Forecasting Fish Stock Recruitment and Planning Optimal harvesting strategies by Using Neural Network

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1 JOURNAL OF COMPUERS, VOL. 4, NO. 11, NOVEMBER Forecastng Fsh Stock Recrutment and Plannng Optmal harvestng strateges by Usng Neural Network Ln Sun 1 1 School of management of Dalan Unversty of echnology, Dalan, 11624, Chna Emal: sunln@yeah.net Hongjun Xao 1, Shouju L 2 and Dequan Yang 1 2 Department of Engneerng Mechancs, Dalan Unversty of echnology, Dalan, 11624, Chna Emal: lshouju@dlut.edu.cn Abstract Recrutment predcton s a key element for management decsons n many fsheres. A new approach usng neural network s developed as a tool to produce a formula for forecastng fsh stock recrutment. In order to deal wth the local mnmum problem n tranng neural network wth back-propagaton algorthm and to enhance forecastng precson, neural network s weghts are adjusted by optmzaton algorthm. It s demonstrated that a well traned artfcal neural network reveals an extremely fast convergence and a hgh degree of accuracy n the predcton of fsh stock recrutment. Index erms neural network, predcton of fsh stock recrutment, optmal harvestng strategy, management decson I. INRODUCION Marne ecosystems are notorously dffcult to study. rophc relatonshps are multdmensonal, relevant bophyscal factors vary wdely n ther spatal and temporal scales of nfluence, and process lnkages are complex and hghly non-lnear showed that the problem s further compounded by naccuraces n measurng envronmental varablty, as well as the botc response. Consequently, appled ecologcal nvestgatons attemptng to relate oceanc physcs, atmospherc physcs, and marne bology to varatons n fsh stock-recrutment are dffcult to carry out. Nonetheless, the collectve mpacts of regme shfts, large mult-decadalscale forcngs of marne ecosystems (such as those attrbuted to the NAO), and natural and man-made nfluences on varablty n fsh populatons and future states of ecosystems are wdely recognzed as mportant areas of study [1]. o set accurate preseason fshng quotas, t s mportant to be able to forecast the bomass of young fsh (recruts) that wll jon the fshable stock for the frst tme before the fshng season opens. Experence has proven that the level of recrutment s dffcult to forecast for Correspondng author: Shouju L. most fsh stocks because the survval of juvenle fsh s affected by a number of varables. For example, the bomass of 3-year-old recruts to the west coast of Vancouver Island (WCVI), Brtsh Columba, Pacfc herrng (Clupea pallas) stock over the last 6 years has fluctuated over a 35-fold range n response to nterannual and decadal tme scale varatons n the spawnng bomass (of parents) and n the state of the envronment, whch n turn affects the Pacfc herrng food supply and mortalty rate [2]. A long-term ecosystem research program has dentfed that the key varables determnng Pacfc herrng recrutment are the lagged bomass of adult spawners, the summer bomass of Pacfc hake (Merluccus productus), whch s a sgnfcant predator, and two lagged envronmental factors (annual sea surface temperature (SS) and salnty). he annual SS s beleved to be a general ndcator of mortalty and the state of the food supply. In many cases, t s dffcult to clarfy and model the mechansm controllng recrutment by usng conventonal mathematcal and statstcal methods because the survval process s nonlnearly related to several factors [3]. Understandng and predctng bologcal productvty s consdered a key queston by lake fsheres scentsts. Several ecologsts and fsheres managers have tred to determne the abundance of lvng stocks or the specfc bodversty n aquatc ecosystems usng some of ther characterstcs,.e. surface of the rver dranage basn, surface area of lakes, flood plan areas, morphoedaphc ndex, depth, coastal lnes, prmary producton, etc [4]. In developng countres, the economcal mportance of fsh and as a food source makes ths topc partcularly relevant. Dverse multvarate technques have been used to nvestgate how the varous rchness of fsh s related to the envronment, ncludng several methods of ordnaton and canoncal analyss, and unvarate and multvarate lnear, curvln-ear, and logstc regressons. However, for quanttatve analyss and more partcularly for the development of predctve models of fsh abundance, multple lnear regresson and dscrmnate analyss have remaned, the most frequently used technques. hese conventonal technques (based notably on multple 29 ACADEMY PUBLISHER

2 176 JOURNAL OF COMPUERS, VOL. 4, NO. 11, NOVEMBER 29 regressons) are capable of solvng many problems, but show sometmes serous shortcomngs. hs dffculty s that relatonshps between varables n scences of the envronment are often non-lnear whereas methods are based on lnear prncples. Non-lnear transformatons of varables (logarthmc, power or exponental functons) allow to sgnfcantly mprove results, even f t s stll nsuffcent. However, the neural network, wth the error back-propagaton procedure, s at the orgn of an nterestng methodology whch could be used n the same feld as regresson analyss partcularly wth the nonlnear relatons [5]. Ecologcal applcatons of multvarate statstcs have expanded tremendously durng the last two decades. Among these methods, the prncpal component analyss (PCA) s now used routnely by ecologsts. It s known as able to smplfy large data sets wth reasonable loss of nformaton and to assess nter-correlaton among varables of nterest [6]. However, the nformaton gven by PCA technques suffers from some drawbacks n that the relatonshps between varables n envronmental scences are often non-lnear, whle the methods used are based on lnear prncples. ransformaton of non-lnear varables by logarthmc, power or exponental functons can apprecably mprove the results, but have often faled to ft the data. In the same way, ecologcally relevant, but unusual observatons, are frequently deleted from the data sets to reduce data heterogenety. Although these deletons satsfy statstcal assumptons, they are lkely to bas the ecologcal nterpretaton of the results. o overcome these dffcultes, the artfcal neural networks whch are known to be effcent n dealng wth heterogeneous data sets should consttute a relevant alternatve tool to tradtonal statstcal methods [7]. II. A NEURAL NEWORK MODEL FOR FORECASING FISH SOCK RECRUIMEN he factors and phenomenon affectng recrutment n marne fsh are complex and not yet fully explored. hus, mechanstc models or model drven statstcal technques poorly result n predcton or utterly fal. Data drven paradgm wth mplct evolvng nature s the best alternatve. NNs, nspred by the functonng of human bran are n a state of maturty wth excellent mappng and predctve characterstcs for both supervsed and unsupervsed two-way data structures. he recrutment of Norwegan sprng-spawnng herrng (Clupea harengus) n Norway, sand eel Ammodytes personatus n Eastern part of seto Island sea, Northern Benguella, Sardne Sardnops, sagax n South Atlantc were modelled wth NNs. Hardman-Mount ford et al. modelled recrutment success of Northern Benguela, Sardne sardnops, sagax n South Atlantc ocean employng a seven year tme seres data. An adequate model for the recrutment of sand eel A. personatus n eastern part of Seto Island Sea n the month of February was developed wth a three-layer FFNN traned wth BP algorthm. he nfluental nput varables of the model are reflected n the magntude of the weghts. Inferences based on the NN ndcated that recrutment was hgher when the water temperature was low n precedng September. SOM could dentfy characterstc patterns based on sea level dfference, whch are related to SS. he Pacfc halbut stock data were analysed for fsh recrutment by models wth dfferent bass assumptons and the results are compared. In the models Pacfc Decadal Oscllaton (PDO) ndex, envronmental varable was employed along wth autoregressve component. Fuzzy-logc model out performed the tradtonal Rcker stock recrutment model. MLP-NNs are tested wth several performance crtera [8]. Artfcal neural networks are computer algorthms that smulate the actvty of neurons and nformaton processng n the human bran. In general, a neural network s an nterconnected network of smple processng layers where typcally the frst layer (nput layer) makes ndependent computatons and passes the results to a hdden layer. hs layer may n turn make an ndependent computaton and pass the results to another hdden layer. hs sgnal process may contnue to produce more hdden layers dependng on the complextes of the problem. Fnally, the last layer (output layer) determnes the output from the network. Each processng layer makes the computaton based on the weghted sum of ts nputs. hs sgnal processng between layers enables neural networks to model complex lnear and nonlnear systems. Unlke the more commonly used regresson models, neural networks do not requre a partcular functonal relatonshp or dstrbuton assumptons about the data. hs makes neural network modelng a powerful tool for explorng complex, nonlnear bologcal problems lke recrutment forecastng [9]. he man factors affectng fsh stock recrutment consst of spawnng bomass (SB n mllon tones,x1), mean annual sea surface temperature (SS n C, x2), and North Atlantc Oscllaton ndex (NAO, normalzed sea level pressure anomaly, x3) [1]. An artfcal neural network model s a system wth nputs and outputs based on bologcal nerves. he system can be composed of many computatonal elements that operate n parallel and are arranged n patterns smlar to bologcal neural nets. A neural network s typcally characterzed by ts computatonal elements, ts network topology and the learnng algorthm used. SB, x 1 SS,x 2 NOA,x 3 v jk µ j Fg. 1 A schematc of neural network model R,y 29 ACADEMY PUBLISHER

3 JOURNAL OF COMPUERS, VOL. 4, NO. 11, NOVEMBER he archtecture of BP networks, depcted n Fgure 1, ncludes an nput layer, one or more hdden layers, and an output layer. he nodes n each layer are connected to each node n the adjacent layer. Notably, Hecht-Nelsen proved that one hdden layer of neurons suffces to model any soluton surface of practcal nterest. Hence, a network wth only one hdden layer s consdered n ths study. here are three nodes n nput layer. he nput of each node s SB, SS, and NAO, respectvely. here s only one node n output layer, whch denotes forecastng fsh recrutment. Before an ANN can be used, t must be traned from an exstng tranng set of pars of nputoutput elements. he tranng of a supervsed neural network usng a BP learnng algorthm normally nvolves three stages. he frst stage s the data feed forward. he computed output of the -th node n output layer s defned as follows [1] Nh N (1) y = f( ( µ f( ν x + θ ) + λ )). j jk k j j= 1 k= 1 Where µ j s the connectve weght between nodes n the hdden layer and those n the output layer; v jk s the connectve weght between nodes n the nput layer and those n the hdden layer; θ j or λ s bas term that represents the threshold of the transfer functon f, and x k s the nput of the kth node n the nput layer. erm N, N h, and N o are the number of nodes n nput, hdden and output layers, respectvely. he transfer functon f s selected as Sgmod functon [11] f ( ) = 1/[1 + exp( )]. (2) he second stage s error back-propagaton through the network. Durng tranng, a system error functon s used to montor the performance of the network. hs functon s often defned as follows Where p P N o p p E ( w) = ( ( y o ). (3) y and p= 1 = 1 p o denote the practcal and desred value of output node for tranng pattern p, P s the number of sample. ranng methods based on backpropagaton offer a means of solvng ths nonlnear optmzaton problem based on adjustng the network parameters by a constant amount n the drecton of steepest descent, wth some varatons dependng on the flavor of BP beng used. he optmzaton algorthm used to tran network makes use of the Levenberg-Marquardt approxmaton. hs algorthm s more powerful than the common used gradent descent methods, because the Levenberg-Marquardt approxmaton makes tranng more accurate and faster near mnma on the error surface [12]. 1 wk ( + 1) = wk ( ) H ( k) gk ( ). (4) Where w(k) s the vector of network parameters(net weghts and element bases) for teraton k, matrx H -1 (k) 2 represents the nverse of the Hessan matrx. he vector g(k) represents the gradent of objectve functon. he Hessan matrx can be closely approxmated by H J J. (5) Where J s the Jacoban matrx, and the gradent of the objectve functon can be computed as E g = = J e. w Where e s an error vector, and t can be calculated as follows (6) e= y o. (7) he teratve formulas of adjustng weghts can be rewrtten as follows 1 wk ( + 1) = wk ( ) [ J ( k) J( k)] J ( kek ) ( ). (8) One problem wth the teratve update of weghts s that t requres the nverson of Hessan matrx H whch may be ll condtoned or even sngular. hs problem can be resolved by the regularzaton procedure as follows H J J + µ I. (9) Where µ s a constant, I s a unty matrx. he weght adjustment usng Levenberg-Marquardt algorthm s expressed as follows wk ( + 1) = wk ( ) 1 [ J ( k) J( k) + µ I] J ( k) e( k). (1) he Levenberg-Marquardt algorthm approxmates the normal gradent descent method, whle f t s small, the expresson transforms nto the Gauss-Newton method. After each successful step the constant µ s decreased, forcng the adjusted weght matrx to transform as quckly as possble to the Gauss-Newton soluton. When after a step the errors ncrease the constant µ s ncreased subsequently. he number of neurons n the hdden layer s determned by the followng equaton N h = 2 N + 1. (11) Where N and N h are the amount of nput, hdden neurons, respectvely. III. CASE SUDY Data for Norwegan sprng-spawnng herrng, potentally the largest of the herrng stocks n the northeast Atlantc, were taken from nformaton presented n oreson [13]. me seres for fsh recrutment and affectng factors were plotted n Fg.2, 3, 4 and 5. Some of data seres were used as tranng neural network; and others were taken to valdate the effectveness of proposed forecastng procedure based on neural network. Fg. 6 depcts the comparson of forecastng and practcal fsh recrutment. 29 ACADEMY PUBLISHER

4 178 JOURNAL OF COMPUERS, VOL. 4, NO. 11, NOVEMBER 29 2 practcal values forecasng values SB Fg. 2 me seres plot for spawnng bomass (SB n mllon tones) Recruts Fg. 6 Comparson of forecastng and practcal fsh recrutment (R n bllons ) SS Fg. 3 me seres plot for mean annual sea surface temperature (SS n C) NA Fg. 4 me seres plot for North Atlantc Oscllaton ndex (NAO) Age 3 Recruts Fg. 5 me seres plot for age-3 recrutment (R n bllons ) IV. OPIMAL HARVESING SRAEGIES FOR FISHERIES MANAGEMENS Bo-economc fsheres models, depctng the economc and bologcal condtons of the fshery, are wdely used for the dentfcaton of Pareto mprovement fsheres polces. he models that have been constructed for ths purpose dffer n sze, detal and techncal sophstcaton. Vrtually all, however, model the fshery as a techncal relatonshp between the use of fshery nputs and the resultng bologcal and economc outcomes. In order to model growth of bologcal systems numerous models have been ntroduced. hese varously address populaton dynamcs, ether modelled dscretely or, for large populatons, mostly contnuously. Others model actual physcal growth of some property of nterest for an organsm or organsms. he rate of change of fsh stock dx/dt s determned by natural reproductve dynamcs and harvestng [14] x& = f( x, t) h( e, x, t). (12) Where f(x,t) s the natural growth rate of fsh stock whch s dependent on the current sze of the populaton x. he quantty harvested per unt of tme s represented by h(e,x,t). he net growth rate dx/dt s obtaned by subtractng the rate of harvest h(e,x,t) from the rate of natural growth f(x,t). Functonal relatonshps commonly used to represent the natural growth rate of fsh stock s the logstc model [15]. x f( x) = rx(1 ). (13) K Where r s the ntrnsc growth rate, K s the envronmental carryng capacty, and x s the constant assocated wth the ntrnsc growth rate. he rate of harvest h(e,x,t) s assumed proportonal to aggregate standardzed fshng effort (e) and the bomass of the stock x; that s [16] hext (,,) = βet () xt (). (14) 29 ACADEMY PUBLISHER

5 JOURNAL OF COMPUERS, VOL. 4, NO. 11, NOVEMBER Where β s the catchablty coeffcent. Once average fshng power has been calculated, the standardzed fshng effort s computed as [8] et () = Pτ n. (15) Where e s the standardzed fshng effort ; P represents average relatve fshng power ; τ s the average fshng days at tme t; and n denotes the number of vessels at tme t. Fshng cost s evaluated by [17] Cext (,,) = cet (). (16) Where C(e,x,t) s the total cost functon. (13) has soluton xt = Kx (). ( K x)exp( rt) + x (17) Let us start by brefly revewng the essental structure of conventonal bo-economc fsheres models. As dscussed above, these models consst of two fundamental components: () a bomass growth functon and () an economc performance functon. her two basc components may be represented by the followng four sets of equatons: max Π= [ p h C]exp( α t) dt = [ p β et ( ) xt ( ) cet ( )]exp( α tdt ). ntrnsc growth rate r=1.,k=1 r=.5,k=1 r=.7,k= Sze of fsh populaton Fg. 7 Natural growth rate of fsh stock versus the sze of fsh populaton Sze of fsh populaton r=1.,x=1,k=1 r=.5,x=2,k=1 r=.4,x=2,k=1 r=.3,x=2,k=1 r=1.,x=18,k= tme Fg. 8 Sze of fsh populaton versus tme wthout catchng (18) x( t > ) = x opt. (19) hext (,, > ) = h opt. (2) & (21) x = f( x, t) h( e, x, t). In ths formulaton, Π s the ultmate performance measure of the fshery. P s output prce of fsheres. s startng catchng tme. x opt s optmal sze of fsh populaton. h opt s optmal rate of harvest. From (17), we can deduce the startng catchng tme Kx ln[( x) / ( K x)] xopt =. (22) r he optmal rate of harvest s expressed as follows: xopt hopt = β eopt xopt = xoptr(1 ). (23) K dhopt Let =, the optmal sze of fsh populaton and x opt the optmal rate of harvest are solved K x opt =. (24) 2 rk h opt =. (25) 4 he optmal fshng effort s deduced as follows e opt xopt r = r(1 ) / β =. (26) K 2β V. SUSAINABLE DEVELOPMEN POLICIES FOR FISHERIES MANAGEMEN here has been much comment n recent years on the nature of sustanable development and, n partcular, on the nternal contradctons mplct n ths term. Rate of havest Sze of fsh populaton r=1.,k=1 r=.5,k=1 Fg. 9 Optmal rate of harvest versus the sze of fsh populaton 29 ACADEMY PUBLISHER

6 18 JOURNAL OF COMPUERS, VOL. 4, NO. 11, NOVEMBER 29 Whle t s generally accepted that sustanable use of natural resources means that ther explotaton by one generaton should not dmnsh ther value for succeedng generatons, applcaton of ths concept remans elusve and s the subject of much debate [9]. Whle we assume that sustanablty s accepted as a desrable outcome of management of any renewable natural resource, there are cases where sustanablty s not the expected outcome. When stocks have a low rate of natural ncrease, and so provde a low contrbuton to present value, but the owners have a hgh dscount rate for ther captal, the stock s lkely to be exploted to extncton. In other words, f the rate of return on captal s greater than the value of the rate of natural producton, for economcally valuable stocks, extncton s a lkely outcome. Ocean fsh stocks have tradtonally been arranged as common property resources. hs means that anyone, at least anyone belongng to a certan group (often a complete naton), s enttled to harvest from these resources. hrty years ago, the common property arrangement was vrtually unversal. oday, at the begnnng of the twenty-frst century, t s stll the most common arrangement of ocean fsheres. It has been known that common property resources are subject to fundamental economc problems of overexplotaton and economc waste. he essence of the fundamental problem s captured by the dagram n Fg. 1. In fsheres, the common property problem manfests tself n: 1). Excessve fshng fleets and effort. 2). oo small fsh stocks. 3). Lttle or no proftablty and unnecessarly low personal ncomes. 4). Unnecessarly low contrbuton of the fshng ndustry to the GDP. 5). A threat to the sustanablty of the fshery. 6). A threat to the sustanablty of human habtaton. Fg. 1 llustrates the revenue, bomass and cost curves of a typcal fshery as a functon of fshng effort. Fshng effort here may be regarded as the applcaton of the fshng fleet to fshng. he revenue and bomass curves are sustanable n the sense that these are the revenues and bomass that would apply on average n the long run, f fshng effort was kept constant at the correspondng level. Beneft x opt x y Optmal effort e opt e y Bo-mass Sustanable bomass Revenues Costs Common property Fshng effort Fg. 1 Sustanable development model for fsheres management Fg. 1 reveals that the proft maxmzng level of the fshery occurs at fshng effort level e opt. At ths level of fshng effort, profts and consequently the contrbuton of the fsheres to GDP s maxmzed. Note that the proft maxmzng fshng effort e opt s less than the one correspondng to the maxmum sustanable yeld (MSY), e MSY. Consequently, the proft maxmzng sustanable stock level, x opt, s comparatvely hgh as can be read from the lower part of Fg. 1. he proft maxmzng fsheres polcy, consequently, s bologcally conservatve. Indeed the rsk of a serous stock declne s generally very low under the proft maxmzng sustanable fsheres polcy. he rate of change of fsh stock dx/dt s determned by natural reproductve dynamcs and harvestng when fshng effort s not equal to optmal value x x& = xr(1 ) βe( t) x( t). (27) K he soluton of Eq. (16) s deduced as follows Px xt () =. x e ( P x ) ( βe r) t + (28) βe P= (1 ) K. (29) r What we are suggestng n terms of sustanablty then, s that f we are talkng about the recreatonal fshng experence rather than just catchng fsh, we do not need to assume that the same fsh wll be avalable n the same proportons/numbers n future, just that the same total experence wll be avalable. hs mples that you can substtute speces, as they become less fashonable, or less avalable n response to human or natural pressures; but there s an obvous bologcal lmt to the extent to whch speces can be substtuted. In any case, f a fashonable speces s droppng n numbers, t probably wll be worth takng steps to arrest the declne. he shareholders n a company would expect the manager to take the most cost-effcent steps and provde the shortest nterrupton to ther dvdends. At present, marne fsheres rely almost wholly on wld stocks. Sze of fsh e=1eopt e=1.5eopt e=2eopt e=3eopt e=.5eopt me Fg. 11 Sze of fsh populaton versus tme whle excessve fshng(x=5,k=1,r=1.,β=.1, eopt =5.) 29 ACADEMY PUBLISHER

7 JOURNAL OF COMPUERS, VOL. 4, NO. 11, NOVEMBER Unlke freshwater fsheres, there s lttle capacty at present for augmentng stocks from hatcheres. A properly prced stock would provde an mpetus for developng more drect methods such as use of hatcheres to accelerate stock recovery, rather than removng fshng pressure and smply watng for natural recovery of stocks. Prudent fsheres managers mght make development of drect methods of restockng a prorty [2]. A practcal tme-scale for sustanablty for natural resource management broadly equates to 8 1 years. After that tme, t would be dffcult for people to magne what socety mght be lke. Even makng predctons of what consttutes sustanablty wthn that tme perod wll be dffcult because of natural changes beyond human control and changes to the way humans use natural resources. hese ssues become more focused when consderng dfferent forms of property rghts, ncludng those nvolvng explotaton for commercal gan, as n fsheres. In ths case, a mnmum expectaton s that those explotng the resources would seek commercal returns on captal nvested n acqurng access, and n harvestng and developng the resources. Open access and some forms of common property ownershp result n overexplotaton and collapse of resources, rather than n sustanable bologcal and socal outcomes. hs s not suffcent reason to argue that renewable natural resources should be mantaned n government ownershp and commercal explotaton prohbted. In realty, natural resources treated n ths manner assume no value to the communty, other than ther ntrnsc ecologcal and exstence values. hese resources are even more lkely to be degraded or lost. VI. CONCLUSIONS Back propagaton of the ANN was used to develop forecastng models of fsh yeld predcton usng habtat features on a macrohabtat scale. hs forecastng approach requred an extensve database and care to obtan relable models. he selecton of nput varables, ther ecologcal sgnfcance and the use of a test data set to assess the model precson and accuracy are mportant elements of ths type of approach. he advantage of ANN over MLR models s the ablty of ANN to drectly take nto account any non-lnear relatonshps between the dependent varables and each ndependent varable. Several authors have shown greater performances of ANN as compared to the MLR. he back-propagaton procedure of the ANN gave very hgh correlaton coeffcents comparng to the more tradtonal models, especally for the tranng calculaton. In the test set, correlaton coeffcents were lower than n tranng but stll remaned clearly sgnfcant. hs dfference between tranng and testng sets s more amplfed when the data set s small, and when each sample s lkely to have unque nformaton ; ths s relevant to the model. hs study demonstrates that neural network models can perform reasonably well n predctng the bomass of fsh that wll recrut to the fshery, gven pror nformaton on the state of several key factors durng the frst year of lfe of the year-class. Specfcally, nformaton on the bomass of ther parents (.e., spawners), the bomass of a key predator speces (.e., Pacfc hake), and some mportant envronmental varables that are beleved to be proxy ndcators of other predators and general feedng condtons s requred. Comparson wth a multple regresson and modfed Rcker model demonstrated the superor ablty of the neural network model to ft the underlyng complex relatonshps between recrutment and the ndependent varables. he recrutmentenvronment problem s a dffcult one, but t does not mean that we should stop explorng models and technques to help understand the factors that control recrutment dynamcs and ther spatal and temporal scales of nfluence. Smple statstcal approaches stll have ther place f used approprately. REFERENCES [1] B. A. Megrey, Y. Lee, and S. A. Mackln, Comparatve analyss of statstcal tools to dentfy recrutmentenvronment relatonshps and forecast recrutment strength, ICES Journal of Marne Scence, Vol. 62, pp , May 25. [2] Robnson, C.L.K., and D.M. Ware, Modellng pelagc fsh and plankton trophodynamcs off southwestern Vancouver Island, Brtsh Columba, Can. J. Fsh. Aquat. Sc, Vol. 51, pp , August [3] D.G. Chen and D.M. Ware, A neural network model for forecastng fsh stock recrutment, Can. 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8 182 JOURNAL OF COMPUERS, VOL. 4, NO. 11, NOVEMBER 29 [13] R. oresen, and O. J. Ostvedt, Varaton n abundance of Norwegan sprng-spawn herrng (Clupea harengus, Clupedae) throughout the 2th century and the nfluence of clmatc fluctuatons, Fsh and Fsheres, Vol. 1, PP , September 2. [14] A. L. Jensen, Maxmum harvest of a fsh populaton that has the smallest mpact on populaton bomass, Fsheres Research, Vol. 57, pp , July 22. [15] B. Lng, and W. Ke, Optmal mpulsve harvest polcy for tme-dependent logstc equaton wth perodc coeffcents, Electronc Journal of Dfferental Equatons, Vol. 121, pp. 1 9, December 23 [16] A. soulars, and J. Wallace, Analyss of logstc growth models, Mathematcal Boscences, Vol. 179, pp , July August 22. [17] S.Y. a, Effort Dynamcs and Alternatve Management Polces for the Small Pelagc Fsheres of Northwest Pennsular Malaysa, Marne Resource Economcs, Vol. 11, pp , February [18] A. Ragnar, Endogenous optmzaton fsheres models, Annals of Operatons Research, Vol. 94, pp , February 2. [19] D. Derrn, and F. G. Donald, Challenges for economc polcy n sustanable management of marne natural resources, Ecologcal Economcs, Vol. 36, pp , February 21. [2] D. S. Martn, Z. Junje, and C.C. Felca, Econometrc modelng of fsheres wth complex lfe hstores: Avodng bologcal management falures, Journal of Envronmental Economcs and Management, Vol. 55, pp , May 28. Ln Sun was born n Dalan, Laonong Provnce, Chna, on July 11, He receved hs B.S degree n nvestng and economc management from Dongbe Unversty of Fnance and Economcs n 1996 and Master of Busness from the MBA College of Dongbe Unversty of Fnance and Economcs n 25. Currently, he s a PH.D research canddate wth techncal economy management at Dalan Unversty of echnology snce 26. Hs research nterest s regonal economy management. He s workng at Dalan Ocean and Fshery Bureau currently. He has been engaged n Dalan regonal ocean economcal and fshery research for approxmately decade. Hongjun Xao was born n Ye County, Shandong Provnce, Chna, n He receved B. S. degree form Dalan Unversty of echnology n 1975 and Master degree form Htotsubash Unversty n Currently, he s a Professor of Dalan Unversty of echnology and conducts research n the areas of busness management, busness fnance and knowledge nnovaton. Shouju L was born n Shenyang, Laonong Provnce, Chna, on October 3, 196. He receved the Ph. D. degree n Engneerng Mechancs from the Dalan Unversty of echnology, Dalan, Chna, n 24. He was Assocate Professor at Department of Engneerng Mechancs, Dalan Unversty of echnology form 1994 to 28. Now he s a Professor of Dalan Unversty of echnology and teaches and conducts research n the areas of neural network, ntellgent optmzaton, parameter dentfcaton appled to sol mechancs and underground engneerng felds. Dequan Yang was born n Nehe County, Helongjang Provnce, Chna, on March 4, He receved the Ph.D. degree n management scence and engneerng from the Harbn nsttute of echnology, Harbn, Chna n Snce 21 he has been an Assocate Professor at School of Management, Dalan Unversty of echnology, Laonng, Chna. He teaches and conducts research n the areas of management scence and system scences. 29 ACADEMY PUBLISHER