The sole resource is modelled by a dynamic Schaefer production model which allows for a drop in the value of the intrinsic growth rate parameter from 2000 onwards. The model is fit to the available CPUE and survey abundance indices. These data are not sufficiently informative to be able to distinguish amongst fairly wide ranges of pre- and post-2000 intrinsic growth rate parameters. Nevertheless, all suggest that the sole resource has never been substantially depleted (being well above its MSY level), and furthermore that the current replacement yield and MSY are reasonably robustly estimated in the ranges of 300-400 and 500-650 mt respectively

Butterworth, Doug S

Glazer, Jean

English

The sole resource is modelled by a dynamic Schaefer production model which allows for a drop in the value of the intrinsic growth rate parameter from 2000 onwards. The model is fit to the available CPUE and survey abundance indices. These data are not sufficiently informative to be able to distinguish amongst fairly wide ranges of pre- and post-2000 intrinsic growth rate parameters. Nevertheless, all suggest that the sole resource has never been substantially depleted (being well above its MSY level), and furthermore that the current replacement yield and MSY are reasonably robustly estimated in the ranges of 275-350 and 490-720 mt respectively. Given that this update 2020 assessment indicates slightly lower values for resource productivity than in 2019, consideration should be given to some reduction in the current TAC of 502 mt

Butterworth, Doug

Cape Town University OpenUCT

  FISHERIES/2020/OCT/SWG-DEM/26 1  2020 sole dynamic Schaefer production model results  JP Glazer1 and DS Butterworth2  Summary  The sole resource is modelled by a dynamic Schaefer production model which allows for a drop in the value of the intrinsic growth rate parameter from 2000 onwards. The model is fit to the available CPUE and survey abundance indices. These data are not sufficiently informative to be able to distinguish amongst fairly wide ranges of pre- and post-2000 intrinsic growth rate parameters. Nevertheless, all suggest that the sole resource has never been substantially depleted (being well above its MSY level), and furthermore that the current replacement yield and MSY are reasonably robustly estimated in the ranges of 275-350 and 490-720 mt respectively. Given that this update 2020 assessment indicates slightly lower values for resource productivity than in 2019, consideration should be given to some reduction in the current TAC of 502 mt.   Introduction  In recent years two hypotheses to explain low CPUEs for the sole resource over the 2012-2016 period have been considered, namely a decrease in abundance and a decrease in catchability. However, by 2018 CPUEs had returned to levels similar to those pre-2013, rendering the first of these hypotheses now scarcely viable – abundance could not have near doubled in such a short period of only some two years.  For the 2019 assessment of the sole resource a simple dynamic production model was fit to the available data under the assumption of a catchability reduction over 2012-2016.  A number of analyses were undertaken related to r (the intrinsic growth rate) and μ (the parameter that quantifies the extent of catchability reduction over the period 2012-2016, which was assumed to explain the lower CPUE values better over that period). Furthermore, r was considered to be period-specific where r1 (ranging from 0.2-0.5) refers to the intrinsic growth rate for the period 1920-1999 and r2 (ranging from 0.05-0.2) to that rate for the period 2000-2018. μ was either estimated or fixed.    For 2020, this assessment approach has again been applied to updated sole data (with CPUE and catches extended to include 2019 data) to assist in TAC deliberations.                                                            1 Fisheries Management Branch, Department of Agriculture, Forestry and Fisheries, Cape Town 2 Marine Resource Assessment and Management Group, Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7700    FISHERIES/2020/OCT/SWG-DEM/26 2   Methodology   The observation error assessment model applied is as follows   The dynamic Schaefer model is of the form:  𝐵𝑦+1 = 𝐵𝑦 + 𝑟𝐵𝑦[1 −𝐵𝑦𝐾] − 𝐶𝑦         (1)  where  𝐵𝑦 is the biomass estimated in year y,  r is the intrinsic rate of population growth (note that as explained further below, the value of r is allowed to change after a specified year),  K is pristine biomass (which is assumed to reflect the biomass at the start of the catch time series in 1920), and 𝐶𝑦 is the annual catch over the period 1920-2019.  The likelihood is calculated assuming that the abundance indices are log-normally distributed about their expected values:   𝐼𝑦𝑖 = 𝑞𝑖𝐵𝑦𝑒𝜀𝑦𝑖           (2)  where 𝐼𝑦𝑖  is the value for abundance index i for year y, 𝑞𝑖𝐵𝑦 is the corresponding model estimate (𝑞𝑖 being the estimated catchability coefficient for each index of abundance), and 𝜀𝑦𝑖  is the observation error for each index, ~𝑁(0, 𝜎𝑖2), for year y.  The contribution of each abundance index to the negative log-likelihood function (after the removal of constants) is given by:  −ℓ𝑛𝐿𝑖 = 𝑛𝑖ℓ𝑛(?̂?𝑖) +𝑛𝑖2          (3)  where ni is the number of annual data values for index I, and the standard deviation for each index is given by:  ?̂?𝑖 = √1𝑛𝑖(∑ ℓ𝑛𝑦 𝐼𝑦 − ℓ𝑛(?̂?𝑖) − ℓ𝑛?̂?𝑦 )2       (4)  where  𝑙𝑛?̂?𝑖 =1𝑛𝑖∑ 𝑙𝑛 (𝐼𝑦?̂?𝑦)𝑦 The following data have been included in the analyses:   sole catches (1920-2019),    FISHERIES/2020/OCT/SWG-DEM/26 3   nominal CPUE index (1986-2019)   autumn survey index (utilizing “old” gear),   autumn survey index (utilizing “new” gear),  spring survey index (utilizing “old” gear), and   spring survey index (utilizing “new” gear).    Note that the nominal rather than the standardised CPUE index was used because the former is available for a much longer period, and also because over the period for which both are available, they do not differ greatly.  Results  A number of analyses have been undertaken related to r (intrinsic growth rate) and μ (an estimable  parameter that quantifies the extent of catchability reduction over the period 2012-2016, which is assumed to better explain the lower CPUE values over that period). Furthermore, r is considered to be period-specific where r1 (ranging from 0.2-0.5) refers to intrinsic growth for the period 1920-1999 and r2 (ranging from 0.05-0.2) refers to intrinsic growth for the period 2000-2019.    Tables1a and 1b report the parameter values obtained from the 2019 and 2020 assessments respectively.  Table 2 shows comparisons of the values of selected parameters from each of the two assessments, with the results for the three models that fit the data best being highlighted (note that the r1/r2 combination of 0.3/0.1 contributes to one of the three models that best fit the data in both the 2019 and 2020 assessments).  Figures 1-7 show the past catch and biomass trajectories, as well as the fits to the respective indices of abundance.  Discussion  Figure 1 shows that catches have been markedly less over the 2004+ period compared to beforehand (this was, at least in part, a consequence of a reduction in the fishing effort applied). However, there is no indication of an associated increase in biomass from the abundance index data available. This results in models with an unchanged value over time of the r intrinsic growth rate parameter being unable to fit the data (without estimating biomass to be at unrealistically high levels).  Consequently, the earlier value of r (r1) is assumed to drop to a lower value (r2) from 2000 onwards. Table 1 shows the results of fits for various input combinations of r1 (from 0.2 to 0.5) and r2 (from 0.05 to 0.2). Some combinations with r2 only slightly less than r1 are omitted; this is because they result in notably worse fits to the data (this is because they suggest recent marked increases in abundance).    The results for the three best fitting models for both the 2019 and 2020 assessments are highlighted in both Table 1 and Table 2. However, there is little to choose between these three and the other combinations for which results are reported. The reasons are clear from the comparisons between abundance data and model predictions in Figures 3 to 7: these data are not really able to discriminate amongst these different r1/r2 combinations.   A notable feature of the results in Tables 1 and 2, which is also evident from the biomass trajectory plots in Figure 2, is the indication that the resource has never been greatly depleted. For the 2020 assessment, the most pessimistic current depletion (B(2020)/K) in these Tables is 73%, with the best fits yielding values in the vicinity of 80%.    FISHERIES/2020/OCT/SWG-DEM/26 4  As regards advice on a TAC, the three best fitting models for the 2020 assessment suggest a current Replacement Yield (RY) in the 310-340 mt range; this estimate seems fairly robust, as estimates for other r1/r2 combinations are not that dissimilar (and estimates for the lowest r2 value shown can probably be discounted as an intrinsic growth rate for sole as low as 0.05 seems implausible).  Overall then RY is likely in the range of 275-350 mt.  As last year, a case can be made for a TAC that is higher than RY, given that the current depletion (about 80%) is estimated to be well above the MSY level of 50%. Some consideration might be given to (a highish proportion of) the MSY estimates, which for r2≥0.1 range from about  490-720 mt.  At present, the sole TAC is set at 502 mt with an associated TAE of 26352 fishing hours. This TAC was set based on MSY estimates.  Given that this update 2020 assessment indicates slightly lower values for resource productivity than last year, consideration should be given to some reduction in this TAC.     FISHERIES/2020/OCT/SWG-DEM/26 5    Tables 1a: 2019 Assessment parameter estimates and TACs under possible harvest control rules from a suite of dynamic Schaefer production model assessments fitted to the nominal CPUE values over 1986 to 2018, and conducted for various fixed input values of r (r1 refers to intrinsic growth for the period 1920-1999 and r2 refers to intrinsic growth for the period 2000-2018). μ is an estimable parameter that quantifies the extent of catchability reduction over the period 2012-2016; such an assumption explains the lower CPUE values over that period than a biomass decline. Biomass and catch units are mt. The three models which best fit the data as indicated by –lnL are highlighted.     MSY Replacement Yield Fmsy Catch MSY Replacement Yield Fmsy Catchr1 r2 μ -lnL K B(2019) B(2019)/K 0.25*r1*K r1*B(2019)*(1-B(2019)/K) 0.5*r1*B(2019) 0.25*r2*K r2*B(2019)*(1-B(2019)/K) 0.5*r2*B(2019)0.2 0.05 0.558 -51.114 31552 23659 0.750 1578 1184 2366 394 296 5910.3 0.05 0.560 -51.070 33092 26328 0.796 2482 1615 3949 414 269 6580.4 0.05 0.561 -51.029 34329 28040 0.817 3433 2055 5608 429 257 7010.5 0.05 0.561 -51.007 35091 29063 0.828 4386 2496 7266 439 250 7270.2 0.1 0.532 -51.157 20078 14436 0.719 1004 811 1444 502 406 7220.3 0.1 0.550 -51.446 20558 16109 0.784 1542 1046 2416 514 349 8050.4 0.1 0.553 -51.383 22204 18203 0.820 2220 1312 3641 555 328 9100.5 0.1 0.554 -51.344 23355 19564 0.838 2919 1588 4891 584 318 9780.3 0.15 0.522 -51.239 14799 11640 0.787 1110 745 1746 555 373 8730.4 0.15 0.537 -51.464 15826 13119 0.829 1583 897 2624 593 337 9840.5 0.15 0.541 -51.467 17005 14501 0.853 2126 1068 3625 638 320 10880.4 0.2 0.509 -51.022 12499 10625 0.850 1250 637 2125 625 319 10630.5 0.2 0.522 -51.297 13329 11619 0.872 1666 745 2905 666 298 1162  FISHERIES/2020/OCT/SWG-DEM/26 6  Table 1b: 2020 Assessment parameter estimates and TACs under possible harvest control rules from a suite of dynamic Schaefer production model assessments fitted to the nominal CPUE values over 1986 to 2018, and conducted for various fixed input values of r (r1 refers to intrinsic growth for the period 1920-1999 and r2 refers to intrinsic growth for the period 2000-2018). μ is an estimable parameter that quantifies the extent of catchability reduction over the period 2012-2016; such an assumption explains the lower CPUE values over that period than a biomass decline. Biomass and catch units are mt. The three models which best fit the data as indicated by –lnL are highlighted.       MSY Replacement Yield Fmsy Catch MSY Replacement Yield Fmsy Catchr1 r2 μ -lnL K B(2020) B(2020)/K 0.25*r1*K r1*B(2020)*(1-B(2019)/K) 0.5*r1*B(2020) 0.25*r2*K r2*B(2020)*(1-B(2020)/K) 0.5*r2*B(2020)0.2 0.05 0.567 -52.582 29667 21735 0.733 1483 1162 2174 371 291 5430.3 0.05 0.569 -52.588 30880 24109 0.781 2316 1586 3616 386 264 6030.4 0.05 0.569 -52.562 31928 25639 0.803 3193 2020 5128 399 253 6410.5 0.05 0.569 -52.548 32580 26555 0.815 4073 2456 6639 407 246 6640.2 0.1 0.538 -51.849 19715 14188 0.720 986 796 1419 493 398 7090.3 0.1 0.559 -52.609 19644 15258 0.777 1473 1022 2289 491 341 7630.4 0.1 0.561 -52.661 21053 17119 0.813 2105 1280 3424 526 320 8560.5 0.1 0.562 -52.670 22063 18340 0.831 2758 1547 4585 552 309 9170.3 0.15 0.525 -51.556 15330 12449 0.812 1150 702 1867 575 351 9340.4 0.15 0.542 -52.259 15671 13097 0.836 1567 861 2619 588 323 9820.5 0.15 0.547 -52.439 16631 14234 0.856 2079 1026 3558 624 308 10680.4 0.2 0.510 -51.157 14458 12872 0.890 1446 565 2574 723 282 12870.5 0.2 0.525 -51.804 14026 12466 0.889 1753 693 3117 701 277 1247  FISHERIES/2020/OCT/SWG-DEM/26 7  Table 2: Comparisons of select statistics related to the r1 and r2 combinations as derived from the 2019 and 2020 assessments respectively, the latter excluding r2=0.05.  The three models which best fit the data as indicated by –lnL are highlighted.    2019 Assessment    2020 Assessment                                                            r1 0.05 0.1 0.15 0.20.2 -51.114 -51.1570.3 -51.070 -51.446 -51.2390.4 -51.029 -51.383 -51.464 -51.0220.5 -51.007 -51.344 -51.467 -51.297r2-lnLr1 0.05 0.1 0.15 0.20.2 -52.582 -51.8490.3 -52.588 -52.609 -51.5560.4 -52.562 -52.661 -52.259 -51.1570.5 -52.548 -52.670 -52.439 -51.804-lnLr2r1 0.05 0.1 0.15 0.20.2 0.750 0.7190.3 0.796 0.784 0.7870.4 0.817 0.820 0.829 0.8500.5 0.828 0.838 0.853 0.872B(2019)/Kr2r1 0.05 0.1 0.15 0.20.2 0.733 0.7200.3 0.781 0.777 0.8120.4 0.803 0.813 0.836 0.8900.5 0.815 0.831 0.856 0.889B(2020)/Kr2r1 0.05 0.1 0.15 0.20.2 394 5020.3 414 514 5550.4 429 555 593 6250.5 439 584 638 666MSY (based on r2)r2r1 0.05 0.1 0.15 0.20.2 371 4930.3 386 491 5750.4 399 526 588 7230.5 407 552 624 701r2MSY (based on r2)r1 0.05 0.1 0.15 0.20.2 296 4060.3 269 349 3730.4 257 328 337 3190.5 250 318 320 298RY based on r2r2r1 0.05 0.1 0.15 0.20.2 291 3980.3 264 341 3510.4 253 320 323 2820.5 246 309 308 277r2RY based on r2  FISHERIES/2020/OCT/SWG-DEM/26 8    Figure 1: Annual sole catches (units: mt).    Figure 2: 2020 assessment biomass trajectories (units: tons) for the r1/r2 combinations that best fit the data in the 2019 and 2020 assessments respectively (as indicated in the legend). The dashed lines relate to the 2019 assessment best fit r1/r2 combinations and the solid lines relate to the  2020 assessment best fit r1/r2 combinations (note that there is only one trend for the r1=0.3 and r2=0.1 combination given that it was one of the best fits in both the 2019 and 2020 assessments). 02004006008001000120014001920192419281932193619401944194819521956196019641968197219761980198419881992199620002004200820122016050001000015000200002500019201924192819321936194019441948195219561960196419681972197619801984198819921996200020042008201220162020r1=0.3, r2=0.1 r1=0.4, r2=0.1 r1=0.5, r2=0.1r1=0.4, r2=0.15 r1=0.5, r2=0.15  FISHERIES/2020/OCT/SWG-DEM/26 9   Figure 3: 2020 Assessment fits to the commercial CPUE index (units: kg/min) for the r1/r2 combinations that best fit the data in the 2019 and 2020 assessments respectively (as indicated in the legend). The dashed lines relate to the 2019 assessment best fit r1/r2 combinations and the solid lines relate to the  2020 assessment best fit r1/r2 combinations (note that there is only one trend for the r1=0.3 and r2=0.1 combination given that it was one of the best fits in both the 2019 and 2020 assessments).   Figure 4: 2020 Assessment fits to the autumn old gear index (units: mt) for the r1/r2 combinations that best fit the data in the 2019 and 2020 assessments respectively (as indicated in the legend). The dashed lines relate to the 2019 assessment best fit r1/r2 combinations and the solid lines relate to the  2020 assessment best fit r1/r2 combinations (note that there is only one trend for the r1=0.3 and r2=0.1 combination given that it was one of the best fits in both the 2019 and 2020 assessments).  .   00.10.20.30.40.50.619861988199019921994199619982000200220042006200820102012201420162018r1=0.3, r2=0.1 r1=0.4, r2=0.1 r1=0.4, r2=0.15r1=0.5, r2=0.15 nominal index010002000300040005000600019881989199019911992199319941995199619971998199920002001200220032004200520062007200820092010r1=0.3, r2=0.1 r1=0.4, r2=0.1 r1=0.5, r2=0.1r1=0.4, r2=0.15 r1=0.5, r2=0.15 observed  FISHERIES/2020/OCT/SWG-DEM/26 10   Figure 5: 2020 Assessment fits to the autumn new gear index (units: mt) for the r1/r2 combinations that best fit the data in the 2019 and 2020 assessments respectively (as indicated in the legend). The dashed lines relate to the 2019 assessment best fit r1/r2 combinations and the solid lines relate to the  2020 assessment best fit r1/r2 combinations (note that there is only one trend for the r1=0.3 and r2=0.1 combination given that it was one of the best fits in both the 2019 and 2020 assessments).    Figure 6: 2020 Assessment fits to the old gear spring index units=mt) for the r1/r2 combinations that best fit the data in the 2019 and 2020 assessments respectively (as indicated in the legend). The dashed lines relate to the 2019 assessment best fit r1/r2 combinations and the solid lines relate to the  2020 assessment best fit r1/r2 combinations (note that there is only one trend for the r1=0.3 and r2=0.1 combination given that it was one of the best fits in both the 2019 and 2020 assessments). 050010001500200025002004200520062007200820092010201120122013201420152016201720182019r1=0.3, r2=0.1 r1=0.4, r2=0.1 r1=0.5, r2=0.1r1=0.4, r2=0.15 r1=0.5, r2=0.15 observed0200400600800100012001400160020032004200520062007200820092010201120122013201420152016r1=0.3, r2=0.1 r1=0.4, r2=0.1 r1=0.5, r2=0.1r1=0.4, r2=0.15 r1=0.5, r2=0.15 observed  FISHERIES/2020/OCT/SWG-DEM/26 11   Figure 7: 2020 Assessment fits to the spring new gear index (units=mt) for the r1/r2 combinations that best fit the data in the 2019 and 2020 assessments respectively (as indicated in the legend). The dashed lines relate to the 2019 assessment best fit r1/r2 combinations and the solid lines relate to the  2020 assessment best fit r1/r2 combinations (note that there is only one trend for the r1=0.3 and r2=0.1 combination given that it was one of the best fits in both the 2019 and 2020 assessments).      01000200030004000500060007000198619871988198919901991199219931994199519961997199819992000200120022003200420052006r1=0.3, r2=0.1 r1=0.4, r2=0.1 r1=0.5, r2=0.1r1=0.4, r2=0.15 r1=0.5, r2=0.15 Observed

2020 sole dynamic Schaefer production model results

  FISHERIES/2019/OCT/SWG-DEM/42 1  Further sole dynamic Schaefer production model results  DS Butterworth and JP Glazer  Summary  The sole resource is modelled by a dynamic Schaefer production model which allows for a drop in the value of the intrinsic growth rate parameter from 2000 onwards. The model is fit to the available CPUE and survey abundance indices. These data are not sufficiently informative to be able to distinguish amongst fairly wide ranges of pre- and post-2000 intrinsic growth rate parameters. Nevertheless, all suggest that the sole resource has never been substantially depleted (being well above its MSY level), and furthermore that the current replacement yield and MSY are reasonably robustly estimated in the ranges of 300-400 and 500-650 mt respectively.   Introduction  Previously there were two hypotheses to explain low CPUEs for the sole resource over the 2012-2016 period: a decrease in abundance and a decrease in catchability. The increase in CPUE over the last two years (so that CPUE is now back to a similar levels to those before 2012 – see Figure 4) renders the first of these hypotheses now scarcely viable – abundance could not have near doubled in such a short period of only some two years.  This document therefore examines fits of simple dynamic production models to the available data under the assumption of a catchability reduction over the 2012-2016 period, in part to ascertain whether these might be able to provide a basis for updated TAC recommendations.   Methodology   The observation error assessment model applied is as follows   The dynamic Schaefer model is of the form:  𝐵𝑦+1 = 𝐵𝑦 + 𝑟𝐵𝑦[1 −𝐵𝑦𝐾] − 𝐶𝑦         (1)  where  𝐵𝑦 is the biomass estimated in year y,  r is the intrinsic rate of population growth (note that as explained further below, the value of r is allowed to change after a specified year),  K is pristine biomass (which is assumed to reflect the biomass at the start of the catch time series in 1920), and 𝐶𝑦 is the annual catch over the period 1920-2018.  The likelihood is calculated assuming that the abundance indices are log-normally distributed about their expected values:    FISHERIES/2019/OCT/SWG-DEM/42 2   𝐼𝑦𝑖 = 𝑞𝑖𝐵𝑦𝑒𝜀𝑦𝑖           (2)  where 𝐼𝑦𝑖  is the value for abundance index i for year y, 𝑞𝑖𝐵𝑦 is the corresponding model estimate (𝑞𝑖 being the estimated catchability coefficient for each index of abundance), and 𝜀𝑦𝑖  is the observation error for each index, ~𝑁(0, 𝜎𝑖2), for year y.  The contribution of each abundance index to the negative log-likelihood function (after the removal of constants) is given by:  −ℓ𝑛𝐿𝑖 = 𝑛𝑖ℓ𝑛(?̂?𝑖) +𝑛𝑖2          (3)  where ni is the number of annual data values for index I, and the standard deviation for each index is given by:  ?̂?𝑖 = √1𝑛𝑖(∑ ℓ𝑛𝑦 𝐼𝑦 − ℓ𝑛(?̂?𝑖) − ℓ𝑛?̂?𝑦 )2       (4)  where  𝑙𝑛?̂?𝑖 =1𝑛𝑖∑ 𝑙𝑛 (𝐼𝑦?̂?𝑦)𝑦 The following data have been included in the analyses:  • sole catches (1920-2016),  • nominal CPUE index (1986-2016)  • autumn survey index (utilizing “old” gear),  • autumn survey index (utilizing “new” gear), • spring survey index (utilizing “old” gear), and  • spring survey index (utilizing “new” gear).    Note that the nominal rather than the standardised CPUE index was used because the former is available for a much longer period, and also because over the period for which both are available, they do not differ greatly.  Results  A number of analyses were undertaken related to r (intrinsic growth rate) and μ (the parameter that quantifies the extent of catchability reduction over the period 2012-2016, which is assumed to better explain the lower CPUE values over that period). Furthermore, r was considered to be period-specific where r1 (ranging from 0.2-0.5) refers to intrinsic growth for the period 1920-1999 and r2 (ranging from 0.05-0.2) refers to intrinsic growth for the period 2000-2018. μ is either estimated or fixed.    Table 1 reports the parameter values obtained from each of the model fits for the r1/r2 combinations for which μ is estimated.  Table 2 shows comparisons of the values of selected parameters, with the results for the three models that fit the data best being highlighted.      FISHERIES/2019/OCT/SWG-DEM/42 3  Table 3 compares results for r1=0.5 and r2=0.15 (which yields the best fit amongst the different r1/r2 combinations considered) for scenarios where μ is either estimated or fixed (at 0.1).    Figures 1-7 show the past catch and biomass trajectories, as well as the fits to the respective indices of abundance.   Discussion  Figure 1 shows that catches have been markedly less over the 2004+ period compared to beforehand (this was, at least in part, a consequence of a reduction in the fishing effort applied). However, there is no indication of an associated increase in biomass from the abundance index data available. This results in models with an unchanged value over time of the r intrinsic growth rate parameter being unable to fit the data (without estimating biomass to be at unrealistically high levels).  Consequently, the earlier value of r (r1) is assumed to drop to a lower value (r2) from 2000 onwards. Table 1 shows the results of fits for various input combinations of r1 (from 0.2 to 0.5) and r2 (from 0.05 to 0.2). Some combinations with r2 only slightly less than r1 are omitted; this is because they result in notably worse fits to the data (this is because they suggest recent marked increases in abundance).    The results for the three best fitting models are highlighted in both Table 1 and Table 2. However, there is little to choose between these three and the other combinations for which results are reported. The reasons are clear from the comparisons between abundance data and model predictions in Figures 3 to 7: these data are not really able to discriminate amongst these different r1/r2 combinations.   Table 3 (and Figure 3) show the consequences of assuming (by fixing μ at the low value of 0.1) that the low 2012-2016 CPUE values were not entirely a consequence of poor catchability; the resultant fit to the CPUE data is very poor.  A notable feature of the results in Tables 1 and 2, which is also evident from the biomass trajectory plots in Figure 2, is the indication that the resource has never been greatly depleted. The most pessimistic current depletion (B(2019)/K) in these Tables is 72%, with the best fits yielding values in the vicinity of 80%.  As regards advice on a TAC, the three best fitting models suggest a current Replacement Yield (RY) in the 320-350 mt range; this estimate seems fairly robust, as estimates for other r1/r2 combinations are not that dissimilar (and estimates for the lowest r2 value shown can probably be discounted as an intrinsic growth rate for sole as low as 0.05 seems implausible).  Overall then RY is likely in the range of 300-400 mt.  A case could be made for a TAC that is higher than RY, given that current depletion (about 80%) is estimated to be well above the MSY level of 50%. Fmsy strategy options, ranging from about 600 to 1200 mt would seem questionably appropriate, including because those values would be expected to decrease over time if such a strategy was implemented. However, some consideration might be given to (a highish proportion of) the MSY estimates, which range from about 400 – 650 mt, or 500 – 650 mt if r2 values of 0.05 are excluded.   FISHERIES/2019/OCT/SWG-DEM/42 4   Note that at present, the sole TAC is set at 627 mt, but with an associated TAE of 16767 fishing hours.    FISHERIES/2019/OCT/SWG-DEM/42 5  Table 1: Parameter estimates and TACs under possible harvest control rules from a suite of dynamic Schaefer production model assessments fitted to the nominal CPUE values over 1986 to 2018, and conducted for various fixed input values of r (r1 refers to intrinsic growth for the period 1920-1999 and r2 refers to intrinsic growth for the period 2000-2018). μ is an estimable parameter that quantifies the extent of catchability reduction over the period 2012-2016; such an assumption explains the lower CPUE values over that period than a biomass decline. Biomass and catch units are mt. The three models which best fit the data as indicated by –lnL are highlighted.     MSY Replacement Yield Fmsy Catch MSY Replacement Yield Fmsy Catchr1 r2 μ -lnL K B(2019) B(2019)/K 0.25*r1*K r1*B(2019)*(1-B(2019)/K) 0.5*r1*B(2019) 0.25*r2*K r2*B(2019)*(1-B(2019)/K) 0.5*r2*B(2019)0.2 0.05 0.558 -51.114 31552 23659 0.750 1578 1184 2366 394 296 5910.3 0.05 0.560 -51.070 33092 26328 0.796 2482 1615 3949 414 269 6580.4 0.05 0.561 -51.029 34329 28040 0.817 3433 2055 5608 429 257 7010.5 0.05 0.561 -51.007 35091 29063 0.828 4386 2496 7266 439 250 7270.2 0.1 0.532 -51.157 20078 14436 0.719 1004 811 1444 502 406 7220.3 0.1 0.550 -51.446 20558 16109 0.784 1542 1046 2416 514 349 8050.4 0.1 0.553 -51.383 22204 18203 0.820 2220 1312 3641 555 328 9100.5 0.1 0.554 -51.344 23355 19564 0.838 2919 1588 4891 584 318 9780.3 0.15 0.522 -51.239 14799 11640 0.787 1110 745 1746 555 373 8730.4 0.15 0.537 -51.464 15826 13119 0.829 1583 897 2624 593 337 9840.5 0.15 0.541 -51.467 17005 14501 0.853 2126 1068 3625 638 320 10880.4 0.2 0.509 -51.022 12499 10625 0.850 1250 637 2125 625 319 10630.5 0.2 0.522 -51.297 13329 11619 0.872 1666 745 2905 666 298 1162  FISHERIES/2019/OCT/SWG-DEM/42 6   Table 2: Comparisons of select statistics related to the r1 and r2 combinations.  The three models which best fit the data as indicated by –lnL are highlighted.      Table 3: Comparison of results for r1=0.4 and r2=0.15 where μ is either estimated (0.537) or fixed (at 0.1). r1 0.05 0.1 0.15 0.20.2 -51.114 -51.1570.3 -51.070 -51.446 -51.2390.4 -51.029 -51.383 -51.464 -51.0220.5 -51.007 -51.344 -51.467 -51.297r2-lnLr1 0.05 0.1 0.15 0.20.2 23659 144360.3 26328 16109 116400.4 28040 18203 13119 106250.5 29063 19564 14501 11619r2B(2019)r1 0.05 0.1 0.15 0.20.2 0.750 0.7190.3 0.796 0.784 0.7870.4 0.817 0.820 0.829 0.8500.5 0.828 0.838 0.853 0.872B(2019)/Kr2r1 0.05 0.1 0.15 0.20.2 394 5020.3 414 514 5550.4 429 555 593 6250.5 439 584 638 666MSY (based on r2)r2r1 0.05 0.1 0.15 0.20.2 296 4060.3 269 349 3730.4 257 328 337 3190.5 250 318 320 298RY based on r2r2r1 0.05 0.1 0.15 0.20.2 591 7220.3 658 805 8730.4 701 910 984 10630.5 727 978 1088 1162r2FMSY  catch (based on r2)MSY Replacement Yield Fmsy Catch MSY Replacement Yield Fmsy Catchr1 r2 μ -lnL K B(2019) B(2019)/K 0.25*r1*K r1*B(2019)*(1-B(2019)/K) 0.5*r1*B(2019) 0.25*r2*K r2*B(2019)*(1-B(2019)/K) 0.5*r2*B(2019)0.4 0.15 0.537 -51.464 15826 13119 0.829 1583 897 2624 593 337 9840.4 0.15 0.1 -8.708 19372 16911 0.873 1937 860 3382 726 322 1268  FISHERIES/2019/OCT/SWG-DEM/42 7    Figure 1: Annual sole catches (units: mt).    Figure 2: Sole biomass trajectories for r1/r2 combinations (units: mt)020040060080010001200140019201923192619291932193519381941194419471950195319561959196219651968197119741977198019831986198919921995199820012004200720102013201605000100001500020000250003000035000400001920192319261929193219351938194119441947195019531956195919621965196819711974197719801983198619891992199519982001200420072010201320162019r1=0.2, r2=0.05 r1=0.3, r2=0.05 r1=0.4, r2=0.05r1=0.5, r2=0.05 r1=0.2, r2=0.1 r1=0.3, r2=0.1r1=0.4, r2=0.1 r1=0.5, r2=0.1 r1=0.3, r2=0.15r1=0.4, r2=0.15 r1=0.5, r2=0.15 r1=0.4, r2=0.2r1=0.5, r2=0.2 r1=0.4, r2=0.15, μ= 0.1 Catch  FISHERIES/2019/OCT/SWG-DEM/42 8   Figure 3: Fits to the commercial CPUE index for r1/r2 combinations (units: kg/min)    Figure 4: Fits to the autumn index (old gear) for r1/r2 combinations (units: mt)    00.10.20.30.40.50.619861988199019921994199619982000200220042006200820102012201420162018r1=0.2, r2=0.05 r1=0.3, r2=0.05 r1=0.4, r2=0.05r1=0.5, r2=0.05 r1=0.2, r2=0.1 r1=0.3, r2=0.1r1=0.4, r2=0.1 r1=0.5, r2=0.1 r1=0.3, r2=0.15r1=0.4, r2=0.15 r1=0.5, r2=0.15 r1=0.4, r2=0.2r1=0.5, r2=0.2 observed r1=0.4, r2=0.15, μ=0.1010002000300040005000600019881989199019911992199319941995199619971998199920002001200220032004200520062007200820092010r1=0.2, r2=0.05 r1=0.3, r2=0.05 r1=0.4, r2=0.05r1=0.5, r2=0.05 r1=0.2, r2=0.1 r1=0.3, r2=0.1r1=0.4, r2=0.1 r1=0.5, r2=0.1 r1=0.3, r2=0.15r1=0.4, r2=0.15 r1=0.5, r2=0.15 r1=0.4, r2=0.2r1=0.5, r2=0.2 observed r1=0.4, r2=0.15, μ=0.1  FISHERIES/2019/OCT/SWG-DEM/42 9    Figure 5: Fits to the autumn index (new gear) for r1/r2 combinations (units: mt)    Figure 6: Fits to the spring index (old gear) for r1/r2 combinations (units: mt)  050010001500200025002004200520062007200820092010201120122013201420152016201720182019r1=0.2, r2=0.05 r1=0.3, r2=0.05 r1=0.4, r2=0.05r1=0.5, r2=0.05 r1=0.2, r2=0.1 r1=0.3, r2=0.1r1=0.4, r2=0.1 r1=0.5, r2=0.1 r1=0.3, r2=0.15r1=0.4, r2=0.15 r1=0.5, r2=0.15 r1=0.4, r2=0.2r1=0.5, r2=0.2 observed r1=0.4, r2=0.15, μ=0.101000200030004000500060007000198619871988198919901991199219931994199519961997199819992000200120022003200420052006r1=0.2, r2=0.05 r1=0.3, r2=0.05 r1=0.4, r2=0.05r1=0.5, r2=0.05 r1=0.2, r2=0.1 r1=0.3, r2=0.1r1=0.4, r2=0.1 r1=0.5, r2=0.1 r1=0.3, r2=0.15r1=0.4, r2=0.15 r1=0.5, r2=0.15 r1=0.4, r2=0.2r1=0.5, r2=0.2 Observed r1=0.4, r2=0.15, μ=0.1  FISHERIES/2019/OCT/SWG-DEM/42 10   Figure 7: Fits to the spring index (new gear) for r1/r2 combinations (units: mt)     0200400600800100012001400160020032004200520062007200820092010201120122013201420152016r1=0.2, r2=0.05 r1=0.3, r2=0.05 r1=0.4, r2=0.05r1=0.5, r2=0.05 r1=0.2, r2=0.1 r1=0.3, r2=0.1r1=0.4, r2=0.1 r1=0.5, r2=0.1 r1=0.3, r2=0.15r1=0.4, r2=0.15 r1=0.5, r2=0.15 r1=0.4, r2=0.2r1=0.5, r2=0.2 observed r1=0.4, r2=0.15, μ=0.1

Further sole dynamic Schaefer production model results

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Further sole dynamic Schaefer production model results

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