Spaial Processes and Managemen of Marine Populaions 539 Alaska Sea Gran College Program AK-SG-01-02, 2001 An Empirical Analysis of Fishing Sraegies Derived from Trawl Logbooks David B. Sampson Oregon Sae Universiy, Hafield Marine Science Cener, Newpor, Oregon Exended Absrac During a fishing rip a fisher mus make a series of decisions regarding where o fish and how long o operae a each fishing locaion. The problem of organizing fishing operaions during a rip is exremely complicaed, especially in a mulispecies fishery. This paper presened preliminary resuls from an ongoing Oregon Sea Gran projec ha is developing quaniaive measures of fishing sraegies for he Oregon rawl fishery for groundfish and evaluaing inra- and inerannual changes in fishing sraegies wih respec o fish prices and fishing regulaions. The erm fishing sraegy here means he fishing gear and sequence of fishing locaions seleced by a fisher during a fishing rip. Principal componens analysis (PCA) was applied o rip-by-rip summary saisics derived from logbooks from a se of 28 rawlers ha operaed every year during 1987-1997. These boas made 9,556 of he 30,455 fishing rips (from 245 differen boas) for which logbook daa are available during 1987-1997. For simpliciy he analysis was limied o daa from hese 28 rawlers for 1988, 1991, 1994, and 1997, a oal of 3,635 rips. The logbook daa files and corresponding landings informaion were provided by he Oregon Deparmen of Fish and Wildlife, whose por agens colleced logbooks each year from 77% o 85% of all groundfish rawl rips and landings receips for all rawl landings. The logbook daa were subjeced o preliminary screening o idenify fishing rips wih incomplee informaion. For he daa se used in his sudy 30 rips (0.8%) were excluded from he analysis because he logbook daa had no informaion on ow locaions, boom dephs, or duraions, or because he logbooks were missing from he daabase. The daa were also screened o idenify infeasible ow saring locaions (ones ha were on land or ha had boom dephs ha were inconsisen wih he repored laiude and longiude).
540 Sampson Analysis of Fishing Sraegies Derived from Trawl Logbooks For he 23,581 ows from he 3,635 rips used in his sudy here were 337 ows (1.4%) wih missing or infeasible ow saring locaions. PCA was used o ransform he 23 aribues associaed wih each fishing rip ino a se of wo scores ha were hen examined graphically and wih sandard saisical mehods. The PCA scores have he propery ha rips wih similar scores have similar aribues and vice versa. The se of rip aribues were: he number of days a sea, he number of ows, he average and range of he ow duraions, he average and range of boom dephs a he ow saring locaions, he proporion of he ow ime spen a four deph classes (1-99, 100-199, 200-299, and >300 fahoms), he proporion of ows made wih boom versus midwaer rawl, he proporion of ows saring norh of he reurn por, he proporion of ow hours ha were during dayligh, he disance of he firs ow from he saring por, he disance of he las ow from he reurn por, he maximum disance from he reurn por, he average disance beween ow sars, he proporion of ow saring locaions on he curren rip ha also had been occupied during he mos recen previous rip, and he proporion of ow saring locaions occupied on rips during he previous 90, 180, 270, and 360 days. Also abulaed for each rip were auxiliary daa: boa idenifier, year, monh, reurn por, and he landings of 20 species or species groups (Pacific hake, Dover sole, hornyheads, sablefish, arrowooh flounder, Pacific ocean perch, widow rockfish, yellowail rockfish, large rockfish, small rockfish, lingcod, perale sole, English sole, rex sole, Pacific sanddab, miscellaneous flafish, Pacific cod, Pacific mackerel, jack mackerel, and oher). The auxiliary daa were no included in he PCA of he rip aribues bu were used o help inerpre he PCA scores. For he 3,635 rips examined he boas on average were a sea for 3.0 days and made 6.5 ows ha lased 3.9 hours. On average he boom deph a he ow saring locaions was 172 fahoms, 70% of he ows were made wih boom rawl gear, and 75% of he ow ime was during dayligh. The saring locaion of he firs ow on a rip on average was 31 nauical miles from he deparure por, he las ow was 34 nmi from he reurn por, and he maximum disance from he reurn por was 45 nmi. The average disance beween ow saring locaions was 8.6 nmi. On average only 18% of ow saring locaions on a rip were wihin 5 nmi and wihin 5 fahoms by deph of one of he ow saring locaions made by ha boa during he mos recen previous rip. Boas usually reurned o ow saring locaions ha hey had occupied previously. On average 47% of ows sared a locaions ha had been occupied during he pas 90 days, 54% of ows were a locaions occupied during he pas 180 days, 58% of ows were a locaions occupied during he pas 270 days, and 64% of ows were a locaions occupied during he pas 360 days. PCA was applied iniially o he daa se for all 3,635 rips. The firs and second principal componens accouned for 31.4% and 17.5% of he variabiliy in he rip aribues. Plos of he PCA scores for he firs wo componens indicaed wo disinc groupings of rips. Examinaion of he
Spaial Processes and Managemen of Marine Populaions 541 aribue and auxiliary daa indicaed ha one group was composed almos enirely of rips ha used midwaer rawl gear, which caugh widow rockfish during 1988 (86% of he rip landings by weigh) and Pacific hake during 1991, 1994, and 1997 (95-99% of he rip landings by weigh). A second PCA was applied o he subse of rips ha used boom rawl gear on a leas one ow of each rip (2,574 rips ha made 21,835 ows). For his PCA he firs and second componens accouned for 32.4% and 11.2% of he variabiliy in he rip aribues. The firs axis was highly negaively correlaed wih he proporion of ows made a locaions occupied during he pas 180, 270, and 360 days (r 2 > 0.58) and wih he proporion of ow ime in he 1-99 fahom deph class (r = 0.758). The second axis was highly correlaed wih he number of ows (r = 0.674), he maximum disance from por (r = 0.630), and he average ow duraion (r = 0.527). The PCA scores in general were no srongly correlaed wih he auxiliary landings daa. The axis 1 scores were moderaely correlaed wih landings of he deepwaer species: hornyheads (r = 0.578); sablefish (r = 0.504); and Dover sole (r = 0.343). The axis 2 scores were moderaely correlaed wih he landings of Pacific ocean perch (r = 0.431) and Pacific cod (r = 0.310). The firs and second axis scores (PCA1 and PCA2) from he second PCA were analyzed using a generalized linear model (GLM) o gauge he imporance as explanaory facors of he auxiliary variables boa, year, monh, and por and heir wo-way ineracions. Wih boh ses of PCA scores he GLM analyses showed ha all main effecs were highly significan (P < 0.001). In he GLM wih PCA1 he facor boa had a paricularly large mean squared error and all wo-way ineracions were significan (P < 0.05), excep for boa wih por and monh wih por. In he GLM wih PCA2 he facors boa and por had large mean squared errors and all wo-way ineracions were significan (P < 0.05). Scaerplos of he PCA scores (PCA2 versus PCA1) were examined for each of he main effecs in he GLM. There was a posiive linear rend in he scores averaged on an annual basis, wih rips from 1997 associaed wih larger values of PCA1 and PCA2. There was an almos-linear rend in he scores averaged by por, wih rips from Coos Bay and Brookings (on he souh coas of Oregon) associaed wih larger values of PCA1 and PCA2, and rips from Asoria (a he norhern border of Oregon wih Washingon) associaed wih smaller values. Also, here was a disinc seasonal componen o PCA1: rips during he winer monhs were associaed wih larger PCA1 values. Addiional analyses are planned ha will examine wheher changes in fish prices or rip limi regulaions have had deecable effecs on fishing sraegies. PCA scores will be derived using he fishing rip aribues from a more complee se of he available logbook daa. Also planned are analyses o idenify fishing sraegies ha generae he greaes revenue flows for a given class of fishing boa and o deermine wheher boas ha leave he fishery afer a few years use differen fishing sraegies from hose ha remain.
Spaial Processes and Managemen of Marine Populaions 543 Alaska Sea Gran College Program AK-SG-01-02, 2001 Disribuing Fishing Moraliy in Time and Space o Preven Overfishing Ross Clayor Deparmen of Fisheries and Oceans, Science Branch, Moncon, New Brunswick, Canada Allen Clay Femo Elecronics Ld., Lower Sackville, Nova Scoia, Canada Absrac In his paper we describe a mehod for measuring he spaial and emporal disribuion of fish school densiies and exploiaion raes. A herring purse-seiner, fishing on nonspawning feeding aggregaions, and a herring gillneer fishing on smaller, highly dense spawning aggregaions, in he souhern Gulf of S. Lawrence, Canada, colleced he daa used in his sudy. Four saisical mehods were esed o deermine he mos appropriae mehod for densiy esimaion from hese daa: inverse disance weighing, Voronoi neares neighborhood, arihmeic, and kriging. No differences in densiy esimae rends were found among he four mehods and he Voronoi-neares neighborhood mehod was chosen. The relaionship beween gillne cach raes (kilograms per ne) esimaed for assessmen of his sock reaches asympoic values a lower han expeced densiies and was no useful for racking daily rends in school densiy. Gillne and purse-seine cach per meer searched were linearly relaed o densiy, and are likely suiable abundance indices for sock assessmen esimaes. An individual boa wih daa colleced in his manner was found o be represenaive of he enire flee. There was a hreshold densiy beyond which exploiaion raes remained low. This hreshold provides managers wih a mehod for idenifying and eliminaing spaial and emporal rends in high exploiaion raes and prevening overfishing. Cach Curren address for Ross Clayor is Deparmen of Fisheries and Oceans, Science Branch, Inverebrae Fish Division, P.O. Box 1006, Darmouh, Nova Scoia, Canada B2Y 4A2.
544 Clayor & Clay Disribuing Fishing Moraliy in Time and Space raes, which use searching as he uni of effor, and densiy were found o be good indicaors of high exploiaion raes in he gillne fishery. Inroducion Two principal goals of sock assessmen are o deermine if fishing moraliy is wihin conservaion arge levels and o mainain he spaial and emporal inegriy of spawning componens. A firs sep in achieving hese goals is o provide managers wih ools ha would allow hem o disribue fishing moraliy in ime and space, relaive o he size of schools being harvesed. For example, we may expec he spaial and emporal srucure of a spawning componen o be compromised if all he fishing moraliy comes from one area and ime, even if he overall fishing moraliy is wihin conservaion limis. If, however, he overall fishing moraliy is kep wihin conservaion limis and is disribued in proporion o he relaive abundance of he various spaial and emporal componens, we may expec o mee our goals. To make hese relaive disribuions in fishing moraliy, informaion on he spaial and emporal disribuion of fish biomass in he fishing area, as well as exploiaion raes on hose schools, is required. In his paper we describe a mehod for measuring he spaial and emporal disribuion of fish school densiies. This mehod is developed using acousic daa colleced during regular fishing aciviy from wo herring fishing flees in he souhern Gulf of S. Lawrence, Canada. Fishery informaion commonly used in assessmens includes cach and effor informaion provided hrough logbooks, dockside monioring, and purchase slips (Clayor and LeBlanc 1999). These sources provide indirec measures of densiy only on areas where fish are caugh. The mehod we describe improves on hese daa sources because i provides informaion on densiies of fish hroughou he enire fishing and searching area of he flee and no jus on where fish were caugh. I also enables us o es he assumpions required of hese indirec measures when hey are used o esimae populaion biomass and o deermine he effec of curren fishing moraliy on he populaion. For example, scieniss are ofen concerned ha cach raes have remained high in spie of populaion densiy declines because of efficien search mehods available o modern fishing flees (Hilborn and Walers 1992). Alernaively, concerns among indusry are ha cach raes have been lowered because of managemen or marke resricions on daily caches, inerference from oher gear, and weaher (Clayor e al. 1998). In his fishery and many ohers (see examples in his volume) here is increasing demand for local area assessmen and managemen. For his o occur, knowledge of he spaial and emporal disribuion of fish densiies in each area is essenial. As a firs sep in his direcion, we se he following objecives for his paper. Firs, deermine he appropriae densiy esimaion mehod for hese daa. Second, deermine he relaionship beween cach per uni of effor, kilograms per ne, and kilograms per meer of searching on he fishing
Spaial Processes and Managemen of Marine Populaions 545 grounds, and densiy observed by boas collecing acousic daa. Third, deermine he spaial and emporal disribuions of exploiaion rae indices and deermine if hey would provide managers wih he necessary ools for adjusing fishing moraliy in hese fisheries. Fourh, deermine if densiy and cach raes are useful indirec measures of he emporal and spaial disribuion of exploiaion indices. Maerials and Mehods Fishery and Flees The daa analyzed in his paper come from wo of he herring flees paricipaing in he fall souhern Gulf of S. Lawrence herring fishery. This fishery consiss of several gillne flees wih a oal of abou 1,500 licenses of which abou 600-1,000 are acive, and a purse-seine flee wih six acive boas. The gillne flees fish inshore on spawning aggregaions in five areas of he souhern Gulf of S. Lawrence. Their allocaion is abou 80% of he oal quoa for he area and recen average landings range from 30,000 o 60,000. Daa from he gillne flee were colleced from 7 Sepember o 30 Sepember 1997 from he Picou, Nova Scoia area, by a commercial boa, he Broke Again (Fig. 1A). In his area, he flee consiss of abou 120 boas. The purse-seine flee fall fishery occurs on nonspawning feeding aggregaions in he Chaleur Bay area and recen average landings have ranged from 6,000 o 16,000. Daa from he purse-seine flee were colleced from 23 Augus o 20 Ocober 1995 by a commercial boa, he Gemini (Fig. 1B). Acousic Daa Collecion and Calibraion The acousic sysem employed on he gillne boa Broke Again consised of a 120-kHz ransducer wih a 14 beam angle, a ransceiver (Femo DE9320 digial echo sounder), and a compuer for logging daa. The digiizing sysem (Femo) used on he purse-seiner was idenical o ha used during acousic research surveys in he souhern Gulf of S. Lawrence (Clayor and LeBlanc 1999) and was aached o a 50-kHz Furuno FCV120 sounder. These sysems are analogous o a black box on an airplane in ha he capain of he vessel urns he uni on when leaving por and off when reurning and digial acousic daa are coninually recorded during he fishing rip (Clayor e al. 1999). The sofware used o process and collec he acousic daa was he Hydroacousic Daa Processing Sysem (HDPS, Femo Elecronics). Calibraion of he acousic hardware consised of a ball and ime varied gain calibraion and proceeded as described by Clay and Clayor (1998). Acousic Daa Preparaion The fishing rack was idenified by recording laiude and longiude once per second using Garmin 45XL porable GPS unis. The acousic signal a every fourh navigaional posiion fix was reained o deermine biomass
546 Clayor & Clay Disribuing Fishing Moraliy in Time and Space densiy along he fishing rack. Selecion a every fourh fix was done o reduce he size of he daa se and o remove small flucuaions in he fishing rack because of errors in GPS saellie signals. Laiude and longiude coordinaes for each remaining fix were convered o disances (meers) from a common reference (45 laiude, 67 longiude) aking ino accoun he curvaure of he earh. The aciviies along each fishing rack were hen idenified as raversing (raveling o or from por o he fishing grounds), searching which included looking for fish and seing he ne on he fishing grounds, hauling he ne, and oher aciviies ha were no par of he direced fishing, such as waiing in por and unloading he cach. Once hese aciviies were idenified he fishing rack was divided ino equal 100-m incremens by aciviy. The area backscaer coefficiens a each of hese posiions were linearized and a disance weighed average of hese linearized coefficiens along each 100-m incremen was calculaed. This calculaion was made by muliplying he disance raveled associaed wih each coefficien imes he value of he coefficien. The sum of hese values was hen divided by he lengh of he inerval, which was 100 m. The cener of each incremen became he daa poin for subsequen analyses. Incremens a he end of an aciviy were less han 100 m and heir weighed average and cener was based on he lengh of hese incremens o he neares meer. The nex sep in he analysis was o esimae arge srengh of he acousic signals during each nigh of daa collecion so ha biomass abundance indices could be esimaed. Samples for esimaing lengh and weigh of he acousically recorded herring for gillne fishing rips were colleced from experimenal gillnes fished in he Nova Scoia area of he souhern Gulf of S. Lawrence on 11 and 18 Sepember 1997. Ne consrucion and sampling proocols are described in Clayor e al. (1998). Samples for esimaing lengh and weigh of he acousically recorded herring for purseseine fishing rips came from daily sampling from he Gemini by shipboard observers (Clayor e al. 1996). The lengh-weigh relaionship from hese samples esimaed he arge srengh using Fooe s (1987) formula: Targe Srengh = (20 log 10 lengh [cm] 71.9) 10 log 10 weigh (kg) The densiy was esimaed by dividing he linearized backscaer coefficien by he linearized arge srengh (Clayor e al. 1998). Spaial Analysis Only he porion of he fishing rack associaed wih searching and seing he ne (see above) was seleced for spaial analysis. Searching was generally riggered a densiies 0.0625 kg per m 2 or abou 1/4 herring per m 2 and seing he ne occurred only in areas ha had been searched. Hauling he ne was always associaed wih seing he ne, bu his aciviy creaed a lo of debris in he waer and hese daa were no suiable for biomass
Spaial Processes and Managemen of Marine Populaions 547 esimaion and were eliminaed. A polygon drawn around he boundary of he searching and seing daa poins defined he area for spaial analysis and biomass esimaion (Fig. 1C). The densiy esimae used in all analyses was he biomass esimae wihin he polygon divided by he area of he polygon. The nex sep in preparing he daa for biomass esimaion was o aggregae idenical daa poins. This aggregaion was done by averaging all poins ha were wihin 1 m of each oher o form a new daa poin. All mapping, daa selecion, and aggregaion were done using Mapinfo (1997) and Verical Mapper (1998) rouines. Inverse Disance Weighing Inverse disance weighing (IDW) is an inerpolaion mehod ha gives more weigh o he closes samples and decreasing weigh as samples become furher from he esimaion poin. Verical Mapper was used o esimae biomass by his mehod. The cell size was 10 m and search and display disances were he defauls, based on a percenage of he oal map area, provided by he sofware. The exponen which described he decay of influence beween poins was kep a he defaul of 2. A maximum of 25 poins were analyzed for each grid node. The number of zones and he minimum number of poins were kep a 1. Inverse disance weighing provides maximum esimaes below and minimum esimaes above hose observed. Voronoi-Neares Neighbor Analysis Neares neighborhood inerpolaion forms a region around each poin so ha he boundary of he region is he perpendicular bisecor beween a poin and each of is neares neighbors. Verical Mapper builds hese regions around daa poins using Delaunay riangulaion. The nework of polygons generaed is called a Voronoi diagram. The area of he region or polygon is hen he weigh for he poin. The Voronoi neares neighborhood mehod mainains observed maximum and minimum values. Arihmeic The arihmeic mehod assumes ha all poins have equal weigh in he esimaion and is simply he arihmeic average of all he poins wihin he polygon. Kriging The spaial srucure of he disribuion in each group was examined using variograms as described by Isaaks and Srivasava (1989). A se of eigh variograms was calculaed from 0 o 157.5 a 22.5 inervals. Iniially he lag disance was se o he average disance beween he daa poins. In some cases, his assumpion abou he iniial lag disance produced variograms wih lile or no spaial srucure. These cases were easily rec-
548 Clayor & Clay Disribuing Fishing Moraliy in Time and Space ognized because he nugge value was equal o or similar o he sill and he model showed no improvemen from using he mean. When his siuaion occurred, he lag disance was reduced or increased unil variograms ha idenified a spaial srucure were obained. Lag olerances were se o 50% of he lag spacing. Angular olerance was generally a 45 bu in some cases i was reduced o 30 o produce variograms ha provided a beer spaial descripion. The variogram for each angle was ploed and he highes variogram value ha occurred was idenified for each angle. The disance corresponding o his value a each angle was hen ploed on a compass plo o deermine he spaial orienaion of he daa poins. This plo was analogous o he rose diagrams discussed in Isaaks and Srivasava (1989). When here was no overall direcionaliy idenified or all he disances were similar, isoropy was assumed and an omnidirecional variogram was modeled for kriging. When direcionaliy was indicaed, an anisoropic variogram was modeled. These analyses were performed using Variowin (Pannaier 1996). A geomeric variogram, wih a common sill bu differing ranges, was assumed for all anisoropic analyses. The final variogram modeling and kriging were as described by Héber e al. (2000). The direcion of he variogram deermined above was imposed on he variogram model assuming a spherical model of he form: Variogram = Co + C [(1.5 (h/a) (0.5 (h/a) 3 ] (Cressie 1991), where Co = nugge; C= sill; h = disance; and a = range The resuls of he variogram modeling were used o obain ordinary kriging esimaes for each region and school srucure analyzed. Kriging is a mehod of esimaing spaial daa such ha poins neares he poin of ineres receive he highes weigh and hose mos disan receive he leas weigh. These weighs are linear combinaions of he available daa. The parameers of he variogram are used o assign hese weighs. Kriging has he advanage over he oher mehods described above because i is a bes linear unbiased esimaor and confidence inervals are readily esimaed (Isaaks and Srivasava 1989). Sock Assessmen Parameers The sock assessmen parameers esimaed for analysis were: densiy of he schools on he fishing grounds as defined above, gillne cach per uni of effor (CPUE) defined as kilograms per ne, gillne and purse-seine cach per meer searched wih searching as defined above, and an exploiaion rae index (ER) defined as he repored cach per biomass esimae from he school as defined above. The source of cach daa for he gillne flee was he 100% dockside monioring program in place in he gillne fishery in 1997. The number of nes used each nigh by he Broke Again, as repored o us each nigh by he capain, was always 5. The average number of nes used by all oher gillneers in he area was also 5 as esimaed by a phone survey conduced
Spaial Processes and Managemen of Marine Populaions 549 each year for he annual assessmen of his sock (Clayor and LeBlanc 1999). The source of cach daa for he purse-seiner was he purchase slip sales recorded a dockside. Saisical Analyses Linear and nonlinear regression echniques, using SAS (1999) procedures, were used o examine he relaionships among he four esimaion mehods, beween densiy and disance searched, and beween cach rae indices and densiy. A P-value < 0.05 was considered significan. The relaionship beween CPUE and densiy was examined using a von Beralanffy ype funcion and a sandard linear regression. A zero inercep was forced in each case because a zero densiy he cach mus also be zero. The von Beralanffy funcion followed he addiive error srucure as defined by Quinn and Deriso (1999) as: CPUE i = CPUE inf {1 exp( k N i )} + e i In his form, CPUE inf is an asympoic value, k describes he rae a which he asympoe is reached, and N i is densiy a each observed densiy i. The linear regression model was defined simply as: CPUE i = b N i + e i Parameers were esimaed wih and wihou logarihmic ransformaion. A nonlinear exponenial model (Exp) and linear reciprocal model were used o deermine he relaionship beween densiy and disance searched on he fishing grounds. The exponenial model was : The reciprocal model was: N i = b 0 exp(b 1 Disance) + e i N i = b 0 + b 1 1/Disance + e i The von Beralanffy and linear models were used o deermine he relaionship beween cach per meer and densiy as described above for purse-seine and gillne boas. In hese analyses, he densiy esimaed from he daa colleced by he Broke Again and he Gemini were compared o heir individual landings as well as o hose of all he boas paricipaing in each of heir flees. Regions for he gillne fishery are defined as: 1, easernmos zone; 2, midzone; and 3, he wesernmos zone of he Picou, Nova Scoia fishing area (Fig. 1A). Regions for he purse-seine fishery are defined as: 1, Rivière-au-Renard; 2, Gaspé side of Chaleur Bay; 3, Poine de la Maisonnee; and 4, Miscou Bank (Fig. 1B).
550 Clayor & Clay Disribuing Fishing Moraliy in Time and Space Figure 1. (A) Fishing and searching racks for Picou area gillneer, Broke Again, collecing acousic daa from 7 Sepember o 30 Sepember 1997. Key o map regions: 1, Easern area; 2, Midzone; 3, Wesern area. (B) Fishing and searching racks for Chaleur Bay area purse-seiner, Gemini, collecing acousic daa from 23 Augus o 20 Ocober 1995. Key o map regions: 1, Rivière-au-Renard; 2, Gaspé side of Chaleur Bay; 3, Poine de la Maisonee; and 4, Miscou Bank. (C) An example of an idenified herring school from Picou area gillneer daa collecion, 26 Sepember 1997. Solid squares are fish densiies 0.0625 kg per m 2, open squares are fish densiies <0.0625 kg per m 2. School is oulined by polygon used o delineae school area.
Spaial Processes and Managemen of Marine Populaions 551 Resuls Biomass esimaes made by each of he four esimaion mehods were all significanly correlaed (P < 0.001, r 2 > 0.96). Differences in esimaes were he leas beween he IDW and Voronoi neares neighbor mehods. Differences were greaes for all comparisons wih he arihmeic mehod. In he resuls, Gillne Boa refers o cach and effor daa only from he Broke Again, he gillneer boa used o collec he acousic daa. All Gillne Boas refers o cach and effor daa from all he boas paricipaing in he Picou, Nova Scoia fishery. Purse-Seine Boa refers o cach and effor daa from he Gemini, he purse-seiner used o collec he acousic daa. Purse-Seine Flee refers o all six purse-seine boas paricipaing in his fishery. In each of hese cases, he disances searched and he esimaed densiy of schools applies only o he boas collecing he acousic daa. The CPUE inf value for he Gillne Boa was larger han he CPUE inf value for All Gillne Boas. The Gillne Boa also reached is CPUE inf asympoe before All Gillne Boas (Fig. 2A). There was a significan curvilinear relaionship (P < 0.005) beween densiy and disance searched on he fishing grounds for he Gillne Boa and Purse-Seine Boa. The fis for he exponenial and reciprocal models were similar for each daa se (Table 1, Fig. 2B,C). Linear and von Beralanffy models significanly explained he relaionship beween cach per meer and densiy (P < 0.001) for Purse-Seine and Gillne Boa models. The linear model provided he bes fi for he Purse- Seine Boa daa and he von Beralanffy model for he Gillne daa and purse-seine flee daa (Table 1, Fig. 2D,E). The reciprocal model significanly explained he relaionship beween exploiaion rae (ER) and densiy for each of he purse-seine and gillne flees (P < 0.001) (Table 1, Fig. 2F). These resuls indicae ha ER increases as densiy decreases. All above-average exploiaion raes for he Purse-Seine Flee occurred afer 13 Sepember 1995 (Fig. 3A,B). All high exploiaion raes in he gillne fishery occurred a he beginning and end of he season when densiies were lowes (Fig. 3C,D). Discussion In his sudy we sough o deermine he relaive rends and relaionships beween densiy and key sock assessmen parameers such as cach raes and exploiaion raes. The high correlaion among he esimaion mehods indicaes ha he mehod used o esimae densiy will no affec conclusions regarding hese relaive relaionships. One reason for his high correlaion may be he raio of disance surveyed o survey area compared o oher survey mehods. For example, during acousic surveys of he souhern Gulf of S. Lawrence he maximum sampling rae does no exceed 0.50 km
552 Clayor & Clay Disribuing Fishing Moraliy in Time and Space Figure 2. (A) Scaerplos and regression lines for relaionship beween gillneer cach raes (CPUE, kg per ne) from boa collecing acousic daa and all boas in he Picou gillne fishery. (B, C) Scaerplo and regression lines for relaionship beween fish densiy and disance searched for fish schools by (B) purse-seine and (C) gillne boa collecing acousic daa. (D, E) Scaerplos and regression lines for relaionship beween cach raes (kg per meer searched) and fish densiy for (D) purse-seine and (E) gillne boa collecing acousic daa. (F) Scaerplos and regression lines for relaionship beween exploiaion rae index (ER) and fish densiy for purse-seine and gillne boa collecing acousic daa.
Spaial Processes and Managemen of Marine Populaions 553 Table 1. Sum of squared residual (SSR) values for indicaed regression models. Gillne All Gill- Purse- Purse-Seine Relaionship Model Boa ne Boas Seine Boa Flee Densiy-Disance Exponenial 114 5.52 Reciprocal 113 5.48 Figure reference Fig. 2C Fig. 2B Densiy-Ca/Me von Beralanffy 0.51 3,770 33 1,090 Linear 0.85 4,480 31 1,210 Figure reference Fig. 2E Fig. 2D Densiy-ER Exponenial 3,700,000 0.17 Reciprocal 4,200,000 0.16 Figure reference Fig. 2F Fig. 2F Figure references are provided. Ca/Me is cach per meer searched, ER is exploiaion rae.
554 Clayor & Clay Disribuing Fishing Moraliy in Time and Space Figure 3. Disribuion over ime by region of ER and fish densiy for (A, B) purseseiner and (C, D) gillne colleced daa. Regions are hose defined in Fig. 1A, B.
Spaial Processes and Managemen of Marine Populaions 555 of ransec surveyed per km 2 of survey area (Clayor and LeBlanc 1999). In his sudy, 2.4 km were surveyed per km 2 of fishing area for he purseseine boa, and 55 km per km 2 of fishing area for he gillne boa. This comparison of survey lengh is imporan because each 100 m is a daa poin. Transecs for acousic and rawl surveys in he souhern Gulf of S. Lawrence are ypically several kilomeers apar (Clayor and LeBlanc 1999). This high sampling rae means ha here is less inerpolaion among he poins han has been encounered in oher invesigaions. An imporan consideraion in he selecion of an esimaion mehod is ha i accouns for he clusering of daa samples. Samples which are close ogeher mus have heir influence reduced in he overall esimae because hey do no represen as large an area as samples ha are more disan from one anoher. The Voronoi, kriging, and IDW mehods accoun for disances beween samples. The arihmeic mehod, which is he unweighed average of all he poins, does no ake clusering effecs ino accoun and i is he reason why his mehod differs he mos from each of he oher mehods (Isaaks and Srivasava 1989). For hese daa and for he purposes of our invesigaion, any of he hree declusering mehods would be sufficien and he Voronoi mehod was chosen primarily for convenience of implemenaion. The nighly limi imposed on each boa in he gillne fishery is similar o he esimaed asympoic CPUE of 1,353 kg per ne for he gillne boa model (Fig. 2A). The boa collecing he acousic daa used 5 nes per nigh. The 7,000 kg nighly fishing limi hen corresponds o a CPUE of 1,400 kg per ne. The maximum CPUE was reached a a densiy of abou 1 kg per m 2 while he densiies observed during he fishing season ranged up o 10 kg per m 2 (Fig. 2A). The maximum CPUE for he enire flee was lower han for he individual collecing he acousic daa bu was sill reached a a densiy of abou 1 kg per m 2 (Fig. 2A). These resuls indicae here is lile change in hese CPUE over mos of he densiies observed during he fishing season and hey would be of limied use in racking daily abundance rends in his fishery. Many fisheries depend upon volunary logbook programs o obain hese ypes of cach rae informaion and i is ofen he individuals wih he highes ineres and highes cach raes ha paricipae in hese programs. If hey are able o consisenly cach heir nighly limis regardless of densiy, hen relaively lile informaion is being obained from such logbook CPUE for he assessmen of he sock. As a resul, he effecs of nighly limis wheher because of boa capaciy, managemen, or marke quoas, mus be considered in inerpreing flucuaion in CPUE for assessmen purposes. Oher problems in using hese ypes of daa in assessmen models may resul from nonlinear relaionships beween CPUE and abundance. Many assessmen models require a linear relaionship (Hilborn and Walers 1992) and logarihmic ransformaions are ofen used o mee his requiremen. In our resuls, no linear relaionship was obained for he gillne CPUE, even afer log-ransformaion.
556 Clayor & Clay Disribuing Fishing Moraliy in Time and Space The purse-seine CPUE (cach per se) shows no relaionship wih densiy. This may be explained by he imporance of search, effor, and caching efficiency for his ype of gear, which resuls generally in poor relaionships beween CPUE and abundance. Consequenly, CPUE indices, defined as cach per ne in he gillne fishery or cach per se in he purseseine fishery, are no useful indices for racking daily populaion rends and exploiaion raes. A principal objecive of his sudy has been o provide managers wih a ool for idenifying and eliminaing high exploiaion raes as a sep in prevening overfishing. The relaionship beween exploiaion rae and densiy implies here is a hreshold densiy beyond which here will be no change in exploiaion rae. The hreshold may be a funcion of he boa limi and may be differen if here were no nighly limis, bu we have no esed his hypohesis. Neverheless, exploiaion raes ha are considerably above average occur only a low densiies for boh ypes of flees. If hese exploiaion raes are resriced in ime and space, hey could be eliminaed by reduced or reallocaion of effor by managers. For example, he gillne fishery in 1997 was scheduled o open on 1 Sepember. The individuals fishing in he area volunarily delayed heir season because of low densiies observed during acousic surveys conduced during he firs week of Sepember. This delay no doub had he effec of eliminaing oher high exploiaion raes from his fishery during 1997. This ype of acousic daa may no be easy o collec and analyze for all laboraories. Thus, we invesigaed wheher CPUE, kg per ne, or cach per meer would be useful indirec measures of emporal rends in exploiaion raes. There was a significan relaionship beween cach per meer and densiy for boh flees. As a resul, where rends in densiy and exploiaion rae occurred i would be expeced ha cach per meer could be used as an indirec measure of emporal rends in exploiaion rae. Gillne CPUE (kg per ne) was below average a he beginning of he season, bu here was lile conras beween early and lae season kg per ne CPUE and hey are unlikely o be a useful ool for managers o idenify high in-season exploiaion raes. Throughou his paper we have resriced our inerpreaions of acousic biomass esimaes o hose of relaive raher han absolue esimaes. Some of he facors ha preclude an absolue biomass inerpreaion are: he variabiliy of backscaering in high arge concenraions, he relaionship beween arge srengh and fish size, vessel avoidance, and acousic exincion from near-surface reverberaion (MacLennan and Simmonds 1992, Clay and Clayor 1998, Fréon and Misund 1999). The fisheries we examined occur over a shor period of ime and on a single species in paricular phases of is life hisory, eiher as spawning or feeding aggregaions. As a resul, our esimaes are likely o be relaively consisen and while we canno claim ha we have esimaes of absolue biomass of he schools, spaial and emporal changes in exploiaion rae in hese fisheries may be idenified from changes in relaive indices.
Spaial Processes and Managemen of Marine Populaions 557 Herring fisheries in he souhern Gulf of S. Lawrence occur on several spawning beds a he same ime. The simulaneous occurrence of hese fisheries makes i impracical, wih curren resources, o use hese rends for making in-season adjusmens in managemen plans. Thus, we view he idenificaion of spaial and emporal rends in exploiaion raes as par of an annual sock assessmen process. This process would be used o derive decision rules ha govern he fishery during he season (Clayor 2000). The success of hese rules in disribuing exploiaion raes, relaive o he size of schools being fished, would be evaluaed a he end of he season. This evaluaion would subsequenly form he basis for advising on changes in decision rules. We expec ha he greaes poenial for using hese analyses for in-season managemen occurs where a single flee sequenially harvess a series of sock componens in ime and space. Collecing acousic daa and informaion on searching effor has several advanages over more radiional forms of daa collecion for fisheries sock assessmens. They provide marked improvemen over kg per ne indices, paricularly when here are daily or rip limis on caches resuling from regulaory, marke, boa capaciy, or environmenal sources. These echniques apply o a wide variey of fisheries where he species of ineres is deecable by acousic mehods eiher as schools or individuals and are paricularly suiable for single species pelagic fisheries. Acknowledgmens We would like o hank he many people involved in he souhern Gulf of S. Lawrence herring indusry who helped wih his projec. Funding for his projec came from he Naional Hydroacousics Program, Human Resources and Developmen, he Province of Nova Scoia, Career Edge Programs, and he Gulf Nova Scoia Herring Federaion. References Clay, A., and R. Clayor. 1998. Hydroacousic calibraion echniques used for souhern Gulf of S. Lawrence herring fishing vessels, 1997. Canadian Sock Assessmen Secrearia Research Documen 98/96. Canadian Sock Assessmen Secrearia, 200 Ken S., Oawa, Onario, Canada, K1A 0E6. 12 pp. Clayor, R. 2000. Conflic resoluion in fisheries managemen using decision rules: An example using a mixed-sock Alanic Canadian herring fishery. ICES J. Mar. Sci. 57:1110-1127. Clayor, R., and C. LeBlanc. 1999. Assessmen of he NAFO Division 4T souhern Gulf of S. Lawrence herring sock, 1998. Canadian Sock Assessmen Secrearia Research Documen 99/54. Canadian Sock Assessmen Secrearia, 200 Ken S., Oawa, Onario, Canada, K1A 0E6. 169 pp.
558 Clayor & Clay Disribuing Fishing Moraliy in Time and Space Clayor, R., A. Clay, and C. LeBlanc. 1998. Area assessmen mehods for 4T fall spawning herring. Canadian Sock Assessmen Secrearia Research Documen 98/97. Canadian Sock Assessmen Secrearia, 200 Ken S., Oawa, Onario, Canada, K1A 0E6. 63 pp. Clayor, R., A. Clay, E. Waler, J. Jorgenson, M. Clémen, and A. S.-Hilaire. 1999. Naional Hydroacousic Program clien paricipaion projecs: Flee acousics, parnership review, poenial users, equipmen invenory. Can. Tech. Rep. Fish. Aqua. Sci. 2272. 76 pp. Clayor, R., C. LeBlanc, J. Dale, G. Nielsen, L. Paulin, C. MacDougall, and C. Bourque. 1996. Assessmen of he NAFO Division 4T souhern Gulf of S. Lawrence herring sock, 1995. DFO Alanic Fisheries Research Documen 96/79. 136 pp. Cressie, N.A.C. 1991. Saisics for spaial daa. Wiley and Sons, New York. 900 pp. Fooe, K.G. 1987. Fish arge srenghs for use in echo inegraor surveys. J. Acous. Soc. Am. 82:981-987. Fréon, P., and O.A. Misund. 1999. Dynamics of pelagic fish disribuion and behaviour: Effecs on fisheries and sock assessmen. Fishing News Books, Oxford. Héber, M., A. Héber, E. Wade, T. Suree, D. Giard, P. DeGrâce, M. Biron, and M. Moriyasu. 2000. The 1999 assessmen of snow crab, Chionoecees opilio, sock in he souhwesern Gulf of S. Lawrence (Areas 12-25/26, E and F). Canadian Sock Assessmen Secrearia, 200 Ken S., Oawa, Onario, Canada, K1A 0E6. 57 pp Hilborn, R., and C.J. Walers. 1992. Quaniaive fisheries sock assessmen. Chapman and Hall, New York. 570 pp. Isaaks, E.H., and R.M. Srivasava. 1989. Applied geosaisics. Oxford Universiy Press, New York. 561 pp. MacLennan, D.N., and E.J. Simmonds. 1992. Fisheries acousics. Chapman and Hall, London. Mapinfo. 1997. Mapinfo professional version 4.5. Mapinfo Corporaion, One Global View, Troy, New York 12180-8399, USA. 557 pp. Pannaier, Y. 1996. Variowin 2.2. Springer-Verlag, New York. 89 pp. Quinn II, T.J., and R.B. Deriso. 1999. Quaniaive fish dynamics. Oxford Universiy Press, New York. 542 pp. SAS. 1999. SAS/STAT User s guide. SAS Insiue, Cary, Norh Carolina. 1848 pp. Verical Mapper. 1998. Verical Mapper version 2.1.1. Norhwood Geoscience Ld., 89 Auriga Drive, Nepean, Onario, Canada K2E 7Z2. 369 pp.
Spaial Processes and Managemen of Marine Populaions 559 Alaska Sea Gran College Program AK-SG-01-02, 2001 In-Season Spaial Modeling of he Chesapeake Bay Blue Crab Fishery Douglas Lipon and Nancy Bocksael Universiy of Maryland College Park, Deparmen of Agriculural and Resource Economics, College Park, Maryland Absrac The Chesapeake Bay blue crab resource is characerized by a high degree of naural variabiliy, which masks srucural relaionships beween harvess and populaions when considered on an annual basis. However, wihin a fishing season here appears o be saisically deecable relaionships beween harvess of differen marke classes of crabs in boh a spaial and emporal dimension. These relaionships are saisically modeled and he parameer esimaes are used as inpu o an opimizaion model of harves. By adjusing effor and landings by ime and area, fishermen can achieve higher revenues from he same biomass and level of effor. The lack of sufficienly long ime series daa conaining appropriae spaial informaion is he major consrain o applying his approach. Inroducion Blue crab (Callineces sapidus) is currenly he mos valuable produc harvesed from he Chesapeake Bay. In 1998, he oal repored Chesapeake Bay harves was 65.5 million pounds, wih an ex-vessel value of $70.7 million. The saes of Maryland and Virginia aemp o manage he harves wih a complex se of regulaions which include size limis, cull rings in crab pos, resricions on fishing days, hours, amoun of gear ha can be used, where gear can be placed, license limiaion, ec. There is lile, if any, published evidence o demonsrae ha his se of rules conribues o he saed managemen goals of opimizing long-erm use of he resource (CBP 1997). Recen concerns have focused on he healh of he Chesapeake Bay crab populaion. To address his, a major sock assessmen was underaken of he blue crab resource o deermine he saus of he sock, and deermine wheher addiional harves resricions are necessary (Rugolo
560 Lipon & Bocksael Spaial Modeling of he Blue Crab Fishery e al. 1997). The resuls of he sock assessmen have generaed a good deal of conroversy regarding heir inerpreaion. Par of he conroversy sems from he sensiiviy of model resuls o parameerizaion of he sock assessmen model. For example, he esimaes of naural moraliy used in he Rugolo model require an assumpion regarding he heoreical maximum age i is assumed crabs can live o. The curren range being debaed, 4-8 years, yields very differen resuls in he model abou wheher or no he resource is currenly biologically overfished. The issue is no easily resolved because of he difficuly in aging and agging blue crabs, or using oher mehods o esimae naural moraliy. Focus on his level of deail abou he sock assessmen model ignores a major facor in crab populaion dynamics, which is ha random climaic and oceanographic facors dominae he populaion dynamics of he resource and obscure he populaion relaionships ha are explici in he sock assessmen modeling. Consequenly, when compared wih acual daa, he models do a poor job of predicing how regulaions change curren harves and he ulimae impac on fuure populaions of blue crabs and heir harves from he bay. Recruimen o he blue crab fishery, which occurs hroughou he year in he Chesapeake Bay, is a random variable ha up o his poin canno be accuraely prediced from year o year using sandard sock assessmen echniques ha rely only on sock-recruimen relaionships. When faced wih an inabiliy o link recruimen o spawning sock biomass, he sandard approach for fishery biologiss is o explore yield-per-recrui relaionships (Thompson and Bell 1934, Beveron and Hol 1957). The focus is herefore on in-season managemen, obaining he greaes value from he given availabiliy of crabs. However, yield-per-recrui models sill require esimaes of populaion parameers such as naural moraliy, growh, and gear seleciviy, which can have a large degree of uncerainy. For example, in rying o characerize crab growh Smih (1997) developed a complex model of crab moling relaed o emperaure exposure over ime (degree days). Despie his level of uncerainy, Miller and Houde (1998) recenly esimaed a deerminisic yield-per-recrui model for Chesapeake Bay blue crab. As an alernaive o he numerical modeling approaches discussed above, his sudy acknowledges he inheren random naure of blue crab abundance hroughou is life cycle in Chesapeake Bay. By aking a more saisically oriened approach, we address he inabiliy o adequaely capure he srucural relaionships ha exis in he blue crab populaion and hus rely on a reduced form approach o help predic consequences of regulaory changes. The approach also reflecs he heerogeneous naure of he crab fishery, which resuls from he differenial migraion of crabs hroughou he bay during he harves season, and he disribuion of fishing and processing indusries ha have developed around his migraion paern. Spaial allocaion of fishing effor is guided by he spaial disribuion of fish abundance, and his appears o be he case in he Chesapeake Bay blue crab fishery.
Spaial Processes and Managemen of Marine Populaions 561 Similar economic approaches o in-season fisheries managemen issues were sudied by Önal (1996), who used mulilevel opimizaion echniques o sudy sequenial exploiaion in he Gulf of Mexico shrimp fishery, and Criddle (1996), who simulaed Yukon River salmon fisheries as a Markov process. Sequenial exploiaion refers o he fac ha in hese species, as in blue crab, exploiaion a a paricular ime and place ineracs wih exploiaion of he same sock a anoher ime and place. The presen sudy more closely resembles Criddle s approach bu differs from boh previous sudies in ha i relies on saisical modeling of he producion relaionships. Anoher major difference wih he Önal and Criddle sudies is ha he sequenial naure of he shrimp and salmon fisheries is essenially unidirecional. For example, salmon swim upsream and a negaive relaionship is expeced beween downsream harves and upsream availabiliy of fish. Blue crab migraion is more complex han hese species during he fishing season and differs for males and females. The basic approach in his paper is o saisically relae harves of differen classes of crabs in a given segmen of Chesapeake Bay in a given monh o harvess of relaed classes of crabs in oher pars of he bay in laer monhs. Classes of crabs refer o he differen marke caegories repored in he Maryland landings daa: #1 males; #2 males; females; mixed; and sof and peeler. For example, he harves of #2 male crabs in he mainsem porion of he bay is posulaed o have a negaive effec on he harves of #1 male crabs in a ribuary of he bay in fuure monhs, since he #2 crabs ha are no harvesed or do no succumb o naural moraliy evenually mol o become #1 crabs. Since we can observe he harvess of he differen size of crabs a differen imes, i is possible o model his relaionship saisically wihou knowing he explici underlying biological relaionships, such as he specific moraliy, growh (moling), or migraion componens. Since he differen crab classes have differen marke demands and he demand varies by season, he profiabiliy of harves will differ depending on he harves paern. Once hese producion relaionships and marke demands are esimaed, i is possible o opimize he sysem by conrolling harves of crab classes during he season. The challenge is o uilize he ime series and spaial naure of he crab harves daa o improve he efficiency of esimaes of he producion relaionships beween an area a one period of ime o anoher area a anoher period of ime. In paricular, he porion of he variabiliy ha is correlaed across ime and space is expeced o conain much of he informaion explaining variabiliy in caches. In he following secion, he general framework for an in-season harves model is developed. This is followed by developmen of a model ha is esimaable given curren daa limiaions. Some discussion of he economeric issues ha may arise in performing he model esimaion is provided. Since his is a work in progress, an empirical example is included o demonsrae he uiliy of he approach, bu more work is needed o obain a working model ha can be used for managemen purposes.
562 Lipon & Bocksael Spaial Modeling of he Blue Crab Fishery An Economeric In-Season Harves Model Tradiionally, he approach o modeling he blue crab fishery would assume some fishery producion funcion: H,i,j = f (E,i, X,i,j ) (1) where H,j,k is he harves in ime period, i indexes he area of harves, and j is he marke class of crab. E,i is a measure of fishing effor such as number of crab pos fished and X,i,j is he fishable populaion size. The dynamics of he populaion are implici in he relaionship beween curren populaion size and he populaion in he previous ime period (Conrad and Clark 1987): X,j,k = g(x 1,j,k, H 1,j,k ) (2) The g() funcion would ypically be relaed o naural moraliy, growh, migraion, and recruimen paerns. However, because of he predominance of random facors ha affec moraliy and recruimen in he crab populaion, he funcion should conain an error erm making populaion a ime a random variable. For he Chesapeake Bay blue crab fishery, when he ime sep is annual he error erm is very large relaive o he nonsochasic par of he funcion, so ha he large error ends o mask whaever srucural relaionship is presen. When i is concluded ha for Chesapeake Bay blue crab here is no sock recruimen relaionship (Miller and Houde 1998), i is his large error erm ha is being observed. In conras, if he ime sep being modeled is less han a year, i may be ha he error erm is smaller relaive o he srucural dynamics. Thus, i may be possible o deec he influence of harves a a paricular area and ime period on subsequen populaion and harves levels in he same and oher areas. We will be esing o see if ha is he case in he empirical secion of his paper. In addiion o he saisical approach menioned above, anoher difference in he approach aken in his paper wih ypical fisheries models is he inclusion of he area index (i) for he sock. Socks are usually managed as a uni, and he spaial disribuion of he populaion is ypically no a major facor in allocaion of harves under a managemen regime unless he sock crosses sae or inernaional boundaries. In our model, where he harves akes place has imporan ramificaions because i may have an effec on he relaive abundance of crabs in oher marke caegories in oher areas, and also due o he fac ha differen segmens of he crab processing indusry have locaed around radiional harves areas. Shifing harves paerns spaially, will affec he coss of hese operaions ha will be refleced in heir derived demands for differen marke caegories of crabs.