Citation
Changes in Target Species and Spatial Population Structure in Stock Assessment Models for Highly Migratory Pelagic Fish Stocks as Exemplified by the South Atlantic Blue Shark

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Title:
Changes in Target Species and Spatial Population Structure in Stock Assessment Models for Highly Migratory Pelagic Fish Stocks as Exemplified by the South Atlantic Blue Shark
Creator:
Carvalho, Felipe Correia
Place of Publication:
[Gainesville, Fla.]
Florida
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University of Florida
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Language:
english
Physical Description:
1 online resource (155 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Fisheries and Aquatic Sciences
Forest Resources and Conservation
Committee Chair:
MURIE,DEBRA JEAN
Committee Co-Chair:
AHRENS,ROBERT
Committee Members:
PARKYN,DARYL CHARLES
PONCIANO CASTELLANOS,JOSE MIGUEL
BIGELOW,KEITH A
CARLSON,JOHN K
HAZINS,FABIO
Graduation Date:
5/3/2014

Subjects

Subjects / Keywords:
Biomass ( jstor )
Fish ( jstor )
Fisheries ( jstor )
Longline fishing ( jstor )
Modeling ( jstor )
Oceans ( jstor )
Parametric models ( jstor )
Sharks ( jstor )
Statistical models ( jstor )
Tuna ( jstor )
Forest Resources and Conservation -- Dissertations, Academic -- UF
assessment -- elasmobranch -- migration -- selectivity -- stock
Atlantic Ocean ( local )
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Fisheries and Aquatic Sciences thesis, Ph.D.

Notes

Abstract:
In 2008 The International Commission for the Conservation of Atlantic Tunas (ICCAT) encouraged future research on movement patterns, habitat utilization, and different stock assessment models that would allow incorporation of these types of information to improve the quality and reduce uncertainty in future Atlantic blue shark (Prionace glauca) stock assessments. Furthermore, the ICCAT working group on assessment methods also expressed concern that some CPUE series used in the assessments might be misleading due to changing fishing strategies within the fishery, such as changes in target species. My dissertation proposal addresses this necessity and focuses on investigating the movements of the South Atlantic blue shark stock using Pop-up Satellite Archival Tags (PSAT), as well as developing and comparing the predictions of a series of stock assessment models for the South Atlantic blue shark. Chapter 2 presents a suite of Bayesian state-space production models fitted to the time series of a South Atlantic blue shark stock in which a single change point in the stationary distribution of the catchability coefficient is specified in order to capture a significant change in target species (hence catchability) in the Brazilian longline fishery. Accounting for a single change point in the catchability coefficient had no significant impact on the status of South Atlantic blue shark (still above BMSY); however, it provided a robust way of accounting for changes in catchability as a result of changing target species. In Chapter 3, satellite telemetry and random mixed-models were used to quantify the factors driving movement patterns in blue sharks across the South Atlantic Ocean. The majority of sharks showed a residency to core areas and showed patterns of vertical segregation between adults and juveniles. In chapter IV, the effectiveness of integrating the vertical spatial structure of the south Atlantic blue shark population in Statistical catch-at-age models (SCAM) was evaluated. Although accounting for vertical spatial structure had no significant impact on the status of SA blue sharks (still above SSBMSY), the model provided a simpler method to capture some of the complexities of a spatially-structured situation. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2014.
Local:
Adviser: MURIE,DEBRA JEAN.
Local:
Co-adviser: AHRENS,ROBERT.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2014-11-30
Statement of Responsibility:
by Felipe Correia Carvalho.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Embargo Date:
11/30/2014
Resource Identifier:
907379240 ( OCLC )
Classification:
LD1780 2014 ( lcc )

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CHANGES IN TARGET SPECIES AND SPATIAL POPULATION STRUCTURE IN STOCK ASSESSMENT MODELS FOR HIGHLY MIGRATORY PELAGIC FISH STOCKS AS EXEMPLIFIED BY THE SOUTH ATLANTIC BLUE SHARK By FELIPE CORREIA CARVALHO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2014

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201 4 Felipe Correia Carvalho

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This dissertation is dedicated in loving memory of my grandparents Jose Lira Soares de Carvalho and Maria Ivone de Carvalho

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4 ACKNOWLEDGMENTS Thank God for the wisdom and perseverance that he has been bestowed upon me during my years in Graduate School, and indeed, throughout my life: "I can do everything through him A special feeling of gratitude to my loving parent s, Gesner Correia and Irany Carvalho, and my brother Eduardo Carvalho for being the pillows, role models, catapults, cheerleading squad and sounding boards I have needed. I also would like to express my sincere gratitude to Dr. Debra Murie, my committee ch airman for her countless hours of reflecting, reading, encouraging, and most of all friendship over the past seven years. You have set an example of excellence as a researcher, mentor, and instructor I could not ask for a better advisor. A special thanks to my committee co was always open whenever I ran into a trouble spot with my statistical models or had a question about my research or writing. Rob makes learning stock assessment a piece of cake. My grati tude also goes to Dr. Daryl Parkyn for encouragement and guidance. He has walked with me through all the stages of this project, and his friendship, instruction, and positive attitude have enabled me to face and overcome various difficulties. I would t o like to thank Dr. Jose Miguel Ponciano for enlightening guidance and inspiring instruction in the development and completion of this study. Dr. Ponciano was always there to help me strength en my quantitative skills and my grounding in data analysis. My experience and research were greatly improved through engagements with and critiques of knowledgeable, dedicated, available, and supportive scientists from the NOAA National Marine Fisheries Service and I especially thank Mr. Keith Bigelow and Dr. John Carlson.

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5 My gratitude and sincere thanks also goes to Dr. Fabio Hazin. His passion for fishery science, but more importantly, the analytical thinking that goes behind it has inspired me since my very first day in college. I also want to thank Dr. Alexand re Aires da Silva and Dr. Mark Maunder for their great support, encouragement, insight, and suggestions during the development of this work. My sincere thanks to Mr. George Burgess from the Florida Program for Shark Research. This journey would not have been possible without his support, guidance, and friendship. To the Pacific Islands Fishery Science Center (NOAA PIFSC), I especially thank Lennon Thomas, Gerard DiNardo, Ben Richards, Yi Jay Chang, Hui Hua Lee, William Walsh, Jon Brodziak, Keith Bigel ow, Darryl Tagami, Penglong Tao, Donald Kobayashi, and Annie Yow My special words of gratitude to Humberto Gomes Hazin, Bruno Leite Mourato, Catarina Wor, John Waters, Charlene da Silva, Yannis Papastamatiou, Mollie Brooks, Jake Ferguson, Rosana Zenil, Ga briela Blohm, Oscar Murillo, Christian Barrientos, Geoffrey Smith, John Hargrove, Dana Bigham, Chelsey Campbell, Pat Gardner, Amanda Croteau, Zy Biesinger, Rui Coelho, Joana Fernandez, Johanna Imhoff, Andrew Pierc y Paulo Travassos, Drausio Veras, Diogo Ma rtins, Andre Afonso, Fabio Caltabellotta, Chris Wall, Laurent Dagorn, Paulo Guilherme Vasconcelos de Oliveira, Danielle Viana, Osman Crespo, Fernando Mendonca, Santiago Montealgre Quijano, and Mariana Travassos, for all their professional help that they ha ve extended to me throughout. To my friends and roommates, thank you for listening, offering me advice, and supporting me through this entire process. Special thanks to my friends from Biology Department and Fisheries Pro gram, soccer, and SURF

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6 Finally, I would like to express my deepest appreciation and thanks to my best friend, my comp anion, my better half, acknowledge my extended family, Jim Nelson, Caro l Banning, Steven, Emily and Donna Zill for their encouragement, support, and friendship. Finally, I would like to express my deepest appreciation and thanks to my best friend, my comp anion, my better half, my love, al so like to acknowledge my extended family, Jim Nelson, Caro l Banning, Steven, Emily and Donna Zill for their encouragement, support, and friendship

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7 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 9 LIST OF FIGURES ................................ ................................ ................................ ....................... 10 LIST OF ABBREVIATIONS ................................ ................................ ................................ ........ 12 ABSTRA CT ................................ ................................ ................................ ................................ ... 14 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 16 1.1 Overview ................................ ................................ ................................ ........................... 16 1.1.1. Stock Assessment For Sharks ................................ ................................ ................ 20 1.1.2. Surplus Production Models ................................ ................................ ................... 21 1.1.3. Age S tructured Models ................................ ................................ ......................... 23 1.1.4. Statistical Catch at Age Model ................................ ................................ ............. 24 1.2. Motivation ................................ ................................ ................................ ........................ 25 2 INCORPORATING SPECIFIC CHANGE POINTS IN CATCHABILITY IN FISHERIES STOCK ASSESSMENT MODELS: AN ALTERNATIVE APPROACH APPLIED TO THE BLUE SHARK ( Prionace glauc a ) STOCK IN THE SOUTH ATLANTIC OCEA N ................................ ................................ ................................ .............. 29 2.1. Background ................................ ................................ ................................ ...................... 29 2.2. Materials and Methods ................................ ................................ ................................ .... 32 2.2.1. Catch and Effort Data ................................ ................................ ............................ 32 2.2.2. Cluster Analysis ................................ ................................ ................................ ..... 33 2.2.3. CPUE Standardization ................................ ................................ ........................... 34 2.2.4. Bayesian State Space Production Model ................................ ............................... 35 2.2.5. Prior Distributions ................................ ................................ ................................ 38 2. 2.6. Biological Reference Points ................................ ................................ .................. 41 2.2.7. Sensitivity Analysis ................................ ................................ ............................... 42 2.3. Results ................................ ................................ ................................ .............................. 42 ................................ .................. 42 2.3.2. CPUE Standardization ................................ ................................ ........................... 43 2.3.3. Biomass Dynamic Model ................................ ................................ ...................... 44 2.4. Discussion ................................ ................................ ................................ ........................ 46 3 HABITAT SELECTION AND TRANS OCEANIC MIGRATION BY BLUE SHARKS IN THE SOUTH ATLANTIC OCEAN FROM SATELLITE TELEMETRY ..... 65

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8 3.1. Background ................................ ................................ ................................ ...................... 65 3.2. Materials and met hods ................................ ................................ ................................ ..... 67 3.2.1. Satellite Tracking ................................ ................................ ................................ ... 67 3.2.2. Space Utilization Distribution ................................ ................................ ............... 68 3.2.3. Analysis of Directionality ................................ ................................ ...................... 69 3.2.4. Overlapping Tracking and Oceanographic Data ................................ ................... 70 3.2.5. Random Effect Models ................................ ................................ .......................... 70 3.2.6. Vertical Habitat Utilization ................................ ................................ ................... 72 3.3. Results ................................ ................................ ................................ .............................. 72 3.3.1. Movements and Utilization Distribution ................................ ............................... 72 3.3.2. Habitat Selection and Mixed Models ................................ ................................ .... 74 3.3.3. Vertical Habitat Utilization ................................ ................................ ................... 76 3. 4. Discussion ................................ ................................ ................................ ........................ 76 4 INCORPORATING VERTICAL SPATIAL POPULATION STRUCTURE INTO STATISTICAL CATCH AT AGE STOCK ASSESSMENT MODELS .............................. 92 4.1. Background ................................ ................................ ................................ ...................... 92 4.2. Materials and Methods ................................ ................................ ................................ .... 94 4. 2.1. Data ................................ ................................ ................................ ........................ 94 4.2.2. Data Analysis ................................ ................................ ................................ ......... 96 4.3. Results ................................ ................................ ................................ ............................ 101 4.3.1. CPUE St andardization ................................ ................................ ......................... 101 4.3.2. Statistical Catch at Age ................................ ................................ ....................... 101 4.4. Discussion ................................ ................................ ................................ ...................... 102 5 CONCLUSIONS ................................ ................................ ................................ .................. 120 APPENDIX A GAMM ................................ ................................ ................................ ................................ 123 B ANALYSIS O F RESIDUALS ................................ ................................ ............................. 125 C TUKEY TEST ................................ ................................ ................................ ...................... 127 D EFFORT DISTRIBUTION ................................ ................................ ................................ .. 135 LIST O F REFERENCES ................................ ................................ ................................ ............. 140 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 155

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9 LIST OF TABLES Table page 2 1 Growth parameters values used in the Demographic analysis for South Atlantic blue shark. ................................ ................................ ................................ ................................ .. 51 2 2 Percentage of each species or group of species per cluster (Asterisks (*) indicates the target species in each cluster). ................................ ................................ ........................... 52 2 3 Deviance analysis of explanatory variables in the Tweedie models for blue shark caught by Brazilian pelagic tuna longline fleet, from 1978 2012. ................................ .... 53 2 4 Estimations of regression coefficients and related statistics for the main effects of the variables included in the GLMs. ................................ ................................ ........................ 54 2 5 Estimated parameters from the southern Atlantic blue shark stock assessment using a Bayesian state space production model. ................................ ................................ ............ 55 2 7 Estimated reference points from the southern Atlantic blue shark stock assessment using a Bayesian state space production model. ................................ ................................ 56 3 1 Summary data for 28 blue sharks tagged with pop off satellite tags in the south Atlantic Ocean. F female; M male ................................ ................................ .............. 81 3 2 Results from the generalized additive mixed models (GAMMs) for presence and absence of tagged blue sharks in areas acros s the south Atlantic Ocean. .......................... 82 3 3 Results from the generalized additive mixed models (GAMMs) for presence and absence of tagged blue sharks in areas across the south Atlantic Ocean. .......................... 83 4 1 Definition of subscripts, input data, and input parameters ................................ ............. 107 4 2 Notation for estimated parameters, age schedule calculations. *Upper and lower case subscripts indicate unfished and fished conditions, respectively ................................ .... 108 4 3 Residuals and likelihoods. ................................ ................................ ............................... 109 4 4 Deviance analysis of explanatory variables in the Tweedie models for blue shark caught by Brazilian pelagic tuna longline fleet, from 2002 2012. ................................ .. 110

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10 LIST OF FIGURES Figure page 1 1 Theorized movements by female blue sharks in the South Atlantic Ocean. ..................... 27 1 2 Spatial distribution of observed (left) and predicted (right) blue shark CPUE (sharks per 1000 hooks) caught by the Brazilian pelagic longline fleet from 1997 to 2008 in the Southwest Atlantic. ................................ ................................ ................................ ...... 28 2 1 Distribution of fishing effort in number of hooks by the Brazilian longline fleet between 1978 and 2012. ................................ ................................ ................................ .... 57 2 2 Annual catches (1978 2012) of blue shark in the South Atlantic Ocean estimated by using data supplie d by ICCAT and methods that use either: 1) the ratio of tunas to sharks in the catch; or 2) the total shark fins in the shark fin trade. ................................ .. 58 2 3 Nominal (red circle) and standardized (black line) CPUE of blue shark caught by the Brazilian pelagic tuna longline fleet from 1978 factor. ................................ ................................ ................................ ................................ 59 2 4 Time series of observed (red circle) and predicted (black line) CPUE from the southern Atlantic blue shark stock assessment using a Bayesian state space p roduction model ................................ ................................ ................................ ............... 60 2 5 Prior and posterior densities for and estimated by the southern Atlantic blue shark stock assessment using a Bayesian state space production model under scenarios I (split catchability) and II (continuous catchability). ................................ ....... 61 2 6 Ti me series of observation error, process error, and catchability estimated by the southern Atlantic blue shark stock assessment using a Bayesian state space production model ................................ ................................ ................................ ............... 62 2 7 Time series of exploitable biomass (mt) estimated by the southern Atlantic blue shark stock assessment using a Bayesian state space production model. .......................... 63 2 8 Estimated trajectories for the posterior median of B/B MSY and F/F MSY from the southern Atlantic blue shark stock assessment using a Bayesian state space p roduction model ................................ ................................ ................................ ............... 64 3 1 Proposed movements by female blue sharks in the south Atlantic Ocean ........................ 84 3 2 Most probable track for tagged blue sharks across the south Atlantic Ocean fit with the Kalman Filter State Space Model. ................................ ................................ ............... 85 3 3 Use areas occupied by tagged blue sharks across the south Atlantic Ocean. .................... 86

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11 3 4 Rose diagrams showing the angular changes for tagged blue sharks that represented r ....... 87 3 5 Boxplot of sea surface temperature (SST) in the quadrants experienced by tagged blue sharks across the south Atlantic Ocean. ................................ ................................ ..... 88 3 6 Boxplot of depth of the mixed layer (DML) in the quadrants experienced by tagged blue sharks across the south Atlantic Ocean. ................................ ................................ ..... 89 3 7 Partial response curves showing the effects of sea surface temperature (SST) and depth of the mixed layer (DML) on presence of blue sharks in quadra nts across the south Atlantic Ocean. ................................ ................................ ................................ ......... 90 3 8 Cluster analysis of the frequency distributions of the proportion of time at depth for each individual and for adult males, adult females, and juveniles (both sexes combined). ................................ ................................ ................................ ......................... 91 4 1 Annual catches (2002 2012) of blue shark by country in the South Atlantic Ocean estimated by ICCAT using the ratio of sharks landed to the total landings of all tunas (including swordfish and billfishes) ................................ ................................ ................ 111 4 2 Distribution of fishing effort in number of hooks by the Brazilian longline fleets between 2002 and 2012 in Areas I and II ................................ ................................ ....... 112 4 3 P roportion of time at depth histograms for adults and juveniles for areas I and II A) Area I. B) Area II. ................................ ................................ ................................ ............ 113 4 4 Histogram of standard residuals (left panel) and quantile quantile (Q Q) plots of the deviance residuals (right panel) of the model fit for Fleets A (Area I) and B (Area II) . 114 4 5 Nominal (red circle) and standardized (black line) CPUE of blue shark caught by the Brazilian pelagic tuna longline fleets A and B from 2002 2012. Shaded region represents the 95% credibility interval for predicted CPUE values. ............................... 115 4 6 Observed and predicted CPUE from the southern At lantic blue shark stock assessment using the SCAM under scenarios I and II. Shaded region represents the 95% credibility interval for predicted CPUE values. ................................ ....................... 116 4 7 Observed age composition (top panel) and Pearson residuals between observed and predicted proportions at age (bottom panel, with negative residuals given by blue circles). ................................ ................................ ................................ ............................. 117 4 8 Selectivity curves constructed using catch at age information of blue sharks caught by the Brazilian pelagic tuna longline fleets A and B from 2002 2012 Dashed black lines represent the estimated age at 50% selectivity. ................................ ....................... 118 4 9 Total biomass and spawning stock biomass (SSB) estimat ed by the southern Atlantic blue shark stock assessment using the SCAM. ................................ ................................ 119

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12 LIST OF ABBREVIATIONS ADMB AD model builder AIC Akaike information criterion ANOVA Analysis of variance ASM A ge structured models BBMM Brownian bridge movement m odel BIC Bayesian information criterion BSH Blue shark CI C redibility intervals CODA Convergence diagnosis and output a nalysis CPUE C atch per unit effort CV Coefficient of variation DIC D eviance information criterion DML Depth of the mixed layer ECDF Empirical cumulative distribution function GAM Generalized additive model GAMM Generalized additive mixed model GLM Generalized linear model HBS Habitat based s tandardization ICCAT International commission for the conservation of Atlantic t unas MCMC Markov chain monte c arlo MSY Maximum sustainable yield PODAAC Physical oceanography distributed active archive center PSAT Pop up s atellite archival t ag

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1 3 RMFO Regional fisheries management organization SA South Atlantic SCAM Statistical catch at age models SPM Surplus production models SRR S tock recruitment relationship SSB Spawning stock biomass SST Sea surface temperature STC Subtropical convergence TAC Total allowable c atch UD Utilization d istributions VPA Virtual population analysis

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14 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CHANGES IN TARGET SPECIES AND SPATIAL POPULATION STRUCTURE IN STOCK ASSESSMENT MODELS FOR HIGHLY MIGRATORY PELAGIC FISH STOCKS AS EXEMPLIFIED BY THE SOUTH ATLANTIC BLUE SHARK By Felipe Carvalho May 201 4 Chair: Debra Murie Co chair: Robert Ahrens Major: Fisheries and Aquatic S ciences In 2008 The International Commission for the Conservation of Atlantic Tunas (ICCAT) encouraged future research on movement patterns, habitat utilization, and different stock assessment models that would allow incorporation of these types of information to improve the quality and reduce uncertainty in future Atlantic blue shark ( Prionace glauca ) stock assessments. Furthermore, the ICCAT working group on assessment methods also expressed concern that some CPUE series used in the assessments might be misleading due to changing fishing strategies within the fishery, such as changes in target species. My dissertation proposal addresses this necessity and focuses on investigating the movements of the South Atlantic blue shark stock using Pop up Satellite Archival Tags (PSAT), as well as developing and comparing the predictions of a series of sto ck assessment models for the S outh Atlantic blue shark. Chapter 2 present s a suite of Bayesian state space production models fitted to the time series of a South Atlantic blue shark stock in which a single change point in the stationary distribution of the catchability coefficient is specified in order to capture a significant change in target species (hence catchability) in the Brazilian longline fishery. Accounting for a single change point in the

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15 catchability coefficient had no significant impact on the status of South Atlantic blue shark (still above B MSY ); however, it provided a robust way of accounting for changes in catchability as a result of changing target species. In Chapter 3 satellite telemetry and random mixed models were used to quantify the factors driving movement patterns in blue sharks across the South Atlantic Ocean. The majority of sharks showed a residency to core areas and showed patterns of vertical segregation between adults and juveniles In Chapter 4 the effectiveness of integra ting the vertical spatial structure of the S outh Atlantic blue shark population in Statistical C atch at A ge M odels (SCAM) was evaluated. Although accounting for vertical spatial structure had no significant impact on the status of S outh Atlantic blue sharks ( SSB 2012 > SSB MSY ), the model provided a simpler method to capture some of the complexities of a spatially structured stock. Overall, accounting for changes in target species directly in the Bayesian surplus production model and spatial struct ure information into the Statistical Catch at Age Models indicated that the South Atlantic blue shark stock is not overfished ( SSB 2012 > SSB MSY ), nor is overfishing occurring ( F 2012 < F MSY ), and the stock is therefore in no danger of overexploitation and c ollapse.

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16 CHAPTER 1 INTRODUCTION 1.1 Overview gear, constituting bycatch that is either discarded at sea or landed for sale. Over the past decade there has been a growing global concern regarding bycatch of sharks in fishing operations (Coelho et al., 2003). However, the historically low economic value of shark products compared to other fishes has resulted in research and conservation of sharks being given a lower priority than traditionally higher value fish spec ies (Barker and Schleussel, 2005). The blue shark is one of the widest ranging sharks, having a circumglobal distribution in tropical, subtropical and temperate seas, including the Mediterranean (Compagno, 1999). The e ( Aires da Silva and Gallucci 2008 ) in addition to its cosmopolitan distribution and presence in multiple and widespread fisheries, has resulted in it being a relatively well studied elasmobranch and there is considerable information available on its bi ology in the North Atlantic Ocean (e.g., Skomal and Natanson, 2003) and in South Atlantic Ocean (Hazin et al., 1990, 1994a, 1994 b, 2000; Amorim 1992). Little is yet known, however, about the stock structure of blue sharks in the oceans ( Aires da S ilva and Gallucci, 2008). In the South Atlantic, the hypothesis of a single stock for management and stock assessment purposes is debatable (Amorim 1992; Hazin et al. 1994a; Castro and Mejuto, 1995; Legat, 2001; Azevedo, 2003; Mejuto and Garca Cort s 200 5 ). Using information from blue sharks caught off northeastern and southeastern Brazil, as well as the Gulf of Guinea off the western coast of Africa, Hazin et al (2000 ) proposed that a single stock of blue sharks undertake a migratory cycle using a large portion of t he South Atlantic Ocean They hypothesized that mating occurs in southern Brazilian waters, primarily from

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17 December to February, and that ovulation and fertilization follows about 3 4 months later from April to June while off northeast Brazil. Pregnant females then move eastward to the African west coast and from there southward to parturition grounds located at higher latitudes ( Figure 1 1 A ) However, Legat (2001), using reproductive and morphometric data from blue sharks caught off southern Brazil, proposed the existence of two separate stocks in t he South Atlantic Ocean Legat (2001) suggests that one stock is based in the western region of the South Atlantic Ocean near northeastern Brazil, where mating, ovulation, fertilization, and the ini tial stages of pregnancy occur. Pregnant females from this population then move towards African waters, with parturition occurring between 5N and 5S and 5E and 10E, near the Angola Gyre. The second stock has mating, ovulation, fertilization and pregnan cy occurring between 20S and 40S, with a nursery area probably located in African waters between 30S and 40S ( Figure 1 1 B ) Currently, there are not enough data to fully support or refute either of these hypotheses. However, we have tagg ed, and are cur rently tagging, blue sharks using Pop up Satellite Archival Tags (PSATs) in the Southwest Atlantic to investigate large scale movements and vertical distribution of this species. Preliminary results indicate trans oceanic migration of female blue sharks, w ith one individual having moved from its tagging site off the northeast coast of Brazil to the Gulf of Guinea area off the we st coast of Africa (F. Carvalho unpublished data). A juvenile blue shark tagged off the coast of Uruguay was also recaptured i n So uth African waters in 2009 (d a Silva et al., 2010) In 2010, a juvenile moved from the southeast coast of Brazil up north towards the equatorial Atlantic after 44 days. These observations support the hypothesis of a single blue shark population in the Sout h Atlantic

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18 In Brazil, blue sharks are taken along the entire coast by fleets targeting tunas and swordfish with pelagic longline gear ( Carvalho et al., 2010) Since 1971, important changes have been observed in fishing gear and strategies in the Brazilian longline fishery that may have caused spatial and temporal trends in shark catches (Amorim, 1992). Between 1972 and 1995, the am ount of sharks landed from the s outheastern coast of Brazil increased greatly, with average annual landings in the Por t of Santos increasing from 7.8 mt (8.6 t) between 1971 and 1976 to 1,136 mt (1,250 t) between 1990 and 1994. In 1996, the landings declined abruptly to 491 mt (541 t) because 40% of the longline vessels operating off the coast of Brazil moved to Panama to fish (Hazin et al., 2000) Recently, the majority of blue sharks caught in Brazil were landed in the city of Itajai, State of Santa Catarina (550 mt /year ), where the main fishing fleet operating off southern Brazil is based Carvalho et al (2010) analyze d the d istribution and relative abundance o f blue sharks in the S outhwestern Atlantic Ocean based on catch per unit effort (CPUE) and length frequencies of blue sharks caught by the Brazilian pelagic tuna longline fleet between 1978 and 2009. Blue shark CP UE showed a relatively stable trend from 1978 to 1995 In 1995 the first sharp increase in blue shark CPUE was observed, which could have been attributed to the introduction of monofilament gear in 1995 1996 to target swordfish, followed by a gradual incr ease in the market value of blue shark with time. In 2001 there was another increase in the trend in standardized CPUE going up to a maximum value in 2008 that was approximately 1.8. This may have been due to a few factors, including: 1) the majority of the national Brazilian longline fleet started to target swordfish instead tunas. Furthermore, good market conditions for swordfish were an extra stimulus for the national fleet, which was reflected in the number of vessels increasing 15% from 2002 to 2003 and 19% from 2004 to 2005 (Hazin 2006) ; 2) t he steady

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19 supply of blue shark meat gradually helped to build a market for the species in Brazil, thereby driving landing values upward; 3) t he value of fins, which were largely exported to Asian markets in the ; and 4) s ince 2000 the Santos and Itaja fleets started to concentrate their fishing efforts in areas close to the oceanic banks of Rio Grande Rise, off the southern Brazil, where the blue shark abundance is much higher as indicated by the pr edicted CPUE in the area ( Figure 1 2) (Carvalho et al., 2 011 ) Carvalho et al. (2010) also analyzed length frequency distribution s of ove r 11 ,000 blue sharks caught in the S outhwest Atlantic Ocean Overall, the spatial distribution of blue sharks by size had a general tendency of large adults to concentrate in lower latitudes and juveniles to be more common in higher latitudes. Seasonal variation in size was also observed for differen t latitudes. The management of blue shark stocks in the Atlantic Ocean is under the responsibility of the International Commission for the Conservation of Atlantic Tunas ( ICCAT ) ICCAT carried out a stock assessment for Atlantic blue sharks using the tw o stock hypothesis (one in the North Atlantic and another in the S outh Atlantic ) and Bayesian surplus production models ( ICCAT 2008) All analyses indicated that the current fishing mortality rates for the blue shark in the North and South Atlantic are sustainable. Although the general conclusion of the assessment was that the blue shark stock in the South Atlantic Ocean was not overfished, the results were interpreted with considerable caution due to data deficiencies and the resulting uncertainty in th e assessment ( ICCAT 2008). ICCAT encouraged future research on different stock assessment models that would allow incorporat ing information such as movement and age to improve the quality and reduce uncertainty in future Atlantic blue shark stock assess ment s

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20 1.1. 1 Stock Assessment For S harks In recent years, there has been increasing concern about the deteriorating status of the ., Cailliet et al ., 2005; Aires da Silva et al ., 2009 ; Dulvy et al ., 2008; Simpfendorfe r et al ., 2008). Whereas there is some uncertainty about the precise status of these species, there is no doubt that populations have declined significantly (Baum et al ., 2003 2005 ; Baum and Myers 2004; Simpfendorfer et al., 2008). Most pelagic shark spec ies are K strategist because of their life history characteristics, including late attainment of sexual maturity, long life span, slow growth and low fecundity ( Gruber and Stout, 1983) These characteristics make them susceptible to heavy fishing pressure and prolonged recovery times from overfishing (Walker 1998 ; Corts 2002 2008 ; Smith et al ., 2008). It is therefore important that management measures are in place to ensure the future sustainability and prevent population collapse of these species. Perhaps the most influential works on shark stock assessment were those of Holden in the 1960s and 1970s (Musick and Bonfil, 200 5 ). Holden was one of the first scientists to consider the problem of shark stock assessment from a general point of view. He c orrectly pointed out that sharks were different from most bony fishes in terms of their biology, but unfortunately he incorrectly concluded that classic fisheries models such as stock production models could not be applied to sharks and rays (Musick and Bonfil, 2005 ). He specifically stated that the assumptions of surplus production models regarding immediate response in the rate of population growth to changes in population abundance and independence of the rate of natural increase from the age compositi on of the stock do not hold for sharks. Currently, surplus production models have been used by many Regional Fisheries Management Organizations (RMFOs) to perform population assessment s for pelagic sharks, such as the bl ue shark in the

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21 Atlantic Ocean, moti vated mainly by the lack of biological information (i.e. age data) ( Simpfendorfer et al ., 2008 ) 1. 1. 2. Surplus Production M odels The input parameters used in surplus production models are catch and effort data. In this approach, consistent with most other stock assessment techniq ues, CPUE is regarded as an index of resource biomass. The problem is to estimate (1) the constant of proportionality linking CPUE to resource biomass, referred to as the catchability coefficient, and (2) to estimate the resource ca rrying capacity. Most surplus production models fit a Schaefer Model and assume that the relationship between surplus production and resource biomass is bell shaped and fairly symmetrical with a maximum about halfway between a resource biomass of zero and the carrying capacity (McAllister et al 1994). In practice surplus production curves are seldom symmetrical and there are a varie ty of surplus production models that accommodate virtually all possible asymmetrical relationships that may be required for different situations. For example, in many finfish stocks the maximum is assumed to occur at a biomass less than the halfway point, whereas for whale stocks it is assum ed to lie at a biomass greater than the halfway point this is due mainly by differences in their life history patterns ( Corts et al ., 2008) Simpfendorfer et al (2008) analyzed the risk of over exploitation for pelagic shark species taken in Atlantic l ongline fisheries using the position of the inflection point of the population growth curve ( r ) as a measure of the level (relative to virgin biomass) at which the biomass at maximum sustainable yield ( B MSY ) may be achieved ( r ~ B MSY ). The results showed for example that blue sharks probably achieve MSY (Maximum Sustainable Yield) at levels of virgin biomass below the halfway point while thresher sharks achieve MSY at much greater biomass than that.

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22 C omputer based techniques have to be used to estimate the catchability coefficient, the resource carrying capacity and the scale of the surplus production curve It is also necessary to provide a value for the resource biomass at the start of the fishery this is normally assumed to be equal to the resource carrying capacity, but a different value may be used in certain circumstances. The computer based techniques involve comparing the implied (or estimated ) CPUE trend for the resource, which one can calculate based on initial estimates of all the model quan iterations the resource carrying capacity and the scale of the surplus production curve are then made to improve this comparison. The model iterations are based on a mathema tical algorithm and the whole process eventually converges to the best possible se t of model quantities. The idea is for the predicted CPUE and the observed CPUE to agree exactly but because of statistical noise this is never possible. Surplus production model s offer an excellent cost/benefit ratio. Data requirements are modest compared with other models, but they can yield critical information for assessment and management such as estimates of virgin and current biomass, level of depletion of the populat ion, MSY, and optimal effort Most importantly, they can be used to make projections of the population under several scenarios of management (quotas or effor ts) and to evaluate the outcome of each scenario. A further advantage of surplus production models is their simplicity which at the same time can be viewed as a criticism because the models lack biological reality and specifically they do not include age structure. These models assume that all the processes occurring in a population can be captured b y the simple processes described above while ignoring the size or age structure of the population and the dynamics of different parts of the population. Pauly

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23 (19 80 ) mention that the main question the Schaefer model is no t able to measur e is the instantane ous changes to the intrinsic rate of natural increase of the population. Therefore the results obtained are limited to the static conditions and do not identify the equilibrium conditions of the stock. Maunder (2003) considered that the Schaefer model shou ld be discarded from use in stock assessment s and replaced by the Pella Tomlinson model ( Pella, 1993; Fletcher 1978 ) which allows for flexibility in the shape of production curve Finally, surplus production models are applied to elasmobranch fisheries as they are one of the easiest to implement and most fisheries databases available for shark stock assessments, such as blue sharks in the Atlantic, consist only of catch and effort data ( Corts et al ., 2008) However, care should be taken when using produ ction models to take the effects of the resource dynamics into account (Schnute, 1977). Most of the surplus production models treat the resource biomass as a lumped variable and do not take direct account of the underlying age structure. In order to take t he transient effects that result from time lags into account, an age structured production model should be applied (Punt et al., 1995), when required data are available. 1. 1. 3. Age Structured M odels Age structured models are a family of stock assessment m ethods that are based on catch at age data These methods are more detailed compared with surplus production models and basically are recursive algorithms that calculate stock size based on catches broken down by each age class. Using these methods it is p ossible to estimate the magnitude of fishing mortality, levels o f recruitment and the numbers at age in the stock for each past year using only catch at age and an estimate of natural mortality ( M ) (Musick and Bonfil, 200 5 ). A fundamental part of age struc tured models is the concept of cohort A cohort comprises all the individuals that were born in the same year. Age structured models track the history of each cohort in the exploited population back in time from the present to the time each cohort was

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24 born or more commonly to the time it recruited to the fishery. These models specifically calculate the number of fish alive in each cohort for each past year, following each cohort back through time. These models reconstruct the entire exploited population in order to estimate fishing mortality and numbers at age for each age class each year (Musick and Bonfil, 2005 ). There are several age structured stock assessment methods, however, the most commonly used in stock assessment for highly migratory species are Virtual Population Analysis (VPA) and Statistical Catch at age Analysis (Porch et al. 2006). 1 .1 4 Statistical Catch at A ge Model Statistical catch at age models take a different approach than the backward projecting virtual population assessment models (VPA). Statistical catch at age models are almost always forward projecting models and often treat the catch as data needing to be fit (rather than assumed known without error). Most statistical catch at age models take the Bayesian approach, which facilitates taking account of the uncertainties related to models and parameter values and permits incorporation of prior information Compared to VPA models, statistical catch at age models use more formalized statistical approaches to link the data to t he population dynamics models. The model fitting exercise for a statistical catch at age model is the same as the generic model fitting procedure. Because of its forward projecting approach, the stock sizes in the projected year s are the least precise (in contrast to virtual population analyses, in which the stock sizes in the earliest years are least precise). While statistical catch at age approaches are still sensitive to aging errors and to errors in natural mortality, the uncertainty in these parameter s can be directly incorporated into the model if, that is, the modeler has some knowledge about how large those uncertainties might be (Methot, 2000 ).

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25 1.2. Motivation Based on Carvalho et al. (2010, 2011 ) and trans oceanic movement of blue sharks observed using satellite tags ( F. Carvalho unpublished data), it is clearly evident that blue shark s in the South Atlantic vary spatially at a large scale. T his variability should be considered in the assessment and management of blue shark stocks. As data collec tion methods improve, more fine scale spatial data become available. These data can be analyzed to get a better understanding of the spatial variability and movements of the stock and fishery dynamics. Management strategies can then be designed to either e xploit this spatial variability or to be robust to it, depending on the situation. Currently, few stock assessment models directly address spatial variability and movements o f stocks (i.e., Stock Synthesis; Methot 2000 ). For the past 5 years, strong research efforts on blue sharks in the South Atlantic Ocean have resulted in a variety of data sets, including information on catch and effort, size, and movements by various agencies and res earch centers in many countries o ff the Brazilian and West Africa n coasts. With this additional data and movement information, it is an opportune time to apply more than the typical surplus production model used to assess blue shark populations in the South Atlantic. The movement, length, age, catch, and effort data av ailable provides a unique opportunity to develop a more realistic stock assessment model for blue sharks in the South Atlantic Ocean. To achieve this goal, I will ( Figure 1 3): 1. First, for continuity with current ICCAT blue shark stock assessments, I will assess the South Atlantic blue shark stock using a Bayesian Surplus Production Model with updated catch and effort data from the South Atlantic longline fisheries. Here, I will also develop an alternative method to integrate changes in fishing strategy dir ectly into stock assessment models; 2. I will then quantify the spatial structure, movement patterns, and habitat utilization of South Atlantic blue sharks using Pop up Satellite Archival Tags (PSAT); and finally

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26 3. To assess whether incorporating age and spatial population structure improves the blue shark stock assessment, I will use a statistical catch age approach. Finally, I will compare the estimates of South Atlantic blue shark F curr /F MSY and B curr / B MSY obtained from the different models developed in the present study, with those suggested by ICCAT.

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27 A B Fig ure 1 1 Theorized movements by female blue sharks in the South Atlantic Ocean A) From Hazin et al. (2000). B) Two stocks st ructure hypothesized by Legat, J.F.A. ( 2001 ) Adapted from Legat, J.F.A. ( 2001 ) Distribuio, abundncia, reproduo e morfometria de Prionace glauca Universidade Federal do Rio Grande, Rio Grande, Brazil (Page 45, Figure 2 7) Santos Itaja

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28 Fig ure 1 2 Spatial distribution of observed (left) and predicted (right) blue shark CPUE (sharks per 1000 hooks) caught by the Brazilian pelagic longline fleet from 1997 to 2 008 in the Southwest Atlantic. A=Argentina, B=Uruguay and C= Rio Grande Rise. The 3000 m isobaths is shown by a solid black line Adapted from Carvalho, F.C., Murie, D.J., Hazin, F.H.V., Hazin, H.G., Leite Mourato, B., Burgess, G.H., 2011. Spatial predictions of blue shark ( Prionace glauca ) catch rate and c atch probability of juveniles in the Southwest Atlantic. ICES J. Mar. Sci. 68, 890 900 (Page 896, Figure 6)

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29 CHAPTER 2 INCORPORATING SPECIFIC CHANGE POINTS IN CATCHABILITY IN FISHERIES STOCK ASSESSMENT MODELS: AN ALTERNATIVE APPROACH APPLIED TO THE BLUE SHARK ( Prionace glauca ) STOCK IN THE SOUTH ATLANTIC OCEA N 2. 1. Background The majority of abundance indices used in stock assessments are derived from estimates of catch per unit effort (CPUE), the number or biomass of fish caught as a function of effort (Quinn and Deriso 1999). The primary assumption behind a CPUE based abundance index is that changes in the index are assumed to be proportional to changes in the actual stock abundance (Maunder and Punt 2004) The c atchability coeffici ent the proportionality constant between an abundance index and a population size, can be an influential parameter in many stock assessment models ( Arregun Sanchez, 1996) In general, the catchability coefficient is assumed to be constant over time and i ndependent of population size. Th ese assumptions are unrealistic because many biological, management based, and fishery dependent factors may influence catchability in fisheries, such as: spatial and temporal aggregation of fish, changes in fishing power, gear selectivity, environmental variability and dynamics of the population or fishing fleet (Maunder et al ., 2006; Carruthers et al ., 2010). In addition to these other factors fishermen often change the species they target without documentation (Hutching s and Myers, 1994; Salthaug and Aanes, 2003) adding ambiguity to the catchability information of the caught species (Carvalho et al ., 2010). A number of alternative methods can be used to account for variation caused by the above mentioned factors in the catchability coefficient over time, represented here as t ime varying catchability. Two methods are commonly used to address this variability: 1) standardization of the CPUE derived indices via generalized linear models (GLMs) with the aim of correcting the raw dataset for known factors before the stock assessment and 2) direct

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30 specification of time varying catchability during the fitting of the dynamic model used for the assessment If the GLM approach is used, o ne way to compensate for changes in target s pecies in a multi species fishery over time is to include changes in target species, along with other factors that are known to influence catchability, in a CPUE standardization process. Carvalho et al (2010), for example, used cluster analysis and GLMs t o incorporate changes in target species of the Brazilian longline fishery when estimating abundance indices for the south Atlantic blue shark ( Prionace glauca ) stock. Their results clearly showed a major change in target species occurring in 1996 when most of the fleet started targeting swordfish ( Xiphias gladius ) instead of tunas ( Thunnus spp.), with a concomitant switch from using multifilament to monofilament longlines with chemically luminescent light sticks Swordfish and blue sharks are commonly caugh t together in the longline fishery (Campana et al ., 2011) and thus t his change in target species also increased blue shark catches. However, it was still unclear if the standardization process was able to fully account for the effects of changes in target species on blue shark CPUE variability, indicating a need for further stud y In the assessment process, state space models are a n alternative method to model time varying catchability. They can be formulated to estimate the catchability coefficient historical abundance, and other parameters simultaneously and allow them to vary over time without specifying the source of variation (Wilberg et al ., 2010). The interest in state space models as modeling tool in fisheries management has increased in the last decade (e.g. Rivot et al ., 2004; Michielsens et al ., 2006 ). One of the most important advantages of state space models is that they can separate an observed process into two components: a system process that models the biological process over time and an observation process that accounts for imperfect detection of the system process, such as measurement error (Buckland et al ., 2004; Dennis et al ., 2006).

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31 Another way to accommodate time varying catchability in stock assessment models is through the esti mation of the variance parameter of the likelihood for the CPUE data (Wilberg et al ., 2010). This method does not explicitly model catchability but estimating an additive variance parameter accommodates additional white noise variation in the catchability coefficient Other methods that explicitly model time varying catchability in stock assessment have also been developed (see Wilberg et al ., 2010 ). The management of blue shark stocks in the Atlantic Ocean is under the jurisdiction of the International Co mmission for the Conservation of Atlantic Tunas ( ICCAT ). In 2008, ICCAT conducted a stock assessmen t for south Atlantic blue shark using a Bayesian surplus production model and multiple CPUE time series from various fishing fleets. All analyses indicated t hat current fishing mortality rates for b lue shark in the south Atlantic are sustainable. However, the general conclusion of the assessment was that the results needed to be interpreted with considerable caution due to data deficiencies and the resulting u ncertainty in the asses sment (ICCAT, 2008). T he ICCAT working group on assessment methods also expressed concern that some CPUE series used in the assessments mig ht be misleading due to target species changing within the fishery. Time varying catchability remains a central concern in fisheries science due to its potential to create biases in stock assessme nts. The present study aimed to improve the understanding of how changes in catchability over time, specifically due to changes in target species, affecte d the CPUE standardization process. Furthermore, we illustrate how specifying a single change point in the stationary distribution of the catchability coefficient can lead to different estimates of biological reference points and subsequent harvest quota o ptions. For this purpose, a methodology to incorporate specific changing points in the catchability coefficient in

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32 a Bayesian state space production model was developed and applied to the south Atlantic blue shark stock. 2. 2. Materials and M ethods Three sequential procedur es were used to relate target species changes catchability, and CPUE time series to produc tion models : 1) a cluster analysis was used to identify target species in the Brazilian longline fishery in the south west Atlantic Ocean; 2) stand ardized CPUE a bundance indices for blue shark identified through the cluster analysis; and 3) standardized abundance (CPUE) indices were fit to a Bayesian state space production model under two scenarios. In scenario I, the CPUE series was split into periods pre and post 1996, the year when there was a marked change (change point) in the targeted species The catchability coefficient values were then estimated for each period. In scenario II, th e CPUE series used in the model was not split and a single value was estimated for the catchability coefficient Biological and management reference point estimates from both scenarios were then compared. 2. 2. 1. Catch and Effort D ata Blue shark catch and effort data used in Carvalho et al (2010) were updated to 2012, increasing the total of longline sets made by the Brazilian pelagic tuna longline fleet to 72,231 including both national and chartered vessels fishing from 1978 through 2012 ( Figure 2 1). Logbooks were made available by the Ministry of Fisheries and Aquaculture within the Brazilian government. Longline sets were distributed throughout a wide area of the south western Atlantic Ocean, ranging from 10 E and 50 W longitude and between 10 N to 45 S latitude. This total fishing ground was divided into two areas, north and south of 15 S, based on differences in the oceanographic characteristics (Carvalho et al 2010) ( Figure 2 1)

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33 The Bayesian state space prod uction model used the total catch per year for the south Atlantic blue shark between 1978 and 2012. Because the catches reported to ICCAT over time are known to represent only a portion of total removals of the species of concern to ICCAT, working g roups h ave resorted to various methods to estimate a time series of the total catch. Two such m ethods were used by ICCAT in it s last blue shark assessment. The first method, developed by Clark et al (2006), estimate shark catches in the Atlantic by all fleets ba sed on a characterization of the global shark fin trade as of 2000, including number and biomass by shark species. In this method, Hong Kong fin trade based estimates for 2000 were scaled to annual global values for 1980 2006 using the observed quantity of imports to Hong Kong an d an s share of the global trade in each year. The resulting global fin trade for each year was then scaled to Atlantic specific values (Clarke, 2008, ICCAT, 2008). The second method was developed by the I CCAT shark working group (ICCAT, 2005). It estimate s the percentage of reported shark catch vs the combined total catch of tunas swordfish and billfish The ratio from this calculation was aggregated by gear and fleet characteristics and applied to strata for which no shark catch information is available in order to estimate possible catch levels of blue shark for non reporting fleets over the period 1978 2012 in the south Atlantic. As it was in the last ICCAT blue shark assessment, the t otal catch i n each year was set equal to the maximum of the catch estimated from the tuna ratio and the catch estimated from the fin trade data. Except when no fin trade estimates were available during 1978 1980, 1 982, 1985, 1989, and 2006 2012 catches were much high er in the fin ratio based estimate than in the tuna ratio based estimate ( Figure 2 2 ). 2.2. 2. Cluster A nalysis We used cluster analysis to account for changes in target species of the Brazilian longline fishery from 1978 through 2012, as described by Carv alho et al. (2010). Data for the cluster

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34 analysis were obtained from the logbooks of the Brazilian longline fishery, which included such information as: vessel identification, fishing locations, starting times of setting and retrieval, number of hooks depl oyed, and number of fish caught by species. Clusters were developed using SAS 9.3 software (SAS Institute, Cary NC). First, we fit a non hierarchical cluster analysis (K means method; Johnson and Wichern, 1988) in order to identify the ideal number of clus ters associated with targeting different groups of fish After the cluster analysis, percentages of the species and species groups were calculated for each cluster. These clusters comprised the 2. 2. 3. CPUE S tandardizati on Two standardizations were performed for blue shark catch and effort data using GLMs. In order to assess the im one of the models. The number of zero blue shark catches was relat ively high in the dataset (56%) and a Tweedie distribution with a log link function was therefore used in the GLMs following Carvalho et al (2010) T he models used the following formula s : and wher e : location parameter; : diffusion parameter; : power parameter (Shono, 2008)

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35 The selection of predictors was evaluated exclusively on AIC (Akaike Information Criterion) values The GLMs were computed in the R language for statistical analysis (R Development Core Team, 2011). 2. 2. 4. Bayesian State Space Production M odel South Atlantic blue shark population dynamics were modeled within a surplus production model framework using AD Model Builder (ADMB; Fournier et al., 2012). Surplus production models are the most commonly used stock assessment approach when data are comprised of only harvest and relative abundance time series (Hilborn and Walters, 1992). South Atlantic blue shark stock dynamics were accounted for by fitting a surplus production model using a logistic difference equation to predict changes in population biomass ( B ) in year y (Eq uation 2 1). In this model, population change is governed by two population parameters w hile the harvest process is linked with changes in population size (Hilborn and Walters, 1992): where B y is the biomass at the start o f year y is the intrinsic growth rate, is the carrying capacity, and C y is the total catch during year y In order for model predictions to be useful for comparison in a management context, it is important to be able to make probabilistic statements regarding the likelihood of a particular outcome. Parameter estimation is therefore done using either a Bayesian or a Maximum Likelihood approach, with both methods incorporating external information of the parameters of interest. In the case of a Bayesian approach, this information comes in the form of a prior; the lack of parameter identifiability does not impose an inferential problem as long as this lack of information can be compensated using priors based on expert knowledge. Under Maximum Likelihood, extra information about the parameters of interest can be incorporated by writing the

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36 Joint Likelihood function of the external data and the focal data of interest. In this latter approach, data, not priors, are elicited to solve the identifiability problem (Ponciano et al., 2012). In the present assessment, an existing Bayesian estimation framework developed by Mey er and Millar (1999) was used. This framework explicitly considers both observation error and process error to estimate south Atlantic blue shark population parameters while also providing probability distributions associated with population predictions. T his model assumes there is a single closed stock and that the dynamics of the stock (e.g. density dependent growth, mortality, and recruitment processes) are well described by the Schaefer model (Schaefer, 1954). Variability is an important feature of nat ural populations and ignoring it often leads to an incomplete representation of the state of a population and an incorrect prediction of its future. The process error model relates the dynamics of a population to natural variability resulting from demograp hic and environmental processes. Here, the process model uses a state space representation of the Schaefer surplus production model. With this parameterization, the deterministic equation (Eq uation 2 1) is rewritten into a stochastic population model with population state values expressed as a proportion of the carrying capacity ( P t = B t / K ) (Equation 2 2 ). The biomass in the first year of the time series was scaled using the model parameter which is defined as the ratio of the biomass in the first year of the CPUE time series to K where are the unknown states and the process error for year t The observation error model connects the state process (Eq. 2) to CPUE ( I ), assuming CPUE is proportional to biomass (Equation 2 3). An "additional variance" approach, where the

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37 variance of measurement errors is the sum of variance estimates from index standardization and additional va riance was also implemented. where q is the catchability coefficient in year t and is the observation error for year t Observation error variance, process error variance, and index standardization variance, are defined by the parameters , and respectively. When evaluating the joint posterior distributions of the observed and uno bservable processes (Equation 2 4), we used a reciprocal prior on the catchability coefficient (uniform on log scale), which is the Jeffrey's prior (i.e. invariant under re parameterization, see Millar, 2002) Separate catchability coefficient ( q ) values were estimated for each period (pre and post 1996) in scenario I, while a single value was estimated in scena rio II. distribution of parameters was specified based on the observed information. The posterior distribution given assumed known catch removals and CPUE data, and is proportional to the product of the priors and the likelihood of the observable and unobservable processes (Equation 2 4):

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38 2. 2. 5. Prior D istributions In the present study we assumed non informative prior distributions for all model parameters except and For and we assigned an inverse gamma prior distribution with the scaling parameters and k set to 0.001 (Brodziak and Ishimura, 2011) (Equation 2 5). The prior for was based on the analysis of historical catch and effort data of the Brazilian pelagic longline fishery, which can be divided in three distinct periods: I (1958 1962); II (1968 1970); and III (1978 to present). The average blue shark CPUE during period II (unpublished data) was 86% of that during period I (Carvalho et al., 2008). Based on this value, was fixed at 0.86. In order to take into account the high uncertainty around this value we set a coefficient of variation (CV) of 45% (e.g. Hampton et al., 2004) There are no records on longline fishing activity by the Brazilian fleet in between these three periods. Additionally, the target species (yellowfin tuna) and gear (Japanese type longline) were the same for periods I and II, meeting the assumptions required for calculating the depletion between these two periods. An informative prior distribution was developed for the population intrinsic rate of increase following the demographic method outlined in McAllister et al ( 2001). In this analysi s, prior distributions for age specific fecundity, maturity, and natural mortality are converted into prior distributions for This conversion is done using the Leslie matrix projection approach. The Leslie matrix model used is based on two equations: 1 ) the survival equation where is the number of age i individuals at time t and the survival rate from age i to age i +1; and 2) the reproduction equation where m i = the expected number of female pups per female. The number of age 0 individuals depends on m i the average number of age zero individuals produced by an individual of age i In

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39 matrix form, the model is written where is the vector of the numbers of individuals in age group i at time t and L = Leslie matrix of the form: When the matrix coefficients are all positive, the rate of population growth is = ln( ), where is the dominant eigen value of matrix L. A distribution of population intrinsic rate of increase was computed and a probability density function was fitted for values of r generated from 20,000 Leslie population matrices. The life history information and parameters used to construct the prior distributions for were sourced from previous studies on blue shark life history and are summarized in Table 1. To account for uncertainty we used a simulation approach as in Corts (2002), where statistical distribution functions were defined for each life history parameter, based on published records. A total of 20,000 independent vectors were randomly drawn to calculate the different components of the Leslie population matrices, i.e., annual survivorship at age i( S i ) (age 1 to age 16; the maximum age in the calculations was based on Aires da Silva and Gallucci, 2008), survival of age 0 (young of the year) (S 0 ), and expected number of female pups per female ( m i ), respectively. The expected number of female pups produced per femal e is given by where is the mean number of age 0 female pups produced per age female, is the sex ratio (1:1 embryonic sex ratio was assumed based on Hazin et al., 2000), is the fecundity at age and is the pr oportion of mature female at age Age specific fecundities for blue shark were calculated according the equation proposed by Mejuto and Garca Corts (2005):

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40 The logistic fu nction that described the proportion of mature female at age is: where is the slope of the positive linear relationship between litter size and fork length of the pregnant females from Mejuto and Garca Corts (2005) and is the age where 50% of the individuals are mature, which is 5 years according Lessa et al., (2004) To estimate natural mortality (hence survivorship, ) we applied five methods, including Pauly (1980), Hoenig (1983), Chen and Watanabe (1989) and at growth coefficient method All these methods rely on parameter estimates derived from the von Bertalanffy growth function (Corts, 2002). As suggeste d by Aires da Silva and Gallucci (2008), we used the mean and coefficient of variation (CV) obtained for across methods as parameter estimates to define a lognormal distribution, which ensures that the transformed estimates and resulting pdf of annual s urvivorship vary between 0 and 1. This demographic analysis resulted in a prior estimate of 0.297 (SD=0.08) for parameter values and is used to make probability ( or credibility) statements regarding parameter values. In the Bayesian framework, samples are generated from the posterior distribution of parameters, which can be implemented using Markov Chain Monte Carlo (MCMC) techniques (MacKay, 2003). The MCMC sample s were calculated using the default algorithm in ADMB (Fournier et al., 2012). MCMC simulations were conducted in an identical manner for each model scenario. Each simulation included five chains with 2 million cycles, discarding the first 200000 iteration s as burn in phase and then thinning the chain by saving every 200th iteration to

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41 reduce autocorrelation. MCMC simulation convergence was tested using the CODA package (Convergence Diagnosis and Output Analysis; Plummer, 2006) in R statistics A minimal th resholds of p (Geweke, 1992) and the two stage Heidelberger Welch stationary test (Heidelberger and Welch, 1992) We also used the Gelman and Rubin (1992) approach to evaluate the mixing and convergence of our MCMC sampler Tests results showed no evidence of failure to converge for all model parameters. The 2.5th and 97.5th percentiles of the posterior distributions are used to represent 95% Bayesian credibility intervals for all parameters, projections, and management quantities. The estimated 95% credibility intervals (CIs) are analogous to 95% confidence intervals and are also conditional on the model. CIs can be interpreted in the sense that there is a 95% probability that the lower and upper credibility intervals include the true value given the prior information and the data. Model fit was evaluated using a graphical assessment of the 95% prediction credibility intervals. To compare alternative models, the deviance information criterion (DIC) was used. The deviance i nformation criterion is defined as: is the posterior mean of the deviance, where are the data, are the unknown parameters of the model, and = = P is the difference in the posterior mean of the deviance and the deviance evaluated at the posterior mean o f the parameters. As a rule of thumb, if two models differ in DIC by more than three, the one with the smaller DIC is considered the best fitting (Spiegelhalter et al., 2002). 2. 2. 6. Biological Reference P oints For each scenario, harvest management measures can be derived from equation 1, including Maximum Sustainable Yield (MSY). The production model provides direct estimates

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42 of biological reference points for blue shark used for determining stock status: B 2012 the stock biomass at the end of the last year of the assessment period; B MSY the stock biomass at which MSY is achieved; F MSY the fishing intensity corresponding to MSY; F 2012 the fishing intensity during the last year of the assessment period; B 2012 /B MSY the ratio of the spawning stock biomass at the end of the last year of the assessment period to that at which MSY is achieved; and F 2012 /F MSY the ratio of the fishing intensity during the last year of the assessment period to that corresponding to MS Y. Time series of the exploitable biomass was plotted using the mean values from model parameter joint posterior distributions. Total Allowable Catch (TAC) was estimated as the product of the exploitation rate that produces the maximum sustainable yield an d the 2012 biomass. 2. 2. 7. Sensitivity A nalysis The assessment of south Atlantic blue shark stock was subject to sensitivity analysis in order to evaluate model performance under alternative priors for and The best model selected between scenarios I and II was used as the base case for the sensitivity analyses. For the alternative prior for a less informative standard deviation of 0.3 was assigned For the parameter was given an uninformative (uniform) prior between 0.2 and 1.1 (ICCAT, 2008) Also, as taking the maximum catch in each year might inflate MSY, a catch sensitivity analysis using the tuna ratio catch series instead of the maximum of the tuna ratio and fin trade catch estimates was performed. 2. 3. Results 2. 3.1. Cluster Analysis actor The cluster analyses resulted in the separation of the catch into six different clusters r epresenting fishing or target strategies, the % composition of species or species group in each cluster are as follow : Cluster 1 = big eye tuna ( Thunnus alalunga 70.5 %); Cluster 2 = yellowfin

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43 tuna ( Thunnus albacares 45.1 %); Cluster 3 = other teleosts (24.6 %) together with other sharks (11.6 %) and swordfish ( Xiphias gladius 10.4 %) ; Cluster 4 = swordfish (58.9 % ); Cluster 5 = blue shark (68.2 %); and Cluster 6 = albacore ( Thunnus obesus 71 %) (Table 2 2) These clusters were the same ones identified in the analysis by Carvalho et al (2010) using data from 1978 2006, with only small differences in the % composition of the main species obse rvable with the data updated to 2012. 2. 3.2. CPUE S tandardization The final model for the blue shark CPUE standardization that did not include the Target variable consisted of four variables and explained 51% of the total deviance. The relative contribut ion from each variable in the total explained deviance for the model showed that Year ( 58 %) was the most important factor, followed by Area ( 30 %), Quarter ( 8 %), and the interaction between Year and Quarter ( 4 %) (Table 3 ). The CPUE model that included Target consisted of five variables and explained 59% of the total deviance. Target (49%) and Year (31%) were the most important factors, followed by Area (1 7 %), Quarter (2%), and the interaction between Year and Target (1%) (Table 2 3 ). The estimations of the regression coefficients for the main effects in both models are shown in Table 2 4 For both models i t can be noted that the estimated catch rate s in area 2 were higher than catch rates for area 1 (reference area). Also, catch rates in quarter 4 (Octob er to December) were similar to catch rates gathered in quarter 1 (reference quarter), while catch rates in third and second quarter were low er than quarter 1 As expected, the model that included Target showed higher catch rates in cluster 5 (cluster with the highest % of blue shark catches (Table 2 2) than in cluster 1 (reference cluster). The standardized CPUE time series showed a stable trend from 1978 through 1995, increasing from 1996 onwards, and reached a peak in 2003 in both models ( Figure 2 3 ). Ho wever, from 2002 onwards the model that

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44 did not include the Target factor showed higher CPUE values ( Figure 2 3A ) than the CPUE model standardized with it ( Figure 2 3B ). 2. 3.3. Biomass Dynamic M odel We fit the two biomass dynamic models to the blue shark standardized CPUE time series that included Target. The DIC analysis indicated better model fitting under scenario I, as it was 87 deviance points smaller than for the model under scenario II. Under scenario I, predicted CPUE appeared to randomly fluctuate throughout the observed CPUE time series with an increase in both predicted and observed CPUE after 1996, followed by relative stability from 2002 until 2012 ( Figure 2 4A) Under scenario II ( Figure 2 4B), predicted CPUE time series showed similar behavio r as scenario I with a stable trend until 1996 and an increase in CPUE afterward. However, predicted and observed CPUEs from the model under scenario II exhibited similar values until 2001, after which the predicted CPUEs displayed markedly higher values t han the observed CPUEs. When comparing the predicted time series between the two models, there was a noticeable discrepancy in the predicted CPUE values. After 2000, scenario II appears to overestimate predicted CPUE values, and the overestimation also see ms to occur for scenario I, but to a lesser extent In 2012, for example, predicted CPUE under scenario II was 26% higher than the model under scenario I. T he posterior median estimates of parameters and using the baseline priors, showed narrow marg inal posterior distributions for both scenarios, and the observed parameter value for within the predicted range obtained by the demographic analysis. The posterior median values of and are greater for scenario II ( = 0.323, SD = 0.082; = 0.8 67, SD = 0.021) than scenario I ( = 0.282, SD = 0.068; = 0.859, SD = 0.019) (Table 2 5, Figure 2 5). For carrying capacity ( the posterior median based on scenario I was 847,322 t (SD=118,625) while the

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45 median based on scenario II was 971,048 t (126,431). Time series of observation and process errors for both models clearly show a positive trend over time, with no negative values occurring after 1995 ( Figure 2 6A B). T he posterior median estimates for observation error were 0.058 (S D=0.0098) for scenario I and 0.144 (SD=0.0271) for scenario II. For process error, the posterior median estimates were 0.0013 (SD=0.0002) for scenario I, and 0.0026 (SD=0.0004) for scenario II (Table 2 5). The amount of change in the catchability coefficie nt over time also showed an increase after 1995 for both models ( Figure 2 6C). Under scenario I median estimates for and were 0.0000013 (SD=0.0000001) and 0.0000027 (SD=0.0000001), respectively, while for scenario II was 0.000 0029 (SD=0.0000008) (Table 2 6). Biological reference points estimates produced a wide range of uncertainty and varied between the two scenarios (Table 2 7). The posterior median estimates of B MSY for scenario I were 14% below the estimates for scenario II The posterior median estimates of MSY for scenario I were approximately 27% below the estimates for scenario II All models provided different estimates for the current biomass (B 2012 ). The highest posterior median estimated value was obtained by scenari o II (Table 2 7). The estimates of TAC and the uncertainty around these estimates also varied between scenarios. The posterior median estimates of TAC were 93,437 mt per year based on scenario I and 104,101 mt per year based on scenario II (Table 2 7). Th ere was no practical difference in the estimates of stock status in 2012 between the two scenarios. In particular, the posterior median estimates of B 2012 were greater than B MSY for both models (i.e., B 2012 /B MSY >1) and the associated probabilities of B 2012 being below B MSY were close to zero as well. For scenario I, exploitable biomass fluctuated above B MSY during the entire model timeframe, with biomass fluctuating around 600,000 mt until 1995 when values started increasing, reaching their highest valu e in 2001, followed by a decrease and subsequent

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46 stabilization ( Figure 2 7A). Biomass estimates for scenario II were similar to scenario I until 1996, after which the model under scenario II presented slightly higher values ( Figure 2 7B) The trajectories of the posterior median estimates of the ratio of fishing mortality to F MSY for both biomass dynamics models are summarized using a stock status plot ( Figure 2 8). The stock biomass displayed similar trends throughout the years for both models, although sc enario I produced a higher estimate of F / F MSY in 2012 (0.28) than scenario II (0.26). The ratio of B 2012 to B MSY showed a lower value (1.49) under scenario I than scenario II (1.55). Both indicated that the stock is currently not overfished (B>B MSY ) and th at overfishing is not taking place (F
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47 standardized CPUE series. Additionally, the variability found in the blue shark stock assessment models for both scenarios indicates that not correcting for time varying catchability directly in the assessment model can lead to incorrect estimates of stock status and poorly informed management decisions. Besides CPUE standardization, several more sophisticated modeling procedures have been developed that incorporate time varying catchability directly in stock assessment models; however, there is little consensus regarding which practice is ideal (e.g., Fox, 1974; Fournier and Archibald, 1982; Freon, 1988; Prager, 1994; Schnute, 1994; Fournier et al ., 1998; Shepherd and Pope, 2002; Walters and Martell, 2004). State space techniques and modeling the catchability coefficient as a function of time do not ascribe causation for changes in catchability (Meye r and Millar, 1999; Punt, 2003), while the use of functions of density or external variables assumes that the variables used are the dominant factors affecting the change. the logistic Schaefer model, mainly because o f a lack of data and computing power. This model often proved inappropriate to model shark population dynamics since it considered the relationship between surplus production and resource biomass to be symmetrical with a maximum at halfway between a resour ce biomass of zero and the carrying capacity (Maunder, 2003). Pella and Tomlinson (1969) proposed the addition of a supplementary shape parameter to allow the production relationship to be skewed to the left or to the right. However, in order to improve th e logistic model approach in the Pella and Tomlinson model, an additional parameter, the shape parameter, must be estimated to fit the model to the data. Despite its flexibility and suitability, this model may perform worse than the Schaefer due to an inve rse relationship between the number of parameters to be estimated and model performance (e.g. precision)

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48 (Prager, 2002). According to Corts (2008), the blue shark is a very productive species with high fecundity and an inflection point near 50% of K (i.e. not skewed). For precautionary management, 50% is a reasonable estimate of the critical value. Subsequently, the use of the logistic Schaefer model would be appropriate for blue shark. The Bayesian estimation approach presented here provided better scie ntific advice than models that do not incorporate time varying catchability. The estimated biological reference points from the two scenarios indicated that varying catchability had no qualitative impact on the status of the south Atlantic blue shark popul ation with respect to MSY based reference points based on current stock size, with both scenarios indicating that the stock is not currently overfished nor undergoing overfishing. Analyses also showed that it was very likely that the south Atlantic blue sh ark population biomass was above B MSY in 2012 with a high degree of confidence, since all scenarios showed B/B MSY > 1.0. Regardless of the scenario and the sensitivity analysis used, it is unlikely that the south Atlantic blue shark population was being fi shed in excess of its optimal equilibrium harvest rate in 2012, similar to the conclusion reached by the south Atlantic blue shark stock assessment in 2008 (ICCAT, 2008). However, it is important to highlight that an evaluation of the stock status for sout h Atlantic blue shark is strongly compromised by limited fishery statistics, as is any other bycatch shark species. Under or non reporting of bycatch, unknown discard levels, unknown status (dead or alive) of discards, and poor knowledge on the extent of finning practices are among the major reasons for the lack of data. In fact, the blue shark catch information provided by ICCAT and catch estimates based on the shark fin trade from Clarke (2008), represent, to date, the only sources of information on blue shark total removals in the south Atlantic Ocean.

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49 Sharks are usually characterized by slow growth rates, long life spans, late maturity, and production of limited offspring after long gestation periods (Bonfil, 1994). This low reproductive output is resp onsible for the vulnerability of sharks to harvest, as shown by many cases of overexploitation (Corts, 2004). However, the magnitude of the decline of the south Atlantic blue shark population is less than in other pelagic shark species in the Atlantic, su ch as the porbeagle ( Lamna nasus ) (ICES/ICCAT, 2009). This seems reasonable in light of their life history characteristics (Aires da Silva and Gallucci, 2008). According to Corts (2002), blue shark have one of the highest fecundities documented among shar ks (mean litter size of 37 pups, Mejuto and Garca Cortes, 2005; reaching up to 82 pups, Pratt, 1979) and surprisingly fast early growth rates that result in near doubling of pup size over the first year (Skomal and Natanson, 2003). Despite the benefits o f the Bayesian estimation approach, it is important to note that the choice of prior distributions can alter posterior estimates of stock status, especially when data is uninformative. As a result, it is preferable to select prior probability distributions that are consistent with data from other populations. In the present analysis, the prior distribution of south Atlantic blue shark intrinsic rate of increase obtained using demographic analyses, encompassed the range of posterior predictions of r from Corts (2002) and Aires da Silva and Gallucci (2008). Graphical analyses of the posterior distributions for and from both models were similar to the prior which indicates the data are uninformative (McAllister and Kirkwood, 1998). The sensitivity a nalyses also confirmed the current assessment results were sensitive to the prior and catch series choice. For example, the estimate of current biomass for the sensitivity analysis using the tuna ratio catch series is 36% smaller than the base case.

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50 Time v arying catchability is a common feature of many fisheries. Unidentifiable trends in catchability can lead to biased results from stock assessment models and erroneous management recommendations (Pope and Shepherd, 1985; Patterson and Kirkwood, 1995; Wilber g and Bence, 2006, Thorson and Berkson, 2010, Thorson, 2011). As suggested by Wilberg et al., (2010), to best account for the many known causes of time varying catchability, CPUE should be standardized for factors known to affect catchability while recogni zing that it will be difficult to correct for all potential causes. This study implemented an alternative method to incorporate time varying catchability in stock assessment models by specifying a single change point in the catchability coefficient, which resulted in significant improvements in model fit. Furthermore, a mo re stable trend and lower values of especially after 1995 for scenario I, indicates that the alternative model also better captures changes in catchability over time. We recommend that the alternative method that includes time varying catchability pres ented here be tested on other fish stocks, along with other recommendations given by Wilberg et al. (2010). We suggest that the proposed method would be most appropriately applied to assessments where the catch data can clearly be separated into time perio ds with different fisheries dynamics.

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51 Table 2 1. Growth parameters values used in the Demographic analysis for South Atlantic blue shark. : asymptotic length; : growth Coefficient; : age at zero length; : age at 50% mature; and : m aximum a ge. Source Parameter Sex Length measurement Pacific Ocean Cailliet et al (1983) Male 295.3 0.175 1.113 4 9 TL Female 241.9 0.251 0.795 5 9 Nakano (1994)** Male 382.9 0.129 0.756 5 10 PCL Female 321.4 0.144 0.849 6 10 Manning and Francis (2005)* Male 410.8 0.088 1.257 6 22 FL Female 320.1 0.126 1.047 7 19 Atlantic Ocean Stevens (1975) Combined 423.0 0.110 1.035 * 6 TL Aires da Silva (1996) Combined 340.0 0.138 1.075 * 5 TL Henderson et al (2001) Combined 376.5 0.120 1.330 * 6 TL Skomal and Natanson (2003)* Male 282.3 0.180 1.350 5 16 FL Female 310.8 0.130 1.770 5 15 Lessa et al (2004) Combined 352.1 0.157 1.010 5 12 TL Jolly et al (2013) Male 294.6 0.140 1.300 5 14 Female 334.7 0.110 2.190 6 16 Distribution Normal Normal Normal Uniform Uniform Given as fork length (FL) or pre caudal length (PCL) and converted to total length (TL) using equation: FL = 0.8313(TL) and PCL = 0.9075(FL) 0.3956 (Kohler et al. 1995) * No information available

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52 Table 2 2 Percentage of each species or group of species per cluster (Asterisks (*) indicates the target species in each cluster). Species Cluster 1 2 3 4 5 6 Yellowfin tuna Thunnus albacares 5.4 45.1* 9.1 8 2.5 4.3 Bigeye tuna Thunnus alalunga 70.5* 10.4 6.8 5.5 4.8 2.1 Albacore Thunnus obesus 5.3 12.3 5.2 9.9 1.5 71* Swordfish Xiphias gladius 3.1 7.5 10.4 58.9* 8.3 9 Sailfish Istiophorus albicans 1.3 2.4 2.1 1.9 0.8 1 White marlin Tetrapturus albidus 0.7 2.2 1.7 0.9 0.6 0.6 Blue marlin Makaira nigricans 0.5 1.3 0.7 1.3 0.4 0.9 Other billfishes 0.1 0.1 2.4 0.7 0.3 0 Wahoo Acanthocybium solandri 0.7 2.9 2.2 0.4 0.3 0.3 Dolphin fish Coryphaena hippurus 0.4 0.7 6.7 1.5 3.4 0.4 Blue shark Prionace glauca 4.9 2.3 6.1 6.7 68.2* 4.9 Hammerhead shark Sphyrna sp. 0 0.5 3.1 0.4 1.6 0 Bigeye thresher Alopias superciliosus 0 0.1 0.1 0.1 0.3 0 Mako shark Isurus sp. 0.3 1.6 1.3 0.8 2.8 0.1 Silky shark Carcharhinus falciformis 0 0.1 5.8 0.1 0.2 0.1 Oceanic whitetip Carcharhinus longimanus 0 0 0.1 0 0 0 Other sharks 2 1.5 11.6 1 2.4 2.4 Other teleosts 3.9 7.1 24.6* 1.9 1.6 2

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53 Table 2 3 Deviance analysis of explanatory variables in the Tweedie models for blue shark caught by Brazilian pelagic tuna longline fleet, from 1978 2012. Df Deviance Resid. Df Resid. Dev Dev. Exp (%) AIC NULL 50108 211401.3 6312 Year 34 51677.2 49872 146803.2 58 5404 Area 1 29654.1 49114 135872.0 30 5309 Quarter 3 7653.7 48983 121642.3 8 5283 Quarter*Area 56 4412.1 48107 102088.0 4 5228 NULL 59444 297334.0 18549 Year 34 49055.1 59131 255334.0 31 17230 Area 1 38142.3 59022 234667.2 17 17004 Quarter 3 4163.6 58897 226456.0 2 16981 Target 5 84557.0 58814 220569.4 49 14187 Quarter*Area 62 2044.8 58731 187408.9 1 14153

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54 Table 2 4 Estimations of regression coefficients and related statistics for the main effects of the variables included in the GLMs for blue shark caught by Brazilian pelagic tuna longline fleet, from 1978 2012. Estimate Std. Error t value Df P(>|t|) Dev Area 2 0.2290 0.0949 2.35 0.0190 Quarter 2 0.2876 0.1106 2.60 0.0093 Quarter 3 0.2898 0.0877 3.30 0.0013 Quarter 4 0.0304 0.1334 0.23 0.8198 Area 2 0.2853 0.0987 2.8355 0.0049 Quarter 2 0.4748 0.2728 3.6468 0.0030 Quarter 3 0.4000 0.2879 2.0840 0.0374 Quarter 4 0.0950 0.0712 1.3476 0.1818 Target 2 0.5381 0.2781 0.1935 0.8466 Target 3 0.0107 0.2390 0.4481 0.6565 Target 4 0.0146 0.3148 0.5732 0.7012 Target 5 1.3956 0.1270 10.9720 <0.001 Target 6 0.0660 2.9587 0.0221 0.9823

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55 Table 2 5 E stimated parameters from the southern Atlantic blue shark stock assessment using a Bayesian sta te space production model under scenarios I (split catchability) and II (continuous catchability). : population intrinsic rate of increase ; : ratio of the biomass in the first year to ; : carrying capacity; : observation error; and : process error. Median (SD) Median (SD) Median (SD) Median (SD) Median (SD) Scenario I (base case) 0.282 (0.068) 0.859 (0.019) 847322 (118625) 0.058 (0.0098 ) 0.0013 (0.0002 ) Scenario II 0.323 (0.082) 0.867 (0.021) 971048 (126431) 0.144 (0.0271 ) 0.0026 ( 0.0 004 ) Sensitivity analysis Scenario I (Less informative ) 0.316 (0.114) 0.863 (0.034) 935259 (168993) 0.053 (0.0091 ) 0.0015 (0.0002 ) Scenario I (Uninformative prior for ) 0.310 (0.091) 0.810 (0.160) 927195 (192331) 0.063 (0.0099 ) 0.0021 (0.0003 ) Scenario I (Tuna ratio catch series only) 0.301 (0.074) 0.852 (0.015) 653972 (91447) 0.055 (0.0094 ) 0.0019 (0.0002 )

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56 Table 2 6 Estimated catchability parameters from the southern Atlantic blue shark stock assessment using a Bayesian sta te space production model under scenarios I (split catchability) and II (continuous catchability). Median (SD) Median (SD) Median (SD) Scenario I (base case) 0.0000013 (0.00000010) 0.0000027 (0.00000011) Scenario II 0.0000029 (0.00000081) Sensitivity analysis Scenario I (Less informative ) 0.0000011 (0.00000009) 0.0000025 (0.00000012) Scenario I (Uninformative prior for ) 0.0000014 (0.00000012) 0.0000021 (0.00000010) Scenario I (Tuna ratio catch series only) 0.0000010 (0.00000011) 0.0000025 (0.00000008) Table 2 7 Estimated reference points from the southern Atlantic blue shark stock assessment using a Bayesian state space production model under scenarios I (split catchability) and II (continuous catchability). B MSY B 2012 MSY TAC Median (SD) Median (SD) Median (SD) Median (SD) Scenario I (base case) 422861 (59200) 632442 (82445) 59736 (8960) 93437 (12146) Scenario II 485631 (67973) 757442 (90893) 78412 (9801) 104101 (15883) Sensitivity analysis S cenario I ( Less informative ) 465362 (84212) 716035 (124611) 73491 (13072) 97807 (18673) S cenario I ( Uninformative prior for ) 466587 (83447) 718338 (111566) 71849 (15508) 96411 (16813) S cenario I (Tuna ratio catch series only) 325441 (39507) 436713 (70114) 49014 (6305) 75124 (9655)

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57 Fig ure 2 1 Distribution of fishing effort in number of hooks by the Brazilian longline fleet between 1978 and 2012

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58 Fig ure 2 2 Annual catches (1978 2012) of blue shark in the South Atlantic Ocean estimated by using data supplied by ICCAT and methods that use either: 1) the ratio of tunas to sharks in the catch; or 2) the total shark fins in the shark fin trade.

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59 Fig ure 2 3. Nominal (red circle) and standardized (black line) CPUE of blue shar k caught by the Brazilian pelagic tuna longline fleet from 1978 factor. Shaded region represents the 95% credibility interval for predicted CPUE values. A) Standardized CPUE without target factor. B) Standardized CPUE wit h target factor

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60 Fig ure 2 4. Time series of observed (red circle) and predicted (black line) CPUE from the southern Atlantic blue shark stock assessment using a Bayesian state space production model under scenarios I (split catchability) and II (continuous catchability) Shaded region represents the 95% credibility interval for predicted CPUE values A) Scenario I. B) Scenario II.

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61 Fig ure 2 5. Prior and posterior densities for and estimated by the southern Atlantic blue shark stock assessment using a Bayesian sta te space production model under scenarios I (split catchability) and II (continuous catchability ).

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62 Fig ure 2 6. Time series of observation error, process error, and catchability estimated by the southern Atlantic blue shark stock assessment using a Bayesian state space production model under scenarios I (split catchability) and II (continuous catchability). H orizontal dashed lines indicates zero and the vertical dashed line indicates the year 1996 A)Observation error. B) Process error. C) Catchability

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63 Fig ure 2 7 Time series of exploitable biomass (mt) estimated by the southern Atlantic blue shark stock assessment using a Bayesian state space production model under scenarios I (split catchability) and II (continuous catchability). Shaded region represents the 95% c redibility interval for predicted biomass values A) Scenario I. B) Scenario II.

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64 Fig ure 2 8 Estimated trajectories for the posterior median of B/B MSY and F/F MSY from the southern Atlantic blue shark stock assessment using a Bayesian sta te space production model under scenarios I (split catchability) and II (continuous catchability).

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65 CHAPTER 3 HABITAT SELECTION AND TRANS OCEANIC MIGRATION BY BLUE SHARKS IN THE SOUTH ATLANTIC OCEAN FROM SATELLITE TELEMETRY 3. 1. Background Open ocean pre dators are faced with complex movement decisions as they strive to obtain resources (e.g. prey, mates) and select habitats in a largely featureless and oligotrophic environment. Unlike animals in coastal marine environments, which may be able to utilize m ore definitive landmarks for navigation (e.g. bathymetry), offshore marine organisms, including pelagic sharks, appear to rely on cues, which may be not apparent (e.g. geomagnetic gradients, haloclines, thermoclines, and patterns of sub surface polarizatio n, and various celestial compasses) (Klimley 1993; Montgomery and Walker 2001; Luschi 2013). Despite these limitations, there can still be predictable locations of high fish abundance, such as within oceanographic fronts (Block et al. 2011 ; Queiroz et al. 2012). Oceanographic conditions are likely to be strong drivers of pelagic shark movements and distribution. While it is common for driving movements are rare (Block et al. 2011 ; Carvalho et al. 2011; Queiroz et al. 2012 ; Bestley et al. 2013). These environmental drivers or processes are important to fisheries management, as marine predators are frequently caught as bycatch in pelagic longline fisheries (Carvalho et al. 2010, 2011). Analysis of fisheries logbook data suggests that shark populations in the Northwestern Atlantic have declined by 53 70% over the last 50 years due, in large part, to bycatch (Baum and Blanchard 2010). The fact that pelagic sharks are considered wide ranging in their movements makes management decisions difficult, particularly when it relates to designating stock structure (Kohler et al. 2002 ; Aires da Silva et al. 2009). However, more recent satellite telemetry dat a suggest that despite populations being distributed over wide geographic areas, some pelagic

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66 sharks show relatively restricted movements and demonstrate philopatry (e.g. Weng et al. 2005 ; Queiroz et al. 2012 ; Howey Jordan et al. 2013). The blue shark ( Prionace glauca ) is one the most wide ranging shark species, with high bycatch rates in pelagic longline fisheries (Compagno et al. 2005). Blue sharks segregate by size and sex in some locations and are known to move across the Atlantic Ocean (e.g. Pratt 1979 ; Kohler et al. 2002 ; Da Silva 2010). In the s outh Atlantic, there are two theories of blue shark migration patterns. Based on fisheries data from Brazilian and African coastal waters, the firs t hypothesis suggests a single s outh Atlantic stock with adults performing clockwise migrations across breeding stages (Amorim 1992 ; Castro and Mejuto 1995 ; Hazin and Lessa 2005 ; Jolly et al. 2012). Under this scenario, copulation occurs off the SE coast of Brazil, ovulation and fertilization off the NE coa st of Brazil, gestation off NW Africa, and parturition in South African waters (Hazin and Lessa 2005, Figure 3 1A). In contrast, a second hypothesis assumes two separate stocks off Brazil and western Africa. Under this scenario, mating, ovulation, fertil ization, gestation, and parturition occurs separately off southern Brazil and Africa (Legat and Vooren 2004 ; Figure 3 1 B). The management of the blue shark stock in international waters of the s outh Atlantic Ocean i s under the responsibility of the International Commission for the Conservation of Atlantic Tunas ( ICCAT ). In 2008, ICCAT carried out a stock assessment for Atlantic blue sharks using one stock for the north and one for the south with a Bayesian surplus production models (ICCAT 2009). All analyses indicated that the fishing mortality rates for t he blue shark in the North and s outh Atlantic at that time were sustainable. Although the general conclusion of the assessment was th at the blue shark stock in the s outh Atlantic Ocean was not over fished, ICCAT

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67 encouraged future research on movement patterns and stock structure of blue sharks to improve the quality and reduce uncertainty of future Atlantic blue shark stock assessments. Differing blue shark stock structure hypotheses might lead to c ompletely divergent management strategies and change our understanding of the drivers of habitat selection and large scale migrations in this apex marine predator. Blue shark movements appear to be clos ely linked to the temperature structure of the water ( Carey et al., 1990; Campana et al., 2011; Carvalho et al., 2011; Queiroz et al., 2012 ) In the North Atlantic, most blue sharks spend summers on or near the continental shelf, encounter ing the warm waters of the Gulf Stream during their eastward movements. I n the winter most or all blue sharks remain in association with the warm waters of the Gulf Stream, its rings, or the Sargasso Sea furth er south (Campana et al., 2011). The ability to predict how oceanographic conditions drive habitat selection decision sound stock assessment models. In the present study, we combined satellite telemetry data of blue shark movements for individuals throughout the s outh Atlantic Ocean, wit h a hierarchical mixed model and oceanographic data, to reveal the factors driving habitat selection and trans Atla ntic migrations in the species. Further, we discuss how these results can assist in implementing stock assessments and management approaches to ensure sustainable populations of this commercially and ecologically important pelagic shark species. 3. 2. Materials and methods 3. 2.1. Satellite T racking Tagging was spatially and temporally stratified to match the reproductive cycl e of female blue sharks in the s outh Atlantic Ocean reported by Hazin and Lessa (2005) ( Figure 3 1 A ). The s outh Atlantic was split into four quadrants, each representing a geographical area in the s outh

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68 Atlantic Ocean (NE Area I; NW Area II; SW Area III; SE Area IV ) (Table 3 1). A total of 28 mature females and males (Total Length, TL > 228 cm and > 225 cm, respectively; Hazin and Lessa 2005 ) and immature male and female blue sharks were caught from longline vessels and tagged with MK10 PAT (Pop up Archival Transmitting) tags (PSATs; Wi ldlife Computers, Redmond, WA). Female and male blue sharks fork length (FL) ranged from 98 to 275 cm (209 69; mean SD) and from 102 to 290 (212 70), respectively (Table 3 1). Mature females tagged off the southern coast of Brazil (Area IV) possessed scars indicative of recent copulation. PSATs were programmed to record depth, temperature and light intensity for a period of 3 to 7 months until release. All 28 tags successfully detached and transmitted data on the movemen ts and habitat variables for each individual. P SAT attachment time f or the 28 individuals averaged 1 07.2 41.7 days with a maximum attachment time of 209 days (Table 3 1). Archival d ata from t he de tached t ags were internally binned at 3 h, 6 h, or 12 h intervals and the summarized data were transmitted to an Argos satellite Light intensity records were pre processed using the global positioning software WC GPE (Wildlife Computers, Redmond, WA, USA) to provide daily raw geo locations ( i.e unfiltered a nd uncorrected estimates) of tagged fish for each day at liberty. To estimate blue shark movement parameters and provide the most probable track for each shark we processed the PSAT data using a Kalman filter model (KFSST) that integrates sea surface temp erature ( SST ) measurements (Nielsen and Sibert 2005; Nielsen et al. 2006). 3. 2.2. Space Utilization D istribution A Brownian Bridge Movement Model (BBMM) was used to estimate the sharks Utilization Distributions (UD) across the s outh Atlantic Ocean ( Bulla rd, 1999; Horne et al. 2007). The BBMM estimates UDs by modeling movements between locations (i.e. KFSST estimated locations ) as a conditional random walk consisting of a series of steps where the step

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69 length, direction, and time interval between steps ar e independent of each other and those of preceding steps ( Bullard, 1999; Horne et al., 2007). The time step (iteration increment) in the model was 24 h ours The BBMM also account s for the error associated with the estimated position of the tracked animal motion ). A grid system consisting of 1.0 latitude 1.0 longitude cells (~ 111 km x 111 km) was constructed for the entire s outh Atlantic Ocean. An animal random actual location estimates. Each cell had its own UD value, and population level probabilities were generated by summing the cell values of all UDs for all individuals (tagged across the s outh Atlantic Ocean) and then re scaling their cumu lative cell values to sum to 1. All calculations were performed using the BBMM package in R 2.13.1 language for statistical computing (R Devel opment Core Team 2011). 3. 2.3. Analysis of D irectionality Directionality in the individual movements of blue sharks was quantified using circular statistics (Zar 2009). Tests were then used to compare the distribution of bearings calculated by moving fro m one point to another along a movement track relative to uniformity (i.e. the probability of the animal going in any particular direction is equal). to quantify directionality in blue sharks (Bergin 1991 ; Bonadonna et al. 200 1). This statistic incorporates the mean directional vector ( ), the angular concentration ( r ) and the cir cular standard deviation (csd). an individual shark was observed to have a bi modal preference in direction, e.g. both 90 and 180 degree bearings (Bergin 1991). Circular histograms were generated for each shark to graphically

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70 demonstrate the preferred directionality. All circular statistics were performed using Oriana 4.0 (Kovach Computing Services). 3. 2.4. Overlapping Tracking and O ceanogr aphic D ata Weekly time series of SST (C) and depth of the mixed layer (DML) were obtained from the Physical Oceanography Distributed Active Archive Center (PODAAC) Jet Propulsion Laboratory/NA SA ( La Caada Flintridge CA). These data were used to construct a database of 1.0 latitude 1.0 longitude quadrats assembled by day, month, year, latitude and longitude for the entire study area. KFSST estimated locations for each shark were then ove rlapped on the 1.0 1.0 quadrats containing the weekly averaged estimated SST for that specific date. Continuous normally distributed SST and DML data for quadrats experienced by tagged blue sharks were expressed as means 1 SD For multiple compariso ns, data were analyzed with a o ne way analysis of variance Post hoc multiple comparisons tests were performed using T ukey's honestly significant difference test. 3. 2.5. Random Effect M odels The inclusion of environmental variables in statistical modeling is often complex. Statistical analysis often assumes a linear relationship between the response and environmental variables (e.g. SST and DML), when actually they are very likely to be nonlinear. To overcome these difficulties, Hastie and Tibshirani (1990) proposed generalized additive models (GAMs). GAMs are extensions of generalized linear models (GLMs) in which a link function describing the total explained variance is modeled as a sum of the variables. T he terms of the GAMs can be local smoothers or simple transformations with fixed degrees of freedom (Maunder and Punt 2004 ; Venables and Dichmont 2004). In regression studies, the coefficients are commonly considered fixed. However, there are cases in which it makes sense to as sume some random coefficients. These cases typically

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71 occur in situations where the primary focus is to make inferences on the entire population from which som e levels are randomly sampled. In the present study, observations were c ollected from t he same individuals over time. Therefore, it is reasonable to assume that correlations exist among the observa tions from the same individual. Consequently, an approach that conserves the additive model framework with both fixed and random ef fects (generalized additive mixed model GAMM) would be more appropriate for these analyses (see Appendix A for details on model formulation and inference). GAMMs were used to investigate the influence of a series of variables on habitat use of blue shar ks across the s outh Atlantic Ocean. The binary response variable for these analyses is presence (1) or absence (0) of blue sharks in the four geographical areas (I, II, III, and IV). The variables included SST (continuous), DML (continuous), and Area (cate gorical). All variables (SST, DML, and Area) wer e considered as fixed effects. Since there were multiple occurrences for each individual, each tracked individual was included in the models as a random effect. Additive mixed effects modeling was conducted using R statistical language and the mgcv package ( Wood 2006). First, the effect of the variable (SST and DML) was compared to the r esponse variable for each area. Second, to determine whether the relationship differed by area, Area was added as a variab le in the model. To find the most parsimonious GAMM model, standard selection criteria based on Akaike Information Criteria (AIC) (Akaike 1973) and Bayesian Information Criteria (BIC) (Schwarz 1978) were used to determine which variables best explained the variability in the data. The model was built with variables independent from each other (Stage I). The best model was selected based on AIC and BIC values and subsequently tested in the next stage. Stages II to III used the initial model, with an ad ditional variable. Likelihood Ratio tests were also used to determine whether the inclusion of additional

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72 variables in the model significantly improved the explanatory power of the model. The relative effect of each variable over the dependent variable o f interest (presence or absence) was assessed using the distribution of partial residuals ( Neter et al. 1989 ). Partial response curves can be interpreted by examining the change in the standardized partial residuals. If the residual value is greater than 0, the variable has a positive influence on the dependent variable (estimated UD) at that particular variable value (Carvalho et al. 2011). The larger the partial residuals are (as long as > 0), the greater the influence of the variable on the depen dent variable. The relative influence of each variable was then assessed based on the values normalized with respect to the standard deviation of the partial residuals. For model diagnostics, normality was assessed using Q Q plot and the histogram of res iduals ( see Appendix B for detailed model diagnostics) 3. 2.6. Vertical Habitat U tilization To compare the vertical habitat utiliza tion of blue sharks across the s outh Atlantic Ocean, we calculated time at depth histograms for adult male, adult female, a nd juveniles (both sexes combined) for each area using vertical data from the PSATs. A non hierarchical clus ter analysis (based on d) was performed using proportion of time at depth data to identify groups of indivi dual s that were similar to each other with regards to vertical habitat utilization 3. 3. Results 3. 3.1. Mov ements and Utilization D istribution Tracking results showed complex and remarkable movement patterns by blue sharks in the s outh Atlantic Ocean with some individuals staying in the vicinity of the tagging location while others performed long trans oceanic migrations (e.g. north to south and west to east, Table 3 1 and Figure 3 2). Most of the individuals tagged in Area I off t he northeastern coast of Brazil stayed in the vicinit y of the ir tagging site with one mature female (BSH 3) performing the

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73 shortest maximum linear distance traveled among all blue sharks tagged in the present study (114 km in 57 days) However another m ature female (BSH 2) performed a previously unobserved trans oceanic migration spanning the entire equatorial Atlantic Ocean in 209 days from the n ortheast coast of Brazil to the Gulf of Guinea, Africa (Area II) (Area II) ( Figure 3 2), a distance of 4456 km. From A rea IV off the eastern coast of Brazil a mature female (BSH 27) arrived in Area I after travelling along a large portion of the Brazilian coast in 175 days a distance of 3,470 km. T he most probable track s of blue sharks tagged in the Gulf of Guinea (Area II) revealed very distinct movement pat terns among individuals Some blue sharks ( BSH 8, 9, and 13 ) tended to move in waters closest to the African coast; some others ( BSH 10, 11, and 14 ) stayed in the central and deeper part of the Gulf of G uinea ; while one mature female ( BSH 12 ) migrated further south to offshore waters of South Africa in Area III Two mature female blue sharks ( BSH 2 and 16 ), which had been tagged in Area s I and III, respectively moved long distances to reach the Gulf of Guinea in Area II Satellite tracking of blue sharks tagged off the coast of South Africa (Area III) also revealed different movement patterns among individuals. BSH 15, 17, 18, and 19 did not move far from the tagging site, with BSH 17 and 19 cross ing t he meridian of 20 E that separates the Atlantic and Indian Ocean s. BSH 20 spent most of its time off the South African coast; however, during the last month of tracking this individual moved northward to the Namibian coast. Long distance movements were o nly performed by mature females. Specifically, BSH 16 traveled 4,000 km to the Gulf of Guinea in 103 days and BSH 21 moved west from the tagging site. Although the tag on BSH 21 popped off prematurely, its most probable track suggests that this mature fe male would have reached Area IV in a few more days. Blue sharks tagged in Area IV also performed a variety of movement patterns with one mature female (BSH 27) swimming

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74 north into Area I. The remaining individuals swam towards the coast to areas surround ing the Rio Grande Rise. A mature male (BSH 28) tagged on the Uruguayan continental shelf break moved south towards the Argentinean coast before returning back towards the tagging site. The utilization distributions demonstrated high use areas for blue sharks off the Northeast region of Brazil (Area I), characterized by the presence of seamounts (Cadeia Norte do Brasil) and oceanic islands (Fernando de Noronha and Atol da Rocas) ( Figure 3 3). Within Area II, high utilization areas were located in the ce ntral part of the Gulf of Guinea and coastal waters of Gabon, Equatorial Guinea, and Cameroon. While in Area III, areas of high utilization were located off the western coast of South Africa. Within Area IV high utilization areas were associated with the Rio Grande Rise, a large seismic ridge with depths of 300 4000 m, and waters off the coast of Santa Catarina State. Most blue sha rks performed movements that had a uniform distribution of directional vectors, a result of the animals maintaining residenc y in a relatively small area formed by the sharks moving in small loops (e.g., BSH 26 and 28 in Figure 3 2) However there were several individuals within each a rea that displayed directed movements, the majority of which were mature individuals (Table 3 1). Easterly movements were performed by BSH 2, 23, and 24 (tagged in Area I and IV), while westerly movements were performed by BSH 13 and 21 (tagged in Area II and III). A number of other individuals performed southeasterly or northeasterly movements ( Figure 3 4). 3. 3.2. Habitat Selection and Mixed M odels Habitat use varied considerably among individuals in all areas (One way ANOVA, Fig ures 3 5 and 3 post hoc (A ppendix B)). Sea surface temperatures and DMLs were relatively similar among individuals in Area I. However, in Area II mature females BSH 8, 9, and 13 used areas close to shore with warmer SST (mean = 27.04 0.81C) and deeper DML

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75 (21.44 5.12 m), while BSH 10, 11, 12, 14, and 16 spent most of their time in locations with cool er SST (mean = 23.47 1.21C) and shallower DML (12.15 9.21 m). In Area III, males BSH 15 and 19 occurred in waters with cooler SST (mean = 9.76 0.61 C) when compared to BSH 16, 17, 18, 20, and 21 (SST mean = 13.17 1.03 C) and BSH 12 (mean = 15.0 0 1.13 C). BSH 15 and 19 also occurred at deeper DML (67.23 26.24 m) compared with all other sharks (mean = 46.41 20.44 m). In Area IV, BSH 22, 23, 24, 25, and 27 occurred in water with significantly warmer SST (mean = 20.01 1.34C) when compare d to BSH 26 and 28 (mean = 18.32 1.26C). BSH 22, 23, 24, 25, and 26 were more likely to occur in shallower DML (39.09 10.38 m) compared with BSH 27 (mean = 51.51 m 9.97 m) and BSH 28 (mean = 67.02 m 10.41 m). Both SST and DML had a statistically significant influence on model predictions, and lowered AIC and BIC values for all areas (Table 3 2). The best fit model that described the effect of the variables on the presence or absence of tagged blue sharks in a specific quadrant was obtained for Ar ea II ( R 2 = 0.61), followed by Area IV ( R 2 = 0.58), Area I ( R 2 = 0.47 ), Area III ( R 2 = 0.41), and all Areas combined ( R 2 = 0.40) (Table 3 2). The output of the fifth GAMM model, investigating the effect of Area on the presence or absence of tagged blue sharks in a specific quadrant, showed that Area has no significant effect as a variable (Table 3 2). In all models, SST was the most important variable in explaining the variance (Table 3 3). Partial response curves showing the effects of SST on the model indicated a higher occurrence of tagged blue sharks in quadrants where SST was between 26 28 C (Area I); 23 24 C and 26 28 C (Area II); 10 13 C (Area III); and 20 22 C (Area IV). Presence of blue sharks in a spec ific quadrant was also more likely to occur when DML wa s between 60

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76 100 m (Area I); 0 20 m and 25 35 m (Area II); deeper than 70 m (Area III); and between 30 70 m (Area IV) ( Figure 3 7 ). 3. 3.3. Vertical Habitat U tilization Time at depth histogra ms show that patterns of segregation vary based on which area sharks were tagged in. Within Area I, adult females and males occupied shallower depths than juveniles. Within Area II, adult females and occupied shallower depths than either adult males or ju veniles Within Area III, all ages and both sexes were found in similar depth ranges; while in Area IV, juveniles utilized shallower waters than either adult males or females. The cluster analysis revealed four groups, of which three consisted of mixtures o f males and females. However, group 4 (the largest group) was composed almost entirely of mature females (Figure 3 8). 3. 4. Discussion Our study is the largest spatially stratif ied satellite tagging study of s outh Atlantic blue sharks to date and reveals that none of the current hypotheses of migration cycles are fully satisfactory. Blue sharks showed relatively high levels of residency to core areas, but there were individuals within each area that swam to an adjacent area, with one of these movements represented as trans Atlantic migrations. These results support a growing number of studies indicating that oceanic sharks show site fidelity within core areas, although some individuals also undertake long rang e movements (e.g. Ko hler et al., 2002; Weng et al.; 2005, Campana et al., 2011; Howey Jordan et al., 2013). The trans Atlantic movement challenges the two stock hypothesis that Atlantic blue shark populations lack connectivity and should be managed as s eparate stocks (Legat and Vooren 2004). However, length frequency distributions and the movement of at least one individual from Area III to Area II also challenges the clockwise migration hypothesis (Carvalho et al. 2010).

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77 Juvenile blue sharks are mo re commonly found off southern Brazil, while adults are more abundant further north (Carvalho et al. 2010). Juveniles are unlikely to perform trans Atlantic migrations from southwestern Africa, suggesting that a nursery location exists within Brazilian w aters. Fishing surveys indicate this nursery may be off the Subtropical Convergence (STC) and that pregnant females migrate south from northeastern Brazil to give birth (Legat and Vooren 2004; Montealegre Quijano and Vooren 2010). However, our tagging s tudy reveals at least one mature female swimming from northeastern Brazil to the Gulf of Guinea, which may suggest two possible parturition areas (STC and South Africa; Hazin et al. 1994). Our study also highlights how a modeling approach can reveal ocean ographic conditions that explain or influence marine predator movements. The movements and distribution of blue sharks were primarily explained by SST and secondarily by DML, particularly for mature females. However, the actual variable values differed b ased on tracking locations of individuals and presumed reproductive stage. The Gulf of Guinea is a highly productive area, which likely offers ample prey sources to gestating females, which supplement developing embryos through placental viviparity in add ition to meeting their own nutritional requirements (Pratt 1979; Hazin et al. 1994). Furthermore, within the Gulf of Guinea, mature female blue sharks selected warmer coastal waters than adult males or immature sharks. Pregnant female sharks are hypoth esized to select warmer waters to reduce gestation and development time of embryos (Hight and Lowe 2007; Jirik and Lowe 2012). Similar strategies of behavioral gestational thermoregulation are employed by terrestrial poikilotherms such as viviparous liz ards and snakes (Shine and Harlow 1993; Gregory 2009). Larger females also occurred in waters with deeper mixed layers, which may also be related to selecting warmer surface waters, as an increased DML is generally associated with warmer surface waters. Diving data indicated that female blue

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78 sharks dive to shallower depths than males when in the Gulf of Guinea, primarily confining their dives to the mixed layer. Blue sharks tracked in the Atlantic and Pacific Oceans show a preference to remain within t he mixed layer, although they will frequently perform short vertical excursions into cooler waters (Weng et al. 2005; Campana et al. 2011; Queiroz et al. 2012). Habitat utilization also revealed trans Atlantic variability both in vertical habitat utiliz ation and the degree of sexual segregation between males and females. Horizontal and vertical sexual segregation is common in elasmobranchs and may be related to females avoiding males outside of the mating season or selecting physiologically optimal cond itions for gestation or parturition (e.g. Sims 2005; Papastamatiou et al. 2006; Hight and Lowe 2007; Wearmouth and Sims ; 2008). Furthermore, fishing records have shown that juvenile sharks will vertically segregate from mature females (e.g. Papastamati ou et al. 2006). Our results show that this behavior varies across the Atlantic, with strong segregation occurring in locations hypothesized to be used for mating, fertiliz ation and gestation (Area I, II and III ) and greater habitat overlap in habitats used for parturition (Area IV). Juveniles occupied different habitats in all areas except in Area III, which may suggest that smaller individuals avoid water where larger sharks occur more often. Alternatively, t his behavior may be related to predator avoidance with juveniles avoiding the sunlit shallow habitats. Male blue sharks in the Pacific Ocean dive to deeper depths than females during the day, although it is unknown how this relates to the reproductive eco logy of the species in the Pacific Ocean (Musyl et al. 2011). White sharks ( Carcharodon carcharias ) also vary their dive behavior as they swim between a California aggregation site and Hawaii and it is hypothesized that male and females switch to similar diving patterns when in an offshore focal area, potentially due to mating (Jorgensen et al. 2012). Interestingly, the vertical habitat

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79 utilization of male and female blue shar ks were very similar in Area IV where mating is hypothesized to occur and whe re females have been caught exhibiting fresh mating scars. Unfortunately, we were not able to develop an all explanatory movemen t model for blue sharks in the s outh Atlantic. Based on the highly directed long distance movements of a few individuals, it is highly likely that blue sharks, like other animals that have an extended period of growth prior to reproduction, perform partial migrations where only a proportion of individuals migrate (Jonsson and Jonsson 1993; Chapman et al. 2012). Therefore, indiv iduals are faced with the decision to remain a resident or migrate, which may be related to reproductive stage, resource abundance, body condition, or the threat of predation (Chapman et al. 2012). However, teasing apart the contributing factors requires selecting the appropriate spatial and temporal scales to analyze. We selected the entire Atlantic Ocean, which was an appropriate spatial scale, but an appropriate temporal scale would cover reproductive chronology of the species (e.g. 1, 2, or 3 year re productive cycles). An important prerequisite for estimating local fishing impacts is that the survey data (e.g. animal tracks) used to estimate fish core habitats covers the same areas and habitats as the fisheries (Vinther and Eero 2013). Our study sho ws that high utilization areas for tagged blue sharks directly overlapped with major fishing grounds for a variety of tuna longline fishing fleets in the s outh Atlantic Ocean (Anonymous 2012), which typically land blue sharks as bycatch. The continuing p roblem of exploited fish populations, local depletions, and recent issues of conservation of essential fish habitats, requires new information from stock assessments and imposes new challenges for population modeling (e.g., Field et al. 2006 ; Tuckey et al 2007). Many of these new challenges require the incorporation of spatial patterns into stock assessment modeling. It has long been known that stock assessments should not be performed assuming that

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80 single populations are isolated units (Beverton and H olt 1957). Even with our relatively small sample size, trans Atlantic movements of blue sharks were revealed, violating the main assumption of single stock assessment models that immigration and emigration are negligible (Hart and Cadrin 2004). Further more, the study demonstrated the first documented movements of a blue shark from the southeastern Atlantic Ocean into the Indian Ocean. However, demonstrating a link between sub populations is not the only consideration, as the rate of movement between loc ations will also influence management strategies. It has been suggested that all sub populations should be assessed together as a single stock unit when movement rates between sub populations are extremely high, while movement should be included in spatia l assessments when there are intermediate and low mixing rates (Aldenberg 1975). The explicit consideration of spatial scale to assess fishing impact is advantageous to marine management (Lorenzen et al. 2010). It is evident th at the blue shark stock i n the s outh Atlantic Ocean varies spatially at a large scale (Carvalho et al. 2010), with a low degree of mixing among blue shar ks from different areas of the s outh Atlantic Ocean and a clear vertical spatial segregation between adults and juveniles Consequently, a spatially explicit assessment may lead to a better understan ding of the spatial aspects of s outh Atlantic blue shark population dynamics, as well as improve fishery management decisions towards this species. Finally, the ability to model the influence of habitat characteristics on marine predator movements and distribution is critical for the development of predictive models of animal movements. These types of analyses will eventually allow u s to predict how changing oceanographic conditions (e.g. climate change; Hulme 2005) may influence the distribution and habitat selection of top level marine predators and potentially how this may impact fisheries interactions and bycatch.

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81 Table 3 1 Summ ary data for 28 blue sharks tagged with pop off satellite tags in the s outh Atlantic Ocean. F female ; M male. Tagging occurred in f our geographic areas (NE Area I, NW Area II, SW Area III, and SE Area IV). test. Individuals highlighted in grey represented r statistically different from a ID TL (cm ) Se x Location tagged (Area) Tagging date Progra med release days Pop up location (Degrees) Pop up date Days at liberty space 1 98 F I 05/21/09 90 33.0 W 6.5 S 08/09/09 81 162.4 2 235 F I 05/22/09 210 3.4 E 3.9 S 12/16/09 209 193.8 3 242 F I 05 12/11 180 37.5 W 8.8 S 07/07/11 57 141.5 4 275 F I 05/12/11 180 36.3 W 4.3 S 06/20/11 40 160.9 5 234 M I 05/14/11 180 28.5 W 4.1 S 09/07/11 117 165.3 6 102 M I 05/18/11 180 26.5 W 8.27 S 09/25/11 131 131.4 7 119 F I 05/19/11 180 32.1 W 8.6 S 09/03/11 108 143.2 8 253 F II 06/09/11 180 5.3 E 3.5 N 10/02/11 116 142.0 9 266 F II 06/12/11 210 5.0 E 3.2 N 09/25/11 106 130.7 10 107 F II 06/12/11 180 2.5 E 4.9 N 12/11/11 183 155.7 11 230 M II 06/14/11 210 0.4 E 3.0 N 09/12/11 91 150.2 12 103 F II 06/17/11 210 8.4 E 33.0 S 11/07/11 144 192.0 13 247 F II 06/17/11 210 9.9 W 4.5 N 10/23/11 119 165.5 14 112 M II 06/18/11 180 5.5 E 1.2 N 09/25/11 101 148.0 15 254 M III 10/26/08 180 18.3 E 37.4 S 02/04/09 102 130.8 16 259 F III 10/26/08 180 3.5 E 3.7 N 02/05/09 103 194.7 17 271 M III 07/06/09 180 15.6 E 31.7 S 10/14/09 101 150.0 18 261 F III 07/08/09 180 12.8 E 32.8 S 08/03/09 27 110.3 19 244 M III 10/29/10 180 22.0 E 35.0 S 01/29/11 93 153.3 20 290 M III 10/30/10 180 13.6 E 24.0 S 01/28/11 91 146.6 21 230 F III 10/14/11 180 19.6 W 35.9 S 03/08/12 147 187.6 22 241 F IV 01/16/09 90 36.0 W 29.4 S 03/19/10 63 151.2 23 102 M IV 01/22/09 90 35.3 W 31.8 S 03/29/09 67 156.6 24 104 F IV 12/11/10 180 37.8 W 31.0 S 04/02/11 113 164.1 25 107 M IV 12/13/10 180 46.0 W 28.7 S 04/29/11 138 157.1 26 260 F IV 11/05/11 90 50.3 W 35.4 S 12/30/11 56 150.7 27 253 F IV 11/06/11 210 28.3 W 7.18 S 04/28/12 175 161.7 28 241 M IV 11/13/11 210 50.0 W 36.0 S 03/14/12 123 137.0

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82 Table 3 2 Results from the generalized additive mixed models (GAMMs) for presence and absence of tagged b lue sharks in areas across the s outh Atlantic Ocean. The best fit model is highlighted in grey. R 2 is the adjusted coefficient of determination and Lr is likelihood ratio test Model R 2 (%) AIC BIC Lr Lr p value Area I Stage I 1) SST 0.441 3101 3115 NA NA 2) DML 0.427 3387 3388 NA NA Stage II 3) SST + DML 0.473 2883 2885 3 vs. 1 18.91 (<0.0001) Area II Stage I 1) SST 0.608 4219 4227 NA NA 2) DML 0.576 4314 4318 NA NA Stage II 3) SST + DML 0.619 4005 4011 3 vs. 1 7.44 (0.021) Area III Stage I 1) SST 0.403 3556 3569 NA NA 2) DML 0.400 3639 3642 NA NA Stage II 3) SST + DML 0.413 3319 3319 3 vs. 1 11.25 (0.004) Area IV Stage I 1) SST 0.572 4762 4773 NA NA 2) DML 0.560 5012 5018 NA NA Stage II 3) SST + DML 0.583 4511 4515 3 vs. 1 17.19 (<0.0001) All areas Stage I 1) SST 0.392 3034 3041 NA NA 2) DML 0.369 3363 3386 NA NA 3) Area 0.351 3609 3612 NA NA Stage II 4) SST + DML 0.408 2908 2917 4 vs. 1 14.08 (0.002) 5) SST + Area 0.387 3714 3719 NA NA Stage III 6) SST + DML + Area 0.361 3837 3845 6 vs. 4 3.62 (0.173)

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83 Table 3 3 Results from the generalized additive mixed models (GAMMs) for presence and absence of tagged b lue sharks in areas across the s outh Atlantic Ocean. Estimated degrees of freedom (Edf) and F values for smooth term variables are given. All variables selected were significant in the models (p < 0.001) Edf F p value Significant codes Area I Smoother term SST 4.027 3.68 E + 01 3.15 E 7 *** DML 2.119 4.30 E + 01 1.49 E 6 ** Area II Smoother term SST 5.185 1.69 E + 01 7.23 E 11 *** DML 4.220 2.44 E + 01 3.05 E 9 ** Area III Smoother term SST 7.582 1.75 E + 1 7.51 E 6 *** DML 2.992 104.239 0.003827 ** Area IV Smoother term SST 6.003 3.65 E + 01 2.35 E 10 *** DML 2.172 7.48 E + 01 9.42 E 8 ** All areas Smoother term SST 8.331 1.08 E + 01 3.95 E 6 *** DML 5.487 22.451 0.004781 **

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84 Fig ure 3 1 A) Proposed movement s by female blue sharks in the s outh Atlantic Ocean (from Hazin and Lessa 2005) and B) two stocks structure hypothesized by Legat and Vooren (2004). A B

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85 Fig ure 3 2. Most probable track for tagged blue sharks across the s outh Atlantic Ocean fit with the Kalman Filter State Spac e Model

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86 Fig ure 3 3 Use areas occupied by tagged blue sharks across the s outh Atlantic Ocean

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87 Fig ure 3 4 Rose diagrams showing the angular changes for tagged blue sharks that represented r statistically different from uniform distributions for

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88 Fig ure 3 5 Boxplot of sea surface temperature (SST) in the quadrants experienced by tagged blue sharks across the s outh Atlantic Ocean. Outliers are represented by a dot at either end of the plot A) Area I. B) Area II. C) Area II. D) Area IV A B C D

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89 Fig ure 3 6 Boxplot of depth of the mixed layer (DML) in the quadrants experienced by tagged blue sh arks across the s outh Atlantic Ocean. Outliers are represented by a dot at either end of the plot A) Area I. B) Area II. C) Area II. D) Area IV A B C D

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90 Fig ure 3 7 Partial response curves showing the effects of sea surface temperature (SST) and depth of the mixed layer (DML) on presence of blue sharks in quadrants across the s outh Atlantic Ocean. The grey shaded region indicates the calculated 95% confidence interval. A) Area I. B) Area II. C) Area II. D) Area IV A A D B B C C D D

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91 Fig ure 3 8 Cluster analysis of the frequency distributions of the proportion of time at depth for each individual and for adult males, adult females, and juveniles (both sexes combined) A) Area I. B) Area II. C) Area II. D) Area IV A B C D

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92 CHAPTER 4 INCORPORATING VERTICAL SPATIAL POPULATION STRUCTURE INTO STATISTICAL CATCH AT AGE STOCK ASSESSMENT MODELS 4. 1. Background The blue shark ( Prionace glauca ) is possibly the most wide ranging shark species occurring in temperate, subtropical and tropical waters (Henderson et al., 2001), with high bycatch rates in pelagic longline fisheries (Compagno et al., 2005). Blue shark is the most commonly caught large shark and is the most abundant pelagic shark (Megalofonou et al., 2009; Stevens et al., 2000). Howe ver, several studies have reported declines in the abundance of blue shark (Baum et al., 2004; Campana et al., 2005), possibly as a result of the impacts of overfishing. In the South Atlantic Ocean (SA) the blue shark stock is managed by the International Commission for the Conservation of Atlantic Tunas ( ICCAT ). In 2008, ICCAT carried out a stock assessment for Atlantic blue sharks assuming a single stock using a Bayesian surplus production stock assessment model (ICCAT 2008). Surplus production models ( SPM) treat stocks as an undifferentiated biomass, ignoring sexual, size, and age based differences among individuals. Ecological differences within and between members of a population suggest that this assumption may overlook important influences on popula tion dynamics. Another criticism is that SPM ignores the spatial structure of the population and assume that the stock is homogeneously distributed (i.e. fully mixed) (Punt and Hilborn, 1997). Nevertheless, fish often disperse in response to spatial habitat features to satisfy particular life history requirements (e.g., foraging, reproduction), which results in non homogenous patterns of abundance across the water at scales usually distinct from conventional mana gement boundaries (Walters and Martell 2004) Consequently, spatially explicit assessment models may lead to a better understanding of the spatial aspects of the population dynamics, as well as improve fishery management decisions.

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93 Different ways to incor porate spatial structure into stock assessments have been described in the literature. One of the first examinations of spatial structure involved a box transfer model, i.e., a discrete approximation to a dispersion model (Beverton and Holt, 1957). This mo del was expanded to make use of tagging data in an application for skipjack tuna, Katsuwonus pelamis (Sibert, 1984), and later for parameter estimation to be based on maximum likelihood estimation, with the tagging data being assumed to be Poisson distribu ted (Hilborn, 1990). With increasing computing power, more complex models were developed, such as advection diffusion reaction models (Sibert et al., 1999), and MULTIFAN CL (Fournier et al., 1998), which fully integrates advection diffusion processes into a length based, age structured model. Despite the attention given to spatial structure in stock assessments in the literature, most fisheries lack the tagging data required to parameterize models of spatial dynamics explicitly. Thus, it is increasingly com mon to approach spatial structure in stock assessment by dividing the geographical area where the stock is distributed into spatial strata, and treating the data from each stratum as coming from a different fleet. In these cases, the catches, indices of ab undance (CPUE), and biological composition data are partitioned by area (Cope and Punt, 2011). This as distributed across its range, and that any differences in age or l ength compositions are due to gear selectivity. This approach can also been used geographical range, the same considerations apply to a stock for which the population age or length structure differs with depth (Berger et al., 2012). In addition, information on spatial population structure based on depth has also becoming more available due the emerging electronic tagging technology (e.g. Pop up Satellite archival Tags) (Block, 2005).

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94 Analysis on depth preferenc e obtained from the present study revealed variability in vertical habitat utilization and size segregation in particular areas, with juveniles utilizing shallower waters than either adult males or females (Chapter 3). This difference in vertical spatial s tructure of the population can strongly affect fishery selectivity, ignoring it in the stock assessment process can produce biased estimates of management quantities and underestimate uncertainty. Here, we implemented a spatial structured Statistical Catch at Age Model (SCAM) using two different fishing fleets as a proxy for spatial process, to describe the status of South Atlantic blue shark population. Furthermore, we evaluated the potential use of vertical spatial structure information obtained from sat ellite archival tags to directly inform selectivity in SCAM 4. 2. Materials and M ethods Two sequential procedures were used to implement a spatially structured SCAM : 1) standardized CPUE abundance indices for blue shark were constructed for two different longline fleets operating in the South Atlantic ocean ; 2) standardized abundance (CPUE) indices were fit to a SCAM Additionally, to evaluate the potential use of t agging information data to inform the shape of the selectivity curve in stock assessment models, we constructed selectivity curves based on tagging data only and compared those with the selectivity curves generated by the SCAM. 4. 2.1. Data For the SCAM, t he total catches per year used in the model were the catches estimated by ICCAT based on the ratios of sharks to tuna method (ICCAT, 2005) for the South Atlantic blue shark from 2002 to 2012. This method was developed by the ICCAT shark working group (ICCA T, 2005). It estimates the percentage of reported shark catch vs. the combined total catch of tunas, swordfish, and billfish. The ratio from this calculation was aggregated by gear and fleet

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95 characteristics and applied to strata for which no shark catch in formation is available in order to estimate possible catch levels of blue shark for non reporting fleets over the period 2002 2012 in the South Atlantic. Total commercial catches peaked in 2011, with Brazil ranking first in number of blue sharks caught by country per year (Figure 4 1). Blue shark catch and effort data were obtained from 37,665 longline sets made by two Brazilian tuna longline fleets, here represented by Fleet A and Fleet B. Longline sets from both fleets were distributed throughout a wide area of the Southwestern Atlantic Ocean, ranging from 10 E and 50 W longitude and between 10 N to 45 S latitude (Figure 4 2). Fleet A is based in the coastal cities of northeast Brazil, including Recife, Natal, and Cabedelo, and its major fishing ground is located in the Atlantic Equatorial zone. This area (Area I) is characterized by the presence of seamounts (North Chain of Brazil) and oceanic islands (Fernando de Noronha Archipelago and Atol da Rocas), and upwelling driven by the equatorial convergence ( Mayer et al., 1998) (Figure 4 2). Fleet B is based in the Southeast and South of Brazil, in the cities of Santos, Itaja, and Rio Grande. The major fishing ground for this fleet is in the vicinity of the Rio Grande Rise, large seismic ridge situated between the Mid Atlantic Ridge and the Brazilian continental shelf. This area (Area II) also is characterized by the presence of the convergence zone between two current system s: 1) the warm, coast hugging, S outhward flowing Brazil Current; and 2) the cold northward flowing Malvinas (Falkland) Current (Garcia, 1997; Seeliger et al., 1997) (Figure 4 2). Fisheries logbooks from both fleets were made available by the Ministry of Fisheries and Aquaculture within the Brazilian government. The logbooks containe d details for each vessel operating within the fishery and included: date, time, start and end coordinates of the set, total number of hooks, and the total number of individuals caught for each set. Length frequency (fork

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96 length, FL, cm) information on blu e sharks was obtained from the Brazilian on board observer program. A total of 26,341 blue sharks were measured from 2002 to 2012 across the Southwest Atlantic Ocean in Areas I and II. Age frequencies were obtained by back transforming the lengths into age s using the von Bertalanffy relationship provided by Lessa et al. (2004). 4. 2.2. Data A nalysis Standardizations were performed for South Atlantic blue shark catch and effort data from each of the fleets using Generalized Linear Models (GLMs). The number o f zero blue shark catches was relatively high in the datasets (56% Fleet A; 51% Fleet B) and a Tweedie distribution with a log link function was therefore used in the GLMs f ollowing Carvalho et al. (2010). T he models used the following formula: where : location parameter; : diffusion parameter; : power pa rameter (Shono, 2008). The selection of predictors was evaluated exclusively on AIC. The GLMs were computed in the R language for statistical analysis (R Development Core Team, 2011). An estimate of historical blue shark abundance in the South Atlantic ocean was reconstructed u sing a SCAM. SCAMs are age structured models that follow cohorts of fish over time and consider the catch at age data to be measured with error (Megrey, 1989). Such models consist of population and observation submodels, where the model parameters are esti mated by fitting the models to data (Megrey 1989). With the development of SCAM more attention was

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97 parameters within the stock assessment model. In most of SCAMs, wh en age composition data is available, selectivity parameter is estimated internally in the stock assessment model. However, age composition data is not mandatory for SCAMs, in such cases the selectivity parameter will have to be fixed. The SCAM used in the present study is based on the framework developed in Martell et al. (2008). The biological parameters used for the calculations as well as subscripts, input data, and estimated parameters are shown in Table 4 1, and model equations in Tables 4 2 and 4 3 For all equations upper and lower case subscripts denotes unfished and fished conditions, respectively. Individual growth was assumed to follow the von Bertalanffy equation, for which expected length l at age a was given by (T2.1) and mean weight at age is given by the allometric relationship in (T2.2). Standard logistic functions were used to estimate maturity at age (T2.3) and vulnerability at age (T2.4). Assuming dome shaped selectivity was also explored in the model. In order to implement a dome shaped selectivity an additional penalty weight is added to the objective function that control how much curvature there is and limit how much dome shaped can occur. Natural mortality was assumed to be age independent and time invariant ( fixed at a constant 0.2 y r 1 assessment) The leading parameters (T2.1 T2.4), along with the age specific information, were used to derive parameters for the Beverton Holt stock recruitment relationship (T2.7 T2.9) assumin g equilibrium, unfished conditions. In the present study a commonly used parameterization of the Beverton Holt stock recruitment model, the so called steepness parameterization, was applied. This parameterization was developed by Mace and Doonan (1988), wh h A steepness of 1.0 implies that recruitment is independent of spawning stock, and the population would th erefore be

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98 highly robust to exploitation. For steepness approaching 0.2, the population would be barely maintaining itself at all levels of spawning stock and would therefore be highly vulnerable to exploitation. To establish the initial age structure, was assumed an initial equilibrium abundance where survivorship ate age a was given by (T2.5). Survivorship for fished equilibrium conditions was calculated by (T2.6). Given the survivorship and maturity at age, the reproductive rate for unfished and fished c onditions was given by (T2.7). Vulnerable biomass for unfished and fished conditions was calculated by (T2.8). Subsequently, equilibrium recruitment (T2.9), virgin and equilibrium biomass (T2.10), and the initial state of the population, were calculated ( T2.11). Fishing mortality was conditioned on the Baranov catch equation (T2.12), while instantaneous total mortality and spawning stock biomass is given by (T2.13) and (T2.14), respectively. The initial numbers at age are projected forward using (T2.15), w here s 0 is the maximum survival rate from egg to age 1 recruit (T2.16) and b determines the asymptotic limit (T2.17). Predicted annual catch at age and total catch in weight are given by (T2.18) and (T2.19), respectively. Finally, the total number of individuals and the total biomass vulnerable to the fishery is given by (T2.20) and (T2.21), respectively. The final step in the SCAM is computing the residuals between the relative abundance indices and the catch at age proportions to be used in the negat ive log likelihoods during parameter estimation or numerical integration of posterior distribution (Table 4 3). Here we assume that the observation errors in the abundance index for each fleet are normally distributed and proportional to the vulnerable bio mass. Regarding the initial conditions of the stock used in the model, we assumed that the first year for which annual catch data are available may not correspond to the first year of (appreciable) exploitation, so that one cannot necessarily make the assu mption in the application of this SCAM that this initial year reflects a population (and its

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99 age structure) at pre exploitation equilibrium. For the first year considered in the model therefore, the stock is assumed to be at 8 0% of its pre exploitation bio mass, based on estimates from Chapter 2. Additionally, to improve model fit a beta prior (0.9, SD=0.2) was assigned for the steepness parameter ( ) of the Beverton Holt stock recruitment relationship. This value is based on previous blue shark stock assess ments in the north Pacific (Kleiber et al. 2009) and Atlantic oceans (ICCAT, 2008). characteristics. According to Corts (2002), blue shark have one of the highest fecundities documented amo ng sharks (mean litter size of 37 pups, Mejuto and Garca Cortes, 2005; reaching up to 82 pups, Pratt, 1979) and surprisingly fast early growth rates that result in near doubling of pup size over the first year (Skomal and Natanson, 2003). Calculated harv est management points were based on Maximum Sustainable Yield (MSY) assuming the Beverton Holt model. The fishing mortality rate that maximizes yield (F MSY ) is calculated numerically using a Newton Raphson approach to solve the instantaneous catch equation (see Martell et. al., 2008) assuming steady state conditions. Given an estimate of F MSY other reference points are derived based on equilibrium recruitment at F MSY and per recruit incidence functions. The selectivity type for each Fleet used on SCAM were chosen based on the shape of the selectivity curve s constructed using the tagging data only. Fishery specific selectivity as implemented stock assessments is represent ed as the product of contact selectivity (the probability a fish is captured when it encounters the fishing gear) and availability (the probability that a fish is in the area where and when the fishery occurs). To construct the selectivity curves based on tagging data we considered availability as the proportion of time that an age specif ic blue shark occupies the depth range of the longline fishing gear, here assumed to range from 0 to

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100 75 m deep This range was based on a study carried on the Brazilian longline Fleets A and B following the methodology proposed by Bigelow et al. (2006), wh ich attaches t emperature depth recorders to pelagic longline gear. The contact selectivity was assumed to be one for all individuals older than one year old. The availability analysis suggests that there is a trend in age across depth in both areas (Figu re 4 3) For Fleet A the depth range of the longline gear is inhabited mostly by adults, which is consistent with an asymptotic selectivity. In the other hand, for F leet B the overlap shifts to younger ages, with older fish located in deeper waters, conseq uently is expected the selectivity to become more dome shaped. This feature would be modeled by assigning two types of selectivity For Fleet A a simple asymptotic logistic curve was chosen to model the availability data, while a spline curve was used to f it these data for Fleet B (Figure 4 3) The SCAM model was developed and implemented using AD Model Builder (ADMB; Fournier et al., 2012 ). A Bayesian approach was used to obtain posterior probability estimates for the parameter values and quantities of interest such as fishing mortality rates, abundance, and total and spawning stock biomass (SSB). In the Bayesian framework, samples are gen erated from the posterior distribution of parameters, which can be implemented using Markov Chain Monte Carlo (MCMC) techniques (MacKay, 2003). The MCMC samples were calculated using the default algorithm in ADMB (Fournier et al., 2012). MCMC simulations w ere conducted in an identical manner for each model scenario. Each simulation included five chains with 2 million cycles, discarding the first 200000 iterations as burn in phase and then thinning the chain by saving every 200 th iteration to reduce autocorr elation. MCMC simulation convergence was tested using the CODA package (Convergence Diagnosis and Output Analysis; Plummer, 2006) in R statistics A minimal threshold of p (Geweke, 1992)

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101 and the two stage Heidelberger Welch stationary test (Heidelberger and Welch, 1983) We also used the Gelman and Rubin (1992) approach to evaluate the mixing and convergence of ou r MCMC sampler t ests results showed no evidence of failure to converge for all model parameters. Model fit was evaluated by assessing whether the distribution of predicted catch rates, calculated using parameters sampled from the joint posterior distributi on corresponding to MCMC simulations, included the corresponding observed catch rate at the 95% credible level (posterior predictive check; Gelman et al., 2004). 4. 3. Results 4. 3.1. CPUE S tandardization The final model for the blue shark CPUE standardization from both fleets consisted of three variables and explained 56% and 54% of the total deviance for fleets A and B, respectively. The relative contribution from each variable in the total explained deviance for the model for fleet A showed th at Target ( 44 %) was the most important factor, followed by Year ( 38 % ), Quarter ( 12 %) a nd interaction Year*Target (6%) (Table 4 4 ). The CPUE model for fleet B explained 55% of the total deviance. Target (48 %) and Year (40 %) were the most important factors, followed by Quarter ( 8 %) and interaction Year*Target (4%) Residual diagnostic plots and Q Q plots showed that good fit was obtained and that the assumed error structure was satisfactory for both models ( Figure 4 4 ). Overall, the standardized CPUE time s eries showed a stable trend from 2002 to 2012 in both models. However, Fleet B showed lower values for observed and predicted CPUE duri ng the entire model frame ( Figure 4 5 ). 4. 3.2. Statistical Catch at A ge Model The SCAMs produced reasonable fits, with p osterior median e stimate of steepness for the stock recruitment relationship extr emely high (0.93 ). For CPUE the model predicted the same stable trend as was observed, producing lower predictions of CPUE fo r Fleet B than for Fleet A

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102 (Figure 4 6 ). Observed age for both fleets showed a stable trend during the study period, with Fleet A catching predominantly adult individuals while most catches from Fl eet B were juveniles (Figure 4 7 ). R esidual patterns in the age composition data from both fleets ear to have any significant pattern that would indicate a major model misspecification (Figure 4 8 ). Selectivities e stimated by the SCAM show a clear difference between Fleet A and B, with 8 years (0.91) and 6 (0.63) years old fish fully selected in are as I and II, respectively (Figure 4 9). In addition these results clearly demonstrates that when fishing effort is concentrated in a shallower depth zone (0 75m) and there is an ontogenetic shift toward deeper waters for older blue shark the result is a d ome shaped selectivity (Figure 4 9). Changes in posterior median estimates of total biomass, vulnerable biomass, and SSB were relatively small throughout the time s eries for both scenarios Posterior median estimate for MSY were 879,490 mt ( SD= 108,637 mt) with corresponding estimates of S SBmsy of 682,741 (SD=88,721 ) The estimates of t he current status suggest that total biomass in 2012 decrease 4% of initial total biomass The percent decreases for SSB were 5 % Posterior median estimates for SSB 201 2 /SSB MSY was 1.49 while F 2012 /F MSY were 0.32 Current stock status relative to MSY (F 2012 /F MSY SSB 2012 /SSB MSY ) suggest that the stock is not overfished ( SSB 2012 > SSB MSY ), nor is overfishing occurring ( F 2012 < F MSY ) and the stock is therefore in no danger of overexploitation and collapse 4. 4. Discussion C urrent scientific understanding of population dynamics and stock status for blue sharks in the South Atlantic are entirely fishery dependent. Therefore, estimates of historical biomas s are ba sed on relative measures of CPUE obtained from various fisheries, which are assumed to be proportional to exploitable abundance. Because the fisheries do not sample the populations in

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103 a random, unbiased manner, fishery dependent data may introduce many pot ential sources of error. Efforts to account for potential biases require an understanding of the relationship between habitat, susceptibility to capture, and the spatiotemporal dynamics of fishing effort (Maunder and Punt, 2004; Bishop, 2006). To estimate account for factors other than abundance that affect CPUE. There are numerous approaches available for standardizing CPUE (Maunder and Punt 2004), including habitat based models ( Hinton and Nakano 1996; Maunder et al. 2006). Habitat based standardization, as opposed to a more traditional linear modeling technique, has been proposed for highly migratory species, because the fisheries responsible for a majority of their fishing mor tality (longline fisheries) have changed target species and target habitats over time (Majkowski 2007). These changes highlight the need to include habitat when estimating the abundance of target and bycatch species from longline fisheries, because no spe cies group is caught randomly across their respective habitats. Habitat based standardization relies mainly on the knowledge of the species vertical habitat use, which in most cases are obtained from tagging studies (Bigelow et al. 2004). External analyse s of tagging data can be also used to directly inform stock assessment models. First, they can be used to generate and/or test hypotheses about population characteristics and dynamics. This can be very influential through its effects on model structure, pa rticularly for information sources such as electronic tags which may provide insights into fish behavior that evolve with time and more data. For example, separate spawning and foraging grounds have been hypothesized from movement patterns observed in Atla ntic bluefin tuna, Thunnus thynnus using electronic tags data (Block et al. 2005, Galuardi et al. 2010) Kurota et al. (2009) tested some of these hypotheses by estimating bluefin movement (and exploitation

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104 rates) by size across ICCAT boundaries; however, only start and end point data were used, ignoring intermediate positions available from electronic tags. In another example, uncerta inty about spatial structure and movement dynamics in the most recent stock assessment of South Pacific swordfish Xiphias gladius (Kolody et al. 2008) motivated the analysis of spatial dynamics with electronic tags by Evans et al. (2014) as part of the ongoing effort to update the data available for the next assessm ent. related factors might affect their spatial structure and vulnerability to being caught. Consequently, the inclusion of appropriate auxiliary information from tagging data should be encouraged. For instan ce, Chapter 3 shows a strong vertical segregation between adults and juveniles occurring in Areas I and II, this behavior may be related to predator avoidance with juveniles avoiding adult habitats (Musyl et al., 2011). It is increasingly common to treat spatial structure in a stock by dividing the range over which the stock is distributed into spatial strata (such as Areas I and II, in the present study) and treating the data for each stratum as though coming from a different fleet (Cope and Punt, 2011). oorest of the approaches may have been related to not allowing the selectivity patterns for fleets to be different (e.g., dome shaped). SCAM is sensitive to the choice of how selectivity is modeled. Incorrect assumptions about selectivity generate errors in the SCAM estimates of biomass (Kimura, 1990), SSB (Punt et al., 2002; Radomski et al., 2005), exploitation rate (Radomski et al., 2005), and the ratio of

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105 stoc k biomass in the first year to stock biomass in the final year of analysis (Yin and Sampson, 2004). At present, the SCAM approach developed by Martell et al. (2008) allows six alternative age specific selectivity options. If the selectivity is assumed to be dome shaped for all the fisheries, its estimation within a stock assessment model may not be possible. It is likely the degree of the dome shape would be confounded with the estimates of mortality. The more common stock assessment practice is to assume asymptotic selectivity unless there is conclusive evidence that certain sizes or ages are being excluded from the fishery ( Cope and Punt 2011) However, using an asymptotic selectivity for all fisheries might cause estimates of fishing mortality to be bias ed high. Recent research indicates that some degree of dome shaped selectivity is to be expected in many situations, due to incomplete mixing of individuals and spatial heterogeneity in fishing intensity (He et al. 2010). Ideally, information should be ava ilable to provide an objective stance for specifying at least one gear type having dome shaped selectivity ( Cope and Punt 2011) Tagging studies have been used to describe selectivity patterns for a variety of fish including chinook salmon (Jones and McP herson, 2000), cod (Myers and Hoenig, 1997, Pederson and Pope, 2003), halibut (Clark and Kaimmer, 2006), red drum (Bacheler et al. 2010), sablefish (Assonitis, 2008), and yellowtail flounder (Cadrin, 2008). However, until this time, there is no documented evidence that data from satellite archival tags have been used to inform selectivity patterns for pelagic species. The satellite archival tagging study developed by Carvalho et al. (2014) on blue shark in the South Atlantic ocean not only showed blue shar related factors might affect their spatial distribution and vulnerability to being caught. The similar parameter estimates of models using estimated and fixed selectivity, presented here, indicate that

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106 data from satel lite tags can be a powerful source of information, specifically assisting to inform the shape of the selectivity in stock assessment model s

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107 Table 4 1 Definition of subscripts, input data, and input parameters Indices Index for age Age of plus group Index for time Data Fishery o bserved catch Fishery r elative abundance Fishery age proportions Life history information Instantaneous mortality rate Von Bertalanffy growth parameters = 352.1 = 0.16 year 1 = 1.01 Allometry for length weight = 1.901*10 6 = 3.134 Age at 50% maturity = 5 years Standard deviation in age at maturity = 0.65 Calculated parameters Average recruitment Average fishing mortality Instantaneous total mortality rate Model predicted catch at age Model predicted total catch Model predicted abundance index Model predicted proportions of catch at age Estimated parameters Age at 50% vulnerability Standard deviation in vulnerability at age Unfished age 1 recruits Recruitment compensation Equilibrium fishing rate Recruitment deviations

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108 Table 4 2 Notation for estimated parameters age schedule calculations. *Upper and lower case subscripts indicate unfished and fished conditions, respectively Mortality T2.1 T2.2 T2.3 T2.4 Survivorship T2.5 T2.6 T2.7 T2.8 where is given by: T2.9 T2.10 T2.11 State dynamics T2.12 T2.13 T2.14 T2.15 T2.16 T2.17 T2.18 T2.19 T2.20 T2.21

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109 Table 4 3 Residuals and likelihoods. Residuals Abundance index where is given by: T3.1 Recruitment T3.2 Age proportions where = ; and = T3.4 T3.5 Negative log likelihoods Catch T3.6 Abundance index T3.7 Recruitment T3.8 Age proportions T3.9 T3.10

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110 Table 4 4 Deviance analysis of explanatory variables in the Tweedie models for blue shark caught by Brazilian pelagic tuna longline fleet, from 2002 2012 Model for Fleet A Df Deviance Resid. Df Resid. Dev Dev. Exp (%) AIC NULL 22318 8776.8 2034 Target 4 37664.8 19402 7541.3 44 1873 Year 10 34705.3 19015 7103.4 38 1247 Quarter 3 28911.5 18387 6891.2 12 1015 Year*Target 54 15438.4 18119 6224.2 6 973 Model for Fleet B NULL 8425 5778.2 9355 Target 4 12889.4 7655 5433.8 48 8961 Year 10 12541.3 7114 5112.7 40 8542 Quarter 3 11654.8 6743 4902.8 8 8249 Year*Target 54 10382.2 6528 4831.5 4 8104

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111 Fig ure 4 1. Annual catches (2002 2012) of blue shark by country in the South Atlantic Ocean estimated by ICCAT using the ratio of sharks landed to the total landings of all tunas (including swordfish and billfishes)

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112 Fig ure 4 2. Distribution of fishing effort in number of hooks by the Brazilian longline fleets between 2002 and 2012 in Areas I and II

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113 Fig ure 4 3. Proportion of time at depth histograms for adults and juveniles for areas I and II A) Area I. B) Area II. B A

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114 Fig ure 4 4. Histogram of standard residuals ( left panel) and quantile quantile (Q Q) plots of the deviance residuals ( right panel) of the model fit for Fleets A (Area I) and B (Area II) A B

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115 Figure 4 5. Nominal (red circle) and standardized (black line) CPUE of blue shark caught by the Brazilian pelagic tuna longline fleets A and B from 2002 2012. Shaded region represents the 95% credibility interval for predicted CPUE values A) Fleet A. B) Fleet B. A B

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116 Figure 4 6. Observed and predicted CPUE from the southern Atlantic blue shark stock assessment using the SCAM under scenarios I and II Shaded region represents the 95% credibility interval for predicted CPUE values A) Fleet A. B) Fleet B.

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117 Fig ure 4 7. Observed age composition (top panel) and Pearson residuals between observed and predicted proportions at age (bottom panel, with negative residuals given by blue circles) A) Fleet A. B) Fleet B. A 0 units 2 units 4 units 6 units A B B

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118 Fig ure 4 8. Selectivity curves constructed using catch at age information of blue sharks caught by the Brazilian pelagic tuna longline fleets A and B from 2002 2012 Dashed black lines represent t he estimated age at 50% selectivity

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119 Fig ure 4 9. Total biomass and spawning stock biomass (SSB) estimated by the southern Atlantic blue shark stock assessment using t he SCAM A) Total biomass. B) Vulnerable biomass. C) SSB

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120 CHAPTER 5 CONCLUSIONS The research studies that comprise this dissertation focused on the role of changes in target species and spatial structure in assessing the stock of S outh Atlantic blue shark. The results of each study have direct implications for blue shark management in the Atlantic. For instance, when a change in target species of the Brazilian longline fishery was directly incorporated into methods u sed for estimating CPUE and in a surplus production model the accuracy of CPUE estimates was improved as well as the per formance of the stock assessment model. However, despite the good fit obtained using the surplus production model, this type of model does not account for spatial variability in the pulation. For assessing the South Atlantic blue shark stock this issue is aggravated, as the results obtained using the satellite telemetry revealed a much more complex spatial population structure than previously thought, with a clear spatial segregation between adult and juveniles in the Southwestern Atlantic. It is also impor tant to highlight that the stock assessment presented here did not include CPUE and age structured information from the eastern South Atlantic, results from the tagging study indicate that spatial segregation between males and females also occur in the Gul f of Guinea area, for example. Consequently, information such as CPUE and age structure of individuals from that area needs to be incorporated in future assessments as soon as it becomes available. The statistical catch at age stock assessment model develo ped here was able to capture this spatial variability in addition it provide an alternative method to include such variability in situations where size composition data are not available. Despite the stock assessment used, the S outh Atlantic blue shark sto ck has not been depleted to overfished levels. These results align with those of ICCAT (2008 ), which posited that the current status of S outh Atlant ic blue shark is being managed sustainably. While changes in target species and spatial structure considerat ions advance the stock assessment and management

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121 of blue shark, the advancements, unfortunately, do not necessarily lead to adequate results. Even when accounting for all sources of bias, the abundance estimated from fishery dependent catch rates still may not reflect true abundance trends. Thus, bias may persist in the stock assessments even in best case scenarios. This clearly emphasizes that independent stock monitoring programs are essential for effective fisheries management. Therefore, nations with an interest in harvesting these important internationally shared resources should collaborate to support implementation of comprehensive scientific monitoring programs. Moreover, given the long history of exploitation of South Atlantic blue sharks without s cientific monitoring, any established programs would be useful for characterizing future population dynamics, while fishery dependent data will continue to serve as the basis for understanding historical abundance patterns. Fisheries management is often g uided by harvest policies that utilize state dependent control rules to translate current population estimates, such as abundance or biomass, into the alternative ass umptions regarding population structure and changes in catchability can considerably affect quantities necessary for rational management (e.g., estimates of population size, fishing mortality, and population age structure), which could ultimately influence harvest policy decisions. However, more research is needed to evaluate how robust exploitation policies are to alternative assessment models and assumptions of spatial population structure and changes in catchability. For example, does accounting for stru cture using spatially referenced parameters affect policy performance in a meaningful way over models that do not spatially reference parameters? Appropriately accounting for spatial structure in assessments appears to be important.

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122 Previous simulation st udies have shown that allowing for spatial structure, when present, can both reduce bias and improve precision of estimates. For example, Punt (2003) found that less biased and more precise estimates resulted from separate stock assessments carried out at small spatial scales as opposed to pooling data across spatial regions. Sub dividing the stock assessment into smaller spatial levels can also be convenient for satisfying assumptions (Quinn and Deriso 1999). The present study illustrated this approach for South Atlantic blue shark and justified incorporating spatial structure information. Satellite archival tags are one of the newest and potentially most informative data sources for developing spatial structured stock assessment. However, the majority of satellite archival tagging research effort, particularly in highly migratory species, has thus far been guided by ecological questions. The information gathered through these endeavors has undoubtedly given invaluable insights, but insufficient study desig n sometimes leads to duplicate data being collected, while other large knowledge gaps persist. As a remedy, satellite archival tags experiments that maximize their value for stock assessment would also provide balance and rigor to ecological research. Stu dies designed to collect observations across the complete range of spatio temporal strata as well as demographic attributes (age, sex, etc.) would address both ecological and behavior questions as well as become a powerful information source in assessments Closer collaboration between stock assessment scientists and ecologists in the planning and implementation of electronic tags research could greatly leverage the value of the data for both disciplines.

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123 APPENDIX A GAMM Generalized Additive Mixed Mod el formulation and inference Generalized Additive models ( GAMs ) are extensions of Generalized Linear M odels (GLMs) in which a link function describing the total explained variance is modeled as a sum of the covariates. The terms of the model can in this c ase be local smoothers or simple transformations with fixed degrees of freedom (e.g. Maunder and Punt 2004). In general the model has a structure of: Where and has an exponential family distribution. is a response variable, is a row for the model matrix for any strictly parametric model component, is the corresponding parameter vector, and the are smooth functions of the covariates, In r egression studies, the coefficients tend to be considered fixed. However, there are cases in which it makes sense to assume some random coefficients. These cases typically occur in situations where the main interest is to make inferences on the entire po pulation, from which some levels are randomly sampled. Consequently, a model with both fixed and random effects (so called mixed effects models) would be more appropriate. In the present study, observations were collected from the same individuals over t ime. It is reasonable to assume that correlations exist among the observations from the s ame individual, so we utilized Generalized Additive Mixed M odels (GAMM) to investigate the effects of covariates on presence and absence of tagged blue sharks in spec ific quadrants. GAMMs ar e an extension of Generalized Linear Mixed M odels (GLMMs) to allow the parametric fixed effects to be modeled non parametrically. Specifically, suppose { Z ij1 Z ijq } are q covariates associated with Y ij GAMMs are given as: Where is an unknown centered smooth function of the k th covariate Z k and b i is a vector of random effects following N{0, D ( The smoothing splines estimators of { maximize the penalized integrated log likelihood. Where (.) in the integrated log likelihood. Application to blue shark tagging satellite telemetry data The data consisted of binary observations (presence in a quadrant yes = 1 and no = 0). The covariates of interest included SST (Sea surface temperature) and DML (Depth of the mixed layer). Suppose observation of the i th of n units consist of an outcome variable y i and p covar iates x i = (1, x i 1 x ip ) T associated with fixed effects and a q x 1 vector of covariates z i associated with random effects. Given a q x 1 vector b of random effects the observations y i are assumed to be conditionally independent with means and variances var where is a specified variance function, is a prior weight (e.g. binomial denominator) and is a scale parameter. Then the final GAMM can be formulated as: Logit ( ) = log (

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124 Where p = P ( Y = 1), Y is the response variable, are smooth functions, is the shark specific random effect and are assumed to be distributed as and is a c x 1 vector of variance components.

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125 APPENDIX B ANALYSIS OF RESIDUALS Diagnostic tools for the analysis of residuals In the present study we used Q Q plots and histogram of residuals as model diagnostics and the Lilliefors test for normality. In the construction of Q Q plots the distribution function of the resi duals, was estimated with the empirical cumulative distribution function (ecdf) as: Then, the Q Q plot is the scatter plot of the collection of points Where, is the quantile function of the distribution function F 0 that in this case is the normal distribution. The Lilliefors te st was used to check normality of both residuals and random coefficients, i.e. the null assumption and the test statistic, which is a modified Kolmogorov Smi rno v statistic, is: Where is the ecdf of the sample vector x and is the distribution function of a normal distribution wit h mean and standard deviation The null hypothesis is rejected for larger values of the statistic. Residuals used in the construction of QQ Where is the th component of the deviance contributed by the datum th, as suggested by Wood (2006) Residuals of all the models produced almost the same patterns. The Q Q plots of residuals shows a slightly departure of residual quantiles from the theoretical normal quantiles, which can be assured in a symmetry presente d in th e histogram of residuals ( Figure B 1). Furthermore, the Lilliefors's test gave non significant results for residuals of all models (Table B 1), which means that it failed to reject the nor mality assumption. In conclusion, that data did not violate the assumptio n s of normality and independence Table B 1 Lilliefors test for normality of residuals and random effects. For each model the statistic L and the corresponding p value are given f or residuals and for random effects respectively. Model (Area) L (residuals) p value L (random ) p value Area I 1.456 0.082 0.238 0.211 Area II 1.094 1.037 0.176 0.799 Area III 2.665 0.954 0.362 0.083 Area IV 3.552 0.701 0.141 0.165

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126 Figure B 1. Diagnostic plots of GAMMs for presence and absence of blue sharks in specific quadrants across the South Atlantic Ocean.

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12 7 APPENDIX C TUKEY TEST Table C 1. Tukey HSD p ost h oc pair wise comparison of the mean sea surface temperature (SST) in quadrants experienced by tagged blue sharks Shade rows indicate statistically significant differences at P<0.05. Area I BSH D iff erence Lower Upper P adj usted 2 1 0.107025 0.286097 0.07204699 0.61154 3 1 0.075325 0.254397 0.10374699 0.90795 4 1 0.05715 0.236222 0.12192199 0.97885 5 1 0.0722533 0.251330 0.10681366 0.92507 6 1 0.0823416 0.261413 0.09673033 0.86009 7 1 0.104325 0.283397 0.07474699 0.64278 27 1 0.845675 1.000755 0.6905941 0.00000 3 2 0.0317 0.147372 0.21077199 0.99946 4 2 0.049875 0.129197 0.22894699 0.99049 5 2 0.034766667 0.144305 0.21383866 0.99901 6 2 0.024683333 0.154388 0.20375533 0.99990 7 2 0.0027 0.176372 0.18177199 1.10023 27 2 0.73865 0.893730 0.5835691 0.00000 4 3 0.018175 0.160897 0.19724699 0.99999 5 3 0.003066667 0.176005 0.18213866 1.00000 6 3 0.00706667 0.186087 0.17205533 1.00000 7 3 0.029 0.208072 0.15007199 0.99970 27 3 0.77035 0.925409 0.6152691 0.00000 5 4 0.01510833 0.194183 0.16396366 1.00000 6 4 0.02511667 0.204263 0.15388033 0.99988 7 4 0.047175 0.226247 0.13189699 0.99321 27 4 0.788525 0.943609 0.6334441 0.00000 6 5 0.01083333 0.191553 0.16898866 1.00000 7 5 0.03206667 0.211187 0.14700533 0.99942 27 5 0.7734667 0.928976 0.6833577 0.00000 7 6 0.02198333 0.210553 0.15708866 0.99995 27 6 0.76333333 0.914142 0.6825244 0.00000 27 7 0.74135 0.896309 0.5862691 0.00000

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128 Area II BSH D iff erence Lower Upper P adj usted 8 2 1.42764347 1.20662894 1.648658 0.00000 9 2 1.41356014 1.19254561 1.63457466 0.00000 10 2 1.7775732 1.998587 3 1.55 55867 0.00000 11 2 1.8123982 2.033 1273 1.591 8367 0.00000 12 2 1.921331 3 2.1 234606 1.700317 0.00000 13 2 1.60278514 1.38177061 1.82379966 0.00000 14 2 1.74298 86 1.9 400439 1.52 97534 0.00000 16 2 3.526941 6 3.77323 57 3.28 64875 0.00000 9 8 0.014 8333 0.217917 3 0.18 75087 1.32 000 10 8 3.2052 667 3.4090 087 3.0013 247 0.00000 11 8 3.2400 167 3.4438 587 3.0362 747 0.00000 12 8 3.348975 3.5528092 3.1451408 0.00000 13 8 0.17514167 0.028 9253 0.37897587 0.16015 14 8 3.1706 333 3.37446 53 2.966 9913 0.00000 16 8 4.95458 13 5.18 58547 4.72358 79 0.00000 10 9 3.19113 33 3.3949 753 2.98 29913 0.00000 11 9 3.22 95833 3.4 979253 3.0221 413 0.00000 12 9 3.3348 167 3.5387 587 3.131 5747 0.00000 13 9 0.189225 0.0146092 0.3930592 0.09355 14 9 3.15655 3.3603842 2.9527158 0.00000 16 9 4.9405018 5.171 0214 4.7095 146 0.00000 11 10 0.034825 0.2386592 0.1690092 0.99985 12 10 0.143 5833 0.34 59253 0.06007587 0.41303 13 10 3.38035833 3.17652413 3.58419253 0.00000 14 10 0.03458333 0.1692 087 0.23841753 0.99985 16 10 1.74936 46 1.9803688 1.51 36812 0.00000 12 11 0.1089 333 0.3127 753 0.09490087 0.77169 13 11 3.41518333 3.21134913 3.61901753 0.00000 14 11 0.06940833 0.134 2587 0.27324253 0.98003 16 11 1.71454 46 1.9455438 1.483 4312 0.00000 13 12 3.52411667 3.32028247 3.72795087 0.00000 14 12 0.17834167 0.0254 253 0.38217587 0.14257 16 12 1.605 1013 1.83 61047 1.37 60979 0.00000 14 13 3.345775 3.5496092 3.1419408 0.00000 16 13 5.1297268 5.360 2714 4.89 72646 0.00000 16 14 1.7839518 2.014 5214 1.5529 146 0.00000

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129 Area III BSH D iff erence Lower Upper P adj usted 15 12 5.20477 751 5.41848 25 4.991 5426 0.00000 16 12 1.9270 2778 2.13 66266 1.71 44289 0.00000 17 12 1.6775 4559 1.889 4154 1.46 44757 0.00000 18 12 1.6796 4281 1.896 5583 1.46 71273 0.00000 19 12 5.30140 378 5.525 8468 5.077 2207 0.00000 20 12 1.91715 354 2.1 086685 1.7034 386 0.00000 21 12 1.97075868 2.187 5342 1.75 36394 0.00000 16 15 3.277717973 3.0585061 3.49692984 0.08632 17 15 3.527176191 3.30841325 3.74593913 0.07002 18 15 0.00901 667 0.1860887 0.18565533 0.16620 19 15 0.096632 28 0.3 727922 0.13401396 0.90963 20 15 3.287620397 3.06733508 3.50790571 0.00000 21 15 3.234012071 3.01112743 3.45689671 0.00000 17 16 0.249458219 0.03177623 2.4671402 0.86005 18 16 0.04772 267 0.343 2387 0.32 00533 0.96655 19 16 3.37435 601 3.60 97219 3.1 472901 0.00000 20 16 0.009902424 0.2093 945 0.229 1429 1.00000 21 16 0.043705 02 0.2 552968 0.17811787 0.99891 18 17 0.00203 722 0.22393 84 0.21985539 1.00000 19 17 3.623 08819 3.853 0187 3.3946 577 0.00000 20 17 0.23955 795 0.45831 73 0.020 9286 0.07041 21 17 0.2931 412 0.51454 26 0.0717 398 0.06156 19 18 3. 62176 097 3.85 3886 3.38 1496 0.00000 20 18 0.2375 6073 0.460 1222 0.014 1992 0.05788 21 18 0.29112 398 0.517 8409 0.06 1647 0.00242 20 19 3.384253024 3.15360643 3.61489962 0.00000 21 19 3.330644699 3.09751428 3.56377512 0.00000 21 20 0.05360 325 0.276492 7 0.16927632 0.99613

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130 Area IV BSH D iff erence Lower Upper P adj usted 23 22 0.06274 16 0.348 85137 0.22289082 0.99513 24 22 0.1873 913 0.4581 6041 0.08333779 0.38783 25 22 0.07764527 0.198 09642 0.35390018 0.98192 26 22 1.0784 766 1.3 8693174 0.8 826214 0.00000 27 22 1.27043006 1.010243718 1.53061639 0.00000 28 22 2.624 2812 2.935 2871 2.314 2753 0.00000 24 23 0.124 5197 0.39022 791 0.14092285 0.80991 25 23 0.14039243 0. 1308 5444 0.4115903 0.72806 26 23 1.0157305 1.2807 3769 0.750687 3 0.00000 27 23 1.33317721 1.078366619 1.58798781 0.00000 28 23 2.562080 6 2.86 192438 2.25 96949 0.00000 25 24 0.2650444 0.009588514 0.52050028 0.06611 26 24 0.89107 53 1.13 990879 0.64 16618 0.00000 27 24 1.45782918 1.219842078 1.69581629 0.00000 28 24 2.437429 2.729685 45 2.145 7285 0.00000 26 25 1.15612 93 1.41102 156 0.9012197 0.00000 27 25 1.19278479 0.948538679 1.43703089 0.00000 28 25 2.70247 39 2.99984 501 2.405 9828 0.00000 27 26 2.34890771 2.111513927 2.5863015 0.00000 28 26 1.54635 46 1.8381 3673 1.2545 726 0.00000 28 27 3.895258 8 4.17776855 3.6127 781 0.00000

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131 Table C 2. Tukey HSD post hoc pair wise comparison of the mean depth of the mixed layer DML in quadrants experienced by tagged blue sharks Shade rows indicate statistically significant differences at P<0.05. Area I BSH Difference Lower Upper P adjusted 2 1 2.82825 9.8209 56 4.1644456 0.9241539 3 1 2.4305 9.4231 56 4.5621956 0.9658546 4 1 1.29875 8.2914 56 5.6939456 0.9992617 5 1 6.5275 0.46 1956 13.5201956 0.087776 6 1 5.29725 12.28 456 1.6954456 0.2951066 7 1 6.67575 13.6 4456 0.3169456 0.0738023 27 1 3.28825 3.704 456 10.2809456 0.8452973 3 2 0.39775 6.594 456 7.3904456 0.9999998 4 2 1.5295 5.46 1956 8.5221956 0.9978747 5 2 9.35575 2.3630544 16.3484456 0.0 7 13124 6 2 2.469 9.46 6956 4.5236956 0.9627878 7 2 3.8475 10.80 956 3.1451956 0.7076185 27 2 6.1165 0.876 956 13.1091956 0.137772 4 3 1.13175 5.860 456 8.1244456 0.9997024 5 3 8.958 1.9653044 15.9506956 0.0 8 2638 6 3 2.86675 9.8594 56 4.1259456 0.9188563 7 3 4.24525 11.23 456 2.7474456 0.5917109 27 3 5.71875 1.273 456 12.7114456 0.2041264 5 4 7.82625 0.8335544 14.8189456 0.0 9 59824 6 4 3.9985 10.99 956 2.9941956 0.6646912 7 4 5.377 12.3 6956 1.6156956 0.2762928 27 4 4.587 2.40 6956 11.5796956 0.4891258 6 5 11.82475 18.81 456 4.8320544 0.0 6 00085 7 5 13.20325 20.1 9456 6.2105544 0.0 730 003 27 5 3.23925 10.231 94 3.7534 56 0.8553036 7 6 1.3785 8.371 956 5.6141956 0.9989112 27 6 8.5855 1.5928044 15.5781956 0.0 8 49222 27 7 9.964 2.9713044 16.9566956 0.0 7 04239

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132 Area II BSH Difference Lower Upper P adjusted 8 2 10.0850408 7.485191536 12.68489 0.000000 9 2 10.6216651 8.021815849 13.221514 0.000000 10 2 1.6205778 0.97 271473 4.220427 0.588634 11 2 0.6402707 3.25 695018 1.970154 0.997792 12 2 1.1124888 1.48 360408 3.712338 0.922713 13 2 11.1141686 8.517777931 13.710559 0.000000 14 2 2.0838962 0.51 952996 4.683745 0.237687 16 2 3.6932063 1.089865653 6.296547 0.000382 9 8 0.5366243 2.04 979056 3.122228 0.999339 10 8 8.464463 11.0 006638 5.87886 0.000000 11 8 10.7253 15 13.3 154795 8.129075 0.000000 12 8 8.9725519 11.55 15531 6.386949 0.000000 13 8 1.0291279 1.5529 7893 3.611254 0.948054 14 8 8.0011445 10.5867479 5.415541 0.000000 16 8 6.3918344 8.9809 8463 3.80272 0.000000 10 9 9.0010873 11.586 9069 6.415484 0.000000 11 9 11.2619 58 13.858 7226 8.665699 0.000000 12 9 9.5091763 12.09 77963 6.923573 0.000000 13 9 0.4925036 2.089 22205 3.074629 0.999646 14 9 8.5377688 11.12 37221 5.952165 0.000000 16 9 6.9284587 9.51757 775 4.339345 0.000000 11 10 2.2608485 4.8570 4941 0.335388 0.146817 12 10 0.5080889 3.09369 303 2.077514 0.999558 13 10 9.4935909 6.911465116 12.075717 0.000000 14 10 0.4633185 2.12228 892 3.048922 0.999778 16 10 2.0726286 0.5164 5453 4.661743 0.239267 12 11 1.7527595 0.84347 921 4.348996 0.475783 13 11 11.7544393 9.161666237 14.347212 0.000000

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133 Area III BSH Difference Lower Upper P adjusted 15 12 24.9466053 19.5281509 30.3650597 0.000000 16 12 0.1173435 5.5357979 5.3011109 1.000000 17 12 1.5709343 6.9893887 3.8475201 0.987882 18 12 3.2642826 2.1541718 8.682737 0.601202 19 12 17.0231739 11.6047195 22.4416283 0.000000 20 12 6.242388 11.66 8424 0.8239336 0.011357 21 12 5.6688074 0.250353 11.0872618 0.052782 16 15 25.0639 88 30.482 032 19.64549 4 0.000000 17 15 26.5175 96 31.935994 21.09 0852 0.000000 18 15 21.682 227 27.1007 71 16.263 683 0.000000 19 15 7.9234314 13.34 8858 2.504977 0.000257 20 15 31.18 9934 36.6074 78 25.770539 0.000000 21 15 19.2 77979 24. 962523 13. 85934 5 0.000000 17 16 1.4535908 6.8720452 3.9648636 0.992395 18 16 3.3816261 2.0368283 8.8000805 0.555683 19 16 17.1405174 11.722063 22.5589718 0.000000 20 16 6.1250445 11.5 34989 0.7065901 0.014253 21 16 5.7861509 0.3676965 11.2046053 0.026666 18 17 4.8352169 0.5832375 10.2536713 0.120829 19 17 18.5941082 13.1756538 24.0125626 0.000000 20 17 4.6714537 10.089 082 0.7470007 0.150749 21 17 7.2397417 1.8212873 12.6581961 0.001348 19 18 13.7588913 8.3404369 19.1773457 0.000000 20 18 9.5066707 14.925 251 4.0882163 0.060003 21 18 2.4045248 3.0139296 7.8229792 0.880960 20 19 23.2655 19 28.684 163 17.847 075 0.000000 21 19 11.3543 65 16.7 28209 5.9359121 0.000000 21 20 11.9111954 6.492741 17.3296498 0.000000

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134 Area IV BSH Difference Lower Upper P adjusted 23 22 0.587839013 1.9156195 3.091298 0.993011 24 22 0.579046881 1.9244116 3.082505 0.993558 25 22 0.886777486 1.616681 3.390236 0.943329 26 22 2.134722278 0.3687362 4.638181 0.153763 27 22 13.25113896 10.7476805 15.754597 0.000000 28 22 28.76614334 26.2626848 31.269602 0.000000 24 23 0.00872132 2.5122506 2.494666 1.000000 25 23 0.298938473 2.20452 2.802397 0.999849 26 23 1.546883265 0.9565752 4.050342 0.532118 27 23 12.66329995 10.1598415 15.166758 0.000000 28 23 28.17830433 25.6748458 30.681763 0.000000 25 24 0.307730604 2.1957279 2.811189 0.999821 26 24 1.555675396 0.9477831 4.059134 0.525070 27 24 12.67209208 10.1686336 15.175551 0.000000 28 24 28.18709646 25.683638 30.690555 0.000000 26 25 1.247944792 1.2555137 3.751403 0.762069 27 25 12.36436148 9.860903 14.86782 0.000000 28 25 27.87936585 25.3759074 30.382824 0.000000 27 26 11.11641668 8.6129582 13.619875 0.000000 28 26 26.63142106 24.1279626 29.13488 0.000000 28 27 15.51500438 13.0115459 18.018463 0.000000

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135 APPENDIX D EFFORT DISTRIBUTION Figure D 1. Maps of effort distribution (in number of hooks) by individual fleets (with observer coverage) for 1995 2009. Published on the ICCAT Report on the 2012 Shortfin mako stock assessment and ecological risk assessment meeting. Brazil

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136 Chinese Taipei

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137 Japan

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138 Namibia

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139 South Africa Spain

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140 LIST OF REFERENCES Aires da S ilva, A 1996. Contribution to the knowledge of the age and growth of the blue shark, Prionace glauca (Carcharhinidae), in the North Atlantic. Undergraduate Thesis. University of the Algarve, Faro, Portugal. Aires da Silva, A. M. Gallucci, V., 2008. Demographic and risk analyses applied to management and conservation of the blue shark ( Prionace glauca ) in the North Atlantic Ocean. Mar Freshwater Res 58, 570 580. Aires da Silva A M Maunder M N Galluci V F Kohler N E Hoey J J ., 2009 A spatially structured tagging model to estimate movement and fishing mortality rates for the blue shark ( Prionace glauca ) in the North Atlant ic Ocean. Mar Freshwater Res 60, 1029 1043 Akaike H ., 1973 Information theory and an extension of the maximum likelihood principle. In: Petran B N Csaaki F ., (E ds ) International Symposium on Information Theory. Akademiai Kiado Budapest, p p. 267 281 Aldenberg T ., 1975 Virtual population analysis and migration, a theoretical treatment. ICES CM 1975/F:32 Amorim A F ., 1992 Estudo da biologia, pesca e reproduo do cacao azul, Prionace glauca L. 1758, capturado no sudeste e sul do Brasil. PhD dissertation, Universidade Estadual Paulista, Rio Claro, So Paulo Arregun Sanchez, F., 1996. Catchability: A key parameter for fish stock asse ssment. Rev. Fish Biol. Fish. 6, 221 242. azul (Prionace Universidade de Sao Paulo, Sao Paulo, Brazil. Barker, M.J., Schleussel, G., 2005. Managing global shark fisheries: suggestions for prioritizing management strategies. Mar. Freshwater Res. 15, 325 347. Baum, J.K., Blanchard, W., 2010. Inferring shark population trends from generalized linear mixed models of pelagic longline catch and effort data. Fish. Res. 102, 229 239. Baum, J.K., Kehler, D., Myers, R.A., 2005. Robust es timates of decline for pelagic shark populations in the northwest Atlantic and Gulf of Mexico. Fisheries 30, 27 30. Baum, J.K., Myers, R.A., Kehler, D.G., Worm, B., Harley, S.J., Doherty, P.A., 2003. Collapse and conservation of shark populations in the Northwest Atlantic. Science 299, 389 392.

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141 Baum, J.K., Myers, R.A., 2004. Shifting baselines and the decline of pelagic sharks in the Gulf of Mexico. Ecol. Lett. 7 135 145. Bergin T M ., 1991 A comparison of Goodness of Fit tests for analysis of nest orientation in Western Kingbirds ( Tyrannus verticalis ). Condor 93, 164 171 Bestley S Jonsen I D Hindell M A Guinet C Charrassin J B ., 2013 Integrative modelling of animal movement: incorporating in situ habitat and behavioural information for a migratory marine predator. Proc R Soc B 280, 20122262 Beverton R J H Holt S J ., 1957 On the Dynamics of Exploited Fish Populations, Volume 19 of Fishery investigations (Great Britain, Ministry of Agriculture, Fisheries, and Food ). Fish. Invest. 2(19). Bigelow, K.A., Hampton, J., Miyabe, N., 2002. Application of the habitat based model t o estimate e ective longline e obesus). Fish. Ocean. 11, 143 155. Bigelow, K Musyl, M.K., Poisson, F., Kleiber, P., 2006. Pelagic longline gear depth and shoaling. Fish. Res. 77, 173 183. Bishop, J., 2006. Standardizing fishery dependent catch and effort data in complex fisheries with technology change. Rev. Fish Biol. Fish. 16, 21 38. Block B A Jonsen I D ., 2011 Tracking apex marine predator movements in a dynamic ocean. Nature 475, 86 90 Bonadonna F Lea M A Dehorter O Guinet C ., 2001. Foraging ground fidelity and route choice tactics of a marine predator: the Antarctic fur seal. Mar Ecol Prog Ser 223 287 297 Bonfil, R., 1994. Overview of world elasmobranch fisheries. FAO Fisheries Technical Paper 341. FAO, Rome. Braccini, J.M., Etienne, M. P., Martell, S.J.D., 2011. Subjective judgment in data subsetting: implications for CPUE standardization and stock assessment of non target chondrichthyans. Mar Freshwater Res 62 73 4 743. Brodziak, J., Ishimura G., 2011 Development of Bayesian production models for assessing the North Pacific swordfish population. Fish Sci 77, 23 34. Buckland, S.T., Anderson, D.R., Burnham, K.P., Laake, J.L., Borchers, D., Thomas, L., 2004. Advanced Distance Sampling. Oxford University Press, Oxford. Bullard, F ., 1999 Estimating the home range of an animal: a Brownian bridge approach. PhD dissertation. University of North Carolina, Chapel Hill, NC

PAGE 142

142 Butterworth, D.S., Ianelli, J.N., Hilborn, R., 2003. A statistical model for stock assessment of southern bluefin tuna with temporal changes in selectivity. Afr J Mar Sci 25, 331 361. Cailliet, G.M., Martin, L.K., Harvey, J.T., Kusher, D., Welden, B.A., 1983. Preliminary studies on the age an d growth of blue, Prionace glauca, common thresher, Alopias vulpinus, and shortfin mako, Isurus oxyrinchus, sharks from California waters. In: Prince, E.D., Pulos L.M. ( E ds) Proceedings of the International workshop on age determination of oceanic pelagic fishes: tunas, billfishes, and sharks. NOAA Technical R eport NMFS 8, 179 188. Cailliet, G.M., Musick, J.A., Simpfendorfer, C.A., Stevens, J.D., 2005. Ecology and L ife History Characteristics of Chondrichthyan Fish. In: Fowler, S.L., Cavanagh, R. D., Camhi, M., Burgess, G.H., Cailliet, G. M., Fordham, S.V., Simpfendorfer, C.A. Musick, J.A. (Eds.), Sharks, Rays and Chimaeras: The Status of the Chondrichthyan Fishes. IUCN SSC Shark Specialist Group. IUCN, Gland, Switzerland and Cambridge, UK, pp. 12 18. Campana, S.E., Dorey, A., Fowler, M., Joyce, W., Wang, Z., Wright, D., Yashayaev, I., 2011. Migration pathways, behavioural thermoregulation and overwintering grounds of blue sharks in the Northwest Atlantic. PLoS One 6, e16854. Campana, S. E. Marks, L., Joyce, W., Kohler, N., 2005. Catch, bycatch and indices of population status of blue shark ( Prionace glauca ) in the Canadian Atlantic. Collect. Vol. Sci. Pap. ICCAT 58 891 934. Carey F G Scharold J V Kalmijn A J ., 1990 Movements of blue sharks ( Prionace glauca ) in depth and course. Mar Biol 106 329 342 Carvalho, F., Hazin, F.H.V., Hazin, H Travassos, P., 2008. Historical catch rates of blue sharks in the southwestern Atlantic Ocean between 1958 1962. Collect Vol Sci Pap ICCAT 62, 1553 1559. Carvalho, F C Murie D J Hazin F H V Hazin H G Leite Mourato B Travassos P Burgess G H ., 2010 Catch rates and size composition of blue sharks (Prionace glauca) caught by the Brazilian pelagic longline fleet in the southwestern Atlantic Ocean. Aquat Living Resour 23, 373 385 Carvalho, F.C., Murie, D.J., Hazin, F.H.V., Hazin, H.G., Leite Mourato, B., Burgess, G.H., 2011 Spatial p redictions of blue s hark ( Prionace glauca ) c atch rate and catch probability of j uveniles in the Southwest Atlantic. ICES J Mar Sci 68 890 900 Carruthers, T.R., McAllister, M.K. Ahrens, R.N.M., 2010. Simulating spatial dynamics to evaluate methods of deriving abundance indices for tropical tunas. Can J Fish Aquat Sci 47, 1409 1427. Castro J A Mejuto J ., 1995 Reproductive parameters of blue shark, Prionace glauca and other sharks in the Gulf of Guinea. Mar Fresh water Res 46 967 973

PAGE 143

143 Chapman B B Skov C Hulthen K Broderson J Nilsson P A Hansson L A Bronmark C ., 2012 Partial migration in fishes: definitions, methodologies and taxonomic distribution. J Fish Biol 81 479 499 Chen, S., Watanabe, S., 1989. Age dependence of natural mortality coefficient in fish population dynamics. Nippon Suisan Gakk 55, 205 208. Clarke S.C., McAllister, M.K., Milner Gulland, E.J., Kirkwood, G.P., Michielsens, C.G.J., Agnew, D.J., Pikitch, E.K., Nakano, H., Shivji, M.S., 2006 Global estimates of shark catches using trade records from commercial markets. Ecol. Lett 9, 1115 1126. Clarke Atlantic Ocean. Aquat Living Resours 21, 373 381. Coelho, R., Bentes, L., Gonalves, J. M. S., Lino, P., Ribeiro, J., Erzini. K., 2003. Reduction of elasmobranch by catch in the hake semipelagic near bottom longline fishery in the Algarve, Southern Portugal. Fish. Sci. 69, 293 299. Compagno, L.J.V., 1999. Chec klist of living elasmobranches. In: Hamlett, W.C. (Ed.), Sharks, Skates and Rays: the biology of elasmobranc h fishes. Johns Hopkins University Press, Baltimore, MD, pp. 471 498. Compagno L Dando M Fowler S ., 2005 Sharks of the World Princeton University Press, Princeton, NJ Cope, J.M., Punt, A.E., 2011. Reconciling stock assessment and management sc ales under conditions of spatially varying catch histories. Fish. Res. 107, 22 38. Corts, E., 2002. Incorporating uncertainty into demographic modeling: application to shark populations and their conservation. Conserv Biol 16, 1048 1062. Corts, E., 2004. Life history patterns, demography, and population dynamics. In: Musick, J.A., Carrier, J.C., Heithaus, H.R. ( E d s .) Biology of Sharks and their Relatives. CCR Press, Boca Renton, FL, pp. 309 322. Corts E., 2008. Comparative life histor y a nd demography of pelagic sharks In: Camhi, M.D., Pikitch, E.K. Babcock, E.A. (Eds .) Sharks of the Open Ocean: Biology, Fisheries and Conservation Blackwell, Oxford, U.K. pp. 309 322. Da S ilva C Kerwath S E Wilke C Meyer M Lamberth S J ., 2010. A note on the first documented southern transatlantic migration of a blue shark ( Prionace glauca ) tagged off South Africa. Afr J Mar Sci 32, 639 642 Dennis, B., Ponciano, J.M., Lele, S.R., Taper, M.L., Staples, D.F., 2006. Estimating densit y dependence, process noise, and observation error. Ecol Monograph 76, 323 341.

PAGE 144

144 Doubleday, W.G., 1976. Environmental fluctuations and fisheries management. ICNAF Selec. Pap. 1, 141 150. Dulvy, N.K., Baum, J.K., Clarke, S., Compagno, L.J.V., Corts, E ., Domingo, A., Fordham, S., Fowler, S., Francis, M.P., Gibson, C., Martnez, J., Musick, J.A., Soldo, A., Stevens, J.D., Valenti, S., 2008. You can swim but you can't hide: the global status and conservation of oceanic pelagic sharks and rays. Aquat. Conserv. 18, 459 482. Field J C Francis R C Aydin K ., 2006 Top down modeling and bottom up dynamics: Linking a fisheries based e cosystem model with climate. Prog Ocean 68 238 270 Fletcher, R., 1978. On the restructuring of the Pella Tomlinson system. Fish. Bull. 76, 515 521. Fournier, D.A., Archibald, C.P., 1982. A general theory for analyzing catch at age data. Can J Fish Aquat Sci 39, 1195 1207. Fournier, D.A., Hampton, J., Sibert, J.R., 1998. MULTIFAN CL: a length based, age structured model for fisheries stock assessment, with application to South Pacific albacore, Thunnus alalunga Can J Fish Aquat Sci 55, 2105 2116. Fournier, D.A., Skaug, H.J., Ancheta, J., Ianelli, J., Magnusson, A., Maunder, M.N., Nielsen, A., Sibert, J.R., 2012. AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear mod els. Optim Method Softw 27, 233 249. Fox, W.W. Jr., 1974. An overview of production modeling. Collect Vol Sci Pap ICCAT 3, 142 156. Freon, P., 1988. A methodology for visual estimation of abundance applied to flying fish stocks. Proc Gulf Caribb Fish Inst 41, 11 35. Garcia, C.A.E., 1997. Coastal and marine environments and their biota: physical oceanography. In: Seeliger, U., Odebrecht, C., Castello, J.P. (Eds.), Subtropical convergence environments: the coast and sea in the southwestern Atlan tic. Springer Verlag, Berlin, pp. 129 136. Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B., 2004. Bayesian data analysis, second ed. Chapman & Hall, Boca Raton. Gelman, A., Rubin, D.B., 1992. Inference from iterative simulation using multiple sequence s (with discussion). Stat. Sci. 7, 457 511. Geweke J., 1992. Evaluating the accuracy of sampling based approaches to calculating posterior moments. In : Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (Eds.) Bayesian Statistics 4 Clarendon Pres s, Oxford, UK pp. 169 194.

PAGE 145

145 Goethel, D.R., Quinn, T.J. II, Cadrin, S.X., 2011. Incorporating spatial structure in stock assessment: movement modeling in marine fish population dynamics. Rev. Fish. Sci. 19, 119 136. Gregory, P T ., 2009 Northern lights and seasonal sex: the reproductive ecology of cool climate snakes. Herpetologica 65 1 13 Grimm, V., 1999. Ten years of individual based modeling in ecology: what have we learned and what could we learn in the future? Ecol Model 115, 1 29 148. Gruber, S.H., Stout, R.G., 1983. Biological materials for the study of age and growth in a tropical marine elasmobranch, the lemon shark, Negaprion brevirostris (Poey). NOAA Tech. Rep. NMFS 8, 197 205. Hampton, J., Fournier, D.A., 2001. A spatially disaggregated, length based, age structured population model of yellowfin tuna (Thunnus albacares) in the western and central Pacific Ocean. Mar. Freshwater Res. 52, 937 963. Hart D Cadrin S X ., 2004 Yellowtail flounder (Limanda ferruginea) off the northeastern United States, implications of movement among stocks. In: Akakaya H R Burgman M Kindvall O Wood C C Sjgren Gulve P Hatfield J S McCarthy M A ( E ds ) Species conservation and management: case studies. Oxford University Press, New York, p p 231 244 Hastie T J Tibshirani R J ., 1990 Generalized Additive Models. Chapman and Hall, New York Hazin, F.H.V., Boeckmann, C.E., Leal, E.C., Lessa, R.P.T., Kihara, K., Otsuka, K., 1994a. Distribution and relative abundance of the blue shark, Prionace glauca in the southwestern equatorial Atlantic Ocean. Fish. Bull. 92, 474 480. Hazin, F.H.V., Couto, A.A., Kihara, K., Otsuka, K., Ishino, M., 1990. Distributi on and abundance of pelagic sharks in the southwestern equatorial Atlantic. J. Tokyo Univ. Fish. 77, 51 64. Hazin, F., Lessa, R., 2005. Synopsis of biological information available on blue shark, Prionace glauca, from the southwestern Atlantic Ocean. Col. Vol. Sci. Pap. ICCAT 58, 1179 1187. Hazin, F.H.V., Lessa, R.P.T., Chammas, M., 1994b. First observations on stomach contents of the blue shark, Prionace glauca from southwestern equatorial Atlantic Ocean. Rev. Bras. Biol. 154, 195 198. Hazin, F. H. V., Pinheiro, P. B., Broadhurst, M. K., 2000. Further notes on reproduction of the blue shark, Prionace glauca and a postulated migratory pattern in the South Atlantic Ocean. Cinc Cult 52, 114 120.

PAGE 146

146 Hazin, H.G., 2006. Influncia das variveis oceanogrficas na dinmica populacional e pesca do espadarte Xiphias gladius Linnaeus 1758, no oceano Atlntico oeste. PhD Dissertation. Universidade do Algarve. Faculdade de cincias do mar e do ambiente. Campus de Faro. Heidelberger P., Welch, P., 198 3. Simulating run length control in the presence of an initial transient. Oper Res 31 1109 1144. Henderson, A.C., Flannery, K., Dunne, J.A., 2001. Observations on the biology and ecology of the blue shark in the North east Atlantic. J. Fish. Biol. 58, 1347 1358. Hight B V Lowe C G ., 2007 Elevated body temperatures of adult female leopard sharks, Triakis semifasciata while aggregating in shallow nearshore embayments: evidence for behavioral thermoregulation? J Exp Mar Biol Ecol 352 114 128 Hilborn, R., Walters, C.J., 1992. Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty Chapman and Hall, New York. Hinton, M., Nakano, H., 1996. Standardizing catch and effort statistics using physiological, ecological, or behavior al constrains and environmental data, with application to blue marlin ( Makaira nigricans ) catch and effort data from Japanese longline fisheries in the Pacific. Bull. I ATTC 21, 171 200. Hoenig, J. M., 1983. Empirical use of longevity data to estimate mor tality rates. Fish Bull 81, 898 903. Horne J S Garton E O Krone S M Lewis J S ., 2007 Analyzing animal movements using Brownian bridges. Ecology 88 2354 2363 Howey Jordan L A Brooks E J Abercrombie D L Jordan L K B Brooks A Williams S Gospodarczyk E Chapman D D ., 2013 Complex movements, philopatry and expanded depth range of a severely threatened pelagic shark, the Oceanic Whitetip ( Carcharhinus longimanus ) in the Wes tern North Atlantic. PLoS One 8, e56588 Hulme P E ., 2005 Adapting to climate change: is there scope for ecological management in the face of a global threat? J Appl Ecol 42 784 794 Hutchings, J.A., Myers, R.A., 1994. What Can Be Learned f rom the Collapse of a Renewable Resource Atlantic Cod, Ga dus morhua of Newfoundland and Labrador. Can J Fish Aquat Sci 51, 2126 2146. ICCAT, 2005. Report of the Intersessional Meeting of the ICCAT Sub Committee on By Catches: Shark Stock Assessment Collect Vol Sci Pap ICCAT 58, 799 890. ICCAT, 2008. Report of the 2008 Shark Stock Assessment Meeting. Collect Vol Sci Pap ICCAT 64 1343 1491.

PAGE 147

147 ICCAT, 2009 Report of the 2009 Porbeagle Stock Assessment Meeting. SCRS/2009/014. Online at: http://www.iccat.int/Documents/Meetings/Docs/2009_POR_ASSESS_ENG.pdf ICCAT, 2010. Repo rt of the 2009 inter sectional meeting of the ICCAT working group on stock assessment methods. Collect. Vol. Sci. Pap. ICCAT 65, 1851 1908. ICCAT, 2012. Report of the 2012 shortfin mako stock assessment and ecological risk assessment meeting. International Commission for the Conservation of Atlantic Tunas. Online at: http://www.iccat.int/Documents/Meetings/Docs/2012_SHK_ASS_ENG.pdf Jensen, A.L., 1996. Beverton and Holt life history invariants result from optimal trade off of reproduction and survival. Can J Fish Aquat Sci 53, 820 822. Jirik K E ., Lowe C G ., 2012 An elasmobranch maternity ward: female round stingrays Urobatus halleri use warm, restored estuarine habitat during gestation. J Fish Biol 80, 1227 1245 Johnson R.A., Wichern D.W., 1988. Applied Multivariate Analysis, second ed., Prentice Hall, Englewood Cliffs, NJ Jolly, K.A., Silva, C., Attwood, C.G., 2013. Age, growth and reproductive biology of the blue shark Prionace glauca in South African waters. Afr. J. Marine Sci. 35, 99 109. Jonsson B Jonsson N 1993 Partial migration: niche shift versus sexual maturation in fishes. Rev Fish Biol Fisher 3, 348 365 Jorgensen S J Arnoldi N S Estess E E Chapple T K Ruckert M Anderson S D Block B A ., 2012 Eating or meeting? Cluster analysis reveals intricacies of white shark ( Carcharodon carcharias ) migration an d offshore behavior. PLoS One 7, e47819 Kimura, D.K., 1990. Approaches to age structured separable sequential population analysis. Can. J. Fish. Aquat. Sci., 47: 2364 2374. Klimley A P ., 1993 Highly directional swimming by scalloped hammerhead sharks, Sphyrna lewini and subsurface irradiance, temperature, bathymetry, and geomagnetic field. Mar Biol 117 1 22 Kohler, N.E., Casey, J.G., Turner, P.A., 1995. Length weight relationships for 13 species of sharks from the western North Atlantic. Fish. Bull. 9, 412 418. Kohler N E Turner P A Hoe y J J Natanson L J Briggs R ., 2002 Tag and recapture data for three pelagic shark species: blue sharks ( Prionace glauca ), shortfin mako ( Isurus oxyrinchus ) and porbeagle ( Lamna nasus ) in the North Atlantic Ocean. Col Vol Sci Pap ICCAT 54, 1231 1260

PAGE 148

148 Legat, J.F.A., 2001. Distribuio, abundncia, reproduo e morfometria de Prionace glauca no sul do Brasil. Fundao Universidade Federal do Rio Grande Rio Grande, Brazil Legat J F A Vooren C M ., 2004 Reproductive cycle and migration of the blue shark ( Prionace glauca ) in the South Atlantic Ocean. In: Freitas, C.E., Petrere Jr., M., Rivas, A.A.F., MacKinlay, D. (Eds), Proc. Symp. Fish Communities and Fisher American Fisheries Society, p p. 25 36 Less a, R., Santana, F.M., Hazin, F.H., 2004. Age and growth of the blue shark Prionace glauca (Linnaeus 1758) off northeastern Brazil. Fish. Res. 66, 19 30. Lorenzen K Steneck R S Warner R R Parma A M Coleman F C Leber K M ., 2010 The spatial dimensions of fisheries: Putting it all in place. Bull Mar Sci 86 169 177 Luschi P ., 2013 Long distance animal migrations in the oceanic environment: orientation and navigation correlates. ISRN Zoology 2013 631839 Online at: http://dx.doi.org/10.1155/2013/631839 MacKay, D.J.C., 2003. Information Theory, Inference, and Learning Algorithms. Cambridge University Press Cambridge, MA. Manning, M.J., Francis, M.P., 2005. Age and growth of blue shark ( Prionace glauca ) from the New Zealand Exclusive Economic Zone. New Zealand Fisheries Assessment Report 2005/26. Martell, S.J.D., Pine, W.E., Walters, C.J., 2008. Parameterizing age structured models from a rspective. Can. J. Fish. Aquat. Sci. 65, 1586 1600. doi:10.1139/F08 055. Maunder, M.N., 1998. Integration of tagging and population dynamics models in fisheries stock assessment. PhD dissertation, University of Washington. Maunder, M.N., 2001. Integrated tagging and catch at age analysis (ITCAAN): model development and simulation testing. In: Kruse, G.H., Bez, N., Booth, A., Dorn, M.W., Hills, S., Lipcius, R.N., Pelletier, D., Roy, C., Smith, S.J., Witherell, D. (Eds.), Spatial Processes and Management of Marine Populations. Alaska Sea Grant College Program Report No. AK SG 01 02, University of Alaska Fairbanks, pp. 123 146. Maunder, M.N., 2003. Is it time to discard the Schaefer model from the stock assessment Fish Res 61, 145 149. Maunder, M.N., Hinton, M.G., Bigelow, K.A., Langley, A.D., 2006a. Developing indices of

PAGE 149

149 Maunder M N Punt M E ., 2004 Standardizing catch and effort data: a review of recent approaches. Fish Res 70 141 159 Maunder, M. N., Sibert, J.R., Fonteneau, A., Hampt on, J., Kleiber, P., Harley, S. J., 2006 b Interpreting catch per unit effort data to assess the status of individual stocks and communities. ICES J Mar Sci 63, 1373 1385. Mayer, D.A., Molinari, R.L., Festa, F.G., 1998. The mean and annual cycle of upper layer temperature fields in relation to Sverdrup dynamics within the gyres of the Atlantic Ocean. J. Geophys. Res. 103, 545 566. McAllister, M.K., Pikitch, E.K., Punt, A.E., Hilborn, R., 1994. A Bayesian approach to stock assessment and harvest decisions using the sampling/importance resampling algorithm. Can. J. Fish. Aquat. Sci. 51, 2673 2687. McAllister, M.K., Pikitch, E.K., Babcock, E.A., 2001. Using de mographic methods to construct Bayesian priors for the intrinsic rate of increase in the Schaefer model and implications for stock rebuilding. Can J Fish Aquat Sci 58 1871 1890. Megalofonou, P., Damalas, D., De Metrio, G., 2009. Biological characteristics of blue shark, Prionace glauca, in the Mediterranean Sea. J. Mar. Biol. Ass. U. K. 89, 1233 1242. Mejuto, J., Garca Corts, B., 2005. Reproductive and reproduction parameters of the blue shark, Prionace glauca on the basis of on board obs ervations at sea in the Atlantic, Indian and Pacific Oceans. Collect. Vol. Sci. Pap. ICCAT 58, 951 973. Methot, R.D., 2000 Technical description of the stock synthesis assessment program. NOAA Technical Memorandum NMFS NWFSC 43. Methot Jr., R.D., Wetze l, C.R., 2013. Stock synthesis: A biological and statistical framework for fish stock assessment and fishery management. Fish. Res. 142, 86 99. Meyer, R., Millar, R.B., 1999. BUGS in Bayesian stock assessments. Can J Fish Aquat Sci 56, 1078 1087. doi:10.1139/CJFAS 56 6 1078. Michielsens, C.G.J., McAllister, M.K., Kuikka, S., Pakarinen, T., Karlsson, L., Romakkaniemi, A., Pe r, I., Mntyniemi, S., 2011 A Bayesian state space mark recapture model to estimate exploitation rates in mi xed stock fisheries. Can. J. Fish. Aquat. Sci. 63, 321 334. Millar, R.B., 2002. Reference priors for Bayesian fisheries models. Can. J. Fish. Aquat. Sci. 59, 1492 1502. Montealegre Quijano S Vooren C M ., 2010 Distribution and abundance of the life stages of the blue shark Prionace glauca in the Southwest Atlantic. Fish Res 101 168 179

PAGE 150

150 Montgomery J C Walker M M ., 2001 Orientation and navigation in elasmobranchs: which way forward? Environ Biol Fish 60 109 116 Musick, J.A., Bonfil, R., 2005 Elasmobranch Fisheries Management Techniques. Asia Pacific Economic Cooperation (APEC) Fis heries Working Group, Singapore, FAO Fish. Tech. Pap. 474 Musyl M K Brill R W Curran D S Fragoso N M McNaughton L M Nielson A Kikkawa B S Moyes C D ., 2011 Post release survival, vertical and horizontal movements and thermal habitats of five species of pelagic sharks in the central Pacific Ocean. Fish Bull 109 341 368 Nakano, H., 1994. Age, reproduction and migration of blue shark in the North Pacific Ocean. Bull. Natl. Res. Inst. Far Seas Fish. 31, 141 256. Neter J Wasserman W Kutner M H ., 1989 Applied Linear Regression Models, 2nd ed ., Irwin Homewood, Ne w York Nielsen, A., Bigelow, K.A., Musyl, M.K., Sibert, J.R., 2006. Improving light based geolocation by including sea surface temperature. Fish. Ocean. 15, 314 325. Nielsen A Sibert J ., 2005 KFSST: an R package to efficiently estimate the most probable track from light based longitude, latitude and SST. Available at https://www.soest.hawaii.edu/tag data/tracking/kfsst Papas tamatiou Y Wetherbee B Lowe C Crow G ., 2006 Distribution and diet of four species of Carcharhinid shark in the Hawaiian Islands: evidence for resource partitioning and competitive exclusion. Mar Ecol Prog Ser 320 239 251 Patterson, K. R., Kirkwood, G.P., 1995. Comparative performance of ADAPT and Laurec Shepherd methods for estimating fish population parameters and in stock management. ICES J Mar Sci 52, 183 196. Pauly, D., 1980. On the interrelationships between natural mortality, grow th parameters, and mean environmental temperature in 175 fish stocks. J Cons Int Explor Mer 39, 175 192. Pella, J., 1993. Utility of structural time series models and the Kalman filter for predicting consequences of fishery actions. In: Kruse, G., Egg ers, D.M., Marasco, R.J., Pautzke, C., Quinn II, T.J. (Eds.), Proceedings of the international symposium on management strategies for exploited fish populations. Alaska Sea Grant College Program Report AK SG 93 02, Univ. of Alaska, Fairbanks. Pella, J.J. Tomlinson, P.K., 1969. A generalized stock production model. Bull I ATTC 13, 416 497.

PAGE 151

151 Plummer, M., Best, N., Cowles, K., Vines, K., 2006. CODA: Convergence Diagnosis and Output Analysis for MCMC. R News 6, 7 11 Ponciano, J.M., Burleigh, G., Braun, E., Taper, M.L. 2012. Assessing parameter identifiability in Phylogenetic models using Data Cloning. Syst Biol 61 955 972. Pope, J.G., Shepherd, J.G., 1985. A comparison of the performance of various methods for tuning VPAs using effort data. J Cons Int Explor Mer 42, 129 151. Porch, C.E., Eklund, A., Scott, G.P., 2006. A catch free stock assessment model with application to goliath grouper ( Epinephelus itajara ) off southern Florida. Fish. Bull. 104, 89 101. Prager, M.H., 1994. A suite of extensions to a nonequilibrium surplus productio n model. Fish Bull 92, 374 389. Prager, M.H., 2002. Comparison of logis tic and general ized surplus production models applied to swordfish, Xiphias gladius in the north Atlantic Ocean. Fish. Res 58, 41 57. Pratt H.L., 1979. Reproduction in the blue shark, Prionace glauca. Fish Bull 77, 445 470. Punt, A.E., 2003. Extending production models to include process error in the population dynamics. Can. J. Fish. Aquat. Sci. 60, 1217 1228. Punt, A.E., Butterworth, D.S., Penny, A.J., 1995 Stock assessment and Risk analysis for the south Atlantic population of albacore (T hunnus alalunga) using an age structured production model. S. Afr. J. Mar. Sci. 42, 287 310. Punt, A.E., Hilborn, R., 1997. Fisheries stock assessment and decision analysis: the Bayesian approach. Rev. Fish Biol. Fish. 7, 35 63. Punt, A.E., Smith, East Fishery. 2. How well can management quantities be estimated? Mar. Freshwater Res. 53, 631 644. Queiroz N Humphries N E Noble L R Santos A M Sims D W ., 2012 Spat ial dynamics and expanded vertical niche of blue sharks in oceanographic fronts reveal habitat targe ts for conservation. PLoS One 7, e32374 Quinn, T.J.I., Deriso, R.B., 1999. Quantitative Fish Dynamics. Oxford University Press, New York. R Development C ore Team 2011 R: a language and environment for statistical computing. R Foundation for Statistical Computing: Vienna, Austria Available at: Rproject.org.

PAGE 152

152 Radomski, P., Bence, J.R., Quinn, T.J., 2005. Comparison of virtual population analysis and statistical kill at age analysis for a recreational kill dominated fishery. Can. J. Fish. Aquat. Sci. 62, 436 452. Rivot, E., Prvost, E., Parent, E., Baglinire, J.L., 2004. A Bayesian state space modeling framework for fitting a salmon stage structured population dynamic model to multiple time series of field data. Ecol Model 179, 463 485. Salthaug, A., Aanes, S., 2003. Catchability and the spatial distribution of fishing vessels. Can J Fish Aquat Sci 60 259 268. Schaefer, M.B., 1954. Some aspe cts of the dynamics of populations important to the management of the commercial marine fisheries. Bull I ATTC 1, 27 56. Schnute, J.T., 1977. Improved estimates from the Schaefer production model: theoretical considerations. J. Fish. Res. Board Can. 34, 583 603. Schnute, J.T., 1994. A general framework for developing sequential fisheries models. Can J Fish Aquat Sci 51, 1676 1688. Schwarz E ., 1978 Estimating the dimension of a model. Ann Stat 6 461 464 Seeliger, U., Odebrecht, C., Castello, J.P., 1997. Subtropical convergence environments: the coast and sea in the southwestern Atlantic. Springer Verlag, Berlin. Shepherd, J.G., Pope, J.G., 2002. Dynamic pool models: Short term and long term forecasts of catch and biomass. In: Hart, P.J.B ., Re ynolds, J.D. (Eds.), Handbook of Fish Biology and Fisheries. Blackwell, Oxford, pp. 164 188. Shine R Harlow P ., 1993 Maternal thermoregulation influences offspring viability in a viviparous lizard. Oecologia 96 122 127 Shono, H., 2008. Application of the Tweedie distribution to zero catch data in CPUE analysis. Fish. Res. 93, 154 162. Simpfendorfer, C., Corts, E., Heupel, M., Brooks, E., Babcock, E., Baum, J., McAuley, R., Dudley, S., Stevens, J.D., Fordham, S., Soldo, A., 2008. An integrated app roach to determining the risk of overexploitation for data poor pelagic Atlantic sharks. Col. Vol. Sci. Pap. ICCAT 23, 56 71. Sims D W ., 2005 Differences in habitat selection and reproductive strategies of male and female sharks. In: Ruckstuhl K E Ne uhaus P ( E ds ) Sexual segregation in vertebrates: ecology of the two sexes. Cambri dge University Press, Cambridge, U.K. p p. 127 147 Skomal, G.B., Natanson, L. J., 2003. Age and growth of the blue shark ( Prionace glauca ) in the North Atlantic Ocean. Fish Bull 101, 627 639.

PAGE 153

153 Smith, S.E., Au, D.W., Show, C., 2008. Intrinsic rates of increase in pelagic elasmobranchs. In: Camhi, M.D., Pikitch, E.K., Babcock, E.A. (Eds.), Sharks of the Open Ocean: Biology, Fisheries and Conservation Blackwell, Oxford, U.K. pp. 288 297. Spiegelhalter, D.J., Best, N.G., Van der Linde, A., 2002. Bayesian measures of model complexity and fit. J Roy Statist Soc Ser B 64, 583 640. Stevens, J.D., 1975. Vertebral rings as a means of age determination in the blue shark ( P rionace glauca L.). J. Mar. Biol. Ass. U.K. 55, 657 665. Stevens, J.D., Bonfil, R., Dulvy, N.K., Walker, P., 2000. The effects of fishing on sharks, rays, and chimaeras (chondrichthyans), and the implications for marine ecosystems. ICES J. Mar. Sci. 57, 476 494. Thorson, J.T. 2011. Auxiliary and focal assessme nt models: a proof of concept involving time varying catchability and fishery stock status evaluation. ICES J. Mar. Sci. 68, 2264 2276. Thorson, J. T., Berkson, J., 2010. Evaluating single and multi species procedures to estimate time varying catchability functional parameters. Fish Res 101, 38 49 Tuckey T Yochum N Hoenig J Lucy J Cimino J ., 2007 Evaluating localized vs. large scale management: the example of tautog in Virginia. Fisheries 32 21 28 Venables W Dichmont C ., 2004 GLMs, GAMs and GLMMs: an overview of theory for applications in fisheries research. Fish Res 70 319 337 Vinther M Eero M ., 2013 Quantifying relative fishing impact on fish populations based on spatio temporal overlap of fishing effort and stock density. ICES J Mar Sci doi 10.1093 / icesjms / fst001 Walker, T. I., 1998. Can shark resources be harvested sustainably? A question revisited with a review of shark fisheries. Mar. Freshwater Res. 49 553 572. Walters, C., Martell, S., 2004. Fisheries E cology and Management. Princeton University Press, Princeton, New Jersey. Wearmouth V J Sims D W ., 2008 Sexual segregation in marine fish, reptile, birds and mammals: behaviour patterns, mechanisms and conservation implications. Adv Mar Biol 54 1 07 169 Weng K C Castilho P C Morrissette J M Landeira Fernandez A M Holts D B Schallert R J Goldman K J Block B A ., 2005 Satellite tagging and cardiac physiology reveal niche expansion in salmon sharks. Science 310 104 106

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154 Wilberg, M.J., Bence, J.R., 2006. Performance of time varying catchability estimators in statistical catch at age analysis. Can J Fish Aquat Sci 63, 2275 2285. Wilberg, M.J., Thorson, J.T., Linton, B. C., Berkson, J., 2010. Incorporating time varying catchability into population dynamics and stock assessment models. Rev Fish Sci 18, 7 24. Wood S N ., 2006 Generalized Additive Models: an introduction with R. CRC Press, Boca Raton Yin, Y., Sampson, D.B., 2004. Bias and precision of estimates from an age structured stock assessment program in relation to stock and data characteristics. N. Am J. Fish Manage 24 865 879. Zar J H ., 2009 Biostatistical Analysis, fifth ed Prentice Hall Inc., Englewood Cliffs, NJ

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155 BIOGRAPHICAL SKETCH Felipe Car valho was born in Recife, Pernambuco Br azil He earned a Bachelor of Engineering in Fisheries Engineering from the Federal Rural University of Pernambuco. He later r in Fisheries and Aquatic Sciences from University of Florida i n the spring of 2010. He entered the doctoral program at the Program of Fisheries and Aquatic Sciences, School of Forest Resources and Conservation at UF in the summer of 2010 and received his Ph.D. in the spring of 2014