SCRS/2008/170 Collect. Vol. Sci. Pap. ICCAT, 64(4): 1191-1198 (2009) EVALUATING THE IMPACT OF CHANGES IN FISHING PRESSURE ON ATLANTIC TROPICAL TUNAS USING YIELD-PER-RECRUIT AND SPAWNER-PER-RECRUIT ANALYSES Shannon L. Cass-Calay 1 SUMMARY The purpose of this document is to describe a flexible method that can be used to estimate the effects of changes in fishing mortality by age, fleet, gear and area on the yield-per-recruit (YPR) and spawner-per-recruit (SPR) values of tropical tunas and other species. In particular, this method could be used to address questions regarding: time area closures, size limits, emigration or immigration of fishing effort and gear restrictions. An example is discussed that is based on the most recent stock assessment of yellowfin tuna. The method could be extended for additional analyses by the Tropical Tunas Working Group. RÉSUMÉ Le but du présent document est de décrire une méthode flexible pouvant être utilisée pour estimer les effets des changements de la mortalité par pêche par âge, flottille, engin et zone sur les valeurs de la production par recrue et de la reproduction par recrue des thonidés tropicaux et d autres espèces. Cette méthode pourrait notamment être utilisée pour aborder des questions sur : les fermetures spatio-temporelles, les limites de taille, l émigration ou l immigration de l effort de pêche et les restrictions d engins. Un exemple basé sur la plus récente évaluation du stock d albacore est discuté. La méthode pourrait être étendue à des analyses additionnelles par le Groupe d espèces Thonidés tropicaux. RESUMEN El propósito de este documento es describir un método flexible que pueda ser utilizado para estimar los efectos de los cambios en la mortalidad por pesca por edad, flota, arte y área sobre los valores de rendimiento por recluta (YPR) y de reproductor por recluta (SPR) de los túnidos tropicales y otras especies. En particular, este método podría utilizarse para tratar temas relacionados con: vedas espacio-temporales, límites de talla, emigración o inmigración del esfuerzo pesquero y restricciones al arte. Se discute un ejemplo basado en la evaluación de stock más reciente de rabil. El método podría ser utilizado en análisis adicionales por el Grupo de trabajo de túnidos tropicales. KEY WORDS Fisheries statistics, effect of management regulations, YPR, SPR 1. Introduction This paper was prepared to present a methodology that would address the concerns expressed in the 2007 ICCAT Panel 1 Report. Specifically, there is concern about the high percentage of juveniles (~70% of the catches by number) in the bigeye catches and their effect on the stock. It is likely that a decline in the catches of juveniles would increase the biomass of adult fish, and that the establishment of a more extensive and longer closed area would reduce the catch of juveniles. At the same time, the recent decline in nominal purse seine fishing capacity could cause a reduction in the catches of juveniles. 1 U.S. Department of Commerce, NOAA Fisheries, Southeast Fisheries Science Center, Miami Laboratory, 75 Virginia Beach Drive, Miami, Florida 33149 U.S.A. Email: Shannon.Calay@noaa.gov 1191
At the 2008 meeting to assess Atlantic yellowfin and skipjack stocks, it was decided that the Tropical Tunas Species Group would analyze and present a range of options to increase the yield per recruit and MSY of bigeye tuna by reducing mortality on small bigeye tuna through various measures. The impacts of such measures on the catches of yellowfin tuna and skipjack tuna would be analyzed as well. The purpose of this document is to describe a flexible method that may be used to estimate the effects of changes in fishing mortality (F) by age, fleet, gear and/or area on the yield-per-recruit (YPR) and spawner-per-recruit (SPR) estimates of tropical tunas as well as other species. In particular, this method could be used to address questions regarding: 1) Time-area closures 2) Size limits 3) Gear restrictions 4) Emigration/Immigration of fishing effort This procedure is an extension of a previous approach described by Restrepo et al. (2006), and implemented to estimate the effects of various size limits on eastern Atlantic bluefin tuna. The proposed method uses gear/fleet/area specific catch ratios to modify the selectivity vector used to calculate YPR and SPR. A hypothetical example (based on the 2008 base case VPA stock assessment of yellowfin tuna) is included to demonstrate the approach, and to facilitate decisions regarding the types of analyses preferred by the working group. 2. Materials and methods The following data is required to use this procedure to estimate changes in YPR and SPR due to size limits or changes in selectivity at age: 1) Weight-at-age, preferably at the peak of the spawning season (for SPR) and at the middle of the fishing season (for YPR). 2) A constant or age-specific estimate of natural mortality 3) Fecundity-at-age or a proxy (i.e. gonad weight, maturity*weight-at-age, etc.) 4) An estimate of F-at-age for the time period of interest. For this analysis, inputs from the 2008 Case 5 stock assessment of yellowfin tuna were used (Table 1). This is one of two base cases identified by the Working Group (Anon, 2008). The time period considered for this analysis was the most recent three years, excluding the terminal year of the VPA model. This was done to minimize the effects of poor estimation of F in the terminal year which is common to backwards recursive models such as the VPA. 2.1 Formulation The following equations provide details about the computations, where a is the age, y the year, g the gear and c is the case selection pattern examined. The average fishing mortality ( ) is calculated as: The selectivity multiplier for each case (c) being examined is: The fishing mortality vector ( ) and total mortality ( ) vector for each case (c) are: where is the natural mortality. 1192
For each case (c) the number of individuals at the beginning of the year ( ) was calculated as: for terminal age (A) a correction was applied: For each case (c) the catch at age ( ) was calculated as: The yield at age ( ) and spawners at age ( ) for each case (c) were: where is the weight at age at the peak of the fishing year and is the weight at age at the peak of the spawning season. Overall yield per recruit ( ) and spawners per recruit ( ) were calculated for each case (c) as follows: For each case, gear (or area or fleet) specific YPR and SPR estimates can be calculated by multiplying the overall and by the average catch fraction ( ) of each gear. The catch fraction ( ) could be calculated across a selection of years (e.g. 2003-2005) as follows: where the ratio of gear specific catch to total catch ( ) was: However, for this analysis, hypothetical catch ratios were created for two gear types (Table 2). Gear 1 was intended to resemble a purse seine gear in that the catch ratios are highest on the youngest ages. Gear 2 is intended to resemble a longline gear, with the highest catch ratios on the older ages. It should be noted that the sum of the catch ratios must equal 1.0 for any given age. For actual datasets, this may require the addition of an Unspecified Catches category. 1193
2.2 Case specific selectivity multipliers For simplicity, and in order to utilize the existing VPA results, the method of calculation proposed in this document assumes that F is distributed evenly throughout the year. The computation of the selectivity multipliers ( ) for each case and a description of the rationale are as follows. The case-specific selectivity multipliers are summarized in Table 3. Case 1: Status Quo. for all ages. The vector from the VPA is applied unmodified. Case 2: A size limit is applied that eliminates fishing on age-0 and reduces F on age-1 by 25%. In this case, and. For all other ages,. Case 3: An increase in fishing on adults is realized that raises F on ages 3, 4, and 5+ by 25%. In this case,,,.. and. Case 4: This case is intended to examine the effects of hypothetical changes in gear-specific F, but identical methods could be used to examine changes in F of fleets, areas or a combination of these factors. Consider the following example: Assume that two gears exist in a fishery and the intention of a management regulation is two reduce the F of gear 1 by 50% while increasing the F associated with gear 2 by 50%. Further, assume that this reduction is implemented by limiting effort, but does not change the selectivity-at-age of either gear (therefore ). To estimate the effect of this change on the overall YPR and SPR, it is necessary to calculate an adjusted F vector ( ). For this example: (Table 4) where, and are the unadjusted values as described in Section 2.1. YPR and SPR are then calculated as described in 2.1, with the exception that the adjusted fishing mortality vector ( ) be used in place of. To calculate gear (or area, fleet, etc.) specific YPR and SPR for any case that modifies F vectors using catch ratios, it is necessary to compute adjusted catch ratios ( ) that reflect the expected change (Table 5). For the Case 4 example, the adjusted catch ratios for Gears 1 and 2 are: = = where are the unadjusted catch ratios (see in Section 2.1). Note that the sum of the catch ratios must equal 1.0 for any given age. Gear (or area, fleet, etc.) specific YPR and SPR are then calculated as in Section 2.1, with the exception that the adjusted catch ratios ( ) be used in place of the unadjusted values ( ). 3. Results and discussion The overall and gear specific YPR values for each case are summarized in Table 6. Case 1 is the status quo (i.e. no modification applied to the selectivity multiplier or catch ratios). All other cases allow the total YPR to increase relative to the status quo. According to this hypothetical example, the largest increase (13.1%) is 1194
realized by reducing the F associated with Gear 1 by 50% while allowing the F associated with the Gear 2 to increase by the same amount (Case 4). Recall that Gear 1 was intended to resemble a purse seine gear in that the catch ratios are highest on the youngest ages while Gear 2 was intended to resemble a longline gear, with the highest catch ratios on the older ages. The largest increase in the YPR associated with Gear 1 (5.3%) occurs for Case 3, which executed a 25% increase in the F of Ages 3+. Decreasing the F associated with Gear 1 by 50% while simultaneously increasing the F associated with Gear 2 by 50% (Case 4) resulted in a 42.2% decrease in the YPR associated with Gear 1, relative to the status quo. All cases presented in this document allowed an increase in the YPR associated with Gear 2, relative to the status quo. The largest increase (74.9%) occurred when the F associated with Gear 1 was reduced by 50% while simultaneously increasing the F associated with Gear 2 by 50% (Case 4). The smallest increase (6.3%) occurred when the F of Ages 3+ was increased 25% (Case 3). The overall and gear specific SPR values for each case are summarized in Table 7. The maximum SPR (12.42) occurs when F = 0. The largest increase in SPR (31.7%) was realized by reducing the F on Ages 0-1 (Case 2). SPR was reduced by 8.6% by increasing F on ages 3+ (Case 3). The results discussed in this paper are hypothetical. They are not intended to inform the Commission. Instead, they are intended to demonstrate a flexible method that can be used to recommend and evaluate the potential of various management strategies. 4. Acknowledgements The members of the ICCAT Tropical Tunas Species Group were pivotal in providing guidance used during the development of this methodology. We would also like to acknowledge the assistance of Víctor Restrepo (NOAA/SEFSC), Mauricio Ortiz (NOAA/SEFSC) and John Walter (NOAA/SEFSC). 5. References ANON., 2008. Report of the 2008 ICCAT Yellowfin and Skipjack Stock Assessment Meeting. Collect. Vol. Sci. Pap, ICCAT, 64 (in this volume). Restrepo, V.R, Arrizabalaga, H., Ortiz de Urbina, J.M. and Fromentin, J.M., 2006. Effect of minimum size regulations on east bluefin tuna (Thunnus thynnus L.) yield per recruit. Collect. Vol. Sci. Pap. ICCAT, 59(3): 794-801. 1195
Table 1. Inputs used for the analysis. The VPA was implemented on ages 0 to 5+. Inputs used for ages > 5 carried the plus group values forward to age 50. Age Weight (fishery) Weight (SSB) Maturity Fecundity Proxy (WAA * Maturity) M Average F (03 05) 0 1.59 1.07 0.00 0.00 0.80 0.16 1 3.16 2.16 0.00 0.00 0.80 0.46 2 15.89 8.72 0.00 0.00 0.60 0.22 3 40.69 29.52 1.00 29.52 0.60 0.39 4 63.42 54.95 1.00 54.95 0.60 0.66 5 87.96 78.54 1.00 78.54 0.60 0.25 6 87.96 78.54 1.00 78.54 0.60 0.25 7 87.96 78.54 1.00 78.54 0.60 0.25 8 87.96 78.54 1.00 78.54 0.60 0.25 9 87.96 78.54 1.00 78.54 0.60 0.25 10 87.96 78.54 1.00 78.54 0.60 0.25 11 87.96 78.54 1.00 78.54 0.60 0.25 12 87.96 78.54 1.00 78.54 0.60 0.25 13 87.96 78.54 1.00 78.54 0.60 0.25 14 87.96 78.54 1.00 78.54 0.60 0.25 15 87.96 78.54 1.00 78.54 0.60 0.25 16 87.96 78.54 1.00 78.54 0.60 0.25 17 87.96 78.54 1.00 78.54 0.60 0.25 18 87.96 78.54 1.00 78.54 0.60 0.25 19 87.96 78.54 1.00 78.54 0.60 0.25 20 87.96 78.54 1.00 78.54 0.60 0.25 21 87.96 78.54 1.00 78.54 0.60 0.25 22 87.96 78.54 1.00 78.54 0.60 0.25 23 87.96 78.54 1.00 78.54 0.60 0.25 24 87.96 78.54 1.00 78.54 0.60 0.25 25 87.96 78.54 1.00 78.54 0.60 0.25 26 87.96 78.54 1.00 78.54 0.60 0.25 27 87.96 78.54 1.00 78.54 0.60 0.25 28 87.96 78.54 1.00 78.54 0.60 0.25 29 87.96 78.54 1.00 78.54 0.60 0.25 30 87.96 78.54 1.00 78.54 0.60 0.25 31 87.96 78.54 1.00 78.54 0.60 0.25 32 87.96 78.54 1.00 78.54 0.60 0.25 33 87.96 78.54 1.00 78.54 0.60 0.25 34 87.96 78.54 1.00 78.54 0.60 0.25 35 87.96 78.54 1.00 78.54 0.60 0.25 36 87.96 78.54 1.00 78.54 0.60 0.25 37 87.96 78.54 1.00 78.54 0.60 0.25 38 87.96 78.54 1.00 78.54 0.60 0.25 39 87.96 78.54 1.00 78.54 0.60 0.25 40 87.96 78.54 1.00 78.54 0.60 0.25 41 87.96 78.54 1.00 78.54 0.60 0.25 42 87.96 78.54 1.00 78.54 0.60 0.25 43 87.96 78.54 1.00 78.54 0.60 0.25 44 87.96 78.54 1.00 78.54 0.60 0.25 45 87.96 78.54 1.00 78.54 0.60 0.25 46 87.96 78.54 1.00 78.54 0.60 0.25 47 87.96 78.54 1.00 78.54 0.60 0.25 48 87.96 78.54 1.00 78.54 0.60 0.25 49 87.96 78.54 1.00 78.54 0.60 0.25 50 87.96 78.54 1.00 78.54 0.60 0.25 1196
Table 2. Initial gear-specific catch ratios ( ) used for this analysis. Gear 1 is intended to resemble a purse seine and Gear 2 is intended to resemble a longline. Age(s) 0 0.9 0.1 1 0.8 0.2 2 0.5 0.5 3 0.5 0.5 4 0.3 0.7 5-50 0.3 0.7 Table 3. Case specific selectivity multipliers ( through to age 50. ) for cases 1-3. Plus group (5+) multipliers were carried Age(s) 0 1 0 1 1 1 0.75 1 2 1 1 1 3 1 1 1.25 4 1 1 1.25 5 to 50 1 1 1.25 Table 4. The average fishing mortality and adjusted fishing mortality, used for Case 4. Age(s) 0 0.16 0.096 1 0.46 0.322 2 0.22 0.220 3 0.39 0.390 4 0.66 0.792 5-50 0.25 0.300 Table 5. Hypothetical gear-specific catch ratios ( ) used for case 4. Gear 1 is intended to resemble a purse seine and Gear 2 is intended to resemble a longline. The table shows the gear-specific catch ratios before and after a hypothetical regulation that decreases the fishing mortality of Gear 1 by 50% while increasing the fishing mortality associated with Gear 2 by 50%. Age(s) Before Regulatory Change After Regulatory Change 0 0.9 0.1 0.75 0.25 1 0.8 0.2 0.57 0.43 2 0.5 0.5 0.25 0.75 3 0.5 0.5 0.25 0.75 4 0.3 0.7 0.13 0.87 5-50 0.3 0.7 0.13 0.87 1197
Table 6. YPR analysis results including overall and gear specific YPR estimates. Case 1: Status Quo Case 2: Size limit to reduce fishing mortality on ages 0-1 Case 3: Increase fishing mortality on ages 3+ Total 1.774 1.996 1.877 2.006 Gear 1 0.937 0.940 0.987 0.542 Gear 2 0.837 1.056 0.890 1.464 Case 4: 50% decrease in F of gear 1 (hypothetical PS) and 50% increase in F of gear 2 (hypothetical LL) Table 7. SPR analysis results including overall and gear specific SPR estimates. Case 1: Status quo Case 2: Size limit to reduce fishing mortality on ages 0-1 Case 3: Increase fishing mortality on ages 3+ Total 3.080 4.055 2.816 3.639 Gear 1 1.207 1.588 1.127 0.680 Gear 2 1.874 2.467 1.689 2.959 Case 4: 50% decrease in F of gear 1 (hypothetical PS) and 50% increase in F of gear 2 (hypothetical LL) 1198