A fisheries management strategy robust to ignorance: rotational harvest in the presence of indirect fishing mortality

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1 2357 RAPID COMMUNICATIONS / COMMUNICATIONS RAPIDES A fisheries mngement strtegy robust to ignornce: rottionl hrvest in the presence of indirect fishing mortlity Rnsom A. Myers, Susnn D. Fuller, nd Dniel G. Kehler Abstrct: We develop simple theoreticl model of yield nd spwning stock biomss per recruit for the Americn se scllop (Plcopecten mgellnicus), which ppers to hve high indirect fishing mortlity when hrvested with dredges, i.e., mortlity cused by the ct of fishing tht does not result in lndings. The ge t nd degree to which individuls re ffected by the indirect mortlity re unknown, nd it does not pper possible to develop robust hrvest strtegy with yerly hrvests unless indirect fishing mortlity is well quntified. We show tht there could be substntil benefits to rottionl hrvest strtegy for sessile species with high indirect fishing mortlity. First, the strtegy ppers to be robust to ignornce bout indirect fishing mortlity nd results in equl or better yields thn yerly hrvest cross wide rnge of indirect fishing mortlities. Second, under most conditions, higher spwning stock biomss is mintined. Third, rottionl mngement is more esily enforced, s it does not require specifying nrrow rnge of fishing mortlity in order to mximize yield. Résumé : Nous vons développé un modèle théorique simple pour étudier le rendement et l biomsse des géniteurs pr individu recruté chez le pétoncle gént (Plcopecten mgellnicus), qui semble subir une mortlité indirecte élevée due à l pêche à l drgue, i.e., une mortlité cusée pr l pêche qui ne résulte ps en des débrquements. L importnce de cette mortlité indirecte et l âge des individus ffectés ne sont ps connus. Nénmoins, il semble qu on ne puisse étblir une solide strtégie de récolte vec pêches nnuelles sns que cette mortlité indirecte ne soit bien quntifiée. Nous démontrons qu il pourrit y voir d importnts bénéfices à étblir une strtégie de récolte pr rottion chez les espèces sessiles qui ont une mortlité indirecte élevée due à l pêche. D bord, ce type de strtégie est pplicble même lorsqu on ne connît ps l mortlité indirecte due à l pêche et donne des résultts semblbles ou meilleurs qu une strtégie de pêche nnuelle, dns un lrge intervlle de mortlités indirectes. En second lieu, dns l mjorité des situtions, il y mintien d une biomsse plus élevée du stock des géniteurs. Enfin, une gestion vec rottion est plus fcile à ppliquer, puisqu elle n exige ps de fixer des limites étroites à l pêche pour mximiser le rendement. [Trduit pr l Rédction] Rpid communictions / Communictions rpides 2362 Introduction Received August 8, Accepted December, Published on the NRC Reserch Press web site on December 20, J5928 R.A. Myers. Killm Chir of Ocen Studies, Deprtment of Biology, Dlhousie University, Hlifx, NS B3H 4J, Cnd. S.D. Fuller. Deprtment of Biology, Dlhousie University, Hlifx, NS B3H 4J, Cnd. D.G. Kehler. Deprtment of Mthemtics nd Sttistics, Dlhousie University, Hlifx, NS B3H 4J, Cnd. Corresponding uthor (e-mil: rnsom.myers@dl.c). Cn. J. Fish. Aqut. Sci. 57: (2000) Fisheries must be mnged using imperfect informtion bout the biology nd stte of stock; thus, successful mngement strtegies must be robust in light of this lck of detiled informtion. We exmine rottionl hrvest of Americn se scllops (Plcopecten mgellnicus) s one such robust mngement strtegy. The scllop fishery commonly uses dredges for hrvesting, which cn result in high indirect mortlity. Indirect mortlity cused by fishing (e.g., discrding or dmge to fish not cught in fishing ger) is one of the mjor problems in the mngement of the world s fisheries (Alverson et l. 994). Although it is now ccepted tht the clcultions of biologicl reference points, such s the mximum llowed fishing mortlity rte, should include indirect fishing mortlity (Chen nd Gordon 997), this is rrely done in prctice. For the se scllop, the problem of indirect fishing mortlity hs long been known to be criticl conservtion issue (Cddy 973). Cddy (973) found indirect mortlity rtes on pr with direct fishing mortlity (3 7%), nd recent ssessment of se scllops (Ntionl Mrine Fisheries Service 999) estimted indirect mortlity to be three times higher thn the direct fishing mortlity on Georges Bnk. Evidence from other scllop species suggests tht indirect fishing mortlity my be s high s four to eight times the direct fishing mortlity (Nidu 988; McLoughlin et l. 993).

2 2358 Cn. J. Fish. Aqut. Sci. Vol. 57, 2000 Fig.. () Yield per recruit nd (b) percentge of the mximum spwning biomss per recruit (when F = 0) for se scllops t different levels of direct fishing mortlity under the ssumption tht (i) there is no indirect fishing mortlity (solid line), (ii) there is indirect fishing mortlity on prerecruits only (dotted line), nd (iii) there is indirect fishing mortlity on ll ges (dshed line). Indirect fishing mortlity is ssumed to equl the direct fishing mortlity. Note tht the direct fishing mortlity resulting in mximum yield per recruit is much lower when indirect fishing mortlity occurs (Fig. ). In this rticle, we propose rottionl hrvesting s n lterntive strtegy nd investigte its robustness to different levels nd types of indirect fishing mortlity using deterministic models. We propose rottionl hrvesting s n lterntive strtegy nd investigte its robustness to different levels nd types of indirect mortlity using deterministic models.

3 Rpid communictions / Communictions rpides 2359 Fig. 2. ( nd b) Averge yield per recruit nd (c nd d) percentge of mximum verge spwning stock biomss for se scllops hrvested over rnge of direct fishing mortlities for four rottionl periods: hrvest every yer (thick solid line), once every 3 yers (dshed line), once every 6 yers (dotted line), nd once every 9 yers yers (thin solid line). Results re shown under the ssumption of no indirect fishing mortlity (Figs. 2 nd 2c) nd indirect fishing mortlity equl to direct fishing mortlity (Figs. 2b nd 2d). Yield per recruit nlysis including indirect fishing mortlity We considered simple discrete time popultion dynmics model in which fishing tkes plce t one time of the yer nd nturl mortlity only occurs between the periods of fishing. The discrete time model will, in generl, give quntittively, but not qulittively, different results thn the stndrd continuous time yield per recruit model (Beverton nd Holt 957) but cn esily be extended to consider rottionl hrvest. The model is more pproprite when the hrvest tkes plce yerly, over short period, s is proposed for the reopening of portions of the groundfish closed res of the U.S. side of Georges Bnk (New Englnd Fisheries Mngement Council 2000). In our model, we divided totl fishing mortlity into two components: direct nd indirect mortlity. Direct mortlity is denoted F y s, where s is the selectivity of the fishing ger to scllop of ge nd F y is the fishing mortlity in yer y of the fully selected ge or ges, i.e., where s =. Indirect mortlity is denoted F y i, where i is the ge-dependent selectivity of the indirect fishing mortlity. To mke our nlyses consistent with the Ntionl Mrine Fisheries Service (999), the yer ws defined to strt t the midpoint of the cohort yer, nd thus, fishing occurs t the end of this yer. We let N y, be the number of scllops of ge t the beginning of yer y nd m be the ge-specific nturl mortlity. We ssumed tht both sources of fishing mortlity re operting simultneously during the fishery. The dynmics of cohort re given by N y+,+ = N y, exp( m F y (s + i )) nd the ctch in numbers from the cohort t ge is s Cy Ny m Fy s i, =, exp( )( exp( ( + ))). s + i In the yield per recruit nlysis, it is ssumed tht recruitment, N y, nd the selectivity t ge do not vry over time. This ssumption is unrelistic, s recruitment will vry with

4 2360 Cn. J. Fish. Aqut. Sci. Vol. 57, 2000 Fig. 3. Proportionl loss of mximum verge yield for se scllops s function of the rtio of indirect to direct fishing mortlity under the four ssumptions for fully recruited fishing mortlity nd the ge tht indirect fishing mortlity occurs t four rottionl hrvest periods: hrvest once every (thick solid line), 3 (dshed line), 6 (dotted line), nd 9 yers (thin solid line). The ssumptions for the fully recruited fishing mortlity (F) nd the indirect mortlity re () F = 0.2 nd indirect fishing mortlity occurs t ll ges > t the sme rte s direct fishing mortlity on ges 4, (b) the sme s Fig. 3 except tht F = 0.5, (c) thesmesfig.3 except tht F =.0, nd (d) F = 0.5 nd indirect fishing mortlity only occurs on prerecruits but t the sme rte s on fully recruited scllops. both bundnce nd environmentl conditions, but simplifies the nlysis considerbly. The nnul biomss yield per recruit t equilibrium, Y*, is obtined by considering scllop popultion derived from cohort exploited over time with fishing mortlity F nd selectivity of (Clrk 990). This will be constnt with time nd is Y *( F) = wc y,, N y, where w is the weight of the scllops t ge t the time of the hrvest. It is lso useful to clculte the spwning stock biomss per recruit in the sme mnner, i.e., SF ( ) = Ny, φw N y, where φ is the proportion of fish of ge tht re mture. Agin, this will not vry over time in our model. We mde the following dditionl ssumptions in developing this model. Growth in weight (grms) ws defined using the von Bertlnffy growth curve with prmeters from the most recent ssessments (Ntionl Mrine Fisheries Service 999): w = 55.( exp( (.454))) Spwning biomss ws ssumed to be proportionl to the met weight of the scllops. As per Ntionl Mrine Fisheries Service (999), scllops were considered mture t ge 4, nd nturl mortlity ws ssumed to be constnt for ll ges t rte of 0. up to ge 20. Senescence ws ssumed to begin t ge 20, with nturl mortlity incresing by 0. every yer fter tht ge. Direct fishing selectivity of the commercil dredges ws ssumed to be 0 below ge 3, 0.5 t ge 3, nd for higher ges (Ntionl Mrine Fisheries Service 999), which mkes the simplifying ssumption tht ll scllops grow t the sme rte. When we considered the effect of the ge of recruitment to the fishery on yield, we

5 Rpid communictions / Communictions rpides 236 ssumed direct fishing selectivity to be for scllops of ge 4. Two lterntive ptterns of indirect fishing mortlity were modeled. First, indirect fishing mortlity ws ssumed to ffect ll ges > eqully nd t the sme rte s the fully recruited fishing mortlity, i.e., i = for ll, which represents n extreme sitution. Second, it my only be the smller, weker scllops tht re ffected by indirect fishing mortlity, nd thus, we ssumed tht for the prerecruits ( < 4), i =, nd for older scllops ( 4), i =0. We begn by compring the pttern of yield given different direct fishing mortlities nd ge of recruitment to the fishery. The typicl pttern of mximum yield t infinite mortlity nd high ge of recruitment (Beverton nd Holt 957) does not emerge. Insted, yield is mximized t lower ge of recruitment ( 4) nd reltively low direct fishing mortlity (0.08). Ignoring indirect fishing mortlity results in estimtes of fishing mortlity tht give the mximum yield per recruit tht re suboptiml (Fig. ). The fishing mortlity tht results in the mximum sustinble yield is smllest when indirect fishing occurs on ll ges (0.07), intermedite when indirect fishing mortlity occurs only on prerecruits (0.09), nd gretest with no indirect fishing mortlity (0.22) (Fig. ). We lso compred the spwning biomss per recruit for the three levels of indirect fishing mortlity with the percentge of the spwning biomss per recruit with no fishing (Fig. b). Incorporting indirect fishing mortlity results in even lower levels of spwning biomss, prticulrly t low levels of direct fishing mortlity. We hve shown using simple model tht ignoring indirect fishing mortlity results in setting optiml fishing mortlities tht re much too high. Rottionl hrvest strtegy We investigted model where fishing is rotted mong p subdivisions of the fishing ground, nd ech subdivision is hrvested every p yers. The clcultion of yield nd spwning biomss per recruit is not strightforwrd for the rottionl hrvest, since the yield per recruit depends upon the ge t which scllop is first subjected to periodic hrvesting. In other words, scllop first hrvested t ge 4 nd hrvested every p yers will hve different yield thn scllop first hrvested t ge 5 nd hrvested every subsequent p yers. Thus, for rottionl hrvest of p yers, we need to verge over the p different possible yields per recruit. Since recruitment ws ssumed to be constnt over time, the sme number of recruits will hve ccumulted in subdivision p over p yers s in the entire fishing ground in yer. If the verge yield per recruit remins the sme between the rottionl nd nonrottionl hrvest schemes, then totl yield (which is of greter interest) will lso remin the sme. We ssessed the rottionl strtegy in terms of verge yield nd spwning biomss per recruit t different fishing mortlities for four different rottionl periods:, 3, 6, nd 9 yers (Fig. 2). In ll cses, the rottionl strtegy resulted in t lest s high n verge yield per recruit s the nonrottionl strtegy, provided the fishing mortlity ws sufficiently high. The rottionl strtegy mintins considerbly lrger stock biomss, thus reducing the risk of stock collpse. The lrger yield per recruit obtined under rottionl mngement results from llowing scllops to rech the ges where the rtio of somtic growth to loss by nturl mortlity is highest. If indirect fishing mortlity only occurs on prerecruits, then there is greter dvntge in yield per recruit for longer rottionl mngement scheme (not shown). From mngement perspective, the rottionl system is ppeling becuse it is not necessry to control fishing mortlities very precisely when p > 5, since ner-optiml yields re chieved cross wide rnge of fishing mortlities. The bove plots suggest tht rottionl period close to 6 yers, with fishing mortlity of round 0.5, would result in close to mximum verge yield per recruit nd would mintin spwning biomss per recruit t cceptble levels, i.e., bove 20% of the spwning stock biomss. We exmined the consequences of nonrottionl hrvesting strtegy by clculting the loss in yield per recruit under different ssumptions bout indirect fishing mortlity. We defined the percent loss of fishing t fully recruited fishing mortlity of F t rottionl period p s L Yp( F) ( F) = 00. mx( Y ( F)) p F, p p We clculted the loss in yield per recruit for four rottionl periods,, 3, 6, nd 9 yers, nd three direct fishing mortlities. To determine the impct of different indirect fishing mortlities, we llowed the rtio of indirect mortlity to direct fishing mortlity to vry between 0 nd 2 (Fig. 3). There is lrge loss under the nonrottionl mngement regime under ll ssumptions of indirect mortlity except when the rtio of indirect to direct fishing mortlity is very smll nd direct fishing mortlity is kept very low, round 0.2. However, the direct fishing mortlity hs been very much lrger thn 0.5 in the res open to fishing on Georges Bnk for the lst 20 yers (Ntionl Mrine Fisheries Service 999). If F = 0.5 nd the rottionl period is between 3 nd 6 yers (Figs. 3b nd 3d), there is reltively little loss under most levels of indirect fishing mortlity. Discussion Controlling the ge of recruitment to the fishery hs been often considered robust pproch to fishery mngement (Myers nd Mertz 998). In our nlysis, we show tht indirect fishing mortlity cn gretly ffect the optiml fishing strtegy nd tht rottionl hrvest strtegy my be resonble pproch to use when the form nd mgnitude of indirect fishing mortlity re uncertin. We hve shown, theoreticlly, tht the primry benefits of rottionl strtegy, reltive to nonrottionl strtegy, re tht it (i) provides equl or greter yield cross most levels of indirect fishing mortlity, (ii) my be more esily enforced, nd (iii) mintins higher spwner biomss. In the nonrottionl pln, the rnge of fishing mortlities resulting in mximum yield per recruit is very nrrow. Fisheries mngers in the pst hve found it very difficult to chieve such precise control. This problem hs led to overfishing on Georges Bnk nd other regions (Wlters nd Mguire 996). In contrst, the rnge of fishing mortlity

6 2362 Cn. J. Fish. Aqut. Sci. Vol. 57, 2000 resulting in mximum yield per recruit for the rottionl strtegy is very brod. Enforcement of the rottionl pln is simpler thn tht of the nonrottionl pln, s it is esier to completely restrict ccess to n re thn to enforce fishing limit on ech individul bot, prticulrly if ll fishing vessels re required to hve electronic loction becons (s scllop vessels re on the U.S. side of Georges Bnk). An importnt conservtion benefit of mny rottionl mngement strtegies is the increse in spwning biomss resulting from rottionl closure. This hs been noted in previous studies (e.g., Slucznowski 984), but the effect is much lrger in fisheries with lrge indirect mortlity, such s scllops hrvested with dredges. As the totl mount of dredging cn be reduced s result of rottionl hrvesting, the impct of scllop dredging on other species cn be reduced. However, the fishing intensity in the hrvested res my be still be quite high (0.5.0), nd we need to insure tht this does not compromise the scllop stock or other components of the ecosystem (e.g., groundfish). There re some obvious disdvntges if very long rottionl periods re used, e.g., the somtic growth of se scllops my decrese becuse of crowding. As well, very long rottionl periods would require the hrvested re to be divided into mny more res for the rottionl mngement, which would increse the complexity of enforcement. For these resons, the period for rottion should probbly be <7 yers. Rottionl mngement must be considered crefully in multispecies fishery, s intense scllop fishing cn hve n impct on groundfish species nd structure-forming epifunl species. Although the rottionl hrvest is very ppeling theoreticlly, it remins to be seen whether it cn be succesfully implemented. One of the key simplifying ssumptions of our nlysis is tht fishing grounds, which re undoubtedly heterogeneous, cn be divided into res of reltively equl productivity. Monitoring is essentil to determine if nd how productivity vries over spce nd time. An idel sitution for the implementtion of rottionl hrvest currently exists on the U.S. side of Georges Bnk, s there re three sections tht hve been closed since 994 to groundfish nd scllop hrvesting. Proposls to open these res do not presently include rottionl pln, which is unfortunte, s such pln could be esily implemented (New Englnd Fisheries Mngement Council 2000). The implementtion of rottionl strtegy could lso contribute to the bility of scientists to evlute the effects of fishing through n experimentl pproch. References Alverson, D.L., Freeberg, M.H., Murwski, S.A., nd Pope, J.G A globl ssessment of fisheries byctch nd discrds. FAO Fish. Tech. Pp Beverton, R.J., nd Holt, S.J On the dynmics of exploited fish popultions. Fish. Invest. Ser. II Mr. Fish. G.B. Minist. Agric. Fish. Food, 9: 533. Cddy, J.F Underwter observtions on trcks of dredges nd trwls nd some effects of dredging on scllop ground. Cn. J. Fish. Aqut. Sci. 30: Chen, Y., nd Gordon, G.N.G Assessing discrding t se using length-structured yield-per-recruit model. Fish. Res. 30: Clrk, C.W Mthemticl bioeconomics. 2nd ed. Wiley- Interscience, New York. McLoughlin, R., Zchrin, W., Crtwright, I., Gwyther, D., Probestl, M., nd Sterling, D New hrvesters for the scllop industry in south est Austrli. Aust. Fish. 52: 2 4. Myers, R.A., nd Mertz, G The limits of exploittion: precutionry pproch. Ecol. Appl. 8(Suppl. ): S65 S69. Nidu, K.S Estimting mortlity rtes in the Icelnd scllop, Chlmys islndic (O.F. Mueller). J. Shellfish Res. 7: 6 7. Ntionl Mrine Fisheries Service Twenty-ninth northest regionl stock ssessment workshop. NEFSC Ref. Doc. 99/4. New Englnd Fisheries Mngement Council Frmework Adjustment 3 to the Atlntic Se Scllop Fishery Mngement Pln with options for the Frmework Adjustment 34 to the Northest Multispecies Fishery Mngement Pln. New Englnd Fisheries Mngement Council, Sugus, Mss. Slucznowski, P.R A mngement oriented model of n blone fishery whose substocks re subject to pulse fishing. Cn. J. Fish. Aqut. Sci. 4: Wlters, C., nd Mguire, J.J Lessons for stock ssessment from the Northern cod collpse. Rev. Fish Biol. Fish. 6: