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Shoaling dynamics and abundance estimation : Atlantic bluefin tuna (Thunnus thynnus) Newlands, Nathaniel K. 2002

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SHOALING DYNAMICS AND ABUNDANCE ESTIMATION: ATLANTIC BLUEFIN TUNA (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. An 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 viList 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 7 2.4 Spectral identification of movement modes 58 2.5 Space trajectories 69 2.6 Theoretical movement model predictions 62.7 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 183.4 Convex hull refinement of ellipsoidal shoal structure 211 3.5 Principal component analysis of structural variables 217 3.6 Shoal dynamics 233.7 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 5 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 49A. l Abbreviations 49B Chapter 2: Background, Derivations, Extended Results 497 B. l Move-speed and turning angle distributions 49B.2 Spectral identification of movement modes 502 B. 3 Space trajectories 51C Chapter 3: Background, Derivations, Extended Results 522 C. l Shoal size and formation: shoal structure histograms 522 C.l.l Nearest-neighbour distance (NND) 52C.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 54D.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 58F 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 5 1.4 Table 1.3 continued 6 1.5 Table 1.4 continued 7 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 1 1.10 Table 1.9 continued 2 1.11 Table 1.10 continued 3 2.12 Summary of geolocation (GPS) and depth records from hydro-acoustic telemetry of BFT (N=ll). 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 BFT, for rii sampled positions, and shoal size, S 42 2.14 Depth-correlated data summary for hydroacoustic tracking of BFT (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 BFT 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 BFT 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(nm2/d) for short-term light archival tagging movement observations of BFT (N = 7) (1998-1999), where d denotes days 84 2.18 Long-term light archival tagging movement observations of BFT (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 obs 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 (A06S) 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 Cl 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 BFT 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 BFT across ages 0-10+ (ICCAT). . . 159 3.31 Reduced x2/df statistics for shoal size-sorted observed histogram fre quencies of NND 174 3.32 Same as Table 3.31 of nearest-neighbour distance (NND) for formation type 173.33 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 183.37 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 BFT 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: PCA 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 4 3.45 Same as Table 3.41 for mixed formation 225 3.46 Same as Table 3.41 for ball formation 6 3.47 Same as Table 3.41 for oriented formation 227 ix 3.48 BFT 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 BFT 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 1994-96 233.51 Classification summary of BFT 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 PCA analysis of BFT 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 PCI (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 BFT (N=10) and each environmental variable. . 306 5.58 Nonlinear least-squares fitting of sigmoidal function for cumulative SPUE 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 (rai,TO2) and asso ciated movement depth distribution. VPA 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 VPA 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 405.66 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 405.69 Summary of diffusion estimates (D) (km2/d) (un-corrected/corrected val ues) for BFT calculated from various data sources used in analyses: Ul 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 LLA observations (n=3), and Single-point pop-up tag ging (SPl)(n=43) 408 5.70 Comparison of calculated BFT diffusion estimates (nm - nautical miles, km - kilometres) with those of other species of tuna available in the literature. BFT - Northern Bluefin (Thunnus thynnus), BET - Bigeye (Thunnus obesus), YFT - Yellowfin (Thunnus albacares), ABT - 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 BFT (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 3 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 GOM region in the North western Atlantic Ocean. Modified from [404] 16 1.3 3D perspective of GOM circulation/Georges Bank system [344]. Cir culation features are superimposed over preferred topographic regions. MCC- Maine Coastal Current, TMF - 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 BFT 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 BFT 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 BFT 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, <pi, measuring the change between successive move-directions) (modified from [293]) 43 2.7 Left: Observed movement path of individual 9601 in 2D with estimated weight, W, and belonging to a shoal of size, a. Right: Frequency distri butions of move-turning angle and move-speed, with frequencies scaled between (0,1) 46 2.8 Sample autocorrelation functions (ACF) (correlation coefficient versus lag in the number of moves) for move- displacement in the observed move ments of BFT individuals 51 2.9 Sample autocorrelation functions (ACF) (correlation coefficient versus lag in the number of moves) for move-speed in the observed movements of BFT individuals 2 xiii 2.10 Sample autocorrelation functions (ACF) (correlation coefficient versus lag in the number of moves) of turning angle in the observed movements of BFT individuals 56 2.11 Mean variation of turning angle versus lag in the number of successive moves 57 2.12 Lomb normalized periodograms (Power spectra) of P(f) (spectral power) versus frequency (Hz=l/s), / = u/2ix for all moves n* — (1, ,.,n). The spectra show relative peak intensities in the signals of rate of change in turning angle, P{f)v, and move-speed, P(f)v relative to background noise fluctuations. Peak intensities change across an individual's move ment path according to the autocorrelation of these parameters between successive moves. Results are shown for individuals 9601-9603 62 2.13 Same as Figure 2.12 for observed movement paths 9604a-9701 63 2.14 Same as Figure 2.12 for observed movement paths 9702-9705 64 2.15 Autocorrelation results for individual 9601. (Top to Bottom): (a) Am plitude variation of the maximum signal, P(f)max with greater than 99% significance above Gaussian white noise versus reference move position, n*, where n* = (1,n) and n is the total number of successive moves. This plot shows variation in the second-order correlation of turning an gle and move-speed (turning rate and acceleration/deceleration) across • '. the observed movement trajectory, (b) and (c) Lomb normalized peri odograms, P(f) (spectral power) versus frequency (Hz=l/s), / = a;/27r profiled for the second n* = (1, ..,n = 300) total moves showing separa ble signal peaks (movement modes) above a noise background 65 2.16 Observed turning statistics derived for the BFT movements. Here, p(r, <p) is the probability distribution of turning for a move of duration r (fre quency with which moves of duration r are observed). The frequency dis tribution for p(r, ip) is theoretically considered to be gamma-distributed T yields the turning distribution, q(r) = 1 - Jp(r', (p)dr', as the proba-ci bility that move-length is equal or greater than r. The distribution of the rate of turning is /3(r). Calculation of the turning statistics show significant differences in turning-rate distributions between two modes mi,m2 identified in the Lomb spectral analysis 67 2.17 Top: Frequency histogram of switching between the modes mi, m2 versus time of day (hrs.) in BFT movement observations, Bottom: Frequency distribution plot showing the relative depth preference (m) below the ocean surface for each mode mi, m2 68 2.18 (Top to Bottom): (a) 3D interpolated observed movement trajectory (9601), (b) time-series profiles of vertical inclination (polar), 6(n) (rad), horizontal directional (azimuthal), </>(n) (rad), turning, <p(n) (rad) an gles, and move-speed (m/s) for each move 70 xiv ( 2.19 GIS display of observed movement path of individual (4235) within the Atlantic Ocean based on geopositions derived from archived light-intensity. 86 2.20 Kalman filtered of observed movement path of individual BFT, 4235. The optimized paths representing filtered geoposition estimates based on the theoretical predictions of the RW and BRW models are shown in relation to the observed geoposition estimates. Latitude is °N, and lon gitude in °W in reference to the equator and prime meridian, respectively. 87 2.21 Same as Figure 2.19 for observed movement path 4364 88 2.22 Same as Figure 2.20 for observed movement path 4364 9 2.23 Same as Figure 2.19 for observed movement path 4745 90 2.24 Same as Figure 2.22 for observed movement path 4745 1 2.25 Schematic showing how mean dispersal area, RT-ANTI time spent search ing, (T — ANT), and foraging time, ANT is calculated from fluctuations in Rnet. These estimates are used to explain the observed variation in their external movement bias on the basis of the attraction of their shoals to areas where they forage on their prey. . . 96 2.26 Distribution of observed (A0bs) and predicted (AT) values of the A statis tics for the Marsh and Jones significance test for the CRW (E(Ab)) and BCRW (E(Aa)) models used in comparing the relative contribution of movement persistence and external bias. Expected values of the CRW and BCRW model test-statistic are shown corresponding to various num ber of total moves observed (n) 102 2.27 Probability density functions (pdf's) of observed values of the A0f,s statis tic in its range (-1,1). Top to Bottom: Changes in the distributions about the origin illustrate how internal orientation (persistence) (left pdf) and external orientation (right pdf) in movement contribute to bias in mean value of the observed statistic, Aabs. Left: Pdf's corresponding to 10 total successive moves, n, and Right: Pdf's corresponding to a 20 total moves. As n increases, the relative separation between the pdf's also increases 103 2.28 Theoretical model predictions of the CRW and BCRW models with con fidence intervals calculated using statistical bootstrapping for observed movement paths 9601-9701: R2et(m2) versus the number of moves, n. Solid Circles: CRW model prediction, Open Circles: BCRW model pre diction, Solid Line: Observed movement path 104 2.29 Same as Figure 2.28 for observed movement paths 9702-9705 105 2.30 Frequency distributions of move-turning angle, </?j(rad), and move-speed, v(km/d), where d denotes day, for the light-archival BFT movement observations. At the spatial scale (elapsed time) of these movements, the observed distribution of turning angles has a bimodal form (refer to Section 2.2). The move-speed distribution is approximately gamma-distributed having a far broader width in the case of path 4745 106 xv 2.31 Theoretical model predictions of the CRW and BCRW models with con fidence intervals calculated using statistical bootstrapping for the ob served movement path, 4235: -R2ei(nm2) versus the number of moves, n. The RW and BRW predictions from Kalman filtering of the path are also shown 107 2.32 Same as Figure 2.31 for observed movement path, 4364 108 2.33 Same as Figure 2.31 for observed movement path, 4745 109 3.34 Schematic of supervised automated digital image analysis (SAIA). . . . 121 3.35 Automated detection of individual tuna within image field of view from image intensity gradients and spatial connectivity yielding the outline signature as shown profiled in x, y axes and xy image plane 123 3.36 Top: Spatial calibration of image histogram, Bottom: Spatial and inten sity calibration of image histogram 129 3.37 (A)-(D): Selected calibrated intensity profiles to illustrate the variation in the degree of variability in object and disturbance peak intensities and their strength relative to image intensity background for the observed shoals used in the image analysis. Variation in the intensity scale was required so that the peaks are visible relative to the background 130 3.38 Depth frequency distributions for BFT individuals across shoal forma tion types, 1995, zm = 10 131 3.39 Same as Figure 3.38 for year 1996 132 3.40 Depth frequency distributions for BFT individuals across shoal size range categories, 1995, zm = 10 133 3.41 Same as Figure 3.40 for year 1996 134 3.42 Selected output of image processing steps: (A) Original digital image, (B) Area-of-interest (AOI) selection as image subregion for grey-scale converted image, (C) Manual object identification, (D) Automated ob ject detection of profile signatures based pixel intensity gradients, (E) Spatial-calibrated measurements of identified objects, and (F) Intensity-calibration of objects 136 3.43 Conversion of apparent length (Ls) and width (Ws) under transformation rotation by shoal polarization angle, \?s aligned with respect to shoal velocity, v to shoal length (L's) and width (W's) 142 3.44 SAIA shoal size estimation: Comparison between estimates from final, corrected (Na), manual (Nm) and automated (Nc) object identification for 1994 146 3.45 Same as Figure 3.44 for year 1995 147 3.46 Same as Figure 3.44 for year 1996 8 xvi 3.47 Structural formations identified in digital image database from aerial survey observations of BFT shoals, 1994-96: (A) Cartwheel, (B) Surface-Sheet, (C) Dome/Packed Dome, (D) Soldier, (E) Mixed, (F) Ball, (G) Oriented 151 3.48 Selected SAlA analysis output revealing 3D structure of BFT formations based on relative intensity, Iz of objects in the 2D images 153 3.49 Same as Figure 3.48 for formation types (D) to (G) 154 3.50 Histograms of shoal size for BFT formations: frequency versus corrected estimates of shoal size, iVs 155 3.51 SAIA shoal size estimation: Comparison of estimates from automated (Nc) and manual (Nm) object identification between different BFT struc tural formations, 1994 data. 156 3.52 SAIA shoal size estimation: Comparison of estimates from final, cor rected (Ns) and automated (Nc) object identification between different BFT structural formations 157 3.53 SAIA shoal size estimation: Comparison of estimates from final, cor rected (Na) and manual (JVm) object identification between different BFT structural formations 158 3.54 BFT total length(m) of member individuals across shoal size for years 1994-96 obtained from measurements in the image analysis 161 3.55 SAIA analysis histograms of total length(m) of individuals for interval range of shoal size, shown in the upper right-hand corner of each his togram, 1995 162 3.56 Same as Figure 3.55 for year 1996 163 3.57 SAIA analysis histograms of total length(m) of individuals corresponding to shoal formations, 1995 164 3.58 Same as Figure 3.57 for year 1996 165 3.59 Age structure of BFT shoal sizes across ages 0-10+ years obtained by conversion of individual lengths using monthly means of length-at-age (m) (see Table 3.30), 1995 166 3.60 Same as Figure 3.59 for year 1996 167 3.61 Age structure of BFT formations across ages 0-10+ years obtained by conversion of individual lengths using monthly means of length-at-age (m) (see Table 3.30), 1995 168 3.62 Same as Figure 3.61 for year 1996 169 3.63 SAIA analysis histograms of nearest-neighbour distance (NND) for indi viduals across interval range of shoal size, shown in the upper right-hand corner of each histogram, 1995 172 3.64 SAIA analysis histograms of nearest-neighbour distance (NND) for BFT formations, 1995 173 xvii 3.65 SAIA analysis histograms of frequency of nearest-neighbours for individ uals across interval range of shoal size, shown in the upper right-hand corner of each histogram, 1995. These distributions are obtained without any restriction on the distance between individual fish. The restriction of a critical distance between nearest-neighbours (NNDcru) determines the mean and variance in number of nearest-neighbours (NNS), partitioning these frequency distributions 176 3.66 Same as Figure 3.65 frequency of nearest-neighbours for formation types, 1995 177 3.67 SAIA analysis histograms of bearing angle (BA) between nearest-neighbours for individuals across interval range of shoal size, shown in the upper right-hand corner of each histogram, 1995 181 3.68 SAIA analysis histograms of bearing angle (BA) between nearest-neighbours for the BFT formations, 1995 182 3.69 Nearest-neighbour distance, NND (BL), versus bearing angle between nearest-neighbours, BA (°) for BFT shoal formations 184 3.70 SAIA analysis histograms of shoal polarization across interval range of shoal size, shown in the upper right-hand corner of each histogram, 1995. 186 3.71 SAIA analysis histograms of shoal polarization for BFT formations, 1995.187 3.72 Shoal size variation of BFT shoal structure, 1995-96: cartwheel formation. 190 3.73 Shoal variable measurements obtained from SAIA image analysis: Surface-sheet formation 192 3.74 Shoal size variation of BFT shoal structure, 1995-96: surface-sheet for mation 193 3.75 Shoal variable measurements obtained from SAIA image analysis: Dome formation 5 3.76 Shoal size variation of BFT shoal structure, 1995-96: dome formation. . 196 3.77 Shoal variable measurements obtained from SAIA image analysis: Sol dier formation 199 3.78 Shoal size variation of BFT shoal structure, 1995-96: soldier formation. 200 3.79 Same as Figure 3.77 for mixed formation 202 3.80 Same as Figure 3.78 for mixed formation 3 3.81 Same as Figure 3.77 for ball formation 205 3.82 Same as Figure 3.78 for ball formation 6 3.83 Same as Figure 3.77 for oriented formation 209 3.84 Same as Figure 3.78 for oriented formation 210 xviii 3.85 Left: SAIA analysis output structure of a shoal in the horizontal (xy) plane, and corresponding vertical projection of individual positions in the vertical, z-plane (depth), Right: Calculation of shoal convex hull in three-dimensions with vertices as individual members on its edge or shoal perimeter. Edge individuals comprising the fitted convex hull to the shoal structure appear outlined as larger circles, in both the 2D and 3D perspectives 215 3.86 Comparison of ellipsoidal surface area (SAS) and volume (Vs) and re finement of surface area (SAh) and volume (14) with fitted convex hull for the surface-sheet formation 216 3.87 Box-Wisker plots of correlation coefficient of PCA components versus shoal structural variables for the BFT formations, showing median, quar-tiles, 5% and 95% percentiles, where Ns is shoal size, L's is length, D's is depth, Vs is volume, NND is nearest-neighbour distance, and BA is bearing angle 229 3.88 PCA Scree plots showing the proportion of variance explained by each principal component across BFT formations. These plots show the lead ing components (PC1,PC2,PC3) are sufficient to explain up to 70% of the observed variance in shoal structure for each of the formations. . . 230 3.89 Top to Bottom: Depiction of the dynamic linkage of the BFT shoaling formations on the basis of increasing mean shoal size between forma tions: (A) Cartwheel, (B) Surface-Sheet, (C) Dome/Packed-dome, (D) Soldier, (E) Mixed, (F) Ball, (G) Oriented, see Table 3.29. Arrows, rep resenting a linear linkage between each formation, are shown oriented in the direction of increasing mean shoal size 234 3.90 Frequency of occurrence of BFT formations for shoals observed in aerial surveys across years 1994-96. Circular numbers are time of day (hrs). . 235 3.91 Framework overview of the virtual-reality (VRML) extension to the SAIA image analysis scheme 238 3.92 VRML visualization of BFT shoal structure: Cartwheel formation . . . 239 3.93 Same as Figure 3.92 for soldier formation 240 3.94 Same as Figure 3.92 for mixed formation 1 3.95 Same as Figure 3.92 for oriented formation 242 4.96 SIBM model and simulation framework: initialization stage 257 4.97 SIBM model and simulation framework, continued 258 4.98 Eastern (Left) and Western (Right) Atlantic regions, and GOM sub-region are outlined. Arrows depict direction of population transfer be tween regions for each transfer parameter in the model 268 xix 4.99 Numbers-at-age (0 — 10+) for the western Atlantic population of BFT from VPA assessment estimation (constant natural mortality, M=0.14/year) and variable age-specific fishing mortality, Fa,t, used to simulate their GOM residency in the model 269 4.100 Theoretical depiction of immigration and emigration of shoals in the SIBM model 273 4.101 Initial spatial boundary locations of shoals/individuals: Large arrows de pict scheduled immigration of individuals/shoals into the Gulf of Maine region from initial spatial locations specified on a grid boundary with movement through the Great South and North Channels, Small arrows: depict hypothetical movement of shoals/individuals within the region. . 274 4.102 Large arrows depict emigration of individuals/shoals out of the Gulf of Maine region independent of their locations for emigration set to occur at a specific simulation time, tm in the south direction, Small arrows: depict emigration direction movement of shoals/individuals emigrating from the region's interior 274 4.103 Individual and shoal-level profiles of fitness functions referenced in the SIBM model (Qf = 10.5,/«, = 0.003, r, = 0.50, QM - 10.5,/ii = 2.0, /x2 - 0.003, rmax=6) 284.104 Three-dimensional mesh/grid for referencing environmental data layers in the SIBM model from a comprehensive coastal circulation model for the GOM region (Numerical Methods Laboratory, Thayer School of En gineering, Dartmouth College, Hanover, NH, USA (see [224], grid GS2). The grid comprises horizontal finite-element nodes, with vertical refer ence layers below each horizontal node 286 4.105 Bimonthly mean sea-surface temperature SST (°C) for the Gulf of Maine, from GOM oceanographic model [224] 291 4.106 Frequency distributions of environmental variables (Current flow ve locity, SST, chlorophyll-a concentration, zooplankton abundance, and bathymetry for BFT shoals observed in spotter-surveying (July, 1994). 292 4.107 Same as Figure 4.106 for August, 1994 293 4.108 Same as Figure 4.106 for September, 1994 4 4.109 Same as Figure 4.106 for October, 1994 295 4.110 Observed frequency distribution of shoals and AVHRR-derived sea-surface temperature (°C) for survey years 1994-95, in July-September. Distribu tions for October are not fitted due to insufficient sample sizes. Normal distributions are fitted to the observations for estimating the mean and variance in SST associated with the annual and monthly survey shoal sightings 296 4.111 Bimonthly, vertically-averaged residual and M2-tide flow velocity vec tors and magnitude (see legend) from oceanographic model predictions, referenced as a data layer in the model for January-June 297 xx 4.112 Same as Figure 4.111 for July-December 298 4.113 Observed distribution of chlorophyll-a in the upper 75 m of the water column from shipboard surveys, 1977-88. In addition to zooplankton spatial abundance, chlorophyll-a is considered to correlate with mean abundance in major BFT prey species. Distributions are formed from sampling observations with the transects used in the Marine Resources Monitoring, Assessment and Prediction Program, (MARMAP) (See [280]).299 4.114 Observed distribution of zooplankton in the GOM (Calanus finmarchicus abundance [96,223,251] 300 4.115 Cross-correlation coefficient for individual movement trajectory 9601, across range in time-lag (number of moves) between successive moves. . 307 4.116 Same as Figure 4.115 for observed movement trajectory, 9703 308 4.117 Testing of the environmental grid spatial resolution in three-dimensions. Horizontal and vertical nodes of the grid are referenced and values from each grid layer are profiled, corresponding to the individual movement trajectory, 9602 319 4.118 Immigration of shoals into the GOM region from the south-western edge of the environmental grid. The movement direction is indicated. Simula tion of 20 shoals and the corresponding locations at 5,6,9,10 run days are shown. During the immigration process shoals are set to move without responding to environmental gradients or prey concentration/abundance level, and they immigrate in aggregations. At a pre-scheduled end of the immigration process, the movement direction angle and response to en vironment gradients leads to partitioning of shoal aggregation 320 4.119 Gamma-distributed move-speed and Von-Mises circular normal turning angle. The distributions are kept fixed for each movement mode (mi,7712) with gamma-distributed move-speed having parameters a = (1.50, 2.25) and (3 — (0.5,0.5) for mi,m2 respectively. Turning angle distribution has direction (0°, +10°) and concentration parameter, c = (1.0,1.0) for movement modes mi and m2 respectively. Randomly sampled deviates axe obtained from these distributions to simulate movement trajectories. 321 4.120 Top: Emigration process test for two shoals containing ten individual fish moving with random turning angle (sampled from a Von-Mises dis tribution at each move). Before the onset of emigration shoals move in the directions indicated as (la,2a). After emigration time, tm, the shoals are re-directed south (lb,2b) maintaining their movement char acteristics. The accompanying figures provide a higher resolution of the simulated movements for each shoal (lb,2b). The random variation here differs from pure random due to a contraction in the deviation range of turning angle and move-speed associated with their assumed distributions. 322 xxi 4.121 Top: Emigration process test for two shoals moving with non-random movement parameters. The harmonic form for alteration in move-speed and turning angle, and correlation in each of these movement parameters is maintained. Non-random and correlated variation in their movement, in contrast to random assumptions, leads to highly advective movement trajectories. Before the onset of emigration shoals move in the direc tions indicated as (la,2a). After emigration time, tm, the shoals are re-directed south (lb,2b) maintaining their movement characteristics. Bottom: The simulated movement trajectories of the two shoals shown at higher spatial resolution 323 4.122 Process testing of turning angle and move-speed variation. Move-speed is fixed as harmonic (non-random), with turning angle varying as non-random, and randomly sampled from a Von-Mises and pure/uniform distribution (-180°,+180°). A model trajectory of an individual BFT is simulated. Sub-figure (A-l) shows a simulated trajectory with harmonic variation in turning angle and move-speed, with no correlation in either variables. Sub-figure (A-2) shows a trajectory resulting from random sampling of turning angle from a Von-Mises circular normal distribution corresponding to the distribution shown in Figure 4.119. Sub-figure (A-3) shows a trajectory with pure random turning angle, and harmonic move-speed. (B-l)-(B-3) show trajectories for each case.as in (A-l)-(A-3) with turning angle correlation" across ten successive moves 324 4.123 Same as Figure 4.122 but with stochastic variation in move-speed, and turning angle varying as non-random, and randomly sampled from a Von-Mises and pure/uniform distribution (-180°,+180°) 325 4.124 Process testing of turning angle correlation. Move-speed is non-random, with turning angle varying as non-random, and randomly sampled from a Von-Mises, and pure/uniform distribution (-180°,+180°). A model trajectory of an individual BFT is simulated. Sub-figure (A-l) shows a simulated trajectory with harmonic variation in turning angle and move-speed, with no correlation in either variables. Sub-figure (A-2) shows a trajectory resulting from random sampling of turning angle from a Von-Mises circular normal distribution corresponding to the distribution. (B-l)-(B-3) show trajectories for each case as in (A-l)-(A-3) with turning angle correlation across 50 successive moves 326 4.125 Same as Figure 4.124 but for correlation in both turning angle and move-speed 327 4.126 Model harmonic variation in turning angle (Cv), and move-speed (Cv), in the model corresponding to each movement mode, mi and m^. Turning angle frequency between each of the movement modes varies, with no change in the frequency of variation in move-speed between the modes. mi is associated with a higher rate of variation/turning angle frequency. 328 xxii 4.127 Simulated profiles of variation in turning angle and move-speed versus number of moves for an individual model trajectory. Both variation in turning angle frequency (i.e., turning rate) and its correlation between successive moves is seen in these profiles. Correlation in each variable was set to extend across ten successive moves. These results correspond to the harmonic coupling variation of C„, shown in Figure 4.126. . . 329 4.128 Simulated model trajectories following each movement mode mi,m2. The first-half of the movement trajectory follows rrt2, with an alter ation in turning rate between m2 and mi as indicated. Simulation of a similar trajectory where turning angle is pure-random and correlation is still present between ten successive moves, a clear division between the characteristics of each movement mode is evident 330 4.129 Percentage of total number of simulated shoals (N=200) in each move ment mode (mi,ra2) versus time of day (hrs) for elapsed run times within a day, for one day and after two days. (A) shows the initial alteration be tween modes. During mode-switching events, such as 777,3, the switching stops and all shoals in the model move according to the characteristics of 777,3, set as a deep vertical dive near times of dusk and dawn. As time elapses, in (B) and (C), the shoals adopt one of the two movement modes as a result of their spatial interaction, whereby during times of shoal mix ing and exchange of individual fish, shoals alter their movement mode as a function of the shoal size that results. After two days, shoals are sufficiently distributed in the spatial dimension whereby interactions are reduced and the population of shoals is separated into movement modes. In cases, where interactions of shoals remain high as time elapses, varia tion in the percentage of shoals before and after the switching events at dusk and dawn occurs. The simulated results show uniformity in mode separation due to a sufficiently small number of interactions 331 4.130 Process testing of mode-switching and shoal interaction. Results are shown for N=200 shoals simulated in the model. (A) shoal mixing over time dependent on the sizes of two interacting shoals. No environmental movement response was assumed. (B-l) shows an example profile of a shoal with movement alterations occurring as a result of its interaction with other shoals as profiled in (B-2), moving according to either m\ or 7772- Shoal interactions that lead to an increase in shoal size for a given shoal are set to correspond to mi, and smaller shoals, to m2. This setting, over elapsed time, leads to larger shoals moving in the mi mode, and smaller shoal sizes moving in the m2 mode. (C-l) is the mode-switching profile that results when alteration in shoal movement modes occurs, not only by shoal interactions (B-2), but with the underlying switching of modes independent of shoal interaction. (C-2) is the shoal interaction profile resulting from this superposition 332 xxiii 4.131 Attraction/repulsion process. Simulation results are shown for a shoal of five individuals (each line), with move steps scaled sufficiently large to reveal attraction/repulsion differences along the trajectories. Case (A) (Left Figures) show movements with non-random move-speed and turning angle, with these variables correlated between successive moves, Case (B) (Right Figures) show movements with pure random turning angle and move-speed, with no correlation in speed and turning angle between successive moves 333 4.132 Shoal size frequency distributions for varying shoal fusion and fission rates (i.e., the number of individual fish mixing per interaction as a ' percentage of shoal size), N=200 shoals 334 4.133 Spatial distribution of shoals (N=200) for varying shoal fusion and fission rates. The radius of the circles scales linearly with shoal size, used to depict the relative difference between the sizes of each shoal 335 4.134 Model predictions of the spatial distribution of shoals (N=200) using fixed parameter values in Table 4.54. Shoals move by responding to all environmental layers in the simulation grid for a time period of ten days. The aggregations shown in the predictions correspond to t=(5,8,10) days elapsed in the model, as shoals move northward, following the coast line. The predictions identify locations of shoal aggregation that ap proximately correspond to those seen in aerial surveys (1994-96) across years. Model predictions explain the location of aggregations seen in the survey distributions on shoals moving by responding to environmental gradients, with predominately northward advection along the coastline. 336 5.135 Survey effort spatial coverage for spotter-directed surveys of BFT in the GOM, 1994-96 355.136 Survey spatial sightings-per-unit-effort (SPUE) with interpolated grid, 1994 357 5.137 Same as Figure 5.136 for year 1995 358 5.138 Same as Figure 5.136 for year 1996 9 5.139 Daily SPUE versus elapsed time (days) 1994-96. 2.1 m/s filter, no depth calibration 364 5.140 Cumulative SPUE for shoals (solid circles) and individuals (open circles), over elapsed time (days) in spotter-surveys, 1994-96 365 5.141 Serial correlation (first-order autoregression) analysis of cumulative SPUE (individuals/185.2km) for surveys 1994-96. For survey years (1994-95) SPUE is correlated at a temporal scale of 8 survey days (best-fitting, AR(8) model), while for 1996, SPUE is correlated between each day (best-fitting, AR(1) model). Plots of the residuals for fitting to the AR(8) and AR(1) fits are shown corresponding to each survey year. . . 366 xxiv 5.142 Monthly SPUE versus elapsed time (days) 1994-96. 2.1 m/s filter, no depth calibration 367 5.143' Probability density distribution of BFT movement depth from hydroa-coustic tracking 1996-97. Distributions corresponding to movement modes mi,rri2, and all movements from the observations are shown. Detection depths for photographic (light attenuation) as 10m, and radar (LIDAR) surface observation, 40m are indicated 369 5.144 Observed depth distribution (hydroacoustic observations) fitted to a Weibull probability density function used to obtain integrated correc tion factors for surface SPUE indices in the spotter-aerial surveys. . . . 369 5.145 Depth-corrected spatial survey SPUE index (individuals/185km), 1994-96.370 5.146 Top: Survey relative abundance of BFT in the study region (1994-96) for (0,0.8,2.1) m/s movement filters, Bottom: Survey abundance esti mates compared to ICCAT-VPA age-specific population estimates for the Western Atlantic management division 373 5.147 Open Circles: Relative abundance (individuals) time-series (2.1 m/s fil ter, depth-corrected) for years 1994-96 in the GOM. Filled Circles: Sur vey abundance time-series are fitted to predicted abundance derived from separated ages (6+,7-f-,8+,94-) portions of the total (ages 1-10+) VPA West Atlantic estimated population (Dashed Line) 378 5.148 Bottom: Open Circles: Survey (observed) abundance (individuals) (2.1 m/s filter, depth-calibrated) time-series for the GOM region. Dotted Line: VPA-time-series for ages 7+ for the total Western Atlantic man agement division. Solid Circles: Best-fitting (predicted) time-series for the GOM region derived from VPA estimates for ages 7+ 380 5.149 Single-point pop-up satellite tagging released in the Cape-Hatteras re gion, south of the Gulf of Maine. Linear interpolated movements between release and final tag locations show immigration of shoals into the study region [26] 382 5.150 Single-point pop-up satellite tagging released in the Gulf of Maine, 1997-2000. Linear interpolated movements between release and final tag lo cations show emigration of BFT out of the GOM [214, 236] 382 5.151 (A) Single-point pop-up satellite tagging returns (number versus time at liberty from Jan 1st.) [26,214,236]. (B)-(D) BFT immigration/emigration rate calibrated annually for years 1994-96 to the predicted population abundance for the GOM region derived from ages 7+ of the VPA-estimated Western Atlantic abundance 383 xxv 5.152 Open Circles: Survey corrected-abundance (spotter surveys), and Solid Circle: predicted GOM abundance comprising ages 7+, derived from: Open Triangles: previous year-estimates for ages 7+ from VPA assess ment for the Western Atlantic population. Western Atlantic population abundance for ages 7+ with immigration and emigration following two mortality scenarios into the GOM region are shown corresponding to Figure 5.151, Scenario (1): Myr=0.U, Fyr=(0.249,0.186,0.345) and Sce nario (2): Myr=0.U, Fyr=(0.519,0.356,0.615) for July-December across years (1994,95,96) 384 5.153 Shoal size frequency distribution for, (A): annual and (B)-(E): monthly observations in survey year 1994 387 5.154 Same as Figure 5.153 for year 1995 8 5.155 Same as Figure 5.153 for year 1996 389 5.156 Log-log plots of frequency of shoals fi^ = f(s) versus shoal size, us = S, for the 1994-96 surveys, fitted to power-law function with exponential decay after a cut-off shoal size, sc (see Chapter 4) [32-34] 390 5.157 (A) Comparison of predicted abundance of BFT in the GOM region with shoal size for 1994-96. (B) Shoal size versus survey year, (C) shoal size versus month in each survey year 391 5.158 Spatial distribution of shoals sighted in spotter-surveying, 1994. Shoals sighted in each survey month (July-October) are also shown 400 5.159 Same as Figure 5.158 for year 1995 401 5.160 Same as Figure 5.158 for year 1996 2 5.161 Relationship of mean aggregation radius (km) and the number of shoals in aggregations from cluster analysis of observed shoal distributions in survey years 1994-95. In (B) and (C), square symbols indicate cluster centroid locations 403 5.162 Standardized variograms (geostatistical measure of spatial autocorrela tion) for shoals observed in surveys, 1994-96 404 5.163 Diffusion estimates (D)(km2/d) versus elapsed time, ET(d), d-days from hydroacoustic tracking, single-point and archival tagging of BFT in the GOM region: Ultrasonic telemetry/hydroacoustic tracking (UT)(n=10), Short-term light archival (SLA)(n=6), Long-term light archival (LLA)(n=3), Single-point approximation of LLA observations (n=3), and Single-point pop-up tagging (SPl)(n=43) _ 406 5.164 Same as Figure 5.163 for diffusion (D)(km2/d) versus time (day of year). 407 xxvi 5.165 Comparison of diffusion and advection estimates across different species of tuna. Plots of estimated ichthyokinematic ratio (R) versus charac teristic length (I)(km) are shown for tuna species using data available in the literature (refer to Table 5.70 for data sources): BFT - North ern Bluefin (Thunnus thynnus), BET - Bigeye (Thunnus obesus), YFT - Yellowfin (Thunnus albacares), ABT - Albacore (Thunnus alalunga), SJT - Skipjack (Katsuwonus pelamis. Values of R less than one indicate that dispersive (diffusive) movements are more important than directed movements over the corresponding characteristic distance, 1 409 5.166 Aerial survey schemes for spatial sampling of BFT abundance: (A) ran dom line-transect, (B) systematic line-transect, (C) systematic stratified transect, (D) adaptive stratified, and (E) spotter-pilot generalized search. 414 5.167 Example simulation realizations of BFT shoal distribution on superim posed survey grid across varying levels of aggregation 415 5.168 Example distribution of transect sampling points for random transect scheme A superimposed on survey grid 415.169 Example search path for a single track of a spotter pilot observer. . . . 416 5.170 Spotter-pilot search paths for aerial survey of BFT in the GOM region, July, 1994 415.171 Simulation results for survey schemes: Precision (coefficient of variation, CV) for shoal encounter/sightings versus the number of transects. ... 431 5.172 Simulation results for survey schemes: Precision (coefficient of variation, CV) for abundance estimation versus the number of transects 432 5.173 Simulation results for adaptive survey schemes: Precision (coefficient of variation, CV) for abundance estimation versus the number of transects for varying spatial stratification 433 B.174 Left: Observed movement path of individual 9602 in 2D with estimated weight, W, and belonging to a shoal of size, a. Right: Frequency distri butions of move-turning angle and move-speed, with frequencies scaled between (0,1). 497 B.175 Same as Figure B.174 for observed movement path, 9603 498 B.176 Same as Figure B.174 for observed movement path, 9604a 49B.177 Same as Figure B.174 for observed movement path, 9604b 499 B.178 Same as Figure B.174 for observed movement path, 9701 49B.179 Same as Figure B.174 for observed movement path, 9702 500 B.180 Same as Figure B.174 for observed movement path, 9703 50B.181 Same as Figure B.174 for observed movement path, 9704 501 B.182 Same as Figure B.174 for observed movement path, 9705 50xxvii B.183 Autocorrelation results for individual, 9602. (Top to Bottom): (a) Am plitude variation of the maximum signal, P(f)max with greater than 99% significance above Gaussian white noise versus reference move position, n*, where n* = (1, ...,n) and n is the total number of successive moves. This plot shows the variation in second-order correlation of turning an gle and move-speed (turning rate and acceleration/deceleration) across the observed movement trajectory, (b) and (c) Lomb normalized peri-odograms, P(f) (spectral power) versus frequency (Hz=l/s), / = u)/2n profiled for the second n* = (1,.., n — 300) total moves showing separa ble signal peaks (movement modes) above a noise background 503 B.184 Same as Figure B.183 for observed movement path 9603 504 B.185 Same as Figure B.183 for observed movement path 9604a 505 B.186 Same as Figure B.183 for observed movement path 9604b 506 B.187 Same as Figure B.183 for observed movement path 9701 507 B.188 Same as Figure B.183 for observed movement path 9702 508 B.189 Same as Figure B.183 for observed movement path 9703 509 B.190 Same as Figure B.183 for observed movement path 9704 510 B.191 Same as Figure B.183 for observed movement path 9705 511 B.192 (Top to Bottom): (a) 3D interpolated observed movement trajectory (9602), (b) time-series profiles of vertical inclination (polar), 6in) (rad), horizontal directional (azimuthal), (j)(n) (rad), turning, </?(n) (rad) an gles, and move-speed (m/s) for each move 513 B.193 Same as Figure B.192 for individual movement path 9603 514 B.194 Same as Figure B.192 for individual movement path 9604a 515 B.195 Same as Figure B.192 for individual movement path 9604b 516 B.196 Same as Figure B.192 for individual movement path 9701 517 B.197 Same as Figure B.192 for individual movement path 9702 518 B.198 Same as Figure B.192 for individual movement path 9703 519 B.199 Same as Figure B.192 for individual movement path 9704. 520 B. 200 Same as Figure B.192 for individual movement path 9705 521 C. 201 Same as Figure 3.63 for year 1996 523 C.202 Same as Figure 3.64 for year 1996 4 C.203 Same as Figure 3.65 for year 1996 526 C.204 Same as Figure 3.66 for year 1996 7 C.205 Same as Figure 3.67 for year 1996 529 C.206 Same as Figure 3.68 for year 1996 530 C.207 Same as Figure 3.70 for year 1996 2 C.208 Same as Figure 3.71 for year 1996. . 533 C.209 Comparison of ellipsoidal surface area (SAS) and volume (Vs) and re finement of surface area (SAh) and volume (14) with fitted convex hull for BFT Cartwheel formations 534 xxviii C.210 Same as Figure C.209 for dome formation. . 535 C.211 Same as Figure C.209 for soldier formation. 6 C.212 Same as Figure C.209 for mixed formation 537 C.213 Same as Figure C.209 for ball formation 8 C. 214 Same as Figure C.209 for oriented formation 539 D. 215 Frequency distributions of environmental variables (Current flow ve locity, SST, chlorophyll-a concentration, zooplankton abundance, and bathymetry for BFT shoals observed in spotter-surveying (September, 1995) 569 D.216 Same as Figure D.215 for August, 1995 570 D.217 Same as Figure D.215 for September, 1995 1 D.218 Same as Figure D.215 for October, 1995 572 D.219 Frequency distributions of environmental variables (Current flow ve locity, SST, chlorophyll-a concentration, zooplankton abundance, and bathymetry for BFT shoals observed in spotter-surveying (July, 1996). 573 D.220 Same as Figure D.219 for August, 1996 574 D.221 Same as Figure D.219 for September, 1996 5 D.222 Same as Figure D.219 for October, 1996 576 D.223 Top: Cumulative frequency versus SST (°C), and Bottom: linearly-interpolated vertical (z-axis) velocity versus SST gradient at temporal resolution corresponding to the movement sampling duration (AT), for observed movements of BFT from hydroacoustic experiments in (N=10, 1996-97) [216]. Values are obtained by intersection and grid-extraction of their movements on the corresponding environmental grid layer. . . . 578 D.224 Same as Figure D.223 for water flow velocity (m/s). A range of gradient response curves corresponding to Equation D.241 are shown for ep = (1.6 - 3.3), Xp = (0.004 - 0.200), Bp=l 580 D.225 Same as Figure D.223 for bathymetry. A range of gradient response curves corresponding to Equation D.241 are shown for ep = (0.0001), Ap = (0.0005 - 0.0600), /?p=l 582 D.226 Same as Figure D.223 for chlorophyll-a (ChlA) concentration (ng/1). A range of gradient response curves corresponding to Equation D.241 are shown for ep = (1.6 - 3.3), Ap - (0.004 - 0.200), 0P=1 584 D.227 Same as Figure D.223 for zooplankton concentration (N/10m2). A range of gradient response curves corresponding to Equation D.241 are shown for ep - (1.6 - 3.3), Xp = (0.004 - 0.200), Bp=l 586 xxix Acknowledgments I was very fortunate over the past several years to be able to work with my two supervisors, Dr(s). Tony Pitcher (UBC) and Molly Lutcavage (New England Aquarium, Boston, U.S.A.). Your guidance helped me to develop and strengthen perspectives and issues relating to my research. I am very grateful for their assistance in my research and for pointing me many a time in the right direction. Many thanks to the Department of Resource Management and Environmental Studies and the affiliated, Fisheries Centre, at the University of British Columbia for all their encouragement and enthusiasm they express towards their graduate students. I greatly enjoyed my course work, and participating in departmental activities. I would like to recognize the primary support of the New England Aquarium and various agencies that funded our collaboration. The work was funded in part by the United States Office of Naval Research (ONR), National Satellite Information Distribu tion Service (NESDIS), and National Marine Fisheries Service (NMFS), and a university graduate research fellowship award (UGF) from the University of British Columbia. I am grateful to Rob Schick, Anne Everly, Jennifer Goldstein, Scott Kraus (Marine GIS program) and other members of the Edgerton Laboratory at the New England Aquarium for their support and assistance during my visits to Boston. My special thanks to the other members of my committee; Dr(s). Carl Walters, Leah Edelstein-Keshet, Daniel Pauly and Les Lavkulich. Our meetings and discussions helped to identify issues regarding my research ideas and tasks, critical examination of results obtained, and to improve my presentation skills. Your unique insights, advice, patience and expertise were critical to my research work and learning. For providing data and technical support, I would like to recognize Dr(s). John Sibert, Laurent Dagorn, Julia Porter, Reg Watson, Richard Brill, Brad Chase, Greg Skomal, and Jeff Tutein for their work in collecting the experimental data used in my analyses. I sincerely thank my parents who taught me to set high goals and achieve them, and who provided strong guidance, encouragement, advice and support. I thank Merlin and Lancelot, two feline brothers, for keeping me sane, waking me up early many a morning, and sitting on my alarm clock when I needed to rest. I especially acknowledge my fiancee, Dr. Tracy A. Porcelli for her love, support and encouragement. Your support helped me through critical stages of my thesis, with additional computing help near the end by converting figures and mastering the I^TpjX-typesetting language. You showed great patience when I would ask you mathematical questions written on napkins during dates when we first met, and also later on when I continued to inundate you with my bluefin tuna research thoughts. I look forward to sharing an exciting, wonderful future ahead with you by my side. xxx Chapter 1 Introduction The introductory sections of this thesis are compiled from several publications listed below, with modifications and additions.1, 2 1.1 Research objectives The goals of my thesis were to investigate the movement, aggregation and distribution of bluefin tuna (BFT) shoals, and how these factors affect the measurement bias and estimation uncertainty of population abundance. The main objectives were to: • investigate the movement and behaviour of individuals, comparing field-derived observations to theoretical movement models and assumptions. • investigate shoal structure and characterize shoal formations from aerial survey data. • investigate how movement, shoal structure and population abundance are coupled by formulating a spatially-explicit, individual-based model based on individuals and their schools, in relation to oceanographic variables and prey. 'Newlands, N. 2001. Learning from Uncertainty: Population monitoring, modelling and simula tion of Atlantic Bluefin Tuna (Thunnus thynnus), pp. 18-38. Proceedings of the 5th Annual Work shop/Symposium of the Institute for Resources and the Environment (IRE) entitled: Addressing the Knowledge Gap in Water and Energy: Linking Local and Global Communities. 19th February, 2001, Univ. British Columbia, Vancouver, BC, Canada. 2Lutcavage, M. and Newlands, N. 1998. A strategic framework for fishery-independent aerial as sessment of bluefin tuna. International Commission for the Conservations of Atlantic Tunas (ICCAT), SCRS Working Document /75/98: 1-4. 1 1.1 Research objectives 2 • compare the relative precision of several aerial survey sampling schemes for abun dance estimation, examining the effects of shoal size, aggregation and distribution. Analysis methods were developed to provide information at the individual, shoal and population scale. The results are compared to theoretical predictions and then integrated into a spatially-explicit, individual-based model. This model provides a new description of fish shoaling dynamics that integrates size, structure, interaction, spatial aggregation and distribution of bluefin shoals. Numerical simulation is used to compare the precision of different aerial survey sampling schemes in estimating regional population abundance. Chapter 1 is an introduction to this thesis providing background information in terms of the research objectives. Chapter 2 provides an analysis of individual movement and behaviour from fishery-independent experiments (hydroacoustic tracking and satellite tagging). Chapter 3 presents an automated image analysis method to analyze shoal structure and behaviour. I apply the method to analyze the structure of bluefin tuna formations. In Chapter 4, I present a spatial, individual based (SIBM) model formulated for bluefin tuna, seasonally resident in the Gulf of Maine/Northwestern Atlantic. This model is formulated as coupled ordinary differential equations (ODE's), in a state-space, La-grangian approach, where the movements of interacting individuals and/or their shoals can be tracked spatially over time. This model is constructed on the basis of empir ical analysis results from open-ocean experiments; aerial spotter surveying, ultrasonic tracking, and satellite tagging. The model integrates processes governing alterations in movement and behaviour of individuals, shoal structure, formation and mixing, and movement responses to the environment. The seasonal immigration and emigration of shoals is also considered. The model environment is specified by scalar (concentrations) and vector (gradients) of a set of environmental variables as data layers referenced on a 1.1 Research objectives 3 heterogenous oceanographic grid. The model assumes that phytoplankton and zooplank ton spatial concentration correlates to the abundance of prey, and includes sea-surface temperature, water circulation flow and bathymetry. The phytoplankton, zooplankton, and bathymetry grid layers are compiled from data, and the sea-surface temperature (SST) and flow circulation layers are predictions of an oceanographic model for the study region. Chapter 5 considers underlying population dynamics and the measurement of popu lation abundance using aerial surveys. Five different aerial survey sampling schemes are developed and compared using simulation-based inference: (1) random line-transect, (2) systematic line-transect, (3) systematic stratified transect, (4) adaptive stratified, and (5) spotter survey sampling. Chapter 6 summarizes results of the investigation and identifies several key areas requiring further research. A tabular summary of the specific objectives of this thesis is provided in Tables (1.1 -1.5) and Tables (1.6 - 1.11) at the end of this chapter. Tables (1.1 - 1.5) are a summary of the sources of empirical data as they pertain to the objectives and to each chapter, and lists the mathematical and statistical techniques used in the data analyses. The numbers accompanying the description of each technique are cross-referenced to each of the specific objectives. Tables (1.6 - 1.11) summarize specific objectives in developing components of the SIBM model, including model validation and statistical tests. Appendices contain a list of abbreviations, and additional derivations, results and discussion. The material contained in the appendices are organized into sections that match the main chapter sections. 1.2 Individual-based spatial models of fish populations 4 1.2 Individual-based spatial models of fish populations Fish populations comprise non-identical individuals that live and move in hetero geneous, fluctuating, open environments. In a recent review of new fish population dy namics models, Tyler and Rose [403] discuss individual-based approaches describing indi viduals as non-identical entities according to different population processes that include behaviour, physiological abilities, genetical, environmental responses, and spatial inter actions between individuals. Spatially-explicit individual-based models combine three components: individual variability (e.g. feeding, growth, risk of predation), individual movement, and a spatially heterogeneous environment. Figure 1.1 depicts these three components of SIBM models [403]. These models offer new ways of exploring the mech anisms, consequences, and relevant detail or complexity required by empirical and the oretical investigations to test hypotheses and generate predictions of population spatial distribution and abundance [84, 95,132, 209]. A great variety of modelling frameworks are available for solving spatial popu lation problems including partial (PDE) and coupled ordinary differential equations (ODE), finite-differencing (FD), cellular automata (CA), pattern-matching neural net work (PMNN), genetic (GA), evolutionary (EA), fuzzy and game-theoretic (GT), agent-based algorithms (AI) and geographical information systems (GIS) [58, 82, 99,105,126, 165,171,225, 231,261,353,368,393,407,423]. SIBM models can be formulated using one or a combination of these frameworks. The choice of an appropriate modelling framework requires a consideration of: (1) whether the variables of space and time are continuous or discrete variables, (2) whether analytic or numerical solutions are feasible or attainable, (3) the relevant degree of complexity deemed necessary to address an hypothesis, and, (4) the model approach that is most likely to generate useful insights and predictions relevant to theory and observation. 1.2 Individual-based spatial models of fish populations 5 Figure 1.1: Venn diagram depicting the primary considerations of SIBM models Our ability to measure a given process or coupled set of processes is not well un derstood. SIBM models are especially useful in problems that cannot be readily solved analytically, whereby numerical solutions are obtained using simulation-based inference techniques [18, 235]. Application of this technique in problem-solving maintains the pos sibility that results of various spatial simulations can mutually support analytic solu tions [126,142]. By combining movement, behaviour and environmental considerations, the structure of SIBM models requires an integrated view for how processes are coupled and interact. The relative strength of coupling between processes may change as a result of the behaviour of individual processes and how their coupled dynamic behaviour scales in relation to natural thresholds [188,262]. Numerical simulations of spatial-interaction type models can reveal new and unexpected, emergent outcomes [171]. SIBM's are therefore especially important as they provide predictions to explain the wide-range of observable dynamics across different spatial or temporal scales [130]. 1.3 Variability and patterns of fish population abundance 6 Since the structure of SIBM's involve explicit treatment of individual and spatial interactions, they can identify how uncertainties in both measurements and models can be reduced, in tandem, for optimizing experimental methods, empirical measurements, and spatial sampling protocols [131]. SIBM's represent an important new class of models, having a flexible structure to enable multiple biological or physical hypotheses to be tested concurrently. One general aim of these models is to characterize and determine the appropriate finite set of measurable and fundamental processes that accurately describes population changes in space and time [142]. SIBM models also address a continuing need in ecological science for synthesizing and unifying concepts from both theoretical and empirical fields. The development and application of these models for simulation-based prediction parallels technological and computational advances. 1.3 Variability and patterns of fish population abundance Caddy and Collie [56], Kawasaki [190], Spencer and Collie [376] have investigated the spatial pattern and population abundance variability over time of different fish species. The methodology applied in these studies, termed meta-analysis, applies separate anal yses of empirical data for different fish species, and compares these results, alongside the predictions of models, in attempting to identify characteristics patterns of abundance variability across species. In one of these studies, Spencer and Collie examine the variability of abundance in fish populations using hierarchical cluster analysis. They compare observed data to the predictions of a simple production model as a first-order ODE equation assuming alternative intrinsic rates of logistic population growth, and a Holling-type III functional response representing the population depletion due to fishing. This model considers vary ing time scales and amplitudes of environmental variability, and generates sets of possible outcomes as model solutions. Numerical fitting of the parameters of this model was able 1.3 Variability and patterns of fish population abundance 7 to reproduce observable catch and abundance time-series for different fish species. The hierarchical cluster analysis (Spencer and Collie, [376]) uses empirical time-series of abundance for thirty different fish populations, chosen to provide a wide contrast of geographical location and life-history characteristics. The results of their study iden tify six characteristic patterns of population abundance variability: (i) steady-state with stable interannual variation (e.g., Pacific cod Gadus macrocephalus) , (ii) low-variation and frequency (e.g., Pacific ocean perch Sebastes alutus), (iii) cyclic, low-frequency vari ation (e.g., Atlantic herring Clupea harengus), (iv) irregular variation (e.g., Norwegian herring Clupea harengus), (v) high- variation and frequency (e.g., South African pilchard Sardinops ocellatus), and (vi) spasmodic variation (e.g., California sardine Sardinops sagax). These groups or clusters had consistent patterns with respect to trophic levels, taxonomic status, and life-history traits. Despite differences in the geographical location and fishing management controls correlations between abundance time-series and inter related properties of fish populations were identified. This suggests reliable abundance estimation, prediction and forecasting is attainable on the basis of an understanding of how consistent population patterns are produced by coupled population processes. While the majority of fish population abundance time-series do not support steady-state model assumptions, or models that consider only interannual variation of fishing harvesting and environmental change [44,334], predicted abundance patterns in the study showed that substantial variation in population abundances occurs over a wide range of time scales. Such variations were primarily linked to fluctuations in recruitment rate and environmental forcing factors at interannual scales, fluctuation in the productivity of pri mary producers at decadal scales (termed regime shifts), and fluctuations at amplitudes attributable to climate change at larger time scales [108,115,371,376]. While technology has aided the development and application of SIBM approaches in ecological modelling and simulation studies, fishing technology has also contributed 1.3 Variability and patterns of fish population abundance 8 to progressively higher fishing pressure and intensive human disturbance. Fishing tech nology has improved with more efficient fishing vessels, larger fishing fleets, and better methods for processing and distribution of catch. Non-selective fisheries and unwanted bycatch, the destruction of habitat, light, sound, and chemical contamination and pollu tion by humans are major disturbances to ocean ecosystems. These disturbances impact fish populations which are open systems, and therefore, inherently vulnerable [232,236]. These impacts may alter population processes responsible for the survival and mainte nance of fish populations by changing their population distribution and abundance. Fishing pressure can lead to shifts in habitat, alteration of sex ratios, selective alter ations for various ages or sizes of fish, alterations in behaviour and migration of social groups (i.e., shoals), spawning or feeding aggregations [365]. Furthermore, significant synchrony of fishing dynamics may accelerate population depletion, especially when man agement controls are not based on time-series fluctuations of abundance indices derived from catch statistics. As discussed by Pitcher and coauthors [227,310-313], when fish populations collapse two linked processes occur, namely stock collapse and range collapse. Stock collapse is a rapid reduction of the population, whereas range collapse represents a progressive and significant reduction in a population's spatial range or extent. This process of spatial range collapse, shown to be generated by shoaling behaviour alone, is an effect of synchrony in fishing dynamics, resulting from improved ability of fishers to search, locate and concentrate harvesting [160, 233,311]. Congruent declines in fish pop ulations within regions where fishing activities have impacted multiple fish populations simultaneously, are explained by ecosystem model predictions. These models consider food web structure and superimpose inter-dependencies (coupling and constraints) be tween populations. The predictions of ecosystem models, supported by empirical data 1.4 Atlantic bluefin tuna (BFT) 9 for fisheries worldwide, explain how in addition to the direct removal (catch and by catch of fish), serial population depletion can cause significant indirect population im pacts [119,121,151,236, 295-297,408]. Fishing affects both coupled processes within populations, necessary for their re silience and sustainability, and interactions between populations in marine ecosystems. Devising reliable management controls for fishing operations, therefore, also requires an understanding of how movement, shoaling and environmental processes regulate the be haviour of different, interacting fish populations. Theoretical models and simulation predictions can help to identify how fishery management measures may impact popula tions differently, because they provide an explicit description of how processes behave and interact. Population assessment frameworks that use SIBM models base theoretical predictions on available experimental data, and can be applied to a wide variety of fish populations having different population dynamics [71]. 1.4 Atlantic bluefin tuna North Atlantic bluefin tuna (Thunnus thynnus) belongs to the suborder Scombroidei and two major subspecies are recognized; T. thynnus thynnus in the Atlantic Ocean, and T. thynnus orientalis in the Pacific Ocean [70]. The suborder is characterized by having evolved endothermy; the ability to maintain elevated body temperatures, and is the only group of large oceanic teleosts where endothermy has been documented [29]. BFT elevate their body temperature using a counter-current circulatory exchange system that provides rapid oxygen delivery to muscles and supports high rates of metabolism and digestion [6,30,382,383]. BFT have evolved retractable pectoral and dorsal fins to minimize turbulence while they swim, and a caudal fin with a high aspect ratio enabling improved hydrodynamic efficiency in propulsion [394,409,414,415]. Pectoral fins provide hydrodynamic lift that helps to counteract their negatively buoyancy [417,419]. They are 1.4 Atlantic bluefin tuna (BFT) 10 ram ventilators, i.e. oxygenation occurs via the intake of water through their mouths and across their gills. They are pelagic, predatory, shoaling fish with a life-history involving foraging and spawning migrations extending over vast expanses of the Atlantic ocean. They are fast cruisers and can travel at speeds between 3-5 body-lengths/s (BL/s) or (0.6-1.0) m/s while foraging. Aerial survey estimates made by fish spotter-pilots of their shoal sizes range from 2-5,000 individuals [218-220]. Bluefin shoals show a strong association with other pelagic species, and their local foraging and searching movements appear directed between regions of high and low prey abundance. Bluefin, like other tuna aggregate for foraging at current flow boundaries, convergence zones and upwelling areas [216,220]. Atlantic Distribution and Migration Bluefin tuna are distributed from Labrador and Newfoundland in the north, and south to the Gulf of Mexico and the Caribbean Sea, and the coast of Venezuela and Brazil. In the eastern Atlantic, they are reported to be distributed off Norway and south to the Canary Islands and the Mediterranean Sea. Many questions remained unanswered regarding the spatial extent of their distribution and rates of mixing between the east-, ern and western Atlantic ocean [10,240]. Inferring whether individuals have migrated across the ocean is problematic, as genetic and larval data indicate that bluefin spawn on both sides of the Atlantic [85,217,249,266]. Two distinct spawning grounds in the Mediterranean (presumed eastern subpopulation) and Gulf of Mexico (presumed western subpopulation) have been used to depict and manage BFT as two separate populations with minimal transatlantic mixing [241,329,400]. Whether BFT spawn elsewhere is currently under debate, and remains unresolved due to a lack of knowledge of their life-history migrations. Pop-up satellite tagging has been used recently to target spawning 1.4 Atlantic bluefin tuna (BFT) 11 aged adult BFT, and now provides evidence of a high percentage of individuals emigrat ing from the GOM and mid-Atlantic coastal region [13,159, 214, 215, 217], with some fish migrating to the Mediterranean [27]. Tuna may migrate in response to a variety of stimuli: chemical stimuli and environ mental cues such as phytoplankton distribution, temperature, salinity, odorant plumes, and social taxis [133,156,195,265]. Gradients in the properties of their environment may provide important cues that individuals use to direct local search movements while navigating along migrational routes. How BFT are able to navigate across ocean basins in relation to these gradients, or what factors induce changes in their distribution and migration paths remains unclear. Aerial surveys of BFT document well-defined forma tions, high and low density shoal aggregations, and local searching-travel routes between seasonal forage areas. The migratory paths followed as shoals enter and exit the North western Atlantic shelf are currently unclear. Solar or lunar light-variation and/or changes in sea-surface temperature as they move northward along coastal regions may provide the movement cue for scheduling immigration of shoals [157,174,199]. New fishery-independent, electronic tags (PSAT's) which archive data from sensors recording in situ ambient temperature, pressure (depth), and light-intensity (geolocation) of individuals now enable an examination of movement responses to shoal structure, prey and environ mental gradients. However, continued testing of the accuracy of geolocation algorithms and concurrent improvements in the data-archiving and storage capacity of these new fishery-independent tags continues. These tags provide more accurate information on the movements of BFT, and current investigations may lead to the use of this tagging tech nology on a larger number of individuals for achieving accurate emigration rate estimates with increased sample size. It is reasonable to expect that the movements of individuals travelling within shoals would be dependent on shoal size, shape and structure. Theoretical studies have shown 1.4 Atlantic bluefin tuna (BFT) 12 that organized grouping with an increasing rate of alignment results in more rapid con vergence (i.e., synchrokinesis). The relationship between shoal size and alignment is an important link between the dynamics of individuals within shoals, and their ability to navigate or maintain synchrokinesis during rapid, directed or advective movements. These movements can occur either when they are searching for prey between foraging regions, or migrating over long-distances to spawning or foraging regions. Shoaling Behaviour The majority of 24,000 known fish species form cohesive social groups at some stage in their life history [311]. The social grouping of fish, termed' shoaling [308] is a key natural phenomenon whereby individuals in a population gain certain life-history and evolutionary advantages [65,68]. Social groups of birds are termed a flock, mammals form herds, and shoal is considered an analogous term for fish. The term, school, is restricted to coordinated swimming groups [308, 312, 318]. Scientists have had difficulty in explaining how the evolution of social grouping leads to the actual persistence of a species because selection operates within individuals [209]. However, selection also determines aspects of behaviour such as movement, response to others and to environmental cues. Shoaling enhances the fishes' ability to search and find food resources and average predation risk. Shoaling may be a mechanism for individuals to engage in social information-transfer and learning. The resilience of populations is governed by the a wide-range of factors that alter the ability of individual fish to survive. The movement and behavioural dynamics of shoals can be considered to depend on individual tuna deciding to join, leave or stay in its shoal. These decisions may result when individuals continually try to balance different risks on their survival: to improve resource acquisition, defend against predators, and to increase mating success. What is not clear is whether a shoal itself benefits from including certain individuals and how 1.4 Atlantic bluefin tuna (BFT) 13 to characterize shoal-level properties in terms of selection. Therefore, to understand the evolution of shoaling, one must understand how shoaling benefits individuals. Ecosystem Interactions Bluefin tuna are one of the major predators in the GOM marine ecosystem. They are opportunistic predators whose prey include teleosts, mollusks, crustaceans, and salps [93,243, 306]. During June through to October, bluefin tuna are common off the eastern United States and Canada [377,378,422]. Their primary prey species, include sand-lance (Ammodytes spp.), butterfish (Peprilus triacanthus), Atlantic brief squid (Lolliguncula brevis), long-fan squid (Loligo pealeii), Atlantic mackerel (Scomber scombrus), Atlantic herring (Clupea harengus) and Atlantic bluefish (Pomatomus saltatrix) [61]. Crane, 1936 [78], Dragovich, 1969 [93] and Chase, 2002 [62] attribute differences in the diet of bluefin tuna to: depth of prey capture, prey availability, spawning, atmospheric/oceanographic conditions, physiology and size of predatory individuals, and the relative size of their prey. How the shoaling dynamics of BFT influence the distribution of their prey is an open question. Foraging studies have recognized the importance of adjustments in search and attack modes based upon predator decision-making, and its consequences for how fish forage [22,90,252]. Belovsky and coauthors [22] constructed two main characteristic searching and foraging modes with simultaneous and non-simultaneous attributes. These movement modes were modelled to interact over space and time to produce different predator-prey dynamics. Such alternative movement modes of individuals may explain how they interact within shoals in searching or foraging on their prey. Aerial survey ob servations of surfacing shoals indicate a strong association with other marine vertebrates: humpback, minke and fin whales, basking sharks, and a variety of seabirds [218-220]. 1.5 Study region: Gulf of Maine/Northwestern Atlantic (NWO) 14 1.5 Study region: Gulf of Maine/Northwestern Atlantic Horizontal and vertical movement boundaries The Gulf of Maine is a semi-enclosed continental shelf area, with a bottom depth generally greater than 100m, with an average depth of 150m [404]. The three largest basins are Georges Basin (337m), Wilkinson Basin (295m), and Jordan Basin (311m). Shallower water (<60m) is mostly confined to a relatively narrow band along the coast and onto Stellwagan Bank and Cape Cod Bay. Smith [374] and Incze [179] have con ducted detailed reviews of vertical transport, exchange processes and biological-physical interactions within the region. Exchange between the GOM and North Atlantic is restrictive, occurring mostly through the deep Northeast Channel located between Georges and Browns Banks. Georges Bank limits the flow of water to the upper 20m, while flow in the Great South Channel is limited to the upper 70m [54]. Water below 70m transfers between the Gulf and the Atlantic Ocean through the Northeast Channel, which is also the principle entry point for slope water into the region. Fresh water enters the Gulf from rivers in Maine, the Bay of Fundy, and the Scotian Shelf from the Gulf of St. Lawrence, with the largest amount of cold and of low-salinity fresh water originating from the Scotian Shelf. Northwestern coastal water is turbid and has reduced transparency due to river run-off in comparison to deeper water within the central basin. GOM rivers deliver a spring plume of brackish, stratified waters into the western part of the region. These rivers contribute significantly to the upper 40m of the water column. Outflowing water from the Bay of Fundy, and the east-to-west flow of shallower water, maintains regional counterclockwise circulation of water flow. Observations show that this circulation has its strongest flow during the spring [362]. Where winds cause the surface water to move away from a coastline or to diverge 1.5 Study region: Gulf of Maine/Northwestern Atlantic (NWO) 15 from another surface water mass, deeper water will move up to the ocean surface, cre ating what is called an upwelling current. Coherent sea-surface temperature fronts are observed throughout the ocean in regions where upwelling takes place. Upwelling occurs along coastal regions in the western part of the Gulf, off Nova Scotia, and on the Sco-tian Shelf [118]. Vertical stratification of water occurs in the Gulf where bottom depth exceeds 20m in warmer months, while at shallower depths, tidal mixing and coastal cur rents prevent stratification. Turbulent mixing by winds and waves establish a mixed surface layer (200-300)m at mid-latitudes in the open ocean, and up to 10m in sheltered coastal waters during summer months. Below (200-300)m and 1000m, temperature de clines rapidly, and this steep thermoclinic gradient is the permanent thermocline, set by denser, colder water below. The mixed layer shows seasonal variations and may extend to the permanent thermocline when sea-surface temperatures are low and wind speeds are high. Summer months are characterized by increasing sea-surface temperatures and reductions in wind speeds, which form a seasonal thermocline that can lie above an exist ing permanent thermocline. These seasonal thermoclines are usually at depths (0-10)m. Diurnal thermoclines form when daily temperatures are high and occur at depths (10-15)m establishing temperature gradients of approximately 1-2°C. Despite seasonal and diurnal temperature variations, the permanent thermocline divides the ocean into three vertical layers, with a mixed surface layer above and the deep layer below. The vertical movement of BFT in this region may be governed by the location at depth of the permanent thermocline and its relationship with salinity and dissolved oxy gen. Together salinity and temperature are major determinants of seawater density establishing water masses, which to a large extent, govern circulation within an ocean basin. Steady-state equations used in oceanographic modelling to balance vertical and horizontal flow can be used to approximate the structure of the thermocline [224,324]. Available calculations suggest that surface currents have a considerable coupling impact 1.5 Study region: Gulf of Maine/Northwestern Atlantic (NWO) 16 70" 68' 66" 6«° Figure 1.2: General circulation and bathymetry of the GOM region in the Northwestern Atlantic Ocean. Modified from [404]. on the thermoclinic gradient. Spatial Aggregation of Bluefin Tuna Shoals The location of tuna near oceanic fronts and regions of coastal upwelling may estab lish the links between distribution and preferred levels of temperature, salinity, oxygen and prey abundance [103,129,174,191,202,208,278,321,405]. Within the GOM region, extensive coastal upwelling occurs from an interaction between the Labrador Current (as an equator-ward surface current) and the Gulf Stream (a pole-ward return current). Upwelling within this region does not extend to the surface, but forces varying volumes of nutrient-rich water to deeper water depths. The spatial and temporal scales of phy toplankton patches within the offshore Georgia shelf is believed to be governed by the dynamics of frontal eddies produced by the Gulf Stream. In contrast, inshore regions, 1.5 Study region: Gulf of Maine/Northwestern Atlantic (NWO) 17 0-50 meters Figure 1.3: 3D perspective of GOM circulation/Georges Bank system [344]. Circulation features are superimposed over preferred topographic regions. MCC- Maine Coastal Current, TMF - Tidal Mixing Front, SSF - Shelf-Slope Front. The colour legend indicates vertical depth (m) contours, also indicated near the circulation flow labels. that lead to spatial scaling of phytoplankton patches appears to be highly dependent on topographic control of the position of a regional salinity front [349, 424]. Regional scaling in ocean dynamics from inshore to offshore regions influence trophic interaction between phytoplankton and zooplankton, and subsequently the spatial distribution of the major prey species of BFT within the GOM [72,96,104,153,180,195,223,251,253,384,425]. Environmental factors are one of many contributing factors influencing BFT shoal ag gregation. 1.6 Fishery-dependent and independent indices of abundance 18 1.6 Fishery-dependent and independent indices of abundance Since 1998, a 20 year rebuilding program aims to increase the BFT population in the western Atlantic to produce a maximum sustainable yield (MSY)/population biomass (BMSY) by 2018 with a 50% or greater probability. MSY is defined as the largest average catch or yield that can be taken in the long-term from a population that corresponds to a biomass reference level, BMSY, and fishing mortality, FMSY- From the late 1980's, esti mated stock size for BFT age-classes consisting of eight years and older is relatively stable. While these previous assessments are stable against measurable population abundance trends, projections of the future stock abundance are less stable between two-year assess ments for the periods (1994-96 and 1998-2000) [11, 55, 399]. Scientific advice for ensuring the rebuilding of the western Atlantic bluefin population is currently based on projections of future recruitment that examine low and high recruitment scenarios. However, implica tions of changes in distribution resulting from mixing between fishery regions and between the current regulatory boundary (45°W) dividing the western and eastern portions of the Atlantic population present additional uncertainty [11,115,116,158,159,401]. Cohort analysis and modified virtual-population analysis (tuned-VPA) methods used in BFT stock assessment are based primarily on fishery-dependent, CPUE indices. Sur plus production and yield-per-recruit (Y/R) models have limited application for this species, although they do have application in other tuna fisheries [10,108,338,340]. Co hort analysis assumes exponential mortality and is used to estimate past stock sizes and fishing mortality rates for cohorts. This method requires cohort analysis and fishing mortality rates for the terminal cohort at oldest age. The assumption that alternative fishing gears produce a constant level of selectivity over years is not supportable in many fisheries, including those that target tuna species. Population projection using the VPA method is based on the assumption that if the annual catch of each year-class and the corresponding natural and fishery mortality can be estimated, then the numbers of each 1.6 Fishery-dependent and independent indices of abundance 19 year-class can be back-calculated to reconstruct the population. When terminal mortal ity is not well estimated, standardized fishing effort data or relative abundance data is used to tune virtual population analysis according to an objective function that mini mizes observed and predicted abundances. Ten out of eleven indices of abundance used in tuned-VPA assessments for BFT are currently based on CPUE measures [10]. Scientific advice can play a major role in devising appropriate fisheries management policies, and progress in this field relies on support for continued experimental evaluation of new techniques and their analyses. Problems in the management of highly migratory species such as bluefin tuna serve to illustrate many scientific concerns regarding pop ulation or stock assessment methodology. Sound fisheries management now recognizes that the consequences of fishing and the underlying population dynamics of fish are both inherently uncertain [201,348]. Furthermore, aspects of the life-history dynam ics of highly migratory fishes cannot be adequately addressed by averaging population parameters over the stock's entire geographic range [110]. The relationship between fishery-dependent abundance indices (CPUE) and true abundance for highly migratory, shoaling fish populations is rarely, if ever, known, and there are serious challenges in characterizing temporal and spatial dynamics within CPUE-based assessment frame works [64,67,114,116,163,318,334,359]. Equating CPUE with population abundance rests on the assumptions that (1) vul nerability of fishing gear is equal, (2) fishing effort is randomly distributed, and (3) fish are randomly distributed [44,45]. Many authors maintain that without knowledge of shoaling dynamics, our ability to understand changes in a shoaling population is lim ited [40,44,107,110,140,263,264,334,347,396,406]. Dynamic processes that are part of shoaling may regulate shoal encounter rates and the size and spatial extent of their spa tial aggregations, shoal fragmentation and coagulation rates and lead to different shoal structural formations. 1.6 Fishery-dependent and independent indices of abundance 20 Spatially-driven abundance trends caused by stock mixing effects may potentially compound biases and levels of uncertainty in abundance estimates over time. A VPA implementation of a mixing model for two stocks with overlapping ranges has recently been applied to catch, abundance, and passive tag (mark-recapture) movement data for BFT [329]. Resulting abundance estimates from this overlap VPA model, when com pared with a VPA model incorporating diffusive movement assumptions, suggests that the overlap VPA model is much less sensitive to assumed values of spatial mixing [11]. Both models fail to fit tagging data well and result in poor estimates of spatial mixing coefficients. This contributes to high uncertainty in the resulting abundance estimates. Previous results incorporating movement considerations in VPA assessments and projec tions indicate that an integration of spatial mixing effects for BFT within and between fishing regions may offer substantial improvements in the accuracy and precision of pop ulation status [325,328,331,399,400]. These previous studies suggest that current stock assessment projections are sensitive to different assumptions and uncertainties relating to mixing or alterations in distribution. The highest levels of uncertainty in BFT pop ulation assessment and fisheries management relate to the lack of knowledge on BFT spawning site fidelity, migration routes, and mixing. In 1993, the New England Aquarium (NEAQ), initiated an aerial survey program in collaboration with the East Coast Tuna Association (ECTA), a commercial fishery industry group. Spotter pilots are employed in tuna fisheries to monitor shoals and to direct harpoon and purse seine fisheries [35,283,377]. Fish spotters were equipped with digital and photographic equipment enabling them to observe and record sighted BFT shoals [218-220]. NEAQ investigators conducted hydroacoustic tracking and satellite tag ging experiments to provide additional information on BFT movement, shoal structure and dynamics, and their association with other marine life. These experiments provide 1.6 Fishery-dependent and independent indices of abundance 21 data on the vertical and horizontal movement, shoaling behaviour, environmental rela tionships, and post-season migration of BFT in the Northwestern Atlantic [73,214-221]. The use of aerial surveys and direct observation of pelagic fish populations is a rela tively new experimental method providing invaluable data and information on movements and shoaling behaviour [17,147-150,220,281,381]. For example, aerial surveys are used in assessing the abundance of juvenile southern bluefin tuna in the Great Australian Bight [75]. Similarly, aerial surveys have provided observations of the spatial structure and variability of marine mammal populations [76,172, 204,282, 356]. More recently, re search has been directed towards the development, testing and application of different aerial survey spatial sampling strategies in providing fishery-independent estimates of population abundance [20,46,48, 51, 75, 77,122,147, 211, 244, 322, 332, 379]. Statistical methods and analyses provide different methods for dealing with bias and uncertainty in population abundance estimation from shoal size estimation, observer-shoal encounter rates, multiple-counting of shoals, observer visibility and sightability, and spatial interpolation errors [74,100,102,106,154,173,176,181, 245, 246, 323,343]. Differ ent analytical and statistical methods are required due to the diversity of survey de tection technologies. Survey methods include tracking and tagging of individuals using fishery-dependent, passive (i.e., mark-recapture), and fishery-independent, active (i.e., ultrasonic, satellite) techniques. Shoals and aggregations have also been surveyed with acoustic transducer, light-detection and ranging (LIDAR) and synthetic aperture radar (SAR) technologies from aerial and satellite platforms [63,86,128,166,168,176,238,247, 248, 276,277,354,385]. Nonetheless, new analytical approaches can integrate variability and uncertainties of biotic and abiotic data on individual movement and behaviour, shoal structure, be haviour, movement, mixing, and coupled responses can improve the accuracy and reli ability of the interpretation of direct-assessment observational data. A primary aim of 1.6 Fishery-dependent and independent indices of abundance 22 these new methods is to integrate direct-assessment experimental techniques to provide reliable spatial and time-series estimates of population abundance. While direct observa tion methods differ from catch related data in the way in which experimental sampling is conducted, a consideration of depletion and mortality effects on populations from fishing is still required. Fishery-independent sampling, analytical and simulation-based methods used to integrate direct-observational data provides an unique perspective of the impacts of harvesting fish populations. This approach to population assessment is especially im portant because movement and population processes have been neglected historically or have been considered in an over-simplified fashion. However, such issues form the eco logical basis on which further interpretation of assessment predictions and forecasts are evaluated [365]. 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Movement paths were re-constructed in two and three-spatial dimensions by interpolating between successive position estimates. I examined the variation in move-displacement, speed and direction parameters in the movement path reconstructions.1 I examine the form of the move-speed and turning angle distributions, calculating statistics for defined movement parameters in two-dimensions. These distributions show unimodal and bimodal variations according to the scale at which movements are sampled. I also examine the statistical correlation between successive displacements, where values of movement parameters at a given position are dependent on values at previous positions, termed autocorrelation. If attractive and repulsive forces are considered to describe the movement interaction between fish moving in shoals, then autocorrelation in velocity and turning angle indirectly show the variation in the strength of these forces over time. Autocorrelations in movement parameters, such as periodic variation in turning angle, may result from a greater number of neighbours, or on neighbours that have a stronger influence on the movement of the individual being tracked. Cross-correlations between movement parameters are also of interest, and are further confounded by the influence ^ewlands, N. and Lutcavage, M. 2001. Prom individuals to local population densities: North Atlantic Bluefin Tuna (Thunnus thynnus), 421-441, In: Electronic Tagging and Tracking in Marine Fisheries, J.R. Sibert and J.L. Nielsen (eds.), Kluwer Academic Publishers, Dordrecht, 484 PP-34 2.0 Individual Movements 35 of shoaling neighbours. Three-dimensional trajectories are formed by linearly correlating the geopositional data, sampled periodically within the range (60-550)s in the 2D paths, with depth data recorded concurrently at smaller (15s) sampling intervals. This enabled an examination of the full resolution of movements as space trajectories. Alternative movement modes are identified using Lomb periodograms which inversely transform movement trajectories into frequency space [212]. Unlike standard Fourier spectral techniques, the Lomb method does not require periodic sampling at equal inter vals of experimental time-series data [111]. The Lomb method was used to extract modal statistics for characterizing movement behaviour on the basis of second-order autocorre lations in the turning angle and move-speed parameters. Move-parameter statistics help to identify characteristic modes of movement and mode-switching events, with the mo tivational decision-making of individuals making trade-offs between foraging, searching for food, or migrating over larger distances [286]. Changes in turning rate and depth preference are detected between two movement modes (m1,m2), occurring over (116.7 ± 57.52)s and (109.2 ± 49.05)s respectively. I ex amine how modal alterations in movement are also important for the interpretation of movements observed at larger spatial extents. Kalman filtering is an efficient, adaptive technique for interpolating between geoposition estimates combining latitude and longi tude measurement uncertainties. I apply this technique to filter PSAT tagging data that provides information on individual tuna movements at larger spatial scales (e.g., 1000km) than the hydro-acoustic observations (e.g., 10-100)km. I characterize the way in which tuna move, based on movement parameter time-correlations and cross-correlations. I compare the full set of observed movements with theoretical predictions generated us ing statistical bootstrapping for simple (RW), correlated (CRW), biased (BRW), and biased-correlated (BCRW) random-walk models, and a significance test on the relative contribution of movement persistence and external bias. The results of these analyses on 2.1 Interpolation of the movement observations 36 observed movements of individual tuna provides empirical estimates on movement pa rameters and correlation dynamics, necessary for formulating a spatial, individual-based model for BFT. 2.1 Interpolation of the movement observations The horizontal and vertical movement and behaviour of giant BFT (110-350) kg tracked by hydro-acoustic telemetry for up to 48 hours in three regions of the Gulf of Maine (GOM) (Stellwagen Bank, Great South Channel, Cape Cod Bay) was recently reported by Lutcavage and coauthors [215,216], shown in Figure 2.4. Giant bluefin rep resent the primary age/size-class cohort comprising their seasonal assemblage in the study region. Individuals travelling in shoals were tracked using an ultrasonic transmitter and single-directional hydrophone having a detection zone of approximately 1.7 km. Succes sive geoposition estimates of individuals were approximated as the coordinate position of the tracking vessel determined using GPS (global positioning system). Three consis tent movement modes were identified: (1) repetitive travel through the thermocline with small move-displacements (<5-40 km/day), (2) travel primarily in the ocean surface layer with large displacements (40-76 km/day), and (3) large, vertical displacements (diving) at dusk and dawn. Further details on the raw data records I compiled for the observed movement paths (N=ll) are provided in Table 2.12. In this table, two separate move ment records for the same individual (9604) are denoted as 9604a, 9604b, and individual 9605 was omitted due to an insufficient length in the geolocation record. New archival satellite tags (PSAT's) can sample movements over larger durations than 48 hours. These archival tags are equipped with sensors designed to sample and archive light-intensity [28,164,267,369,420]. A determination of movement path end-points using GPS for pop-up tags is provided by the Argos satellite, which receives and relays the streams of archived data, once a tag, programmed to detached from 2.1 Interpolation of the movement observations id o o CD cc I.S1 CO co co CO LO LO Tf CO o 00 oo CO LO LO 00 tr-CO 3.450 oi CN co Tf oi CN co Tf Tf' CN 06 rH co Tf 0 co 3.450 LO co 03 ir-Tf cr- co ^ 00 P CO OO H ^ •• CO _ CO CN ri « LO CN LO p2 co CN 00 IT-00 co 00 co Tf LO co CN CN lr-Oi . co co" 22 '00" co LO Tf LO Oi rH CN LO CO CN ^1. tr- ^ ^ T—1 ^ ^ CN ^ ^ Tf 0 , „ LO , n LO , „ co , _ co t~- O rH LO CN co Oi rH rH LO LO O LO CN co CN rH LO Oi CO O CN CO LO Tf CO Oi co rH co LO co co co CO Tf CO Oi CO rH LO rH CO CO LO CO O LO CN Tf Tf 00 CO CN Tf CN rH Tf rH Tf CO CN Tf Tf LO LO LO rH O s rH ^—' rH -—' H -— rH ~ rH ^—' rH ^—' CN co rH Oi CN rH IT- Oi CN Oi rH 0O 00 rH CO CN tr- Tf 00 Oi O CO CO Tf CN LO rH rH O CO rH 1-- LO rH CO CN rH 0O rH Oi rH o cj . 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Further information on these observations is provided in Table 2.12. 2.1 Interpolation of the movement observations 39 an individual after a given time duration, rises to the ocean surface. The successive geopositions between GPS starting and end-point position fixes of tagged individuals are then derived with astronomical algorithms and equation fitting procedures to match the observed intensity variations expected on the basis of day-length and time of dusk and dawn (corresponding to a given latitude and longitude respectively) on the earth spheroid for a given time of year (see [421] for relevant astronomical equations). The last few successive position estimates determine the extent to which a tag, once detached from a fish, has drifted on ocean currents before satellite detection. The attenuation of light below the ocean surface can also be considered in such calculations. Additional miniature sensors also record temperature and pressure. Interpolation equations Cartesian (xyz) coordinates, referencing the positions of an individual along its move ment path, relate to movement parameters, (k, Qi, fa), defined within polar and spherical coordinate systems. Movement parameters are depicted in two-dimensions (X, Y) using polar coordinates, and in three-dimensions (X, Y, Z) in spherical coordinates, as depicted in Figures 2.5 and 2.6. The equations defining the transformation between the cartesian and spherical coordinate systems are, n xn = li sin 9{ cos fa (2.1) i=l n n zn ='Y^k COS 8i (2.3) i=l The corresponding equations for the 2D case are obtained by setting 9i = n/2 in the above equations. For each successive move, i, where i — (1, ...,n) of n total moves; U is 2.1 Interpolation of the movement observations 40 y Figure 2.5: Definition of parameters used in the iwo-dimensional interpolation of BFT move ments. Each move displacement of variable length, U, has a corresponding directional angle, fa, referenced to the fixed axis, X, and turning angle, </?;, measuring the change between successive move-directions (adapted from [239]). 2.1 Interpolation of the movement observations 41 defined as the length of successive move-displacements, fa is the directional (azimuthal) angle [0, 2ir], measured positive in the counter-clockwise direction relative to a fixed axis, X, and 9i is the vertical inclination (polar) angle [0,7r], measured positive clockwise from the Y axis. The directional angle (fa) of the ith move is related to the sum of previous turning angles (ifi), j = (1,n—1) [—7r, IT], representing the angular change in successive move-direction, i-1 0i = + (2-4) 3=1 Time-series profiles of successive alterations in the movement parameters accompany the 3D interpolated trajectories for each individual (Figure 2.18 in Section 2.5 and Fig ures B.192- B.200 in Appendix B). Mean statistics for the movement parameters includ ing mean move-length (u), mean-squared move-length (fi2), mean move-duration (r), and mean cosine and sine of the turning angle, (cos <p) are calculated for each path, = -X> (2-5) n . TT2 = - £ l\ (2.6) n 1 i r ^9 <"> i=i x ' ^ n 1 " c = cos 09 = — > cos tfi, s = sin </?= — > sin (pt (2.8) n *7~! n i=i i=i Estimates of these measures for movement observations are provided in Table 2.13. 2.1 Interpolation of the movement observations 42 Table 2.13: Statistics of move-length (k), time duration (r,), vertical inclination directional (fa) and turning (ipi) angles in movement observations of BFT, for sampled positions, and shoal size, S. ID S Ti(s) k(m) Vi(m/s) <Pi(°) 9601 500 522.1 679.88 1.33 89.39 29.56 40.11 9602 150-200 60.17 101.61 1.69 86.86 42.26 19.03 9603 >1000 16.52 100.41 6.07 88.18 48.37 21.87 9604a 40-200 75.23 89.120 1.18 87.47 54.16 19.10 9604b - 65.67 119.56 1.82 87.40 52.64 17.39 9701 12 89.07 150.34 1.69 88.21 42.36 19.52 9702 6 60.65 85.750 1.41 87.36 44.01 18.75 9703 12 61.57 72.880 1.18 87.50 42.25 20.06 9704 200-300 60.96 115.28 1.89 87.76 45.10 18.36 9705 200 65.77 101.58 1.54 86.49 46.80 38.58 161.64 ± 57.970 1.98 ±0.460 87.66 ± 0.2500 44.75 ±2.150 23.27 ±2.710 2.1 Interpolation of the movement observations 43 7. Figure 2.6: Definition of parameters used in the i/iree-dimensional interpolation of the BFT movements. Each move displacement of variable length, /j, has a corresponding directional angle, fa, referenced to a fixed axis, X, vertical inclination angle, 0, (spherical, azimuthal and polar angles respectively, and turning angle, tpi, measuring the change between successive move-directions) (modified from [293]). Table 2.14: Depth-correlated data summary for hydroacoustic tracking of BFT (N=10). ID YY Date(DD/MM) Depth-Correlated Record n Start End Duration(h) 9601 1996 11-12/09 205 11:02:00 (39720) 16:30:00 (145800) 29.47 9602 1999 20-22/99 2787 14:15:43 (51326) 12:49:00 (218940) 48.56 9603 1996 26-27/09 1752 12:51:38 (46298) 20:54:02 (161642) 29.45 9604a 1996 6-8/10 2477 12:12:37 (43957) 10:15:55 (209755) 46.06 9604b 1996 12-13/10 1183 10:25:37 (37537) 07:59:34 (115174) 21.57 9701 1997 15-17/08 1888 12:52:34 (46369) 11:30:00 (214186) 46.62 9702 1997 19-21/08 1820 17:47:48 (64048) 00:26:17 (174376) 30.64 9703 1997 25/08 352 12:51:55 (46315) 18:51:33 (67893) 5.990 9704 1997 16/09 180 14:35:05 (52505) 17:36:49 (63409) 3.030 9705 1997 17-19/09 2567 15:47:23 (56843) 14:39:30 (225572) 46.87 2.2 Move-speed and turning angle distributions 44 2.2 Move-speed and turning angle distributions Frequency distributions in two-dimensions provide an indication of the variability of movement parameters, averaged across the length of an observed path. They are formed by aggregating parameter values for each successive move observed. Mean tendencies in movement observations at a specific spatial or temporal scale are revealed when fre quency distributions are compared to theoretical probability distributions. Because the motivation of animal's decision making is not usually known, simulation of movement models and significance testing of simulated outcomes often relies on sampling from em pirical frequency distributions, or the corresponding forms of theoretical distributions for movement parameters. Siniff and Jessen [372] demonstrate how 2D distributions of movement parameters are used in simulating movement model patterns and generating comparisons to telemetry data. Two-dimensional distributions are also useful in identi fying relationships between animals and permanent or seasonal habitat features. I compare theoretical distributions to the observed frequency distributions for the move-speed and turning angle parameters. This comparison indicates the extent to which individuals move left or right, and the range of their movement speed. The von Mises circular (normal) distribution function occurs when turning angles are concentrated symmetrically about a specific bearing. This distribution has parameters (m, c), where m is the angle of maximum probability (modal direction), c - concentration parameter (alters distribution skewness), "M - ^wf,{v-m) <2-9> where, ID(c) denotes the Bessel function of order zero (see [15]). This distribution is unimodal for 1, and uniform when c = 1 (i.e., constant f(<p), over all <p). A theoret ical probability distribution or 'density function' useful in describing the turning angle distribution has a bimodal form. This bimodal distribution of turning angle has a central 2.2 Move-speed and'turning angle distributions 45 symmetry, where the von Mises distribution applies within angles for periodic nir (radi ans) (i.e., 180° sectors), for an integer n. The bi-modal form (n = 2) of the von Mises density function [372], is p(<p) = -i—eccos(^-) (2.10) 27T0(CJ The frequency distribution of move-speed shows the form of a gamma-distribution, pW = ^f|c7TT)"°exp("i) (2'H) where v is move-speed, a and 8 are parameters of the distribution function (a > — 1, 8 > 0,0 < x < oo) and T() is the gamma function [15]. The gamma distribution is a general type of statistical distribution that arises naturally in processes which generate observed events separated in time, termed waiting times. Events are here considered to be associated with changes in the speed of movement. If the occurrence of events is random and rare, then the expected distribution function for an event is expected to follow a Poisson distribution. The Poisson distribution describes a number of discrete events in a sequence, where the number of events over time is exponentially distributed. When a — 1, the gamma distribution reduces to an exponential distribution. The probability of events for a Poisson process is assumed to be small. To avoid having multiple events at same time, the expected number of events that occur is assumed to depend only on the time-interval or duration over which they are counted, but not on time or previous history [330]. Frequency distributions of move-speed and turning angle for the observed movements of individuals were interpolated in two-dimensions. These distribution are provided in Figures 2.7, with additional results for the other tracks provided in Appendix Bl. The frequency distributions of turning angle having been defined within the range of [—IT, IT] (Figure 2.5) are shown shifted by a factor of IT, in the positive range of [0, 2TT], measured from the fixed x-axis. 2.2 Move-speed and turning angle distributions 40 These results show that considerable variability exists in the distribution of move-speed and turning angle across the observed movement paths, with the effects of differ ences in sampling rate, body weight and shoal size. The parameter distributions show significant alterations in their shape (mean, variance, kurtosis). The general form of these distributions supports theoretical functional forms of the Gamma and von Mises distributions. Figure 2.7: Left: Observed movement path of individual 9601 in 2D with estimated weight, W, and belonging to a shoal of size, a. Right: Frequency distributions of move-turning angle and move-speed, with frequencies scaled between (0,1). 2.3 Move-speed and turning angle autocorrelations 47 2.3 Move-speed and turning angle autocorrelations Autocorrelations of move-displacement, speed and turning angle in the hydroacoustic observations were examined and compared to analytical functions for autocorrelation from a theoretical perspective. Move-speed autocorrelation Niwa has formulated a stochastic dynamical equation for the centroid (shoal-centre) motion of a foraging shoal comprising S individuals (S - shoal size), in 2D space as [271], -_L = K ^1 - V - K(3V2V + r}(t) (2.12) where every individual swims at a steady speed of the shoal, /?-1/2, J is the tendency of shoaling individuals to swim parallel to each other (schooling tendency), and «_1 is a relaxation movement time-scale for individual fish. The centroid velocity, V, of the shoal is allowed to fluctuate according to «5-correlated noise, fj(t) in Equation 2.12, such that two successive points in time t and t' are correlated as, <»/(«)> = 0, mr?{t')) = 2J8(t-t>)\ (2.13) where e is a fluctuation measure for this correlation, I is the 2D identity matrix, and 5(t — t') is the Dirac-delta function defined as, ,1 t = t 5(t-t') = { (2.14) 0 t±f In the above equations, (x) denotes the expectation value of x (often denoted as E[x] or x). The first term appearing in Equation 2.12 represents the magnitude of fluctuation in shoal velocity due to changes in the mean and variance of velocity of individual fish. The second term represents the correlation in shoal velocity over time, and the third term is random noise. The main assumptions of this model are that: 2.3 Move-speed and turning angle autocorrelations 48 • individual fish move with speeds that fluctuate about a most probable speed of their shoals. • individual fish in shoals move in directions determined by a fixed coefficient repre senting the degree of polarity. • changes of individual swimming velocity over time are considered statistically in dependent - fish interact randomly such that the rate of change in velocity and tendency to swim parallel to each other is the same. Under these assumptions, the collective movement of individuals in shoals is main tained by correlation in their velocities. This theoretical model shows that for individual fish, the correlation in movement parameters over time, such as velocity, has a large effect on the collective motion of their shoals. The model demonstrates that correlation between velocity and other movement parameters, such as turning angle, are important. However, the model does not consider: (1) a relative ability of individual fish to respond to their neighbours to maintain distinct formations while moving collectively, and (2) non-random movement responses to changes in their environment that would require re alistic assumptions on how mov