BIOECONOMIC DYNAMIC MODELLING OF THE CHILEAN SOUTHERN DEMERSAL FISHERY

IIFET 21 Monpellier Proceedings BIOECONOMIC DYNAMIC MODELLING OF THE CHILEAN SOUTHERN DEMERSAL FISHERY Rene Cerda- D'Amico, School of Marine Sciences, Ponificia Universidad Caolica de Valparaiso, rcerda@ucv.cl Exequiel Gonzalez Poblee, School of Marine Sciences, Ponificia Universidad Caolica de Valparaiso, exequiel.gonzalez@ucv.cl Renao Molina Hernandez, School of Marine Sciences, Ponificia Universidad Caolica de Valparaiso, renao.molina@ucv.cl ABSTRACT The demersal fishery of souhern Chile is a complex sysem including muliple species, fishing flees and markes. Fishing aciviy is conduced under a righs-based sysem for souhern hake (Merluccius ausralis) and hoki (Macroronus magellanicus), where a TAC is allocaed in an even manner among flees and operaors. New managemen approaches no only call for he need of he simulaneous consideraion of biological, echnologic, economic, social, legal and insiuional facors bu also, sakeholders percepions and ineress are becoming increasingly relevan for decision making. In spie of he undeniable imporance for sakeholder inclusion in fisheries managemen, heir percepion of he sysem saus and expecaions are frequenly parial and biased by shor erm needs and ineress. Thus, informaion on expeced impacs of alernaive managemen measures are a valuable guiding inpu o improve sakeholder percepion. This paper, herefore explores he value of dynamic simulaion model in providing illusraive informaion on bioeconomic impacs o he fishery sysem from alernaive managemen measures. The dynamic simulaion model is based on wo main modules. A biologic module depicing he fish populaion dynamics, considering recruimen based on Beveron and Hol funcion. A bioeconomic module depicing flee dynamics based invesmen funcions by Clark e al. (1979) Munro and Munro (1998) and cach per uni of effor proporional o biomass. The model oupus are he species biomass, flee size, effor level, flee and vessel ne benefis presened on a year basis. Fishery and flee cumulaive NPVs are also presened. Keywords: dynamic simulaion, groundfish fishery, economic benefis, social equiy, susainabiliy BACKGROUND This paper has been developed as par of he projec "Technical Basis for he Managemen Plan for he Chilean Souhern Demersal Fishery", which aimed o lay down he foundaions for a paricipaory managemen plan including large-scale and small-scale users and inegraing heir various visions and ineress under a susainable developmen approach. The souhern demersal fishery is one of he mos complexes of he Chilean fisheries, ranging from parallel 41 º 28.6 'L.S. o he parallel 57 º 'L.S. I is defined as a complex sysem based on he exploiaion of souhern hake (Merluccius ausralis), hoki (Macruronus magellanicus), souhern blue whiing (Micromesisius ausralis), pink cusk-eel (Genyperus blacodes), paagonian oohfish (Dissosicus eleginoides) and yellownose skae (Dipurus chilensis). The souhern demersal fishery (SDF) is conduced by muliple fishing flees including differen scales of producion and echnologies, grouped in an indusrial or large-scale segmen operaing in he open sea and a, arisanal or small-scale segmen operaing in fjords and channels. The geographic spread of hese flees, he fragmenaion and isolaion of he landings, he organizaional srucure of he small-scale flee and is exensive monopsonisic supply chain characerizes his as a complex fishery and inricae adminisraion sysem, under which he radiional command and conrol managemen mechanisms are no effecive enough. 1

IIFET 21 Monpellier Proceedings This work focuses on he fishing aciviy based upon souhern hake and hoki fish socks, which represens wo hirds of he oal landing and gross value generaed by he SDF. Souhern hake is argeed by a large number of small-scale longline flee and he large-scale rawling fishing flee. Hoki is argeed only b y he large-scale fishing flee. This fishery presens srong echnological ineracions since boh species are caugh simulaneously and in addiion, here are biological ineracions souhern hake predaes over hoki. Prior o 21 he fishery was regulaed by a oal allowable cach (TAC) for he large-scale secor, in addiion o area resricions, laer wen ino effec a sysem of non ransferable individual quoas, which noneheless, allowed for annual effor parnership beween differen quoa owners a he vessel level for harves purposes. Simulaneously, he small-scale fishing secor is governed by a quoa sysem allocaed o fishermen's organizaions and regionally disribued. The disribuion of he organizaion quoa among individual members is auonomously decided and managed by hese organizaions. The TAC of souhern hake is disribued in equal proporions beween he small-scale and large-scale secors, while he hoki TAC is enirely allocaed o he laer secor. The biomasses of boh resources have long-erm declining rends, even when he hoki shows signs of recovery in recen years. Fishing yields are sabilizing in andem wih he decline in indusrial fishing capaciy, resuling from he individual quoa sysem. However, he coss of fishing have a endency o increase. The general appraisemen of he fishery indicaes i is no viable in he long run, his may be due o flaws in he applicaion and conrol of he managemen sysem in place and o weak governance of he fishery as refleced by exising problems in he decision making srucure and o sakeholder low levels of paricipaion and compliance (Cerda e al. 29). In his conex, ex-ane knowledge of poenial impacs of policies for he conservaion of fishery resources is considered o be imporan if efficien and effecive fishery managemen, based on good ineracion beween users and decision makers, is o be achieved. Accordingly, he developmen of operaional models o measure such impacs are considered o be imporan o guide he decision-making process. The purpose of his paper is o illusrae he relevance of such models in generaing ex-ane knowledge of poenial impacs of managemen policies, hrough a dynamic simulaion model under cerainy condiions. This analysis is focused in he deerminaion of poenial socioeconomic impacs of changes in TAC levels and overall quoa allocaion beween large-scale and small-scale secors considering a hreshold of susainabiliy of he fishery. THE MODEL Even hough he fishery model developed in his work includes wo fish socks (souhern hake and hoki) and five flees (facory rawlers and rawlers for he large-scale secor and wo ypes of small-scale fishing flees disribued in hree regions), for he sake of presenaion simpliciy he model is presened as including only one fish sock and one fishing flee. The following general diagram depics he dynamics of he fishery including fish sock dynamics and sock-fishing flee ineracions, hrough fishery biological, producion and economic modules (Figure 1). 2

IIFET 21 Monpellier Proceedings Figure 1 Dynamic diagram of he Souhern Demersal Fishery (SDF) As shown in Figure 1, he biological module of he fishery includes he fish sock size, measured in number of individuals (i.e., abundance) wha is he ne resul of he ineracion beween naural moraliy and recruimen. Recruimen is considered o be dependen upon he size of a parenal sock and i will be modeled as a Beveron-Hol relaionship which includes parameers and (Sparre and Venema ). The producion module is represened by he ineracion beween exploiable sock size and harves represened as cach in Figure 1. Cach is he resul of he ineracion beween fishing effor per vessel, he number of vessel in he fishing flee he size of he exploiable fish sock. The economic module represens he relaionship beween income, fishing coss, capial invesmen as flee size and ne benefis. Flee size is dependen upon he ineracion beween expeced ne benefis per vessels and he level of ne benefis generaed by he fishery in previous periods. Flee size deermines in urn he level of fishing effor, cach and fish sock abundance. Mahemaical formulaion of he relaionships of his model is presened as follows. The populaion dynamics of he fishery resources is modeled as dn (1) mn y R d Where N fish populaion abundance a ime, y fishing flee yield or harves rae a ime, R recruimen o he fishery a ime and m is he insananeous naural moraliy rae. The recruimen funcion considered is of he familiar Beveron and Hol form (Sparre and Venema 1997). Nr yr (2) R N y r r 3

IIFET 21 Monpellier Proceedings Where and are parameers represening he maximum recruimen level and he abundance level generaing a recruimen equal o /2, respecively. The sub-index r is age of recruimen o he fishery in years. The harves rae is modeled as he familiar Cobb-Douglas producion funcion, radiional in fishery models. (3) y qe N qek N Where E is he fishing effor of he fishery and he parameer q is he cachabiliy coefficien of he fishing vessel. Noice ha N and E E max = e*k. Where E max is he maximum effor capaciy in days a ime, K is he amoun of capial invesed in he fishery a ime and e is he annual effor per vessel in days per year. K represens he number of sandardized fishing vessels of a given fishing flee and secor exising in he fishery. Thus, he maximum effor capaciy is considered o be equal o he number of vessels available and he acual level of effor employed a any ime canno exceed E max. Adjusmens o he number of vessels in he fishery are modeled as follows Clark e al. (1979) and Munro (1998). dk (4) I K, K K d Where I is he gross invesmen rae a ime (expressed in physical erms) and is consan rae of depreciaion and > and - I +. The discouned ne cash flow generaed by he fishery is presened in equaion (5) and he ne presen value of ne cash flow is presened in equaion (6). (5) NB e py ce I (6) PVNB e py ce I d Where δ is he insananeous rae of discoun, p is he price of landed fish, c is he operaing cos per uni of effor and π is he purchase or replacemen price of capial. All hese parameers are considered as consan and posiive. I is assumed ha enry and exi o he fishery will be given by he relaionship beween he expeced annual ne benefis per vessel and he level of ne benefis being generaed by he fishery as whole. I is also assumed ha enry and exi will be modulaed by he availabiliy of vessels (from oher fisheries or by shipyard capaciies) or by he possibiliy of reallocaing vessels o oher aciviies. Scrap value and marke are no considered. NB (7) K I Where φ is he expeced ne benefi per vessel and μ is a modulaion facor for enry and exi of vessels o or from he fishery. The exising pray-predaor relaionship ineracion beween hoki and souhern hake is modeled hrough relaional funcions beween he insananeous moraliy rae of one fish sock and he corresponden sock size of he oher fish sock. This relaion is negaive for hoki wih respec o souhern hake and posiive for souhern hake wih respec o hoki (Figure 2). 4

IIFET 21 Monpellier Proceedings Figure 2 Dynamic diagram depicing he iner-specific ineracions beween of souhern hake and hoki. Finally, o assess he poenial impacs of he curren managemen policies, he simulaion model is run under four scenarios, namely: BASELINE, TAC4%, TAC2% and SMALL7%. Scenario BASELINE represens he curren managemen policy and considers a TAC of 3% of he sock size for each of he fish resources, souhern hake and hoki. I also considers ha he TAC for souhern hake is allocaed in equal shares o he large-scale and small-scale secors. The TAC for hoki is enirely allocaed o he largescale secor. Scenario TAC4% considers an increase of 1% in he TAC level for boh souhern hake and hoki, bu no changes in TAC allocaion beween boh fishing secors. Scenario TAC2% considers a 1% decrease in he TAC level for boh fish resources and no changes in TAC allocaion beween secors. Scenario SMALL7% considers he curren 3% level for he TAC of boh fish resources and a 2% increase in he allocaion of souhern hake TAC o he Small-Scale secor. I does no consider changes in he allocaion of he TAC for hoki beween secors. Table 1 summarizes he daa used o calibrae he model o he fishery curren condiions, which is based upon several official echnical repors from IFOP 21a,b,c and official saisics. Table 1 Operaional and economic daa for he SDF Large-Scale Flee Small-Scale Flee Trawller Refrigeraed Trawller Facory XII h Region ITEM Unis X h Region XI h Region Operaional days days/year 2 25 5 5 9 Cachabiliy coeff. (q) Hoki 1,13E-4 1,14E-4 Souhern Hake 5,66E-5 7,3E-5 3,81E-6 8,93E-6 3,37E-6 Cos per uni of effor USD/day 5.72 9.57 127 127 725 Manainance USD/year 382.799 956.997 746 746 4.785 Vessel price (π) USD 4.784.987 9.569.973 21.54 21.54 34.452 Landing coss Ex - vessel price Hoki Souhern Hake Enry/Exi facor (μ) Expeced benefi per vessel (φ) Depresiaion facor (g) USD/on USD/on USD/on 159 96 9 1.78 1.78 5% 1% 5% Source: elaboraed from IFOP 21 a,b,c and SERNAPesca saisics. 5

Sock Biomass (on) Thousand Thousand IIFET 21 Monpellier Proceedings RESULTS Poenial impacs of he exising managemen policies for he SDF and possible changes are presened in Figures 3 o 6 and hey are depiced by he levels aained by sock size of boh fish resources 1, flee size for large and small scale fishing secors involved in he fishery, he annual ne benefi generaed by hese fishing flees and he cumulaive ne presen value of ne benefis generaed a he fishery and flee levels. Noice ha iniial levels for all considered variables have been calibraed o he siuaion observed in year 27 in he SDF. Curren managemen policy, represened by scenario BASELINE indicaes ha fish sock size (Figure 3) for boh resources would reach equilibrium levels. Hoki sock size (depiced by he black line) would increase from approximaely 16 housand ons o 59 housand ons in 25 periods, approximaely. Souhern hake sock size (depiced by he brown line) would decrease from approximaely 93 housand ons o 78 housand ons in 35 periods, approximaely. Simulaneously, flee size for he large-scale secor would increase reaching 29 vessels in 18 periods as depiced by he solid brown line in Figure 4. Flee size for he small-scale secor, would show an early increase in he number of boas probably reaching of 1.129 boas in period 19, o laer sar an ever declining rend (solid blue line in Figure 4). 8 4 7 35 6 3 5 25 4 2 3 15 2 1 1 5 1 4 7 1 13 16 19 22 25 28 31 34 37 4 43 46 49Years Hoki-BL Hoki TAC4% Hoki TAC2% Souhern Hake-BL Souhern Hake TAC4% Souhern Hake TAC2% Figure 3 Sock size in biomass under scenarios BASELINE(BL), TAC4% and TAC2% Accordingly o his flee dynamic, he level of annual ne benefis for he large-scale flee would sabilize a a level of 71 million USD per year, solid brown line in Figure 5. Annual ne benefis for he small-scale flee would experience a decreasing rend, possibly reaching a level of approximaely 4 million USD per year a he end of 5 year horizon used for modeling purposes, solid blue line in Figure 5. Figure 6 shows ha he cumulaive ne presen value of he SDF would reach 65 million USD in approximaely 43 periods, he large-scale secor would accoun for 91% of he oal value (ligh brown area) and he small-scale secor for only he remaining 9% (brown area). 6

PVNB Flow (USD/Year) PVNB Flow (USD/Year) Millions Millions Small-scale flee size (Boas) Large-scale flee size (Vessels) IIFET 21 Monpellier Proceedings 1.6 7 1.5 1.4 6 1.3 1.2 5 1.1 1. 9 4 8 7 3 6 5 2 4 3 2 1 1 Years 1 4 7 1 13 16 19 22 25 28 31 34 37 4 43 46 49 Small-Scale-BL Small-Scale TAC2% Small-Scale TAC4% Small-Scale SMALL7% Large-Scale-BL Large-Scale TAC4% Large-Scale TAC2% Large-Scale SMALL7% Figure 4 Flee size under scenarios BASELINE(BL), TAC4%, TAC2% and SMALL7% 1 9 8 12, 1, 7 6 5 4 3 2 1 8, 6, 4, 2, Years 1 4 7 1 13 16 19 22 25 28 31 34 37 4 43 46 49 Large-Scale-BL Large-Scale TAC4% Large-Scale TAC2% Large-Scale SMALL7% Small-Scale-BL Small-Scale TAC4% Small-Scale TAC2% Small-Scale SMALL7% Figure 5 Flow of Ne Presen Value of Ne Benefis of flees under scenarios BASELINE(BL), TAC4%, TAC2% and SMALL7%, 7

Million Cumulaive PVNB (USD) 8 7 6 5 4 3 2 1 IIFET 21 Monpellier Proceedings 8 7 6 5 4 3 2 1 1 4 7 1 13 16 19 22 25 28 31 34 37 4 43 46 Years 49 Small-Scale-BL Large-Scale-BL Fishery TAC4% Fishery TAC2% Small-Scale SMALL7% Large-Scale SMALL7% Figure 6 Cumulaive Ne Presen Value of Ne Benefis of he flees and he fishery under scenarios BASELINE(BL), TAC4%, TAC2% and SMALL7% The TAC4% scenario could be depiced as a policy prone o economic developmen and is expeced effecs on sock size, flee size and ne benefis are also shown in Figures 3 o 6. Figure 3 shows ha under his policy boh fish sock would be reduced, hoki sock would reach of proximaely 5 housand ons in 43 years (blue line), bu souhern hake would reach only 5 housand ons in he same ime (ligh brown line). Large-scale flee would experimen a sligh increase reaching 32 vessels (ligh brown solid line in Figure 4). Small-scale flee, noneheless, would experimen a relevan increase during he firs 2 periods, experimening a larger decreasing rend han he one expeced under curren managemen policy in he long-run (solid ligh blue line in Figure 4). Figure 5 shows a consisen increase in annual ne benefis for he large-scale flee, wih relevan increases in early periods bu sabilizing a levels only a 4% higher han he ones expeced under he curren managemen policy (solid ligh brown line). Expeced annual ne benefis for he small-scale flee (solid ligh blue line) are larger during he firs 1 periods, han he ones expeced under he curren managemen policy, bu significanly lower in he long-run ( 23% lower in average). Figure 6 shows ha he overall effec of his policy would be an increase in he ne presen value of ne benefis generaed by he SDF, generaing a 14% increase in 43 periods wih a oal of approximaely 741 million USD (solid blue line). The effecs of he conservaion prone policy represened by TAC2% scenario show relevan posiive effecs on fish sock biomass, no only wih expeced increases in equilibrium levels of boh fish sock biomasses (ligh blue and yellow lines in Figure 3), bu revers he decreasing endency for souhern hake, whose sock size shows now an increasing endency over ime. Effecs in flee size show a relevan decrease of 21% in he expeced number of large-scale vessels operaing, wih 23 unis since he 19 h period (solid yellow line in Figure 4). Small-scale fishing flee size experimens a change, expecing a slower bu longer increasing rend (cyan solid line in Figure 4), wih a 8

IIFET 21 Monpellier Proceedings final number of small-scale fishing boas slighly larger han 1.1 unis in he long-run. Figure 5 shows a reduced level of annual benefis for he large-scale fishing flee, bu increasing levels of annual ne benefis for he small-scale fishing flee wih larger long run annual expeced ne benefis. Figure 6 shows, however a significanly lower level in he presen value of ne benefis generaed by he SDF, which are expeced o be 23% lower han under he curren managemen policy, wih a oal of 5 million USD. The SMALL7% scenario represens a policy prone o favor he small-scale secor which refers o people wih low levels of income. As his scenario only includes changes in he allocaion of he currenly exising TAC level for he souhern hake, effecs of his policy are shown wih respec o flee sizes (Figure 4), annual ne benefis of each fishing secor (Figure 5) and he share of he cumulaive presen value ne benefis generaed by he SDF corresponding o each fishing secor (Figure 6). Figure 4 shows ha he effec of he 2% increase in he share of he souhern hake TAC for he smallscale secor has relevan effecs on he number of small-scale boas in he SDF (dashed ligh green line) bu, marginal effecs on he large-scale flee size (dashed green line). Small-scale flee size is expeced o increase in average by 42% in he long-run, moving from approximaely 95 fishing unis o 1.36 fishing unis. Large-scale flee is reduced in he long-run by only one vessel. Figure 5 shows a significan increase in annual ne benefis o be generaed by he small-scale fishing flee (dashed ligh green line) and a minor decrease in annual ne benefis o be accrued by he large-scale fishing flee (dashed green line). Figure 6 shows ha he overall level of he cumulaive presen value of ne benefis generaed by he fishery is reduced by 5%, amoun ha is ransferred o he small-scale secor whose share would represen a 14% of he oal value of he SDF in he long-run. This would represen a relevan increase of 49% in cumulaive presen value of ne benefis o be generaed by he small-scale secor and only a 1% decrease in ha of he large-scale secor. DISCUSSION AND CONCLUSIONS Resuls obained for he four scenarios considered may be analyzed on he ligh of he hree simulaneous objecives of susainable developmen, ha is: environmenal susainabiliy, economic growh, and social equiy. Thus, curren managemen policy, represened by BASELINE scenario, may be seen as clearly complying wih susainabiliy condiions for hoki fish sock. This is no so clear for souhern hake, as he fish sock size for his resource reaches equilibrium level in he long-run a a smaller biomass level han he curren ones. I is no clear o he auhors wheher he long-run equilibrium esimaed is above criical values for precauionary purposes. The TAC4% scenario has a larger effec on boh sock sizes furher reducing heir long-run equilibrium levels. Hoki resuls sill show an increase in sock size level compared o he curren or iniial levels, hus his resource would no be a risk under his policy. TAC4% may no be advisable for souhern hake under environmenal susainabiliy grounds as i furher reduces he long-run equilibrium sock size level compared o BASELINE. The TAC2% scenario is clearly posiive on environmenal susainabiliy grounds as i favors he growh of he exploiable sock size for boh hoki and souhern hake resources. From he poin of view of economic growh and social equiy, here may no always be clear cu answers. Thus, when only looking a overall ne benefis, i is clear ha scenarios generaing he highes level of ne benefis in erms of presen value of ne benefis are TAC4% and BASELINE. On he conrary, scenario TAC2% generaes he lower level for his variable. Thus, from his perspecive he adopion of a policy like TAC2% would mean a relevan level of forgone overall ne benefis o sociey. 9

IIFET 21 Monpellier Proceedings Social equiy aspecs may be relaed o employmen and income variables and, flee size levels and annual ne benefis may be used as proxy for hese. BASELINE and TAC4% scenarios grealy favor he largescale fishing hrough larger flee sizes and annual ne benefis bu, mean smaller flees and annual benefis for small-scale fishing secor in he long-run. TAC2% scenario generaes smaller flee size for he large scale secor bu, a larger flee size for he small-scale secor in he long-run. Annual ne benefis for he small-scale fishing flee are significanly larger for his scenario in he long-run. The SMALL7% scenario shows posiive effecs on social equiy grounds as he posiive impacs on he small-scale fishing secor are significanly larger han he negaive impacs ha would experimen he large-scale secor. Posiive effecs on overall economic benefis (cumulaive ne presen value of ne benefis) o he small-scale secor would also be significanly larger han negaive effecs on he largescale fishing secor and he whole SDF. The minor effecs of he policy on he large-scale fishing secor are mos probably due o he low dependence of his secor on he souhern hake resource. This scenario has he same effecs on he resource sock as he curren managemen policy, scenario BASELINE. In summary, even hough expeced effecs of he more conservaive managemen policy (TAC2% scenario) may show relevan posiive impacs on he fish resource and on he small-scale fishing secor, i also would generae he larges level of forgone ne benefis a he SDF level. Curren managemen policy (BASELINE) may generae reasonable overall economic benefis and employmen levels bu, i shows large unbalance on social equiy grounds as i clearly favors he large-scale secor. TAC4% would show significan increases in economic benefis and employmen in he shor-run bu, i would generae negaive impacs on he small-scale fishing secor in he long-run as well as i would grealy srain he souhern hake resource. Therefore, scenario SMALL7% may be advisable no only on social equiy and economic growh grounds bu, i also does no impose changes on he curren policy on resource susainabiliy or environmenal susainabiliy grounds. BIBLIOGRAPHICAL REFERENCES Cerda, R., G. Marínez, E. Yáñez, E. González, P. Arana, H. Trujillo, H. Morales y J. Sepúlveda. 29. Bases écnicas para el plan de manejo de la Pesquería Demersal Ausral, Informe Final Proyeco FIP Nº 27-29. Esud. y Doc. Nº 1/29, Escuela de Ciencias del Mar, Universidad Caólica de Valparaíso. pp. 467 más Anexos. Collin W. Clark, Frank H. Clarke and Gordon R. Munro. 1979. The Opimal Exploiaion of Renewable Resource Socks: Problems of Irreversible Invesmen. Economerica, 47(1), pp. 25-47. Hannon, Bruce and Ruh, Mahias, 1994, Dynamic Modeling. Springer, USA. Ed. 2. 4 pp. IFOP, 21a, Invesigación del esaus y evaluación de esraegias susenables en la merluza del sur, 21. Valparaíso: Insiuo de Fomeno Pesquero y Subsecrearía de Pesca. IFOP, 21b. Invesigación del esaus y evaluación de esraegias de exploación en merluza de cola, 21. Valparaíso: Insiuo de Fomeno Pesquero y Subsecrearía de Pesca. IFOP, 21c, Invesigación Siuación Pesquería Demersal Ausral, 28. Valparaíso: Insiuo de Fomeno Pesquero y Subsecrearía de Pesca. Kirkwood, C.W. 1998. Sysem Dynamics Mehods: A Quick Inroducion. College of Business, Arizona Sae Universiy. Arizona, Unied Saes. 117 pp Munro, Gordon R., 1998, The Economics of Overcapializaion and Fishery Resource Managemen: a review. Vancouver: Deparmen of Economics, The Universiy of Briish Columbia. Discussion Paper No.: 98-21. Sparre, P. and S.C. Venema, 1997, Inroducion o ropical fish sock assessmen. Par I. Manual. FAO Fisheries Technical Paper Nº 36.1, Rev. 2 Rome. 1

IIFET 21 Monpellier Proceedings ENDNOTES 1 The dynamics of he sock size in he model is worked in number of individual or abundance as we are working wih a global populaion model and individual growh was no included. Resuls are presen in biomass as abundance is ransformed in biomass using he mean average weigh for he average individual comprising he exploiable sock 11