Table II, where it is compared with the Schaefer surplus production carrying capacity, K, fishery KE, and recovery reference points BREC for 0.4K and 0.4KE, as well as the expected fishery biomass due to phytoplankton production.

Table II indicates all the fisheries were overfished except Sardine (Sardinops sagax) and Horse mackerel (Trachurus symmetricus murphyi), which have their reported biomass higher or about the same as expected by phytoplankton production. Conversely, although all the fisheries were predicted to recover in Table I, all except three are expected to recover with support by the PP. The tree fisheries not expected to reach BREC 0.4KE are Sardine and Horse mackerel, with large limits to recovery by the local phytoplankton production, and Saithe (Pollachius virens), which had BREC about 30% lower than expected by the PP. The higher Schaefer surplus production recovery BREC 0.4K indicated Herring (Clupea harengus), as well as the other three fisheries, may not recover due to PP limitation. Note that the lower recoveries than the PP can support were due to the fisheries recovering from low biomass with limited growth by their r values.

Table II is also relevant to the predicted recovery of data-limited fisheries in Fig. 7. The Herring-based notional biomass was predicted by (7) to reach a biomass of 1.484 t/km2 and not limited by the fishery phytoplankton production. Likewise, the King Mackerel (Scomberomorus cavalla) with PP 1809 t/km2/year (with biomass 7.95 in dry weight/km2 converted to tww/km2 by multiplying by five and P/B 45.5) was expected by the regression to support a biomass of 1.809 tww/km2 while the predicted recovery was supported to 1.113 tww/km2 in about 10 years.

Discussion

Aquatic ecosystem and fishery population dynamics theory has shown how overfished, data-rich, and data-limited fishery managers could estimate recovery times and maintain the fishery biomass using sustainable fishing mortalities. The precautionary factor applied to KE used to estimate recovery reference points, together with FE and EBFM FMSY for severely depleted fisheries, predicted the ten reference fisheries to recover within the target time of ≤10 years, as suggested by Melnychuket al. (2020). However, the predicted increase in biomass and catch over time may vary due to other factors, such as local phytoplankton production, as shown above for Sardine, Horse mackerel, and Saithe. The other factors to consider are fishery demand, ability to catch the fish and by-catch mortality, implying ongoing management of the recovery progress. The findings here explain how fishery managers and stakeholders could select various fishing mortalities and fishing strategies applicable to the fishery characteristics of carrying capacity and intrinsic rates of natural biomass increase. In that regard, a decision to close a fishery or reduce to a sustainable fishing mortality may be considered, but it has economic considerations, requiring the fishery stakeholders to decide.

The fishery examples used for comparison of the derived recovery time theory confirmed the finding by Melnychuket al. (2020) and ICES (2020a) that environmental changes in the fishery area could affect recovery times from overfishing and may require adaptive management of F values to maintain the recovery process. That process was demonstrated by the Namibian shelf Sardine (Sardinops sagax) fishery and for the European Hake (Merluccius merluccius) fishery with F values adjusted to address the decrease in SSB. In both cases, by not applying high F values prior to the shelf environmental changes, sustainable r/2 fishing mortality was expected to give a more consistent increase in biomass and higher catch, other than the last two years of the Hake recovery. It was also found by the Hake recovery that the effects of environmental changes could be accounted for by adjusting the P/B value, indicating environmental effects on the rate of biomass regeneration in the fishery area, as well as adjusting the fishery carrying capacity as the biomass increased.

Although the above analyses for data-limited fisheries are theoretical, they show the importance of undertaking a trial recovery for a particular species before applying to prized fish in a mixed fishery area. Importantly, the fishery characteristics of the reference fisheries and the biological process indicated a possible way for a data-limited fishery to be recovered from overfishing. Hence, further research is suggested to investigate additional development of the recovery methodology for data-limited fisheries, particularly estimation of the fishery area biomass, using variable sustainable fishing mortalities for recovery within ten years or less and potential increase in catch with a higher biomass and less effort.

Recovery from overfishing is an integral part of fishery management, and it is hoped that the insights from this study will be of assistance to both data-rich and data-limited fisheries, fish biologists, fishery managers, policymakers, and fishery modelers for recovery to sustainable fisheries.

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