S H O A L I N G D Y N A M I C S A N D A B U N D A N C E E S T I M A T I O N : A T L A N T I C B L U E F I N T U N A (THUNNUS THYNNUS) Nathaniel K . Newlands M.Sc , University of Calgary, 1997 B.Sc , University of Guelph, 1995 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY RESOURCE MANAGEMENT AND ENVIRONMENTAL STUDIES by in THE FACULTY OF GRADUATE STUDIES We accept this thesis as conforming to the reqjLiired standard The University of British Columbia June, 2002 © Nathaniel K . Newlands, 2002 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Resource Management and Environmental Studies The University of British Columbia Room 426E, 2206 East Mall Vancouver, B.C., Canada V6T 1Z3 Date: Abstract The Atlantic bluefin tuna (Thunnus thynnus) is a long-lived, highly migratory species that attains sizes of 2.20 m, and weights of 300 kg or more. Adults undertake cyclic migrations between coastal feeding zones, offshore wintering areas and spawning grounds. During June through October, bluefin tuna are common off the eastern United States and Canada, entering the Gulf of Maine, a semi-enclosed continental shelf area. The population is currently believed to have plummeted to 20% of 1970's levels, yet there is significant uncertainty in their population status and size. This thesis investigates bluefin tuna movement, aggregation and distribution, size and structure of bluefin shoals, and examines how these factors can affect the measurement bias and estimation uncertainty of population abundance. Data analysis methods applied include: interpolation of movement data, Lomb spectral analysis, statistical bootstrap simulation, Kalman filtering, and geostatistics. A n automated digital image analysis system (SAIA) is developed for the three-dimensional analysis of fish shoal structure. A theoretical model is also formulated to describe the movement and behaviour of shoaling tuna leading to changes in shoal aggregation, distribution and abundance. The preci-sion in abundance estimation of random, systematic, stratified, and spotter-search aerial survey sampling schemes are simulated under changes in the size, distribution and ag-gregation of shoals. Correlated and biased random walk models can predict lower and upper limits on displacement and spatial movement range over time. Bluefin tuna move by respond-ing to changes in temperature gradients and to the local abundance of prey, preferring to be situated in the warmest water available, while also showing a weak response to flow and bathymetric gradients. The effect of aggregation on the distribution of shoals considerably reduces precision of population estimates under random transect sampling. Stratified sampling is shown to increase precision to within 5%, with adaptive stratifica-tion leading to further increases. Movement and shoal aggregation introduce relatively equal levels of bias and uncertainty in estimating abundance. Results indicate that re-liable estimates of abundance can be attained under systematic and stratified survey schemes. However, further reductions in uncertainties associated with the shoal aggre-gation process are necessary to achieve acceptable precision in abundance estimation. ii Table of Contents Abstract ii List of Tables vii List of Figures xiii Acknowledgments xxx 1 Introduction 1 1.1 Research objectives ' ; 1 1.2 Individual-based spatial models of fish populations 4 1.3 Variability and patterns of fish population abundance 6 1.4 Atlantic bluefin tuna 9 1.5 Study region: Gulf of Maine/Northwestern Atlantic 14 1.6 Fishery-dependent and independent indices of abundance 18 2 Individual Movements 34 2.1 Interpolation of the movement observations 36 2.2 Move-speed and turning angle distributions 44 2.3 Move-speed and turning angle autocorrelations 47 2.4 Spectral identification of movement modes 58 2.5 Space trajectories 69 2.6 Theoretical movement model predictions 69 2.7 Kalman filtering of geoposition data from light-archival data 80 iii 2.8 Significance testing: observations and model predictions 92 2.9 Summary 110 3 Shoal Structure and Behaviour 113 3.1 Supervised automated image analysis scheme (SAIA) 117 3.2 Shoal formations 149 3.3 SAIA calculations of shoal formation structure 189 3.4 Convex hull refinement of ellipsoidal shoal structure 211 3.5 Principal component analysis of structural variables 217 3.6 Shoal dynamics 231 3.7 Summary 243 4 Spatial, Individual-Based Model of Bluefin Tuna 251 4.1 Model and simulation framework 252 4.2 Initial and boundary conditions 263 4.3 Seasonal population 266 4.3.1 Seasonal immigration and emigration of shoals 270 4.3:2 Shoal size frequency distribution 275 4.4 Lagrangian equations 276 4.5 Movement and behaviour dynamics 280 4.5.1 Individual/shoal fitness: foraging rate and predation risk 280 4.6 Multi-layered spatial environment 285 4.7 Model validation tests 309 4.8 Summary and future work 337 5 Abundance Estimation: Measurement and Precision 342 5.1 Survey sampling . . 345 5.2 Analysis of aerial survey data (1994-96) 350 iv 5.3 Survey measurement schemes 411 5.4 Results, summary and future work 423 6 Summary and Conclusions 441 6.1 Regional population abundance 442 6.2 Movement: immigration and emigration 443 6.3 Spatial aggregation and distribution 445 6.4 Shoal size and structure 446 6.5 Movement: foraging, short and long-range searching 453 6.6 Interaction of individuals and shoals 456 Bibliography 461 Appendices 495 A Abbreviations and Notation 495 A. l Abbreviations 495 B Chapter 2: Background, Derivations, Extended Results 497 B. l Move-speed and turning angle distributions 497 B.2 Spectral identification of movement modes 502 B. 3 Space trajectories 512 C Chapter 3: Background, Derivations, Extended Results 522 C. l Shoal size and formation: shoal structure histograms 522 C . l . l Nearest-neighbour distance (NND) 522 C.1.2 Frequency of nearest neighbours 525 C.1.3 Bearing angle between nearest-neighbours (BA) 528 C.l .4 Shoal polarization 531 v C. 2 Convex hull refinement of ellipsoidal shoal structure 534 D Chapter 4: Background, Derivations, Extended Results 540 D. l Seasonal population 540 D.2 Shoal size frequency distribution 545 D.3 Lagrangian equations 548 D.4 Adaptive step-size Runge-Kutta integration 551 D.5 Movement and behaviour dynamics 552 D.5.1 Movement correlations, modes and mode-switching events . . . . 552 D.5.2 Move-speed movement mode (mi ,777,2) variation 552 D.5.3 Move-angle operator 553 D.5.4 Move-speed and turning angle autocorrelation functions 555 D.5.5 Shoal mixing: join/leave/stay decisions, mode alterations 556 D.5.6 Neighbour individuals: attraction and repulsion 564 D.5.7 Movement response to environment and prey 565 D. 6 Multi-Layered spatial environment 568 D.6.1 Observed environmental association of shoals 568 D.6.2 Observed movement response to environmental gradients 577 E Chapter 5: Background, Derivations, Extended Results 588 E. l A review of spatial statistics in survey design 588 F Curriculum Vitae 598 vi List of Tables 1.1 Summary of Objectives, Data Sources and Data Analysis Techniques . 23 1.2 Table 1.1 continued 24 1.3 Table 1.2 continued 25 1.4 Table 1.3 continued 26 1.5 Table 1.4 continued 27 1.6 Summary of Objectives, SIBM Model and Validation/Confidence Tests 28 1.7 Table 1.6 continued 29 1.8 Table 1.7 continued 30 1.9 Table 1.8 continued 31 1.10 Table 1.9 continued 32 1.11 Table 1.10 continued 33 2.12 Summary of geolocation (GPS) and depth records from hydro-acoustic telemetry of B F T (N=l l ) . Start and End times for each record are in format of HH:MM:SS and Elapsed time, ET(s) 37 2.13 Statistics of move-length (k), time duration (TJ ) , vertical inclination (#j), directional ((pi) and turning (c/?j) angles in movement observations of B F T , for rii sampled positions, and shoal size, S 42 2.14 Depth-correlated data summary for hydroacoustic tracking of B F T (N=10). 43 2.15 The number of segments, /V(mi) and N(rri2), for mi and m.2 modes, and the number of mode-switching events, S(m\^) identified within the individual B F T movement trajectories from the Lomb spectral analysis. 61 2.16 Modal (mi and m^) statistics of move-length (lt), time duration (ri), ver-tical inclination (<9j), directional (fa) and turning (ipi) angles calculated for the observed individual movements of B F T 66 2.17 Estimates of Fork Length (FL)(m), Longitude (LGT)(°W), Latitude (LAT)(°N), elapsed time (ET(d)), mean speed (v(m/s)) and diffusion, D(nm 2/d) for short-term light archival tagging movement observations of B F T (N = 7) (1998-1999), where d denotes days 84 2.18 Long-term light archival tagging movement observations of B F T (N=3, 1999-2000) with time at liberty/elapsed time (ET) ranging from 77-279 days (d). Parameter estimates of advection velocities (u,v) and diffusion (D) obtained from Kalman filtering for BRW, RW models. Estimates of diffusion (D) as would be calculated with a start and end track location without archived geolocation data (i.e., single-point pop-up) (DM) are also shown 85 vii 2.19 Results of fitting move-speed autocorrelations (ACF) observed from hy-droacoustic tracking of BFT to the general form v = (Vj) exp~^TN, for t = nAt, over n successive lags between moves. These results are used to determine values for persistence time, TJV and shoal searching efficiency for each movement path 97 2.20 Searching efficiency and diffusion estimates based on self-intersections of observed R^et o b s over time with Rnet,CR\v predictions. S - shoal size, T - total foraging time, AT/v - mean foraging time, (T — ATN) - searching time, TTV - persistence time, - characteristic length, D - diffusion, mean dispersal area - (RT-&TN)-> swath width - b^, self-intersection parameter - v, searching distance - LT-ATN, searching efficiency - SN 99 2.21 Testing of observed statistic (A 06 S) for individual movements of BFT to 95% confidence intervals (2cr-intervals) about the expected values, BCRW (see Equation 2.72) for the BCRW, and AT,CRW (see Equa-tion 2.71) for CRW theoretical models 101 3.22 Summary of the spotter observer aerial sampling records of BFT shoals. 120 3.23 Summary of shoal images sorted by background quality: From (Cl)-(C5) in order of decreasing image quality. (*) number of shoal images in class C l were analyzed in the image analysis and results presented. The 1994 images were used in testing of the SAIA image analysis scheme and post-analysis algorithms for which selected results were compiled. Main results were compiled for years 1995-96 122 3.24 Monthly frequencies for analyzed shoal images. The 1994 images were used in testing of the SAIA image analysis scheme and post-analysis algorithms for which selected results were compiled. Main results were compiled for years 1995-96 122 3.25 Definition of variables in post-processing of SAIA digital image analysis used in the measurement and characterization of BFT shoal structure and behaviour. (-) units denote dimensionless measures. 138 3.26 Reduced yf/df for manual (Nm), automated (Nc) and final-corrected, (Ns) of SAIA image analysis school size estimates for each year, 1994-96, shown in Figures (3.44)-(3.46) 145 3.27 Reduced x2/df for manual {Nm), automated (Nc) and final-corrected, (Ns) of SAIA image analysis school size estimates for different shoal formations pooled over years 1994-96. Formations are denoted as: A-cartwheel, B-surface-sheet, C-dome, D-soldier, E-mixed, F-ball, G-oriented shown in Figures (3.51-3.53) 150 viii 3.28 Frequencies of different shoal formations for analyzed shoal images. For-mations are denoted as: A-cartwheel, B-surface-sheet, C-dome, D-soldier, E-mixed, F-ball, G-oriented (H-solitary individuals). The percentage in the number of images for each formation type in each year with respect to the total numbers are provided in brackets 152 3.29 B F T shoal size statistics (mean shoal size, Ns, standard error in the mean (SE), 95% confidence intervals (C.I) and minimum and maximum shoal size for identified structural formations pooled across years 1994-96 (Refer to Figure 3.50) 152 3.30 Monthly mean fork-length(m) for B F T across ages 0-10+ (ICCAT). . . 159 3.31 Reduced x2/df statistics for shoal size-sorted observed histogram fre-quencies of N N D 174 3.32 Same as Table 3.31 of nearest-neighbour distance (NND) for formation type 174 3.33 Reduced x2/df statistics for shoal size-sorted frequency of nearest neigh-bours. Unless otherwise indicated, degrees of freedom (df=36) 178 3.34 Same as Table 3.33 of nearest neighbour frequency for formation type. . 178 3.35 Reduced x2/df statistics for shoal size-sorted observed histogram fre-quencies of nearest neighbour bearing angle (BA) 183 3.36 Same as Table 3.35 of nearest neighbour bearing angle (BA) for forma-tion type 183 3.37 Reduced x2/df statistics for shoal size-sorted observed histogram fre-quencies of shoal polarization. Unless otherwise indicated degrees of freedom (df=20) 188 3.38 Same as Table 3.37 of shoal polarization for formation type 188 3.39 Summary of linear regression of convex hull refinement of ellipsoidal surface area (SAS), and volume (Vs) denoted as SAh and 14, respectively.213 3.40 Surface area and volume estimates for ellipsoidal (SAS, Vs), and convex hull (SAh, 14) approximations to the shape of B F T shoal formations. Estimates of the mean number of edge individuals, Np, and shoal size, Ns (from Table 3.29), for each formation are also provided 214 3.41 Cartwheel formation: P C A correlation matrix and PC1-PC7 eigenvec-tors for shoal variables 221 3.42 Same as Table 3.41 for surface-sheet formation 222 3.43 Same as Table 3.41 for dome formation 223 3.44 Same as Table 3.41 for soldier formation 224 3.45 Same as Table 3.41 for mixed formation 225 3.46 Same as Table 3.41 for ball formation 226 3.47 Same as Table 3.41 for oriented formation 227 ix 3.48 B F T formation frequencies with associated visual shoal size estimates from aerial surveys conducted, 1994-96. These observations provide a larger set of observed frequencies than data set corresponding to quality classed aerial shoal images selected for the SAIA image analysis 233 3.49 Reduced X2/df statistics comparing observed frequency of occurrence at time-of-day (hrs.) between B F T formations. See Table 3.22 for sample sizes of the formations determined by aerial observers 236 3.50 Same as Table 3.49 comparing observed frequency of occurrence at time-of-day (hrs.) between years 1994-96 236 3.51 Classification summary of B F T shoal formations based on approximate means and range in values of internal and external variables. Listed are packing density, ps(BL~3), mean shoal size, N3±5NS, nearest-neighbour distance, NND(BL) , mean number of first nearest neighbours, NNS, modal values for bearing angle between first neighbours, BA(°), max-imum number of edge individuals for maximum observed shoal size, Na, observed range in shoal polarization ( — $ s ) , and a generalized shape description 249 3.52 Summary of P C A analysis of B F T shoal formations. Listed is the per-centage of variance explained by the first two principal components (PC1,PC2) for each formation type, and shoal variables listed in order of decreasing positively correlation associated with P C I (shoal shape) and PC2 (internal structure) 250 4.53 Associations between model variables in forming a reduced model rep-resentation, denoted as model, M . . . . . 254 4.54 Fixed model parameters (N=19 (no grid layers), N=27 (5 grid layers)), aggregated parameter settings, and variables in simulation for process test-results 256 4.55 Definition of SIBM model parameters and variables. (-) units denote dimensionless measures 259 4.56 Aggregation of model variables/parameters into reference categories: en-vironment, population, shoal and individual-scales 260 4.57 Test results of cross-correlation coefficient at zero time-lag (where time-lag interval coincides with mean move-duration) for observed hydroa-coustic movements of B F T (N=10) and each environmental variable. . 306 5.58 Nonlinear least-squares fitting of sigmoidal function for cumulative S P U E versus time (days). r=5 fitting parameters (a,b, c,tQ, SPUEt0), degrees of freedom (d.f.)=(n-r), where k is the number of independent variables (k=l: time) 363 5.59 Monthly sightings-per-unit-effort (SPUE)(individuals/1.8km) for move-ment filters, no depth correction 368 x 5.60 Same as Table 5.59 but with depth correction/calibration 371 5.61 Depth-corrected survey abundance (1994-96) with calibration coefficients based on superimposed behavioural movement modes ( r a i , T O 2 ) and asso-ciated movement depth distribution. V P A Abundance refers to estimates of their abundance (numbers) in the West-Atlantic, for comparison to survey estimates for the Gulf of Maine region 372 5.62 Results of fitting age-specific V P A abundance for the west-Atlantic with transfer parameters and survey calibration coefficients, N=10,000 iter-ations, precision<0.001 using Conjugate-Gradient optimization. Cal-culated x2/df statistics indicate large significant differences using the three available annual estimates (1994-96) in the observed (survey) and predicted (west-Atlantic abundance for ages 7+ and transfer to/from the Gulf of Maine region) time-series. The best-fit, indicated as '*' is obtained for age 7+ of the total western Atlantic abundance, with asso-ciated transfer portions at the end of each year, t 379 5.63 Estimation of aggregation coefficient from fitting of observed shoal size ' frequency distributions to Weibull distribution function (a,b,c,x0,y0), and transformed parameter for power-law/exponential decay function form. Mean and variance of the number of shoals are used to calculate the aggregation coefficient, k (negative binomial spatial distribution of shoals). Parameter standard errors (SE), and associated 95% confidence interval ranges (C.I.) on transformed parameters are provided 392 5.64 Relative abundance estimates, spotter-aerial surveying (1994-96) 405 5.65 Number of shoals and size estimates for BFT in the GOM 405 5.66 Daily observer transects/effort estimates, spotter-surveying (1994-96). . . . 405 5.67 Daily encounter rate of BFT shoals, spotter-surveying (1994-96) 405 5.68 Population density estimates of BFT in the GOM 405 5.69 Summary of diffusion estimates (D) (km2/d) (un-corrected/corrected val-ues) for B F T calculated from various data sources used in analyses: U l -trasonic telemetry/hydroacoustic tracking (UT)(n=10), Short-term light archival (SLA)(n=6), Long-term light archival (LLA)(n=3), Single-point approximation of L L A observations (n=3), and Single-point pop-up tag-ging (SPl)(n=43) 408 5.70 Comparison of calculated B F T diffusion estimates (nm - nautical miles, km - kilometres) with those of other species of tuna available in the literature. B F T - Northern Bluefin (Thunnus thynnus), B E T - Bigeye (Thunnus obesus), Y F T - Yellowfin (Thunnus albacares), A B T - Albacore (Thunnus alalunga), SJT - Skipjack (Katsuwonus pelamis) 410 5.71 Definition of survey model parameters and variables. (-) units denote dimensionless measures 413 xi D.73 Univariate test results for statistical differences in observed movements of B F T (hydroacoustic tracking, N=10) comparing the cumulative distri-butions in relation to sea-surface temperature (SST). Table entries show the value of the test statistic and in brackets the probability (p value) for having the test statistic value (randomized), equal to or greater than the observed value 579 D.74 Same as Table D.73 for water flow 581 D.75 Same as Table D.73 for bathymetry 583 D.76 Same as Table D.73 for chlorophyll-a (phytoplankton concentration). . 585 D.77 Same as Table D.73 for zooplankton (Calanus finmarchicus) abundance. 587 xii List of Figures 1.1 Venn diagram depicting the primary considerations of SIBM models . . 5 1.2 General circulation and bathymetry of the G O M region in the North-western Atlantic Ocean. Modified from [404] 16 1.3 3D perspective of G O M circulation/Georges Bank system [344]. Cir-culation features are superimposed over preferred topographic regions. M C C - Maine Coastal Current, T M F - Tidal Mixing Front, SSF - Shelf-Slope Front. The colour legend indicates vertical depth (m) contours, also indicated near the circulation flow labels 17 2.4 Individual movements of B F T observed during hydro-acoustic tracking experiments within the Gulf of Maine region [216] (from Lutcavage and coauthors [215,216]). Further information on these observations is pro-vided in Table 2.12 38 2.5 Definition of parameters used in the ^o-dimensional interpolation of B F T movements. Each move displacement of variable length, k, has a corresponding directional angle, fa, referenced to a fixed axis, X, and turning angle, ipi, measuring the change between successive move-directions (adapted from [239]) 40 2.6 Definition of parameters used in the three-dimensional interpolation of the B F T movements. Each move displacement of variable length, U, has a corresponding directional angle, fa, referenced to a fixed axis, X , ver-tical inclination angle, (spherical, azimuthal and polar angles respec-tively), and turning angle, (n) (rad), turning,
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SH g CP C3, 43 T J 5 a co T J P CP ' M 1.2 5 cp - f l —, o CP o CD fl TJ fl > * TJ 42 fl SP CO ^ bO r - 1 . fl CO 43 fl CP T J CP > co „ , cp cp CP co co 43 O CP T J O a "3 a o T J fl cd -3 *>• o CP •C cd CD ft* g a Q CO fl O CP T ) 43 TJ 43 CP T T SH CP fl 2 CP OH s a 9- fl 43 += CP (X > CP SH T J fl CO 43 g .2 a cp CP CD O CP CP CP > >» 2 fl cd • 2 ^ 5 fl S.2 fto'*3 • 2 T J $ 4-= cd to cd 43 43 43 o co w ^ § 5 CP JH .fe -s fl C A cd cp 43 xJ TJ 'C fl +^ fl -—'TJ cd TJ CP . f l CP cj fl fl g T J a s in s o o CJ a g a § co cr CP to , „ fl tS -2 fl fl 2 cr 3 CP S fl o 2 fl bO C fl •S cd CP SH fl bO cd 43 ^ .SP fe 1—1 to 43 IT) O fl 0 3 13 cp 2 a fl H cd o cp 43 S a •s .2 43 O o +3 DH 1.6 Fishery-dependent and independent indices of abundance CO u fl I! fl .2 , * I* fl 0 a S o U i—N '1 1 ~ X? a: e l -s' <2 CD O 3 ^ O co co , CO "ft cp o 0 3 fl i_fl 2 s 2 CP CO CP CO CO fl _o rt cp co 2 » fl CP CO +| s I cp •T3 fl Q> fl N O 'to CJ WJ O co rt O 8 ^ CO CP * s O * CO cO "cO fl cO rt fl cp fl o OH o o fl CO rt PH 'co |xf !3 9 >, « 3 co cO £ CP rt >> co cS cp .2 .5 cic „ o fl rf rt ^ ^ fl fl — fl § rti o -2 1—I rt CO fl CP O ax) rt cO rt - H CO JC3 fl X) CT* cp .§-rt _ CJ ^ 2 2 £ - f l CO CO pH rtl O 'co xl •—i CO s CO 05 3 —- CO CP SH fl . 3 SH O !H CO XJ H lo x) PQ o v a, .H rt 'in -fl cp cp rt y -CO cp -fl CJ CO I I CO fl -rt CO .3 O cp ~ cO fl CO OH rt CP CJ CJ cO 3 CO" OH cO cp rf " "-S o =3 % ° fl "g fl O OH O X _ "rt fl rt I CP co y Co Ti CP -—i co fl cO fl fl . . CO ° 2 - — ' CO O > bO cp 'Lo X) .3 3 1.6 Fishery-dependent and independent indices of abundance CO CO -CD CD CJ A CD X> cd fl o o fl . 2 +J CO TJ • t—H X? fl CO CD JH fl +3 O fl (H CO "3 TJ O pq i—i co co" .!> CJ CD -O O fl co T) CD fl fl "•s O cj CD 0O X E2 i f CJ ? +^ cu X 8 8 y CJ 2 S S f 2 <*> - f l CO co >H fl N fl O 2 fl rf CO g bp""1 - 1 .3 lo i-i rf O rH cO rf -—' (rt CO -2 'SH rt CD -2 ^ X) cj O co fl fl CD a CD CO fl CD ^ a 2 3 -—' CO j, co r^f CO CD O CD X> u cS CD T : -fl CQ h—I CO bO fl co CD fl CO Xi cO 0 2 S CD ^ cj v O C O SH rt PH rH O a 2 § fl--3 A ° rt O fl X) CJ rf CD - P S D Ti CO ' fl CO CD CD 4J CJ cO fl bO co co fl rf rt CD CJ fl 2 CD >-* 6 ^ •-3 co g co CD CD 3 3 .5 CO rt >CO CD > I* " e g CO CD fl fl 'rt Jrf CD CQ ^ £ CD n o C J rt fl CD a CD > g< S'-fl fl _fl 3 S co e o fl g) CD fl S3 CQ X3 CD 2 fl 'I & J3 c§ TJ _ MA fl V S Hfl ° fl "S ° o & § CQ 3* CD CO o -fl fl CD CO CO CO .fl ^ Hfl 13 .SP II-IS § 2 ^ co . f l CD ^ co > fl Xi ^ TJ fl fl CO cQ cO CD co fl CO X) fl CO X CD _ Xi co .a a in O CD .H CO rt -H CD C J fl fl 1.6 Fishery-dependent and independent indices of abundance CO CP cp fl CP - d cG fl o O o X) 31 fl CO CP j-i fl +J CJ fl rf. •p CO "cp X) O CQ h—I co co" cj _CD o fl o a 'm fl GO xi CP fl fl • -H fl o CJ oo di - a CO CP CP 1^ rt CO fl ^ cp .2 > S X> § x) -C •-j X3 co 13 o -fl CO fl fl fl CO fl CP O > trt rt O +j bo a o 3 S ° -fl cc .'53 > cd CO o a, o CJ Lo-fl i o fl cd ^ CP cp e CP" cd ^ 1 3 cp fl o cfl CP X i o fl cd O CP rt cd 1 rf CO fl CP 3 M 5b rt J-J CP CO CP rf rt JJ CO CP 1- cd fl CJ-co CO J= fl CO O cd rt QJ rt rt fl (H •2 cs 'C cp +5 fl CO rt 5 § cd fl o ^ rtl CO CO rt >> 10" O g irt ,—v CQ 2 S CS