University of Florida Thesis Or Dissertation Formatting

USING VESSEL MONITORING SYSTEM DATA TO UNDERSTAND THE SPATIAL AND TEMPORAL DYNAMICS OF THE COMMERCIAL VERTICAL LINE FISHERY FOR REEF FISH IN THE GULF OF MEXICO

NICHOLAS DAVID DUCHARME-BARTH

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

2018

To Meghan Sarah for being the reason I follow my dreams

ACKNOWLEDGMENTS

There are a number of individuals who are responsible for getting me through (and furthering my research) these last five years at the University of Florida. First and foremost, I would like to thank my two funding sources the NOAA Fisheries - Sea Grant Population and

Ecosystem Dynamics Fellowship (grant # NA15OAR4170182) and the NOAA Fisheries – RTR program (grant # NA11NMF4550121) as well as the following current and former NOAA-

Fisheries scientists: Liz Scott-Denton, Neil Baertlein, and Carlos Rivero for making this research possible. Additionally, I would like to thank Andre Punt (University of Washington), Tom

Carruthers (University of British Columbia) and several anonymous reviewers for their thoughtful commentary which greatly improved the quality of Chapters 2 and 3 as well as Sarah

Glaser (One Earth Future Foundation) and Hao Ye (University of Florida) for their help thinking through the EDM analysis in Chapter 4.

My supervisory committee played a large role in my development as a scientist and I thank them for helping me grow intellectually over the last 5 years specifically Kai Lorenzen for making me realize that you can only learn so much from analyzing data at a computer and that it is often much simpler to get your answer if you just talk to people; Sherry Larkin for teaching me that research questions with well-defined, testable hypotheses are a lot easier to answer; Bill

Lindberg for instilling in me the importance of having a solid theoretical understanding of the processes being studied before jumping into the modeling and the analysis; and Kyle Shertzer for taking the time to help me develop interesting questions relevant to the needs of NOAA Fisheries and for going above and beyond as a mentor to help me achieve my career goals after graduation.

I would also like to thank my major advisor Rob Ahrens for taking a chance on someone straight out of undergrad that, in retrospect, had no idea how to be a scientist. I thank Rob for being patient, for being willing to talk to me at (mostly) all hours of the day, and for giving me

the guidance I needed even if I didn’t always like hearing it. I thank Rob for giving me the freedom to work through my challenges and create opportunities for myself because in doing so you allowed me to gain belief in myself. I know I still have a long way to go and a lot to learn, but I feel confident in my own abilities moving forward having learned from Rob these last five years.

Most importantly, I would like to thank those that provided me the social support and inspiration needed on a project of this scale. I thank all of those in the greater Gainesville area and the University of Florida community; friends, family, and lab mates, that have made these last five years so enjoyable. I thank the Crockett family for welcoming me to Florida and teaching me how to be a proper Gator. I thank my parents for all the opportunities that they provided me over the years (including many visits to aquariums worldwide) that allowed me to develop intellectually and that prepared me for this challenge. I thank my sister for being an inspiration to me and someone that I look up to because no matter life’s challenges she always finds a way to rise to the occasion while looking out for others at the same time. Lastly, I would like to thank my wife Meghan. Without her none of this would have been possible. Meghan is the reason I went to grad school and the reason I’m still smiling five years later.

TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ...... 4

LIST OF TABLES ...... 8

LIST OF FIGURES ...... 9

LIST OF ABBREVIATIONS ...... 11

ABSTRACT ...... 13

CHAPTER

1 OVERVIEW ...... 15

2 CLASSIFICATION AND ANALYSIS OF VMS DATA IN VERTICAL LINE FISHERIES: INCORPORATING UNCERTAINTY INTO SPATIAL DISTRIBUTIONS ...... 21

2.1 Introduction ...... 21 2.2 Methods ...... 26 2.2.1 Data ...... 26 2.2.2 Classification ...... 29 2.2.3 Uncertainty in Spatial Predictions ...... 31 2.2.4 Analysis ...... 33 2.3 Results...... 37 2.4 Discussion ...... 41

3 INDICES OF ABUNDANCE IN THE GULF OF MEXICO REEF FISH COMPLEX: A COMPARATIVE APPROACH USING SPATIAL DATA FROM VESSEL MONITORING SYSTEMS...... 61

3.1 Introduction ...... 61 3.2 Material and Methods ...... 65 3.2.1 Study Frame ...... 66 3.2.2 Data ...... 67 3.2.3 Abundance Indices ...... 68 3.2.3.1 VMS ...... 68 3.2.3.2 Delta-GLM (status-quo) ...... 69 3.2.4 Abundance Index Agreement ...... 70 3.2.5 Simulation ...... 73 3.2.5.1 Base simulation ...... 73 3.2.5.2 Scenarios ...... 75 3.2.5.3 Abundance indices ...... 76 3.2.5.4 Multivariate analysis ...... 78

3.2.5.5 Sequential depletion simulation ...... 78 3.3 Results...... 79 3.4 Discussion ...... 83

4 SPATIAL CHARACTERIZATION OF THE COMMERCIAL VERTICAL LINE FISHERY FOR REEF FISH IN THE GULF OF MEXICO ...... 100

4.1 Introduction ...... 100 4.2 Methods ...... 104 4.2.1 Study Frame ...... 104 4.2.2 Data ...... 104 4.2.3 Métier Identification ...... 106 4.2.4 Spatially-Explicit Characterization of Species Dynamics ...... 107 4.3 Results...... 110 4.3.1 Métier Identification ...... 110 4.3.2 Characterization of Spatial Stock Dynamics ...... 111 4.4 Discussion ...... 114

5 CONCLUSION...... 133

APPENDIX: CHAPTER 2 – SUPPLEMENTARY MATERIAL ...... 140

A.1 Variables Used in Random Forest Classification ...... 140 A.2 Selection of Classification Threshold ...... 141 A.3 Lee’s L and Bounded Permutation ...... 141 A.4 Comparison to Null Model ...... 142

LIST OF REFERENCES ...... 148

BIOGRAPHICAL SKETCH ...... 166

LIST OF TABLES

Table page

2-1 The trip and set level characteristics...... 48

2-2 Species included in the Gulf of Mexico FMP...... 49

2-3 Species used to identify target groups by fishing set in the OBS data...... 50

2-4 Variables included in the RF model sorted in decreasing order of importance as defined by relative % increase in Mean Squared Error ...... 51

2-5 Confusion matrix calculated from an out-of-sample evaluation of the OBS data for the proposed classification model...... 52

2-6 The number of species per catch and region combination or CPUE and region combination where mean shifts were detected. There are a total of 23 species per combination...... 53

3-1 Species occurring in the top 25 of catch by the vertical line fleet...... 88

3-2 The 15 species used to inform the simulation and their approximate geographic distribution denoted as proportion of abundance in each region...... 89

3-3 Description of each scenario used in the simulation...... 90

3-4 Description of variables used in PCA ...... 91

3-5 The metrics of agreement, mean correlation and mean inferred change in stock abundance, and their respective overlapping coefficients (OVLs) between the two estimated indices of abundance...... 92

4-1 Species included in the Gulf of Mexico FMP...... 122

4-2 Species retained for the analysis...... 123

LIST OF FIGURES

Figure page

2-1 The five spatial regions considered in the time series analysis. The black dot denotes the location of the Deepwater Horizon oil spill. The entire gulf (AG) is the union of the 4 regions labeled...... 54

2-2 The proportion of total catch across time and by region for the 23 most commercially encountered species by the fleet...... 55

2-3 The mean total fishing effort of the 201 fishing scenarios from January 2007 through January 2014 with uncertainty...... 56

2-4 The spatial residuals by target species group, Grouper, Snapper, and other Reef Fish, from the classification model...... 57

2-5 Lee’s L values for catch and CPUE by species...... 58

2-6 Example of a time series created from the spatial distribution of fishing effort for each spatial region...... 59

2-7 Stoplight plot showing the catch and CPUE by species combinations where mean shifts were determined to have occurred...... 60

3-1 The Gulf of Mexico EEZ with the spatial regions considered in the analysis...... 93

3-2 Diagram explaining how to calculate the correlation between two indices...... 94

3-3 Indices of abundance with associated uncertainty constructed using the two methods. ...95

3-4 Simulated abundance indices for five selected species...... 96

3-5 Violin plots showing the RMSD between predicted and true abundance for five selected species...... 97

3-6 Principal components biplot for six of the nine variables used in the analysis...... 98

3-7 Violin plots showing the RMSD from Scenario 6 for two methods...... 99

4-1 Delineation of the 5 sub regions within the Gulf of Mexico and their relation to the 10 different county groups that catches were landed in...... 124

4-2 Plot of fisheries closures impacting the Gulf of Mexico vertical line fishery for reef fish...... 125

4-3 Abundance time series for each of the 23 reef fish species and each of the 6 regions (5 sub-regions and 1 Gulf of Mexico)...... 126

4-4 Radar plot of the mean proportion of the total catch for each species (from the vessel weeks) for each species group...... 127

4-5 Radar plot of the mean proportion of species group and county group variables defining each métier...... 128

4-6 This figure denotes the spatial regions typically fished by each métier along with the county group that their catch is predominantly landed in...... 129

4-7 The proportion of abundance contained in each region for each species...... 130

4-8 Co-prediction dendrograms within species and across regions using Convergent Cross Mapping...... 131

4-9 Co-prediction dendrograms within regions and across species using Convergent Cross Mapping...... 132

A-1 The density distributions for 12 of the 13 continuous variables used in the classification model...... 144

A-2 Diagnostic plots for the classification model used...... 145

A-3 The trajectories from 4 randomly selected trips from the OBS data...... 146

A-4 The spatial residuals by activity type, Fishing and Non-Fishing, from the classification model denoted as the proportion of entries in a given cell classified correctly...... 147

LIST OF ABBREVIATIONS

AC Region of the Gulf of Mexico affected by any spatial closure following the Deepwater Horizon oil spill.

AG Region corresponding to the entire Gulf of Mexico within the US Exclusive Economic Zone.

AIC Akaike information criterion

AU The approximately unbiased p-value for hierarchical clusters calculated by the pvclust package in R.

AUC Area under the receiver operator characteristic curve.

CCM Convergent cross mapping

CLB Commercial logbook catch record

CPUE Catch per unit of effort

CV Coefficient of variation

DH Deepwater Horizon oil spill

DWG Deep-water grouper

EDM Empirical dynamic modeling

EEZ Exclusive Economic Zone

EGOM Eastern Gulf of Mexico

FMP Fishery Management Plan

GLM Generalized linear model

GoM Gulf of Mexico

GPS Global Positioning System

IFQ Individual fishing quota

NEGOM Northeast Gulf of Mexico

NGOM Northern Gulf of Mexico

NMFS National Marine Fisheries Service

NOAA National Oceanic and Atmospheric Administration

NPV Negative predictive value

OBS Gulf of Mexico Reef and Shrimp Observer Program

OVL Overlapping coefficient

PCA Principal Components Analysis

PPV Positive predictive value

RF Random forest machine learning algorithm

RMSD Root mean squared deviance

ROC Receiver operator characteristic curve

SC Small region localized to the Deepwater Horizon spill site and closed during the May 17, 2010 closure. Represent a 10% closure of the US Exclusive Economic Zone in the Gulf of Mexico.

SEDAR Southeast Data Assessment and Review

SEGOM Southeast Gulf of Mexico

SWG Shallow-water grouper

VMS Vessel Monitoring System

WGOM Western Gulf of Mexico

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

USING VESSEL MONITORING SYSTEM DATA TO UNDERSTAND THE SPATIAL AND TEMPORAL DYNAMICS OF THE COMMERCIAL VERTICAL LINE FISHERY FOR REEF FISH IN THE GULF OF MEXICO

Nicholas David Ducharme-Barth

August 2018

Chair: Robert N. M. Ahrens Major: Fisheries and Aquatic Sciences

Commercial fishing fleets play a critical role in the population dynamics of exploited stocks. Understanding the spatial distribution of fleets allows managers to anticipate how fishing pressure on exploited stocks changes in response to perturbing events. By anticipating how fishing pressure changes, managers can develop proactive responses to protect stocks that are vulnerable to overfishing. Modern fisheries monitoring techniques including VMS have advanced this endeavor. This research presents a framework for using VMS data to develop spatial distributions of catch, fishing effort, and CPUE as well as associated estimates of uncertainty in a socioeconomically important vertical line fishery for reef fish in the GoM.

Indices of abundance derived from fishery dependent CPUE data are an important input to the assessment of these stocks. Traditionally, these indices were derived from standardized logbook data, at coarse spatial scales, and were limited to generating predictions for observed spatiotemporal strata. Understanding how CPUE is spatially distributed can help identify range contractions and avoid hyperstability or hyperdepletion, both of which can mask the true population dynamics. Here two methods are compared — spatial averaging of VMS-derived catch and effort data and the result of GLMs applied to logbook data for generating indices, to

evaluate the use of VMS-derived abundance indices in assessments of reef fish stocks. Lastly, there are a number of reasons why it may be advantageous to move management frameworks and assessment models to finer spatial scales that more closely match the spatially heterogeneous distributions of fishing fleets and the species that they target. Assessments may be able to estimate management reference points with greater precision and regulations, and can be fine- tuned to better handle multispecies interactions and spatially differential fishing pressure.

However, a necessary first step is identifying if the fishing fleet and or targeted stocks exhibit spatial structure. Multivariate clustering was used to identify spatial métiers within the fleet defined by individual vessel catch histories, landing and fishing locations. Additionally, empirical dynamic modeling (EDM) was used to identify if spatial stock structure exists based on the temporal dynamics of species relative abundance time series in 5 spatial regions in the

GoM.

CHAPTER 1 OVERVIEW

Fisheries management is a dynamic field requiring information and knowledge of several highly complex systems (Lorenzen 2008). In order to effectively manage exploited marine resources, it takes an understanding of the biology of the target species, as well as its biotic and abiotic ecosystem interactions. Outside of the biological system, managers must consider the stakeholder groups participating in the fishery, their motivations and how they may respond to fluctuations in stock status or regulatory change. More critically however, the sustainable management of exploited marine resources hinges on a proper understanding of the spatial structure and dynamics of these component systems.

Fish are not distributed homogenously across the landscape. At micro-scales, there is an inherent spatial patchiness to fish distributions as they seek to balance the mortality risks of acquiring food for growth and reproduction within a limited foraging arena (Ahrens et al. 2012;

Walters and Juanes 1993). Moving to population level scales, a simple explanation to observed distributional patterns is that fish are scattered across the landscape in proportion to available food resources or habitat suitability (Fretwell and Lucas 1969). These broad population level patterns may differ within the same species across age and maturity gradients due to ontogenetic preferences or spawning requirements. Sudden environmental phenomena (e.g. red-tide events, summer hypoxic zones, extreme thermal events, and anthropogenic disasters) can introduce spatiotemporal anomalies to the expected distributional patterns. Additionally, natural fluctuations in abundance can manifest themselves as shifting distributions as species move in and out of core population areas (MacCall 1990).

Fishers follow fish. As a result, fishers are unlikely to be distributed in a spatially homogenous way either. Fishers are commonly thought to distribute spatially according to a

gravity model (Caddy 1975; Walters et al. 1993) where the probability of fishing in a given location is proportional to the relative utility of that location. Commercial fishermen are traditionally viewed as profit maximizers, so the relative utility of a given location is a combination of spatiotemporally varying costs and benefits. Apart from opportunity costs associated with the decision to go fishing, costs can be viewed as a function of distance from the fishing site (Andersen et al. 2012; Smith and Wilen 2003), or regulatory incentive to avoid areas due to lack of species quota in multispecies fisheries (Walters and Bonfil 1999). Furthermore, costs can vary regionally since fuel, supply and labor costs are not likely to be constant across large geographical regions. Benefits in commercial fisheries correspond to revenues. Revenues are a product of the amount of fish landed, and regional variability in ex-vessel prices (Andersen et al. 2012; Hilborn and Ledbetter 1979; Holland and Sutinen 1999; Huang et al. 2012; Ran et al.

2011). Exogenous factors such as spatial closures or regulatory incentive to avoid areas can otherwise cause deviations from the expected distribution of fishing effort. Additionally, behavioral differences across fishers due to available knowledge (Branch et al. 2006; Holland and Sutinen 1999; Hutton et al. 2004; Vignaux 1996) or risk profile (Holland and Sutinen 1999;

Ran et al. 2011) can also result in heterogeneous spatial distributions and violations to the assumed distribution model.

Given these heterogeneities, catches across the landscape are not created equally. If the stock exhibits a clear spatial metapopulation structure with distinct genetic or age based sub- units (Berkeley et al. 2004; Hedgecock 1994), spatial variation in effort could disproportionately target groups of individuals with different reproductive capacities, reducing the long term productivity of the stock. Absent spatial information, hyperstability – abundance declining faster than catch rate, and hyperdepletion – catch rate declining faster than abundance (Hilborn and

Walters 1992), in the catch rate can mask the true trajectory of the stock (Beverton and Holt

1957; Harley et al. 2001) leading to population collapse in worse case scenarios (Kulka et al.

1996; Rose and Kulka 1999; Sadovy and Domeier 2005). Additionally, in multi-species fisheries, differing distributional patterns across species could result in regulations having differential effects across the management region as separate components of the fishery interact with multiple species complexes.

Despite the importance of explicitly accounting for spatial dynamics in the assessment

(Booth 2000) and management (Wilen 2004) of fisheries resources, as a field there is still a long way to go before this becomes a widespread and common practice. Though assessment models and management frameworks become progressively more challenging to implement in a spatially explicit context, one of the biggest remaining hurdles is acquiring data at the appropriate scale and resolution to inform these more complex frameworks and models. Fisheries independent surveys are expensive to operate and as a result often fail to achieve adequate levels of spatiotemporal coverage to be useful. Fisheries dependent data can be a useful source of information as they typically represent a more spatiotemporally complete and cost effective sample than fisheries-independent data (Ward 2005). Frequently, the catch data reported by vessel operators in their logbooks is at a coarse spatial scale which limits the utility of these data.

Onboard observers placed on fishing vessels greatly increases the spatial resolution of the data collected. However, spatiotemporal coverage can still be problematic if the proportion of observed vessels is small or if observer assignment to vessels is non-representative.

Vessel monitoring systems (VMS) have become increasingly present in commercial fisheries within the last 15 years. Though implemented for the primary purpose of enforcement and ensuring that marine protected areas (MPAs) are respected, VMS data have been used

globally (Gerritsen et al. 2013; Joo et al. 2011; Walker and Bez 2010) as an economical source of high-resolution, spatiotemporally complete fisheries dependent data. Predominantly used as a tool for understanding fisher behavior (Davie and Lordan 2011), tracking effort (Vinther and

Eero 2013), and mapping abundance distributions (Bertrand et al. 2008), VMS data products can be used as inputs to spatial assessment models or in the design of spatial management frameworks (Hall-Spencer et al. 2009).

A careful understanding of the spatiotemporal dynamics is especially important in the commercial vertical line fishery for reef fish in the Gulf of Mexico (GoM). The GoM is a large ocean basin characterized by a broad, shallow continental shelf covered with predominantly sandy substrate and lower relief live-hard-bottom habitat in the east. The western GoM is characterized by deeper – muddy bottom interspersed with high relief hard-bottom communities.

Culturally and economically (NOAA 2017), this is a valuable fishery to the region. However, the aggregating nature (Duffy 1970) and association with targetable habitat (Grimes 1978; Grimes and Huntsman 1980; Lindberg et al. 2006) of the predominant species in the GoM reef fish complex combined with the high-resolution targeting capable with vertical line gear (Pollack et al. 2013; SAFMC 2009a) predisposes this fishery to hyperstable catch rate information.

Additionally, current management and assessment frameworks in the GoM treat the fishery and vertical line fleet as single spatially homogenous units. This assumption is unlikely to be correct given the multi-species nature of this fishery and the changing patterns in species distributions as a function of habitat and geographic scale. Identifying sub-fleets (or métiers) within this fishery or the presence of spatial stock structure can improve management by informing spatially explicit assessment models and giving a better understanding for how components of the fleet may respond differently to perturbing events.

This research addresses the current lack of understanding of the spatiotemporal dynamics of the commercial vertical line fishery for reef fish in the GoM through a three-part analysis using VMS data from 2007-2013. In Chapter 2, a framework was developed to produce spatial distributions of catch, fishing effort, and catch-per-unit-of-effort (CPUE) from VMS data linked to commercial logbook catch records. A machine learning approach, random forest, was used to identify fishing locations from the VMS data. Spatial estimates of uncertainty were calculated using a two-step parametric bootstrap to account for both the classification and process uncertainty. This analytical approach was applied to assess changes in the fishery as a result of two (confounding) perturbing events that occurred in 2010: the shift to a grouper-tilefish individual-fishing-quota (IFQ) and the Deepwater Horizon oil spill. Chapter 3 took a comparative approach to creating indices of abundance for reef fish species in the GoM using spatial data from vessel monitoring systems. Two methods for creating indices were compared – spatially averaging, imputed VMS-derived CPUE distributions and using generalized linear models in a delta framework to standardize commercial logbook catch records. This chapter demonstrated a method for creating spatially explicit indices of abundance using high-resolution

VMS data and used a simulation to evaluate each methods’ ability to track the true abundance trend under a variety of effort and species abundance scenarios. Lastly, a two-part analysis is used in Chapter 4 to spatially characterize the commercial vertical line fishery for reef fish in the

GoM. The first component used multivariate clustering to identify métiers as a function of individual vessel catch histories and landing locations from the commercial logbook along with fishing locations from the VMS data. The second component used the methodology developed in

Chapters 2 & 3 to create spatially explicit abundance indices for targeted reef fish species as inputs to a non-linear non-parametric time series modeling approach (empirical dynamic

modeling EDM) in order to identify the presence of spatial stock structure. In combination, this research uses VMS data to produce the first spatiotemporally complete characterization of the commercial vertical line fishery for reef fish in the GoM.

CHAPTER 2 CLASSIFICATION AND ANALYSIS OF VMS DATA IN VERTICAL LINE FISHERIES: INCORPORATING UNCERTAINTY INTO SPATIAL DISTRIBUTIONS

2.1 Introduction

It is critical to consider spatial relationships in marine fisheries to manage them successfully. Failing to properly account for spatial dynamics between stocks and fleets has led to some of the most notorious stock collapses in the modern history of fisheries management including northern cod Gadus morhua (Rose and Kulka 1999), the multispecies fishery for rockfish in the Pacific (Walters and Martell 2004; Williams et al. 2010), and New Zealand orange roughy Hoplostethus atlanticus (Hilborn et al. 2006; Roberts 2002).

Managing marine commercial fisheries is difficult in part due to technological advancements that have enabled fleets to maintain unsustainable levels of catch even while stocks are declining (Dayton et al. 1995). In some cases, this has led to hyperstability in catch rates that managers have misinterpreted as no change in stock abundance (Bishop et al. 2004;

Harley et al. 2001). There are numerous examples of marine fisheries that have targeted and exploited commercially valuable stocks at unsustainable levels (Jackson et al. 2001; Lotze et al.

2006; Worm et al. 2006). Species that are benthic or structure oriented and that are characterized by aggregating or range collapsing behavior are particularly likely to exhibit hyperstable indices of abundance, especially when the indices of abundance are based solely on fishery dependent catch-per-unit of effort (CPUE). In these cases, the spatial monitoring and management of fishing fleets represent necessary tools for rebuilding and successfully managing stocks (Worm et al. 2009).

 Reprinted with permission from Ducharme-Barth, N.D., Ahrens, R.N.M., 2017. Classification and analysis of VMS data in vertical line fisheries: incorporating uncertainty into spatial distributions. Can. J. Fish. Aquat. Sci. 74 (11), 1749–1764. http://dx.doi.org/10.1139/cjfas-2016-0181.

Vessel monitoring systems (VMS) represent a powerful data collection tool that can be used to develop effective spatial monitoring and lead to successful management of marine fisheries. Spatial distributions of fishing effort and catch more accurately track distributions of targeted stock abundance (Babcock et al. 2005). Spatial data can also guide managers on how to restructure fisher incentives by defining access rights through spatially heterogonous policy instruments that can provide an effective bottom up control and lead to economic and biologic sustainability (Hilborn et al. 2004; Sanchirico and Wilen 2005; Wilen 2004).

The growing prevalence of VMS in fisheries science has helped provide high-resolution vessel position data which allow for the inferences about spatial distributions of fishing effort and species-specific CPUE when linked with self-reported catch data recorded in commercial logbooks (Chang 2011; Gerritsen and Lordan 2011; Witt and Godley 2007). This allows managers to track fishing behavior (Davie and Lordan 2011), identify shifts in exploitation patterns (Vinther and Eero 2013), and create distributions of the underlying stock (Bertrand et al.

2008). Analysis on VMS data has enjoyed global application, particularly in European and

American benthic and demersal trawl fisheries targeting groundfish (Gerritsen et al. 2013;

Murawski et al. 2005) as well as purse seine fisheries in the Indian and Pacific oceans targeting tuna and anchovetta respectively (Joo et al. 2011; Walker and Bez 2010). Though still predominantly used as a tool to better understand the spatial dynamics of commercial fishing fleets, VMS has been used to directly improve management by increasing the precision of in- season real time closures (Little et al. 2015; McCraken 2012) and in the design of a marine protected area (Hall-Spencer et al. 2009).

The full utility of analysis on VMS data is derived from the ability to distinguish between fishing and non-fishing data points (Mills et al. 2007). This is the crucial step in the process for

estimating spatial distributions of fishing effort from VMS data. The rest of the process is summarized in a simple framework (Lee et al. 2010): data cleaning, identification of gear used via link to commercial logbook, determine fishing or non-fishing status, and aggregate fishing data to a grid to estimate the spatial distribution. In fisheries lacking comprehensive observer coverage, various models have been used to classify VMS data as fishing or non-fishing: simple cut off rules based on vessel speed (Campbell et al. 2014; Lee et al. 2010), to more complex

Bayesian Hidden Markov models (Bez et al. 2011; Vermard et al. 2010), and artificial neural network models (Joo et al. 2011).

This type of classification problem is not unique to fisheries and alternative methods have been developed in other fields. Borrowing from remote sensing, biological and ecological applications, random forest (RF) models have been shown to be an accurate and computationally efficient classification and regression algorithm capable of handling large data sets and nonlinear relationships between variables as well as being robust to data noise and overfitting

(Breiman 2001; Cutler et al. 2007; Diaz-Uriarte and de Andres 2006; Pal 2005). In simple two- case classification problems, such as the one considered in this paper, it is acceptable to do classification via binary regression using a nearest neighbor predictive approach (Hastie et al.

2009). Since RF models represent an adaptive nearest neighbor method (Berk 2008), binary regression using an RF model can be used to classify VMS data as fishing or non-fishing.

Additionally, an established method exists for identifying the process uncertainty around binary regression outcomes from an RF model (Sexton and Laake 2009).

Vertical line fisheries are commercially and socioeconomically important within the Gulf of Mexico, coastal waters off the South East U.S. and Hawaii (GSAFFI 2008; Hospital and

Beavers 2011). Within the context of this paper, vertical line fishing refers to fishing multiple

baited hooks (gear) on a single line or multiple lines deployed vertically from a stationary or slowly drifting vessel. Lines are retrieved predominantly using mechanical means such as electric or hydraulic reels. Vertical line fishing occurs in spatiotemporally distinct sets where a set is defined as the period of time that hooks are being fished from a vessel at that spatial location. However, multiple drops of the gear can occur during each fishing set. A change in location or prolonged period with hooks out of the water represents a change to a new fishing set.

Specifically, a substantial vertical line fishery operates in the Gulf of Mexico, targeting a reef-species complex containing multiple populations of particular economic value and concern of overfishing risk. Trip and set characteristics for the Gulf of Mexico vertical line fleet as well as a map of the study site can be found in Table 2-1 and Figure 2-1 respectively. This vertical line fishery targets hard bottom structure by making multiple short fishing sets within a single fishing trip (SAFMC 2009a; Scott-Denton et al. 2011) resulting in the harvest of a range of species. The ability for vertical line fleets to specifically target habitat structure — namely live hard bottom habitat, ledges, and coral reefs, unlike bottom longline gear (Pollack et al. 2013) — makes having an acute awareness of the spatial distribution of these fleets paramount. Currently, the monitoring and management regime in the Gulf of Mexico lacks a complete, high-resolution understanding of the vertical line fishery’s spatial distribution. The Gulf of Mexico Reef and

Shrimp Observer Program (OBS) (Scott-Denton et al. 2011) is able to provide high-resolution spatial data but is spatiotemporally incomplete due to incomplete observer coverage. Spatial information provided by the commercial logbook (CLB) is spatiotemporally complete, however this data is self-reported to a low-resolution statistical grid and reported fishing areas are un- verified and un-validated. A spatial analysis of VMS data can address the lack of acute spatial awareness by providing complete, high-resolution distributions of effort, catch and CPUE.

The Gulf of Mexico reef fish complex is principally characterized by the presence of snappers, Lutjanus spp., and groupers, Epinephelus spp. (Scott-Denton et al. 2011) and represent at least 14% of the $204.967 million in total finfish revenues for the region, and at least 57% of the total revenues associated with red snapper (Lutjanus campechanus) and groupers in the Gulf in 2013 (NMFS 2015, 2016). Many members of this complex are particularly susceptible to over exploitation since they are associated with aggregating behaviors and hermaphroditic sexual patterns where certain sexes are disproportionately targeted (Coleman et al. 1996; Coleman et al.

2000; Sadovy and Domeier 2005). Specifically, 4 species (red snapper, vermilion snapper

Rhomboplites aurorubens, red grouper Epinephelus morio, and gag grouper Mycteroperca microlepis), responsible for roughly 80% of monthly catches by the Gulf of Mexico vertical line fishing fleet, are highly vulnerable to fishing pressure due to their strong association with targetable habitat (Grimes 1978; Grimes and Huntsman 1980; Lindberg et al. 2006; Moran

1988), aggregating nature (Duffy 1970), high site fidelity (Coleman et al. 2010; Coleman et al.

2011), and spawning behavior (Coleman et al. 1996). The most targeted species within this fishery are expected to be most at risk of having hyperstable and misleading CPUE time series.

Despite this troubling combination of fleet and species’ behavior, a research gap exists for applying spatial VMS analysis to vertical line fisheries and fisheries targeting reef fish. This is a management problem. Without appropriate spatial accounting it is challenging to identify how the stock – fleet relationship may change given a spatial perturbation to the system.

Furthermore, there does not currently exist a method to estimate the error associated with VMS derived spatial distributions. This uncertainty is important to quantify so that it can be incorporated in the creation of higher level products generated from the derived spatial distributions. To address these research gaps, this paper presents a method for spatial analysis of

VMS data and for generating estimates of error associated with spatial predictions. This method is comprised of four parts. In this study, a random forest algorithm was developed to classify

VMS data points from vertical line fishery trips in the Gulf of Mexico as fishing points and non- fishing points. A method for partitioning the uncertainty around the classification of fishing points is devised and applied to generate estimates of error around spatial predictions. Spatial distributions of catch and CPUE were estimated at monthly intervals in 5 regions of the Gulf of

Mexico for 23 commercially encountered species. Regional trends over time were analyzed to identify potential shifts within the commercial vertical line fishery. Application of these methods will allow management to develop a better understanding of fleet behavior as well as set the foundation for spatial ecosystem-based management of commercially targeted species.

2.2 Methods

2.2.1 Data

This study utilized 3 data sets to generate spatial distributions of effort, catch, and CPUE for the commercial vertical line fleet targeting reef fish in the Gulf of Mexico. The first data set was the VMS data set spanning the study period, January 2007 through February 2014 (except for July and August 2010; these data were requested but never received), for vessels holding a commercial Gulf of Mexico reef fish permit (Rivero 2015). This represented 19,198,140 unique vessel locations. Each VMS entry contained several variables; however, for this analysis we considered only GPS location, date and time of day, the unique vessel identifier (to link to the catch record), as well as vessel characteristics such as horsepower, length, vessel weight and vessel hold capacity. VMS data are reported every 60 minutes and the position is recorded at a resolution of ~0.1 meters.

The second data set was the CLB catch records. There were 31,643 unique vertical line fishing trips targeting reef fish linked to VMS records within the study period. Trips targeting

reef fish were defined as those trips that caught at least 1 fish of any species listed in the Gulf of

Mexico Reef Fish FMP (Table 2-2). Trips were retained if they indicated a vertical line gear

(hand line, hand gear, or hydraulic/electric reel) was used, and less than 2% of retained trips indicated multiple gears used on a trip. The CLB variables considered in this analysis were unique vessel identifier, unique trip identifier, start date, unloading date, gear used, species harvested, total weight, and depth fished (in-water depth where majority of catch occurred).

VMS records were linked to specific CLB entries if their unique vessel identifiers matched and the time of the VMS entry fell between the CLB start and unload dates.

The final data set is the OBS data, where vertical line fishing trips accommodated onboard observers. The OBS data associated with vertical line vessel activity were used to unequivocally identify 54,486 VMS vessel locations over the time interval considered in this analysis (22.8% fishing points and 77.2% non-fishing points). Observer coverage was allocated proportional to historical fishing effort across strata (regions and gear) to ensure comparable levels of sampling of high and low fishing effort strata (Scott-Denton et al. 2011). Variables considered in this analysis were the vessel identifier, and the date, start time, end time, and position of each fishing set. The start date and end date of the observed trip were also recorded.

For each fishing set, the start and end times corresponded to the time the first hook entered the water to the time the last hook left the water. Position of observed sets were recorded at a resolution of 30 meters. VMS records were linked to an observed trip if their unique vessel identifiers matched and the time of the VMS entry fell between the start and end dates of the observed trip. If a VMS entry corresponded to an observed trip and fell within a window of observed fishing activity for that vessel, it was classified as a “fishing” point. All other points for that observed trip were classified as “non-fishing”.

In the Gulf of Mexico, VMS is reported on an hourly interval meaning that each VMS point represents an instantaneous snapshot of activity in time. Activity occurring at a fishing point includes dropping the gear, allowing the gear to soak and retrieving the gear. Soak times ranged from 1 minute to 107 minutes with a median of 20 minutes. In the case of multiple drop sets, fishing points also account for rebaiting hooks and removing fish from hooks. Activities at a non-fishing point include everything that occurs when hooks are out of the water such as steaming, maintenance, and etc. In vertical line fisheries where detailed information about fishing sets is available, effort can be defined in hook hours (# hooks set * hours fished)

(McCarthy and Cass-Calay 2006; Scott-Denton et al. 2011), hours fished, or number of sets fished. For each trip within the OBS dataset, total hook hours fished per trip, hours fished per trip, sets fished per trip, and VMS fishing points per trip were calculated. Across trips, number of

VMS fishing points per trip was positively correlated with sets fished, hook hours fished and hours fished (Pearson correlation: 0.68, 0.65 and 0.83, p-values for all correlations with hypothesis H0 = 0 were less than 2.2e-16). These correlations provided sufficient support for using the VMS fishing points as a proxy for fishing effort.

To ensure that the classified VMS data represent vertical line fishing activity, and not trolling or other types of fishing activity, several steps were taken. Fishing points from trips that did not fish a vertical line gear were excluded. The target group for each fishing point within the

OBS data was identified. The target species for each fishing point was recorded in the OBS data set for 82% of the observed fishing points. From these observed target species, the following target groups were created: snappers, groupers, reef fish, pelagic, and other (Table 2-3). Where the target species was not recorded in the OBS data set, the target group was determined from the modal species group (catch by weight) for that fishing set (11% of observed fishing points) or

from the modal species group (catch by weight) for that fishing trip (7% of observed fishing points). The breakdown of observed fishing points by species group is: snappers 35%, groupers

59.2%, reef fish 3.1%, pelagic 2.4%, and other 0.2%. Fishing points that targeted the pelagic or other species groups were excluded as it is possible that those fishing points did not represent vertical line fishing activity.

Data cleaning and preparation of the unobserved VMS data set followed the framework initially laid out by (Lee et al. 2010). Due to the scope of the study, VMS entries falling outside of the Gulf of Mexico Exclusive Economic Zone were removed. VMS in the Gulf of Mexico is required to capture vessel location at 1-hour intervals regardless of vessel activity, and as a result, a large proportion of VMS points corresponded to dock or land positions. Therefore, VMS entries located within 5km from shore as calculated by the minimum Haversine distance to the

Global Self-consistent Hierarchical High-resolution Shorelines were not assumed to be fishing locations and were removed from the analysis. Further, VMS entries that could not be linked to the CLB as well as incomplete VMS entries (missing values for variables used in the classification model) and entries that contained implausible variable values were removed from the analysis. VMS entries linked to CLB records were retained if they indicated a vertical line gear was used on that trip. After data cleaning and preparation, 2,769,857 unobserved VMS entries were available for classification. These entries represent vessels at sea potentially engaging in fishing activity.

2.2.2 Classification

VMS entries of unobserved trips were classified as either fishing or non-fishing using a two-part process. The first part used a binary RF regression model resulting in a prediction of behavior bounded between 0 and 1 for each VMS entry. VMS entries were classified as fishing

(1) if their corresponding RF prediction was greater than or equal to a classification threshold

value or non-fishing (0) if it was less than the classification threshold value. The RF model was constructed using the randomForest package in R (Liaw and Wiener 2002), was trained on a random 75% subset of the OBS entries and was grown to 500 trees. The threshold of 500 trees was chosen since model positive predictive value (PPV), determined from an out-of-sample evaluation of the remaining 25% of the OBS entries, had reached an asymptote by this point, and it minimized computational resources required. Positive predictive value (PPV) is defined as the number of fishing points correctly classified as fishing points divided by all points classified as fishing points. Negative predictive value (NPV) is defined as the number of non-fishing points correctly classified as non-fishing points divided by all points classified as non-fishing.

Variables were included in the RF model (Table 2-4) if they contributed to an increase in the PPV. These included calculated variables that characterized vessel movement

(Time_from_previous, Distance_from_previous, Speed_from_previous, FIRST_NN,

SECOND_NN, and BEARING_DIFF), timing of fishing activity (FRACTION_DAY,

JULIAN_DATE, REL_TRIP_TIME, TOTAL_TRIP_TIME, and LunarPhase), or location choice

(DEPTH and DEPTH_DIFF). Recorded variables (variables that were not calculated) were also included to account for variability related to vessel characteristics. Since the first two nearest neighbor distances were highly correlated, additional nearest neighbor distances were not included in the model. There is a clear difference between the distributions of fishing and non- fishing points in the OBS data for the two variables most important to classification (See Figure

A-1 for distributions of the variables used; See APPENDIX Variables Used in Random Forest

Classification for a description of how the variables are used in the classification model).

The performance of the classification algorithm was evaluated through a comparison with a null model and examination of the spatial residuals. Distributions of the spatial residuals for

OBS entries by activity and by target group were derived to test if spatial patterns existed in the

RF model’s predictive ability. Global Moran’s I, a measure of spatial autocorrelation bounded from -1 to 1, was calculated for the spatial distributions of residuals using the ape package in R

(Paradis et al. 2004).

2.2.3 Uncertainty in Spatial Predictions

This paper proposes a two-step approach to account for uncertainty in spatial predictions of effort due to both the RF modeling process and the choice of the classification threshold, 0.43

(See APPENDIX Selection of Classification Threshold for the determination of the classification threshold value). The prediction for a VMS entry from a RF binary regression model is the average prediction across all trees in the RF model and is represented as a decimal value bounded between 0 and 1. Values closer to 1 are more likely to be fishing. Therefore, the prediction for a VMS entry is an average value with an accompanying standard error. The prediction for each VMS entry can then be characterized by a distribution with mean equal to the average prediction across all trees in the RF model for that entry and the standard error associated with that average prediction. The first step is to account for the uncertainty associated with the distribution of predictions for each VMS entry. Separately, the second step is to account for uncertainty related to the classification using the probability that a predicted fishing (or not fishing) point was actually fishing (or not fishing).

Currently there is no method in the literature that describes how to simultaneously account for these two sources of uncertainty. Alternatives to the proposed approach include reporting the uncertainty in classification but not incorporating it in the spatial predictions, or incorporating one source of uncertainty in the spatial predictions and ignoring the other. These alternatives would either ignore or underestimate the derived uncertainty in spatial predictions and are not preferable. However, it is possible that correlation between the two sources of

uncertainty exists and as a result, the proposed approach could overestimate the derived classification uncertainty.

A binary RF regression model and classification based on a cutoff was used instead of a

RF classification model in order to be able to quantify the standard error for each prediction.

There is an existing method for estimating the variance associated with the average of individual tree classifications from a RF classification model (Wager et al. 2014), however the implementation of this method was computationally infeasible given the size of the data set.

Differences in classification accuracy (PPV, NPV, sensitivity and specificity) between the binary

RF regression and cutoff classification model proposed, and an RF classification model built using the same variables and trained on the same data were less than 1% when calculated using the same out-of-sample test data set. Sensitivity is defined as the number of fishing points correctly classified as fishing points divided by all points observed as fishing points. Specificity is defined as the number of non-fishing points correctly classified as non-fishing points divided by all points observed as non-fishing.

A computationally efficient algorithm, the Noisy-Bootstrap algorithm, exists for estimating the variance associated with the average of individual tree predictions from a binary

RF regression model (Sexton and Laake 2009). In the first step for quantifying uncertainty, a

Noisy-Bootstrap algorithm, with 200 bootstrapped iterations (b) of 10 tree (r) binary RF regression models, was used to estimate the variance around the mean regression value for each unclassified VMS entry. Combinations of b x r that are 2-4 times greater than the number of trees used in the initial RF model (in this case 500) give meaningful estimates of the variance around the mean regression value (Sexton and Laake 2009). The mean regression value is the average of individual tree predictions from a binary RF regression model for a given entry. Using

the classification mean () and variance (2) associated with each VMS entry, samples were drawn from a truncated normal distribution (bounded by 0 and 1) to generate 201 possible scenarios for each of the 2,769,857 VMS entries. A truncated normal distribution was used for consistency as opposed to a beta distribution because for a small number of VMS entries, where

휎2 ≮ 휇 (1 − 휇), a valid beta distribution was not able to be parameterized. The 201 scenarios for each VMS entry were converted to binary fishing states (1 for fishing, 0 for non-fishing) using the classification threshold.

Incorporating the classification accuracies calculated for the given classification threshold was the second step in quantifying uncertainty. The PPV represents the probability that an entry is a true fishing point given that it was classified as a fishing point, and the NPV is the probability that an entry is a true non-fishing point given that it was classified as such. Using the

PPV and NPV, each binary fishing scenario was replaced with a random draw from a Bernoulli distribution with success probability equal to the PPV if the binary fishing state was 1 or with success probability equal to 1-NPV if the binary fishing state was 0. An odd number of scenarios was used so that the median scenario was not a composite of two other scenarios. Additionally,

201 scenarios were selected because estimates of uncertainty did not meaningfully change when including more than 100 scenarios and calculations on greater than 201 scenarios became computationally challenging. This step propagated the uncertainty from both the RF modeling process and the classification error into the spatial distributions.

2.2.4 Analysis

Spatial distributions were generated at monthly intervals for each of the 201 fishing scenarios and, using the GPS information associated with each VMS entry, classified fishing points were aggregated on a 10km by 10km grid to account for vessel movements within the 1-

hour reporting window. A distribution of the CV (coefficient of variation) of the average monthly fishing effort was found by first calculating the average monthly fishing effort for each scenario. Then the mean and standard error for each 10km by 10km grid cell was calculated across the scenarios to generate a distribution of the CV of average monthly effort. Additionally, distributions of spatial catch and CPUE, for 23 species comprising the greatest proportion of the total catch by the fleet (2 species grouped in the pelagic category were excluded) during the study period (Figure 2-2), were created at monthly intervals for each of the fishing scenarios. For each CLB trip the associated species-specific catch for that trip was uniformly allocated to each classified fishing point corresponding to that trip for each fishing scenario. For a very small percentage of the catch (<2% of the total catch considered) we were unable to directly allocate it to classified fishing points if there were no predicted fishing points for that scenario. In these situations, unallocated catch was distributed among cells proportionally to the catch that had already been allocated. Spatial CPUE by species was determined individually for each grid cell as the total catch of a given species within the grid cell divided by the total number of classified fishing points within the grid cell.

Given that set specific catch information exists for the OBS data set, the assumptions of uniform catch allocation across fishing points and how CPUE is defined could be evaluated.

Average monthly distributions of catch and CPUE across the entire Gulf of Mexico were created for each species for both the VMS and the OBS datasets. The VMS derived distributions were the average distribution across both months and fishing scenarios. Catch was allocated uniformly across fishing points for a given trip and CPUE was defined as catch divided by fishing points within each grid cell. For the OBS derived distributions the average distribution was taken as the average across months. Catch was distributed to the location specific fishing set it came from and

CPUE was defined for each fishing set as catch divided by hook hours fished. In both cases the data were aggregated to the scale of a 10 km x 10 km grid. This process created paired distributions (VMS and OBS) of catch for each species and CPUE for each species. A bivariate spatial association metric, Lee’s L, was used to assess the spatial correlation between the paired distributions. This metric retains the direction and some of the magnitude of the bivariate point- to-point association, Pearson’s correlation, between the two distributions as well as incorporating the degree of spatial association between the distributions using an extension of a univariate measure of spatial autocorrelation, Moran’s I (Lee 2001). This metric is bounded on the interval

-1 to 1, with positive values indicating a positive point-to-point Pearson’s correlation. A bounded permutation, where the point-to-point correlation between the two distributions remains constant, is used to determine if there is a significant spatial association between the two distributions (Lee

2001; Lee 2004).

To evaluate shifts within the fishery, time series (of effort, catch by species and CPUE by species) in five spatial regions within the Gulf of Mexico were created by aggregating the data points within each spatial region for each of the 201 fishing scenarios. The regions considered were (Figure 2-1): (1) all waters of the Gulf of Mexico contained within the US EEZ (AG); (2) waters that were ever affected by spatial closures caused by the Deepwater Horizon (DH) oil spill beginning in May 2010 (AC); (3) waters closed during the May 17, 2010 closure which are localized to the spill site and represent a 10% closure of the US EEZ in the Gulf of Mexico (SC);

(4) waters not affected by spatial closures east of the mouth of the Mississippi River (EGOM); and (5) waters not affected by spatial closures west of the Mississippi River (WGOM). All told there were 235 combinations of effort, catch by species and CPUE by species each with 201 time series resulting in the analysis of 47,235 total time series.

To incorporate classification uncertainty, the presence of mean shifts in each of the 201 time series of effort, catch by species and CPUE by species were tested using the breakpoints function in the strucchange package in R (Zeileis et al. 2003; Zeileis et al. 2002). Mean shifts are defined as changes in the mean from one segment of the time series to another. The breakpoints function allows for the detection of mean shifts when their locations are not known by testing for changes in the coefficients of linear regression models on the underlying time series of data (Zeileis et al. 2003). We modeled each time series from March 2007 to June 2013 to ensure the same amount of observations (38) pre-spill to post-spill. A gap in the data occurred in July and August of 2010 and linear interpolation of the time series between June and

September 2010 was used to fill this gap. January and February 2007 were excluded from the analysis because those months showed anomalously low effort estimates and mandatory usage of

VMS was not in effect at that time.

A simple, intercept only linear regression model was used to identify breakpoints corresponding to mean shifts in the time series. We allowed for the calculation of a mean shift in each time series subject to the condition that the time series segments were at least 18 months long. This was done to identify periods of persistent, structural change in the time series.

Location of the breakpoints was determined by minimizing the residual sum of squares using the breakpoints function. Confidence intervals around the locations of the breakpoints were calculated using the confint function in the strucchange package. A mean shift was determined to have occurred if it occurred in at least 95% of the 201 time series of effort, catch by species or

CPUE by species. A mean shift was determined to be contemporaneously associated with the

DH spill if the confidence interval for a breakpoint contained the DH spill month (May 2010) in at least 95% of the 201 time series of effort, catch by species or CPUE by species.

It is important to note that confounding effects such as regulatory changes affects the ability to assign causation to mean shifts. Though the DH spill represents a large perturbing event there were several regulatory changes within the study period that also affected the fishery.

Notable changes include regular increases in red snapper (Lutjanus campechanus) quota

(GMFMC 2015), reductions in quota for gag grouper (Mycteroperca microlepis) from 2009-

2012 (GMFMC 2011), and a switch to an individual fishing quota (IFQ) management system for commercial groupers in 2010 (GMFMC 2008).

2.3 Results

The development of a RF model to classify unobserved VMS entries allows for the description of the full spatial distribution for the commercial vertical line fishery targeting reef fish in the Gulf of Mexico (Figure 2-3: top panel, Disclaimer: All spatial distributions have been appropriately aggregated to protect vessel confidentiality). The RF algorithm used for classification of the unobserved VMS entries had a PPV of 60.2%, an NPV of 89.0%, a model sensitivity of 61.6% and a model specificity of 88.4% as determined from the out of sample evaluation of OBS entries (Table 2-5). Keeping in mind that the OBS data set was unbalanced in terms of fishing and non-fishing points, a random classifier would have a PPV of ~22%. The RF model used correctly classifies fishing points at a rate 3x better than random (See APPENDIX

Comparison to Null Model for additional details on model performance relative to a null model).

Classification accuracy also did not appear to vary spatially for either fishing or non-fishing points as there was only negligible positive correlation among the spatial residuals (See Figure

A-3 for classification accuracy relative to spatially anonymous vessel trajectories; See Figure A-

4 for the spatial residuals of fishing and non-fishing points).

Classification accuracy by target group (snappers, groupers, and other reef fish) showed some variability. Since we were unable to identify target species for non-fishing points,

sensitivity was used as a metric of accuracy since it only relies on fishing points. The RF model was able to correctly classify fishing points targeting groupers at the highest rate, 68.3%, followed by other reef fish, 57.8%, of the time and snappers, 50%, of the time. These differences in classification rate do not appear to be driven by spatial patterns of classification success rate within species (Figure 2-4), as there is no spatial correlation among the residuals for fishing points targeting groupers and only negligible positive correlation among residuals for fishing points targeting reef fish or snappers. Spatial differences in targeting between species could explain the discrepancy between the classification accuracies of groupers and snappers. Groupers are predominantly targeted in the eastern Gulf of Mexico which is where a greater proportion of

VMS and OBS points are located, however snappers are primarily targeted in the northern and western portions of the gulf. Differences in the fishing signature across regions combined with the classification model being trained on data that is not equally distributed across regions could explain the discrepancy between the classification accuracies.

The bivariate analysis of spatial correlation indicate that the assumptions made in terms of uniform catch allocation and how CPUE was defined may be appropriate for this fishery since a statistically significant bivariate spatial correlation was found for species that make up a large portion of the fishery (Figure 2-5). A positive point-to-point correlation was found to be statistically significant for catch in 82% of species considered, and for CPUE in 78% of species considered. A statistically significant bivariate spatial correlation was found for 78% of catch species distributions (these species represented 98% of landings during the study period) and

52% of CPUE species distributions (these species represented 93% of landings during the study period). Species where there was not a significant correlation were characterized by species that aren’t commonly caught throughout the Gulf indicating that the OBS data may not appropriately

sample them relative to their spatial distributions. Hogfish (Lachnolaimus maximus) and black grouper (Mycteroperca bonaci) are typically caught in the south-eastern Gulf and lane snapper

(Lutjanus synagris) in the western Gulf.

Hot spots of effort exhibit low variability relative to the effort predicted to occur there.

Though variability and effort density appear to be positively correlated, they do not increase at the same rate (Figure 2-3: middle panel). As the density of predicted effort decreases, the relative variability of predicted effort increases in an inverse relationship (Figure 2-3: bottom panel).

This indicates consistent estimates of effort across scenarios in the most heavily fished regions.

Grid cells on the landward side of the fishing grounds likely represent a transition zone between behaviors, fishing and steaming to and from port. These cells show higher levels of relative variability which is reflective of the uncertainty in classification.

Since variability and density of effort did not increase at the same rate, the scale at which effort was analyzed becomes an important consideration. The variability in effort across a broad spatial scale becomes negligible (Figure 2-6). Within the 5 spatial regions considered, a mean shift was only detected in the area most proximately located to the DH spill. A breakpoint was detected in the month preceding the spill, after which effort never recovered to the pre-spill mean. This mean shift was detected in all 201 time series indicating that even at this smaller spatial scale variability was negligible.

Accounting for variability in spatial distributions was relevant when analyzing time series for the 230 combinations of catch by species and CPUE by species in the 5 spatial regions

(Figure 2-7). Variability across time series for combinations of CPUE by species was not negligible. Analysis of CPUE combinations across all 5 spatial regions showed several instances where results were inconsistent across all 201 time series. Mean shifts were determined to have

occurred in 50% of CPUE by species combinations and 53% of catch by species combinations

(Table 2-6). However, an additional 27% of CPUE by species combinations and 4% of catch by species combinations recorded mean shifts in any of their 201 time series, but not in at least 95% of time series. Where mean shifts were determined to have occurred, 32% of CPUE by species combinations and 43% of catch by species combinations could be contemporaneously associated with the DH spill. An additional 47% of CPUE by species combinations and 10% of catch by species combinations contained the DH spill month fell within the 95% confidence interval for the breakpoint, however contemporaneous association could not be determined as this did not occur in at least 95% of time series.

Consistent regional and species group trends existed within both catch and CPUE by species combinations. Catches and CPUE increased in the eastern Gulf and tended to decrease in the region most proximally located to the spill as well as in the western gulf. Across species groups, a mean shift was detected in roughly two-thirds of grouper catch and CPUE combinations and in less than half of combinations for snapper or other reef fish. Within each species group, there were more species that showed increases over the study period than decreases.

As an aggregate, the vertical line fishery targeting reef fish appeared relatively resilient to the shock caused by a large perturbing event, the DH spill, as this study did not detect meaningful negative change in the total effort or species catches at the Gulf-wide scale during the study period. Breaking it down further, the majority of detected mean shifts were not found to be contemporary to the DH spill. This observation was consistent for both catches and CPUE, though there was a higher proportion of catch by species combinations that were associated with

the DH spill. Intuitively, mean shifts were more likely to be found contemporary to the DH spill within the two regions directly affected by spatial closures.

2.4 Discussion

This paper established methods allowing for the spatial analysis of vertical line fisheries by developing a routine for classifying vertical line VMS data and incorporating uncertainty in the resultant spatial distributions. In addition to providing information on how the fishery may have changed within the study period, this tool is useful for a range of management tasks.

Science based spatial management for socially and commercially important fisheries targeted by vertical line fisheries is facilitated because of the development of a satisfactorily successful classification system. Accurately tracking spatial effort and catch can improve our understanding for how effort may shift across areas and species as a result of perturbations to the system like oil spills or regulatory changes. This can ease the transition from managing fisheries in a single stock framework to ecosystem based fisheries management (Hilborn 2011). Additionally, the increased capacity for spatial monitoring of fishing fleets allows the estimation of slow, long term changes (Walters and Bonfil 1999; Walters and Martell 2004) in variables like catchability, due to increased targeting capabilities, or deviations in species-habitat associations tied to climate change.

Preceding VMS analyses have investigated how sensitivity to the model training dataset

(namely classification threshold) alter classification accuracy (Joo et al. 2011) or how changes in grid size or track interpolation technique alter the predicted effort distribution (Lambert et al.

2012; Russo et al. 2011a). However, this is the first study to explicitly estimate the uncertainty in the predicted spatial distributions as a result of the model classification uncertainty and classification threshold used. Understanding both sources of variability in the resultant spatial distributions allows for a more complete accounting of the uncertainty in estimates of effort,

catch, and CPUE within temporal and spatial strata. This was an important consideration when analyzing catch and CPUE data. Since catch was allocated uniformly to VMS points within a trip, and not across all VMS points, the differences in which VMS entries were classified as fishing between fishing scenarios resulted in relevant levels of variability. The scale of the strata being analyzed is also important to consider when accounting for uncertainty. In the current analysis and level of spatial and temporal aggregation, despite the lower classification accuracy of the model, the inferences drawn were fairly consistent, particularly for effort, across all 201 fishing scenarios indicating reliability at the considered scale. However, at finer spatial and temporal scales this may no longer be the case, so explicitly accounting for uncertainty becomes much more important.

The two-step framework described in this paper for quantifying the uncertainty in spatial distributions has application beyond use with RF models or analysis of VMS data. The use of an

RF model allows for the estimation of variability around individual entries. However, if a classification model is used where uncertainty around the individual entries due to the modeling process is not available the proposed framework can be implemented beginning at the second step to describe spatial uncertainty with respect to classification error. This method has a logical extension to any binary spatial classification problem, beyond VMS, such as species presence- absence modeling.

While this study established a protocol for classifying VMS data within vertical line fisheries, it is important to note that, relative to other VMS analyses, the classification accuracy was comparatively poor. In a literature review of 18 journal articles detailing VMS type analyses the reported classification accuracy ranged from 76% (Joo et al. 2011) to 99% (Mills et al. 2007) while the PPV of this study was just over 60%. There were several potential factors that could

contribute to this lower level of classification accuracy. The first is the large quantity of VMS data in question; 2,769,857 unobserved VMS entries (post-data-cleaning) over the course of 8 years could result in a greater variability of entries attempted to be classified, leading to poorer model classification. In the only study of comparable temporal breadth, Joo et al. 2011 achieved a 76% classification rate albeit with a much smaller data set (97,877 VMS entries). Many classification methods indicated that the intrinsic vessel speed reported within the VMS dataset was an important variable to classification accuracy (Mills et al. 2007; Murawski et al. 2005;

Witt and Godley 2007). In the VMS dataset used for this analysis the intrinsic vessel speed was valid for less than 10% of entries and as such we had to rely on an approximate speed calculated from the distance traveled within the one-hour reporting window. A shorter reporting window would improve estimates of vessel speed and as such would lead to higher classification accuracy. Decreasing the reporting interval could also aid model accuracy in another way.

Vertical line fisheries make a lot of short sets (typically <1hr and as short as 15min) targeting specific habitat, and as such may move and fish many times within a small spatial and temporal window. Since VMS represents an instantaneous snapshot of the vessel’s activity, classification accuracy could suffer if the vessel engaged in multiple fishing and non-fishing activities within the preceding hour. The behavioral signature of the vessel over the previous hour would be a combination of both fishing and non-fishing activities and not clearly one or the other. A shorter reporting window would increase the chance that activity in the previous time window was all of one type or the other. The results also indicated that differences in classification ability across species target groups could be explained by differences in spatial targeting. Including a spatial covariate in the classification model or using separate classification models on subsets of data from different spatial regions could improve model performance. Lastly, the classification model

used was trained on the observed subset of VMS points. Current observer levels account for observation of roughly 2% of total VMS entries for the fleet. An increase in the observer coverage would allow for greater classification accuracy as the classification model could be trained on a data set describing greater variability.

A short-coming of the proposed method is the reliance on a regression based RF model rather than a classification based RF model. Though acceptable to use for the current binary classification system, regression as a general rule is not appropriate for classification due to the problem of masking intermediate classes when attempting to use regression for more than 2 classes (Hastie et al. 2009). Additionally, using a regression approach limits the RF model’s ability to handle data with unbalanced classes. Altering the relative cost of misclassifying specific classes by changing the proportions of each class in the training data is a common approach to addressing this problem (Berk 2008). The built-in options for changing the proportion of each class in the training data are unavailable for regression in the randomForest package. Applying the proposed approach using a classification-based model would be more flexible as it would be better able to handle unbalanced data and could be used with multi-class problems.

The analysis of the bivariate spatial correlation between the VMS and OBS distributions of catch and CPUE indicated that the assumptions made to allocate catch uniformly and define

CPUE as catch divided by fishing points may be valid due to significant correlations for species that comprised greater than 90% of catches within the study period. Though the catch divided by fishing point approach correlates spatially with the hook hour derived CPUE, it is not standardized to account for differences in gear configuration and fishing power across vessels.

Therefore, it is important to consider these CPUE distributions as raw CPUE representing fishing

efficiency and not necessarily reflective of the underlying species distribution. Furthermore, the bivariate analysis revealed differences in the spatial distributions of catch and CPUE for species that comprise a smaller proportion of the total catch. This indicates that for comparatively rarer species the OBS data may not appropriately sample them across spatial and temporal strata.

Linking the CLB data to the VMS data and working with a spatiotemporally complete data set could more appropriately identify fisheries impacts to these species. It is important to note that the CLB data is fisher reported landings data and as such could underreport rare or bycatch species relative to the OBS records. This does not appear to be the case as the proportion of total catch for 77% of species outside of the top 5 species is greater in the CLB data than the OBS records.

An application of these techniques showed that at the Gulf-wide scale the vertical line fishery targeting reef fish appeared to be resilient to a single large perturbation such as the DH oil spill. As referenced in the results, our inability to identify a meaningful negative change in the fishery at the Gulf-wide level for the time period considered was unexpected given a pair of general economic forecasts for the region (McCrea-Strub et al. 2011; Sumaila et al. 2012) that predicted severe economic damages due to the oil spill resulting primarily from decreased catches and marketability of Gulf of Mexico seafood. Additional economic data (NMFS 2015) shows that reef fish revenue and total fisheries related revenue increased following the DH spill.

Though the spill location and closures missed highly targeted and productive fishing grounds in the eastern and western portions of the Gulf of Mexico, the switch to a commercial grouper IFQ and increases to the red snapper quota could also have contributed to the increase in reef fish revenues.

Within the study period, there is evidence to suggest a more specific shift within the fishery occurred in terms of effort. Effort declined contemporary to the spill in the region immediately around the spill site and never fully rebounded. The literature regarding spatial effort dynamics with respect to spatial closures predicts that effort redistribution will occur when a closure impedes access on areas of high effort concentration (Dinmore et al. 2003) which will result in a build-up of effort along the boundary (Murawski et al. 2005; Stelzenmueller et al.

2008) before a return to the area following the lifting of the closure (Rijnsdorp et al. 2001). In this case, effort returned to the closed area but not in the same magnitude as before. This suggests other factors influenced the choice of fishing location. Public perception of and consumer trust in Gulf of Mexico seafood dropped (Upton 2011) and remained low (Graham et al. 2015; Susskind et al. 2016) as a result of media coverage (Greiner et al. 2013) following the

DH oil spill. Media coverage and public sentiment could have influenced the fleet to avoid the area closest to the spill despite extensive seafood sampling indicating that catches from the Gulf were safe to consume (Fitzgerald and Gohlke 2014; Ylitalo et al. 2012). Further study incorporating fisher interviews to determine factors influencing location choice are needed to diagnose this issue. Understanding why effort shifted is important from both a fisheries management and a regional economics perspective. Effort shifts to other regions may be placing additional exploitation on a different complex of species especially in a fishery harvesting a broad array of species such as this one. From a regional economics perspective, communities closer to the impacted region could be targeted by recovery efforts as fishers may be traveling further to avoid the impacted region incurring higher costs. Coastal communities may also process fewer landings resulting in reduced revenues.

This analysis takes a broad view in assessing how the vertical line fishery may have changed over the study period by developing a method for classifying unobserved vertical line

VMS data and accounting for the uncertainty in the classification process. This creates a framework for which uncertainty in the spatial distributions can be propagated through to the creation of time series and other secondary data products. Though accounting for uncertainty did not appear to make much of a difference in the analysis of effort time series, it was important to account for it in two quantities (catch and CPUE by species) that are of interest to managers and assessment scientists. Most importantly, this type of analysis lays the foundation for future work investigating fishermen behavior with respect to their targeted stocks and fleet dynamics in vertical line fisheries in general as well as specifically in the Gulf of Mexico.

Table 2-1. The trip and set level characteristics. Characteristic Median Mean SD

Trip Area (km2) 979.8 2,373.9 4,866.3 Trip Length (days) 3.14 3.70 3.08 Set Length (hours) 0.32 0.48 0.65 Hooks Fished per Set (hooks) 18 32.34 35.08 Note: Trip level characteristics are calculated from all vertical line trips (n = 31 643) within the VMS data set. Trip area is defined as the minimum convex area that contains all VMS points (fishing and non-fishing) for that trip. For reference, the Gulf of Mexico EEZ has an area of ~714 890 km2. The set level characteristics are calculated from all observed vertical line fishing sets (n = 24 069) within the OBS data set.

Table 2-2. Species included in the Gulf of Mexico FMP. Scientific Name Common Name Balistes capriscus Gray Triggerfish * Caulolatilus chrysops Goldface Tilefish Caulolatilus cyanops Blackline Tilefish Caulolatilus intermedius Anchor Tilefish Caulolatilus microps Blueline Tilefish Diplectrum bivittatum Dwarf Sand Perch Diplectrum formosum Sand Perch Epinephelus adscensionis Rock Hind Epinephelus drummondhayi Speckled Hind Epinephelus flavolimbatus Yellowedge Grouper * Epinephelus guttatus Red Hind Epinephelus itajara Goliath Grouper Epinephelus morio Red Grouper * Epinephelus mystacinus Misty Grouper Epinephelus nigritus Warsaw Grouper * Epinephelus niveatus Snowy Grouper * Epinephelus striatus Nassau Grouper Etelis oculatus Queen Snapper Lachnolaimus maximus Hogfish * Lopholatilus chamaeleonticeps Tilefish Lutjanus analis Mutton Snapper * Lutjanus apodus Schoolmaster Snapper Lutjanus buccanella Blackfin Snapper Lutjanus campechanus Red Snapper * Lutjanus cyanopterus Cubera Snapper Lutjanus griseus Mangrove Snapper * Lutjanus jocu Dog Snapper Lutjanus mahogoni Mahogony Snapper Lutjanus synagris Lane Snapper * Lutjanus vivanus Silk Snapper * Mycteroperca bonaci Black Grouper * Mycteroperca interstitialis Yellowmouth Grouper Mycteroperca microlepis Gag Grouper * Mycteroperca phenax Scamp * Mycteroperca venenosa Yellowfin Grouper Ocyurus chrysurus Yellowtail Snapper Pristipomoides aquilonaris Wenchman Rhomboplites aurorubens Vermilion Snapper * Seriola dumerili Greater Amberjack * Seriola fasciata Lesser Amberjack Seriola rivoliana Almaco Jack * Seriola zonata Banded Rudderfish Note: The * indicates species also present in Figure 2-2 and retained for analysis. On average the * species represent ~ 91.5 % of the catch by weight.

Table 2-3. Species used to identify target groups by fishing set in the OBS data. Scientific Name Common Name Target Group Acanthocybium solandri Wahoo Pelagic Balistes capriscus Gray Triggerfish Reef Fish Caranx crysos Blue Runner Reef Fish Caulolatilus microps Blueline Tilefish Reef Fish Coryphaena hippurus Dolphin Pelagic Diplectrum formosum Sand Perch Reef Fish Epinephelus drummondhayi Speckled Hind Grouper Epinephelus flavolimbatus Yellowedge Grouper Grouper Epinephelus morio Red Grouper Grouper Epinephelus niveatus Snowy Grouper Grouper Epinephelus nigritus Warsaw Grouper Grouper Etelis oculatus Queen Snapper Snapper Haemulidae Grunt (Family) Reef Fish Haemulon Grunt (Genus) Reef Fish Haemulon aurolineatum Tomtate Reef Fish Haemulon plumierii Grunt, White Reef Fish Lachnolaimus maximus Hogfish Reef Fish Lutjanus analis Mutton Snapper Snapper Lutjanus campechanus Red Snapper Snapper Lutjanus griseus Mangrove Snapper Snapper Lutjanus synagris Lane Snapper Snapper Lutjanus vivanus Silk Snapper Snapper Mycteroperca bonaci Black Grouper Grouper Mycteroperca microlepis Gag Grouper Grouper Mycteroperca phenax Scamp Grouper Mycteroperca venenosa Yellowfin Grouper Grouper Ocyurus chrysurus Yellowtail Snapper Snapper Pagrus Porgy (Genus) Reef Fish Pagrus pagrus Red Porgy Reef Fish Rachycentron canadum Cobia Pelagic Rhomboplites aurorubens Vermilion Snapper Snapper Sarda sarda Bonito Pelagic Scomber colias Chub Mackerel Pelagic Scomberomorus cavalla King Mackerel Pelagic Scomberomorus maculatus Spanish Mackerel Pelagic Seriola Jack (Genus) Reef Fish Seriola dumerili Greater Amberjack Reef Fish Seriola rivoliana Almaco Jack Reef Fish Seriola zonata Banded Rudderfish Reef Fish Sphyraena barracuda Great Barracuda Reef Fish Thunnus atlanticus Blackfin Tuna Pelagic Fish (Superclass) Other Fish, Miscellanous Bait Other Unknown Fish Other

Table 2-4. Variables included in the RF model sorted in decreasing order of importance as defined by relative % increase in Mean Squared Error. Variable Description FRACTION_DAY (358%)* the time of day represented as a ratio, where 0 is midnight and 1 is 23:59.59. REL_TRIP_TIME (123%)* for entries within the same logbook trip, how much time has passed since the start of the trip, normalized from 0 to 1.

TOTAL_TRIP_TIME (104%)* for entry in the same logbook trip, total trip length in hours

DEPTH (81%)* Depth associated with an entry. Calculated by extracting the depth for that position from the 3 arc second (~90m resolution) NGDC Coastal Relief Model for the Gulf of Mexico.

DEPTH_DIFF (72%)* for entries within the same logbook trip this is the absolute value of the difference in depth between the depth at that entry and the mean depth that fish were caught at on that trip adjusted for catch weight JULIAN_DATE (61%)* the day of the year represented as a ratio, where 0 is Jan 1 and 1 is Dec 31

VS_NET_TONS (60%) vessel weight

LunarPhase (56%)* lunar phase for that date as a decimal where 0 is new moon and 1 is full moon

VS_LENGTH (56%) vessel length VS_HP (53%) vessel horsepower

VS_HOLD_CAPACITY (46%) vessel hold capacity

Speed_from_previous (42%)* for entries within the same logbook trip this is the Distance_from_previous/ Time_from_previous.

SECOND_NN (38%)* for entries within the same logbook trip this is the second closest nearest neighbor in km BEARING_DIFF (38%)* for consecutive entries A,B, and C within the same logbook trip, the bearing along a Great Circle was calculated for a vessel travelling from A to B and then from B to C using the geosphere package in R (Hijmans 2014). The difference in between the two bearings was assigned to entry B. Distance_from_previous (33%)* for entries within the same logbook trip this is the distance traveled since the previous position was recorded. FIRST_NN (30%)* for entries within the same logbook trip this is the closest nearest neighbor in km Time_from_previous (30%)* for entries within the same logbook trip this is the amount of time that passed since the previous position was recorded. Note: The * indicates derived variables.

Table 2-5. Confusion matrix calculated from an out-of-sample evaluation of the OBS data for the proposed classification model. Observed

Fishing Non-Fishing Fishing 1,863 1,234 Predicted Non-Fishing 1,163 9,362

Table 2-6. The number of species per catch and region combination or CPUE and region combination where mean shifts were detected. There are a total of 23 species per combination. Metric AG AC SC EGOM WGOM Catch - Detected in at least 1 time series 13 16 10 17 10 Catch - Detected in 95% of time series 13 13 10 15 10 Catch - Contemporary to DH spill 5 8 6 5 2 CPUE - Detected in at least 1 time series 20 18 16 22 13 CPUE - Detected in 95% of time series 14 12 8 15 9 CPUE - Contemporary to DH spill 6 5 4 2 1

Figure 2-1. The five spatial regions considered in the time series analysis. The black dot denotes the location of the Deepwater Horizon oil spill. The entire gulf (AG) is the union of the 4 regions labeled.

Figure 2-2. The proportion of total catch across time and by region for the 23 most commercially encountered species by the fleet. The colored polygons represent the proportion of total catch by species and the white line represents the time series of total catch of all species.

Figure 2-3. Top panel: The mean total fishing effort of the 201 fishing scenarios from January 2007 through January 2014. Cells shown averaged at least 1 fishing point per month. Note that the color scale has been non-linearly transformed to differentiate areas of low and medium levels of effort. Middle panel: The standard error associated with the mean total fishing effort. Bottom panel: The associated coefficient of variation (CV) of the total fishing effort calculated from the 201 fishing scenarios.

Figure 2-4. The spatial residuals by target species group, Grouper, Snapper, and other Reef Fish, from the classification model denoted as the proportion of entries in a given cell classified correctly.

Figure 2-5. Lee’s L values for catch and CPUE by species. The large colored dot is the Lee’s L point estimate for that species. Green indicates a positive point-to-point correlation significant at the 95% level, red denotes a statistically insignificant result. The blue dots are the Lee’s L values from the 1000 iterations of the bound permutation. The orange bar indicates the 95% quantile of the iterations and the vertical orange bar indicates the median (50% quantile).

Figure 2-6. Example of a time series created from the spatial distribution of fishing effort for each spatial region. The pink polygon represents the 95% quantile around the estimate of total effort allocated to that spatial region. The gray bar represents the period of time when spatial closures due to the DH spill were in effect. The spill occurred at the start of the gray period. The dotted blue line represents the null model that is tested against and the solid blue line represents the best fit model with resulting mean shift. The orange circle is the best fit estimate of the breakpoint location and the orange bar represents the 95% confidence interval around that breakpoint location.

Figure 2-7. This stoplight plot shows the catch and CPUE by species combinations where mean shifts were determined to have occurred. Gray squares indicate that a mean shift was not detected. Colored squares indicate a shift was detected but was not contemporary to the DH spill. Circles indicate shifts contemporary to the spill, they are sized in proportion to how far away the best fit estimate of the breakpoint is to the spill month. Color indicates the nature of the change from the pre-shift to post-shift period.

CHAPTER 3 INDICES OF ABUNDANCE IN THE GULF OF MEXICO REEF FISH COMPLEX: A COMPARATIVE APPROACH USING SPATIAL DATA FROM VESSEL MONITORING SYSTEMS

3.1 Introduction

Abundance indices are an important input for stock assessments. Fisheries-dependent data, such as catch-per-unit-effort (CPUE), are a common source of information for estimating trends in abundance, as they typically represent a more spatiotemporally complete and cost effective sample than fisheries-independent data (Ward 2005).

Despite the availability of fishery dependent data, they may not be reliable as catch rates may not adequately track abundance. Nominal CPUE are widely regarded as disproportionate to abundance (Beverton and Holt 1957; Harley et al. 2001) due to hyperstability - abundance declining faster than CPUE, or hyperdepletion - CPUE declining faster than abundance (Hilborn and Walters 1992). These sources of non-linearity between CPUE and abundance can be introduced through gear effects (saturation and handling time; (Deriso and Parma 1987)), changes in fishing power (Bishop et al. 2004; Ye and Dennis 2009), and interference between vessels (Gillis and Peterman 1998). In addition, discrepancies between the spatial distributions of species abundance and fishing effort can exacerbate the issue if fishers are not representatively sampling the underlying abundance distributions (Clark and Mangel 1979; Paloheimo and Dickie

1964; Rose and Kulka 1999; Rose and Leggett 1991; Swain and Sinclair 1994).

Bias in the relationship between CPUE and inferred abundance due to spatial distributions are typically addressed using one of two approaches: standardization or spatial

 Reprinted with permission from Ducharme-Barth, N.D., Shertzer, K.W., and Ahrens, R.N.M., 2018. Indices of abundance in the Gulf of Mexico reef fish complex: A comparative approach using spatial data from vessel monitoring systems. Fish. Res. 198, 1–13. http://dx.doi.org/10.1016/j.fishres.2017.10.020.

imputation. Catch rates can be standardized using generalized linear models (GLMs) (Maunder and Punt 2004; Nelder and Wedderburn 1972) to separate the abundance trend from other factors. If spatial nominal CPUE data are available, they can be used to infer abundance trends provided they are spatially and/or temporally imputed to account for unfished areas and changes in the distributions of fishing effort (Walters 2003). Abundance indices generated from spatially imputed nominal CPUE data that randomly sample the entire underlying distribution have been shown to track abundance accurately (Yu et al. 2013). However, for both of these approaches, the level of data aggregation is important to consider. Bias in the inferred abundance can occur if the level of data aggregation is too coarse such that fishing effort is no longer randomly sampling abundance within spatiotemporal strata (Campbell 2004; Carruthers et al. 2010). Spatially averaging data on a fine spatial scale is more likely to represent the underlying abundance distribution of non-transient species (Carruthers et al. 2011).

Vessel monitoring systems (VMS) have transformed the analysis of fisheries-dependent spatial information. The high-resolution vessel location data provided by VMS have given fisheries scientists and managers a better understanding of the spatial distribution of effort (Lee et al. 2010; Mills et al. 2007), fisher behavior (Davie and Lordan 2011; Vermard et al. 2010), and the abundance distributions of targeted stocks (Bertrand et al. 2008; Vinther and Eero 2013).

Linking self-reported logbook catch records to VMS data has allowed for the creation of species- specific distributions of CPUE in European trawl fisheries for groundfish (Gerritsen and Lordan

2011; Witt and Godley 2007) and the vertical line fishery targeting reef fish in the Gulf of

Mexico (Ducharme-Barth and Ahrens 2017).

The vertical line fishery in the Gulf of Mexico is a valuable commercial fishery (NMFS

2015; 2016) that targets a diverse complex comprised primarily of snappers, e.g. Lutjanus spp,

and groupers, e.g. Epinephelus spp (Scott-Denton et al. 2011). The four most commercially encountered species (red snapper Lutjanus campechanus, vermilion snapper Rhomboplites aurorubens, red grouper Epinephelus morio, and gag grouper Mycteroperca microlepis) can be characterized by an association with easily identifiable hard bottom structure (Grimes 1978;

Grimes and Huntsman 1980; Lindberg et al. 2006; Moran 1988) and high site fidelity (Coleman et al. 2010; Coleman et al. 2011). The vertical line gear (multiple baited lines dropped vertically from a stationary or slowly drifting vessel) fished in multiple short sets (~20 minutes) allows for high resolution spatial targeting of the hard bottom structure and the targeted fish stocks (Pollack et al. 2013; SAFMC 2009b; Scott-Denton et al. 2011). This combination of targeting behavior and species characteristics predisposes the fishery to the risk of hyperstability, particularly in the absence of spatial information on where catches occur.

Given the unique set of coinciding circumstances between vertical line fisheries and reef fish behavior, it is worthwhile to evaluate if developing abundance indices from higher resolution catch and effort data from VMS gives a more accurate approximation of the underlying abundance trends. Ideally, one would be able to work with data at a spatial resolution where sampling is representative of the underlying abundance (Walters 2003). However, the fishing behavior of the vertical line fleet makes it unlikely that data aggregated at all but the finest scales (e.g. reef or artificial structure) meet this criterion. The current practice for generating abundance indices in this fishery is through the standardization of commercial logbook catch records aggregated to a coarse statistical grid, at best a 1 degree spatial grid, using a two-step delta-GLM (Lo et al. 1992; Stefansson 1996). A delta-GLM is the product of two

GLMs: a logistic model that describes the presence-absence of positive catches and an additional model (with normally distributed error structure in this case) that describes the magnitude of

log(CPUE) for catches greater than 0. This paper evaluates two methods of creating abundance indices as applied in a vertical line fishery for reef fish, and more generally in fisheries able to achieve a high level of spatial targeting of non-transient species.

We conducted analyses to compare abundance indices derived from the same input catch data using two methods: the delta-GLM standardization (status-quo) and spatial averaging of

VMS derived CPUE distributions. The first analysis evaluated the agreement between indices generated from the two methods utilizing as input commercial logbook catch records from a suite of reef fish stocks that make up a large proportion of the catch by the vertical line fleet in the

Gulf of Mexico. Agreement was assessed in two ways: (i) by calculating the correlation between the indices from the two methods, and (ii) by calculating the change in abundance inferred by each method. Instances of poor agreement between the two methods provided motivation for determining which method more accurately tracked abundance.

A simulation analysis was used to assess how well each method captured the true population abundance trend under different effort and abundance scenarios. Corresponding catch and VMS records were simulated and passed as input to the two methods to create abundance indices. The deviations of the indices from the true trend were calculated to determine which method was more accurate under the various scenarios. A principal component analysis (PCA) identified characteristics of scenarios where there were large disparities in the accuracy of the two methods. Previous simulation studies investigated the effects of spatial aggregation, changing distribution of effort, and imputing unfished spatiotemporal strata on indices for pelagic fisheries standardized with GLMs (Campbell 2004; 2015; Carruthers et al. 2011;

Carruthers et al. 2010; Lynch et al. 2012). Other have studies investigated how geostatistical averaging of VMS-informed catch rates compared to a fisheries-independent measure of

abundance in a scallop fishery (Walter et al. 2014a; b). This work represents the first direct comparison of abundance indices derived from delta-GLM standardization and spatial averaging of VMS derived CPUE distributions.

3.2 Material and Methods

This study aimed to address the potential fine-scale spatial targeting problem in conventional CPUE standardization by evaluating the use of VMS data for estimating population trends. Multiple analyses, conduct in R 3.3.2 (R Core Team 2016), were used to compare the delta-GLM and VMS methods. An overview of the fishery and the species included in the study can be found in section 3.2.1 and a description of the two data sources informing each method can be found in section 3.2.2. The first step was to use the same fisheries data to estimate abundance indices using the two methods for every study species. Detail on how abundance indices were constructed for each method can be found in section 3.2.3. The next step was to assess the agreement in species abundance indices estimated using the two methods. This was done using a non-parametric approach described in section 3.2.4. Calculating the agreement between indices constructed using the same catch data, but with different methodologies allowed us to identify if there were noticeable differences between the abundance indices created.

A simulation study was used to evaluate which method was more accurate in estimating abundance under a suite of scenarios governing how effort and abundance were distributed spatially. The base simulation described in section 3.2.5.1 was designed to simulate fine scale targeting in a multi-species fishery on a 1/12th degree spatial grid. Section 3.2.5.2 describes how the base simulation was modified for each scenario. In each scenario, abundance indices for each species were calculated using the two methods along with the deviation from the true simulated population trend (described in section 3.2.5.3). This allowed us to identify how sensitive the accuracy of each method was with respect to changes in broad patterns of effort and abundance.

A multivariate analysis (described in section 3.2.5.4.) was used to identify the effort and abundance characteristics of species-scenario combinations where the two methods predicted diverging abundance trends.

The base simulation made the simplifying assumption that sampling by the fishery did not affect abundance, as this feedback was not necessary in the direct comparison of the ability of the two methods to handle fine-scale spatial data. However, making this assumption ignored the potential effects of in-year sequential depletion occurring at scales smaller than the spatial grid used in the simulation. Hyperstability could occur in fisheries targeting small aggregations or reefs within a cell if vessels move from reef to reef fishing down each in turn. A modification to the base simulation (described in Section 3.2.5.5) was used to explore how sequential depletion at the cell level affected the estimated abundance indices’ ability to capture the true abundance trend.

3.2.1 Study Frame

The study frame for this project was the vertical line reef fish fishery within the Gulf of

Mexico EEZ (Figure 3-1) during 2007‒2013. Vertical line fishing consists of dropping multiple baited hooks on a single line or multiple lines deployed vertically from a stationary or slowly drifting vessel. These lines are predominantly retrieved using mechanical means such as electric or hydraulic reels though they may also be retrieved by hand. Fishing occurs in distinct spatiotemporal sets defined as the period that hooks are being fished from a vessel at that location. Multiple drops of the gear can occur during each fishing set. A change in location or prolonged period with hooks out of the water represents a change to a new fishing set. Species were included in the analysis if they were within the top 25 of catch by weight over the study period (Table 3-1). Two pelagic species in the top 25 were excluded as they were likely targeted using non-vertical line gear.

3.2.2 Data

This study used two data sets: VMS-derived spatial CPUE and commercial logbook self- reported catch records (CLB). VMS use was required for all vessels holding a commercial Gulf of Mexico Reef Fish Permit starting in 2007. Vessel positions are reported every 60 minutes at a resolution of ~0.1 meters. Reported positions were excluded from the analysis if they occurred outside of the study frame, were assumed not to represent fishing activity (<5 km from land), or corresponded to non-vertical line gear. The resulting data set contained 2,769,857 VMS entries spanning the study period (except for July and August 2010; these data were unavailable).

To determine whether the vessel positions corresponded to fishing activity, VMS points were classified as fishing or not fishing using a two-step random forest classification algorithm

(Ducharme-Barth and Ahrens 2017). A unit of effort in the fishery was defined to be a VMS point classified as fishing. Spatial distributions were generated at monthly intervals using the

GPS information associated with each VMS entry. Effort points were aggregated on a 1/12th degree spatial grid (roughly 10 km x 10 km). The species-specific catch in pounds for each trip in the CLB was uniformly distributed to all effort points associated with that trip. Spatial CPUE by species was defined in each grid cell as the total catch weight across all trips divided by the number of effort points across all trips.

A Monte Carlo simulation method was used to propagate classification uncertainty into the spatial distributions by generating 201 CPUE values for each grid cell. The method applied a two-step process that combined variability in the predicted state (fishing or not-fishing) for each

VMS entry due to the random forest model and uncertainty in the predicted state accounting for the classification accuracy of the model. Thus, each of the 201 values represent an alternative fishing scenario that can be used to create an individual abundance index. The number of values,

201, generated for each cell was selected because variability across scenarios had stabilized

when including more than 100 scenarios, and using greater numbers of scenarios became computationally challenging. Ducharme-Barth and Ahrens (2017) provide further detail of the

VMS classification process and Monte Carlo simulation methods.

The second data source was the CLB records that corresponded to the VMS points.

Within the study period, the CLB contained 31,643 unique vertical line fishing trips targeting reef fish. Trips were retained in the analysis if they indicated that a vertical line gear (hand line, hand gear, or hydraulic/electric reel) was used on that trip. A small percentage of retained trips

(2%) indicated that multiple gears were used. Logbook variables considered for CPUE standardization included year, month, area fished, days away, number of crew, season, and region. Season was determined from month (1 – Jan, Feb, March; 2 – April, May, June; 3 – July,

August, September; 4 – October, November, December). The region (Figure 3-1) was assigned based on the reported area or statistical zone. Species CPUE by trip was defined as catch in pounds per hook-hours fished. Hook-hours fished is the product of number of lines fished, hooks fished per line, and total hours fished.

3.2.3 Abundance Indices

3.2.3.1 VMS

Annual abundance indices were created from VMS-derived spatial CPUE distributions for each of the 201 fishing scenarios using a combination of temporal imputation and spatial averaging (Walters 2003). Within a fishing scenario, 82 monthly spatial CPUE distributions were computed to span the time series of seven years (minus two missing months). Cells were identified for temporal imputation if they were empty in a month but fished in another month.

Empty cells were filled with the average value of that cell from the two previous months. If a cell was empty to begin the study period, but was fished in a later month, all months leading up to the first month fished were filled with the value of the first month fished. Following imputation, cell

values were averaged within month to generate a monthly abundance index. For the two missing months of data (July and August 2010), CPUE was imputed as the average of the two adjoining months. The monthly abundance indices were summed within year to create the annual abundance indices. Repeating this process across fishing scenarios resulted in 201 annual abundance indices. This allowed for the calculation of uncertainty as the 95% inter-quantile range around the median for each year in the abundance index. The resulting indices were rescaled to Z scores e.g. mean of zero and standard deviation of one.

3.2.3.2 Delta-GLM (status-quo)

The most practical comparison would be between the VMS-derived abundance index and a corresponding commercial vertical line index used in the SouthEast Data, Assessment, and

Review (SEDAR) process. The SEDAR process provides assessments for stocks in the southeast

United States, including the Gulf of Mexico. Unfortunately, there was not a complete set of indices from the SEDAR process spanning the study period for all species. Additionally, variables used to standardize CPUE tended to vary slightly among different species (Bryan 2013;

Bryan and McCarthy 2015; McCarthy 2011; Saul 2013; Smith et al. 2015; Smith and Goethel

2015). For this study, species-specific indices derived from CLB data were created using a common framework that best approximated the various approaches used in the SEDAR process.

Abundance indices were created from CLB records corresponding to trips that likely encountered the target species. These trips were identified using a logistic regression model of multi-species presence-absence data taken from the CLB records (Stephens and MacCall 2004).

Then a delta-GLM (Lo et al. 1992; Stefansson 1996) was used to standardize the log(CPUE) of the target species. Explanatory variables were selected for inclusion separately in each of the two delta-GLM sub-models according to Akaike information criterion (AIC), with the candidate variables being year, temporal strata (season or month), region, days away, and crew. All

variables were categorical, and days away and crew number were binned (1,2,3,4,5,6,7,8,9,10+ and 1,2,3,4,5+ respectively). At minimum, the two sub-models had to contain a year effect, a temporal effect (season or month), and a region effect. Only one temporal effect could be considered in a sub-model at a time. All effects in the model were assumed to be fixed.

Interactions between spatial and temporal strata were not considered as there were incomplete observations of strata combinations for some of the species considered. Imputing the catch rate of missing strata was not considered since this technique is not commonly used in the SEDAR process. To ensure that bias did not enter the delta-GLM parameter estimates due to the uneven distribution of observations across spatiotemporal strata in the models (Campbell 2004), the observations were reweighted such that each spatiotemporal strata received equal weight in the models (Campbell 2015).

The predictions for both sub-models across a table of all possible spatiotemporal strata

(Walters 2003) were multiplied together and back transformed from log space to give a single expected CPUE in each strata. For models where days away and crew were selected, the modal observation for that variable was used in all predictions across spatiotemporal strata (Campbell

2015). Predictions within year were averaged across temporal strata (season or month) and a weighted average across regions was used to generate the annual abundance index (Campbell

2015). When averaging across regions, the assigned weights were proportional to the areas of the regions. The standard error for the annual abundance index was constructed from the uncertainties associated with the two sub-models according to the method described in Campbell

(2015). Lastly, the indices were rescaled to Z scores.

3.2.4 Abundance Index Agreement

One of the purposes of this study was to assess the agreement between the indices generated from the two methods, VMS (V) and delta-GLM (C). We assess agreement using two

methods: a standard metric of agreement, correlation, and a metric relevant to fishery managers that measures whether the two indices imply the same overall change in abundance.

Given the autocorrelation in time series data, a conventional calculation of correlation and significance would not be appropriate. To account for the auto-correlated nature of the data as well as the uncertainty in each index, we used a non-parametric modification of surrogate data testing to test if the temporal structure of the indices resulted in a meaningful correlation between the two methods. Surrogate data testing is a proof by contradiction technique used in time series analysis to detect non-linearity (Schreiber and Schmitz 2000; Theiler et al. 1992). Surrogate data testing works by calculating a given metric for the original time series and comparing it to a distribution of metrics calculated from many surrogate data sets generated by some null model. If the metric from the original time series falls outside of the distribution of metrics from the surrogate data, then the original time series is different from the null model. In our case, because there is uncertainty around each time series, we compared two distributions to each other rather than a point estimate to a distribution. This modification is outlined in Figure 3-2. For each pair of indices, V and C (Figure 3-2 A), two new indices, v and c, were created (Figure 3-2 B):

푣푡~푁표푟푚푎푙(휇푉,푡, 휎푉,푡 ) (3 − 1)

푐푡~푁표푟푚푎푙(휇퐶,푡, 휎퐶,푡 ) (3 − 2) where 휇푉,푡 and 휇퐶,푡 correspond to the means of V and C at time t, and 휎푉,푡 and 휎퐶,푡 correspond to the standard errors of V and C at time t. The new indices, v and c, account for the uncertainty associated with the abundance indices while maintaining the temporal structure of those indices.

A Pearson’s point-wise correlation can then be calculated between each pair of the indices v, c.

Two surrogate indices, v’ and c’, can be formed by taking v and c and randomly rearranging their order (Figure 3-2 C). A correlation is then calculated between each pair of the indices v’ and c’.

Repeating the process of creating indices v, c, v’, and c’ (Figure 3-2 B, C) 10,000 times resulted in a distribution of correlations where the temporal structure was preserved and a surrogate distribution of correlations where the temporal structure was rearranged (Figure 3-2 D). The mode of the distribution where temporal structure was preserved gives the correlation between the two indices. Values closer to 1 show a positive correlation between indices and values closer to -1 show a negative correlation between indices.

The overlapping coefficient (OVL) is a commonly used metric for assessing the similarity between two distributions (Inman and Bradley 1989; Rom and Hwang 1996) and non- parametric estimates of OVL are robust to strong assumptions on the shape and variance of the distributions (Clemons and Bradley 2000; Stine and Heyse 2001). An OVL of 0 indicates the two distributions are completely dissimilar and an OVL of 1 indicates the two distributions are identical. The OVL, referred to as OVLCorr, between the two distributions indicates the similarity of the correlations between the two indices accounting for the temporal autocorrelation and error associated with each index. In the current case, low OVL values indicate that the distributions of correlation with and without temporal structure are highly dissimilar and that the temporal structure resulted in a meaningful correlation. High OVL values indicate that a random temporal structure was just as likely to achieve the same level of correlation between indices.

We used the same 10,000 simulated indices, v and c, to asses if both indices inferred the same change in stock abundance. Inferred change in stock abundance for each index was calculated as the difference between the mean of the first two years of the index and the mean of the last two years of the index. Each index was already scaled relative to its mean and standard deviation so this allowed for comparisons of the change in inferred stock abundance between indices. For each of the 10 000 indices the inferred change in stock abundance was calculated.

This resulted in two distributions, one for the change in stock abundance inferred by the VMS method and the other for the change inferred by the delta-GLM method. The OVL, referred to as

OVLChange, between these two distributions was calculated. Low values of OVL indicated that the two distributions were dissimilar and that the two methods, VMS and delta-GLM, inferred different changes in stock abundance.

3.2.5 Simulation

3.2.5.1 Base simulation

To further evaluate the two methods, we designed a spatial simulation test to replicate the spatiotemporal dynamics of the underlying species abundance distributions and the vertical line fishery. A simulated fishing fleet was distributed across a multi-species fishery comprised of 15 species. Fishing and species abundance patterns were simulated at an annual scale for 7 years and across a 1/12th degree spatial grid.

The spatial distributions of abundance were simulated to be representative of reef fish species encountered in the Gulf of Mexico (Table 3-2). For each species, the base abundance distributions were smoothed versions of average annual distributions of spatial CPUE from the

VMS data. Each base abundance distribution was rescaled to sum to 3 × 106 so that each species started the simulation with the same abundance. An annual abundance trend was applied to each species using a first order random walk:

푎푖,푠,푡+1 = 0.8 푎푖,푠,푡 + 휖 (3 − 3) where 푎푖,푠,푡 is the abundance of species s in cell i in year t, and 휖 is a normally distributed error term applied to each cell (휖 is defined in more detail in Section 3.2.5.2.). Summing abundance across cells within years gave the true abundance trend for each species.

Fishing trips were simulated to be representative of the characteristics observed in the

CLB and VMS datasets. The total number of trips, 푇표푡푎푙푇푟푖푝푠푡, in any given year t of the simulation was a random draw from the following distribution.

푇표푡푎푙푇푟푖푝푠푡~ 푁표푟푚푎푙(휇 = 4480, 휎 = 740) ( 3 − 4)

Three variables defined each fishing trip f where 푓 ∈ 푇표푡푎푙푇푟푖푝푠푡: the number of VMS points or locations fished on a trip, 푉푀푆푓; the trip length in days, 퐷퐴푌푆푓 ; and the number of crew,

퐶푅퐸푊푓. The parameters used to define the distribution for these variables were estimated from the VMS and CLB data sets.

푉푀푆푓 ~ 푁푒푔푎푡푖푣푒퐵푖푛표푚푖푎푙(휇 = 19.6, 푠푖푧푒 = 1.06) (3 − 5)

퐷퐴푌푆푓 ~ 푃표푖푠푠표푛(휆 = 0.13 푉푀푆푓 + 1.8) (3 − 6)

퐶푅퐸푊푓 ~ 퐿표푔푁표푟푚푎푙(휇 = 0.88, 휎 = 0.4) (3 − 7)

In any trip, if 0 was drawn for any of these variables it was replaced with 1. Additionally,

퐶푅퐸푊푓 was rounded to the nearest integer value. The spatial distribution of effort was simulated by selecting an initial fishing location for each fishing trip, and then allowing additional movements to other cells for the remaining locations in 푉푀푆푓. The initial location or cell for a fishing trip was allocated in accordance with a simple gravity model such that near shore cells with high expected revenues had the greatest chance of being selected.:

푟푖,푡 = ∑ 푝푠,푡푎푖,푠,푡 (3 − 8) 푠=1

푙푓,푡~푀푢푙푡푖푛표푚푖푎푙(푑푖 + 2 푟푖,푡) (3 − 9) where 푙푓,푡 was the initial cell for fishing trip f in year t, 푑푖 was the relative distance from shore in cell i, 푟푖,푡 was the relative expected revenue in cell i in year t, and 푝푠,푡 was the value of species s in year t. The annual value of species was taken as the average annual price per pound reported

in the NOAA Annual Commercial Landing Statistics (NOAA 2017). Movement to adjacent cells within a fishing trip was simulated according to a Queen’s Case random walk with a 60% chance of staying in the same cell at each move. Out of bound cells were either on land or had a depth beyond 600m as either of these represent unlikely fishing locations for vertical line gear.

Each simulated fishing trip recorded the grid cells fished, the region corresponding to the initial fishing location, and the total catch of each species. The catch at each location, 퐶푓,푖,푠, was a function of abundance, 푎푖,푠,푡, and vessel catchability, 푄푓,푖. The vessel catchability was defined by 퐶푅퐸푊푓 and a spatiotemporally correlated normally distributed random error, 휙푖,푡.

푄푓,푖 = 0.2 + 0.05 퐶푅퐸푊푓 + 휙푖,푡 (3 − 10)

퐶푓,푖,푠~ 푁푒푔퐵푖푛표푚푖푎푙(휇 = 푎푖,푠,푡푄푓,푖, 푠푖푧푒 = 0.06 휇 + 0.54)퐵푒푟푛표푢푙푙푖(0.8) (3 − 11)

The parameters used to define 푄푓,푖 and 퐶푓,푖,푠 were selected so that the simulation produced realistic catch rates, representative of what the CLB data showed, given the scale of abundance.

Additionally, we assumed that vessels with greater numbers of crew would be able to achieve higher catch rates because of reduced handling times. The species-specific catch was zero- inflated to account for occasions where no catches were made at that cell despite fishing effort.

The error term 휙푖,푡 was constructed as a first order random walk of Gaussian random fields

(GRF) using the RandomFields package in R (Schlather et al. 2015):

휙푖,푡+1 = 0.8 휙푖,푡 + 퐺푅퐹(휇 = 0, 휎 = 0.025, 푠푐푎푙푒 = 5) (3 − 12)

3.2.5.2 Scenarios

The simulation applied a full factorial design considering three factors, each with two levels, resulting in eight scenarios (Table 3-3). To quantify variability, each scenario was simulated 100 times. The factors considered were species abundance pattern, how effort was distributed, and changes in spatial targeting. For the first factor, species included in the simulated

fishery could have one of two abundance patterns, global or local. In the global case, the 휖 in Eq.

3-3 was the same for each cell. In the local case, 휖 was different for each cell and defined as a first order random walk of GRFs in the same way as 휙푖,푡 but with 휎 = 0.25. This approach simulated a scenario where there were localized patterns in abundance due to regional patterns in oceanographic conditions. For the second factor of the simulation, effort was distributed in one of two ways. In the first case, there were no restrictions on the initial fishing location (푙푓,푡). The second case allocated 푙푓,푡 to the four main spatial regions in proportion to the observed regional effort distribution from the fishery. This represented a scenario where vessels were unwilling to travel very far from their home port. The third factor controlled changes in spatial targeting by manipulating 푟푖,푡 in the gravity model. The first case did not force a change in spatial targeting, and the values of 푟푖,푡 were held constant across years. The second case forced a spatial targeting change midway through the simulation, by manipulating revenues (푝푠,푡) for two of the 15 species. The baseline values for species 7 and 9 were $3.34/pound and $2.65/pound, respectively. However, in this second case, in years 1-3 the value for species 9 was set to

$107/pound and in years 5-7 the value for species 7 was changed to $107/pound. This had the effect of concentrating effort in the SEGOM region over the first three years of the simulation, opening the distribution of effort up in the fourth year, and then driving effort to the WGOM region in the final three years of the simulation. This case demonstrates an instance where the fishery dramatically changed its spatial targeting behavior due to changes in species desirability driven by regulatory or socioeconomic factors.

3.2.5.3 Abundance indices

Species-specific abundance indices were calculated for each simulation using the methods described in Section 2.3, albeit with slight changes accounting for simplifying

assumptions made in the simulation. In the VMS method, spatial distributions of species CPUE were constructed at an annual scale by uniformly allocating 퐶푓,푠 across all cells visited by a specific trip. Temporal imputation followed the method in Section 3.2.3.1, but at an annual time step instead of a monthly time step. Species abundance indices were created by taking the average of each imputed annual CPUE distribution.

The simulation testing approach provided an opportunity to test the effects of spatial strata size and the inclusion of spatial interactions in the status-quo standardization procedure.

Four delta-GLM formulations were used in each simulation to estimate abundance indices: large strata and no interactions (delta-GLM I), large strata with interactions (delta-GLM II), small strata and no interactions (delta-GLM III), and small strata with interactions (delta-GLM IV).

The large strata correspond to the four main regions in the Gulf of Mexico (Figure 3-1), and the small strata to the 10 subdivided regions (Figure 3-1). Formulations with interactions allowed for sub-models that include year and region interactions to be included in the selection of the best model. Each of these formulations modified the same base delta-GLM. The base delta-GLM standardized log(CPUE) as a function of year, region, days away, and crew. CPUE from a given trip was defined at the set level as 퐶푓,푠/ 푉푀푆푓.

Species abundance indices were created following Section 3.2.3.2. Trips from the simulated logbook that were likely to have targeted a given species were identified using the method of (Stephens and MacCall 2004). CPUE from these trips were standardized using the delta-GLMs described in the previous paragraph. Inclusion of interaction terms in the construction of species abundance indices followed the suggestions made in Campbell (2015).

The ability of each method to capture the true trend was assessed in each simulation and for each species by calculating the root-mean-square deviation (RMSD) between the estimated abundance index and the true index. The RMSD between two indices is defined as:

∑푛 (푒푠푡푖푚푎푡푒 − 푡푟푢푒 )2 푅푀푆퐷 = √ 푡=1 푡 푡 (3 − 13) 푛

All indices, both true and estimated, were scaled relative to their means and standard deviations, making values of RMSD comparable across species and scenarios.

3.2.5.4 Multivariate analysis

We used a principal component analysis (PCA) to identify the characteristics of scenarios of particular concern where the two methods estimated diverging trends in abundance. PCA is a multivariate technique that clusters observations in ordination space (McGarigal et al. 2000), and gives meaning to where observations are positioned relative to each other based on the principal component axes and the included variables. Principal component axes are orthogonal compositions of the included variables, with each axis explaining some proportion of the total variability in the observations. When plotted, observations and variables with positive values for a given principal component indicate positive correlation with that axis, and conversely negative values for an axis indicate negative correlation. Nine variables (all scaled relative to their mean and standard deviation) characterizing the simulations (Table 3-4) were used in the PCA. The first two principal components, respectively explaining 37.91% and 15.39% of the total variability, were retained for this analysis.

3.2.5.5 Sequential depletion simulation

We made three modifications to scenario 6 (Table 3-3) of the base simulation to explore the potential effects of in-year sequential depletion on the method’s ability to estimate the true abundance trend. We chose the effort and abundance patterns of scenario 6 as our baseline since

it provided a realistic approximation of the fishery without drastic changes in spatial targeting.

The three modifications were 1) within cell abundance ( 푎푖,푠,푡) was distributed across reefs, 2) within cell effort was distributed across reefs, and 3) catches were subtracted from abundance at that reef within year. The number of fishable reefs in cell i was defined as a random draw from a

Poisson distribution.

푅푒푒푓푠푖 ~ 푃표푖푠푠표푛(휆 = 7) (3 − 14)

If the value 0 was drawn for any cell, it was replaced with 1. In the base simulation, fished cells were visited approximately 4-5 times a year. We simulated the number of reefs per cell with 휆 =

7 to ensure the likelihood of sequential depletion occurring at the cell level. Cell abundance at the start of a year was randomly allocated across reefs associated with that cell. Effort characteristics and cells fished within each trip were simulated in the same way as in the base simulation. For each cell fished on a trip, a reef within that cell was then randomly selected using a multinomial distribution. The probability of selecting a particular reef within a cell was equal to the proportion of total cell abundance at that reef. Catch was then defined at the reef level according to Eq. 10 and Eq. 11, and then subtracted from the available abundance at that reef in that year. If the catch value generated by Eq. 11 was greater than the available abundance at that particular reef, the catch was set equal to the available abundance. Abundance indices were then calculated in the same way as described in Section 3.2.5.3 for the VMS and delta-GLM I methods. When calculating the RMSD, the true abundance was taken as the mean of the starting and ending abundances for each year.

3.3 Results

Using the same catch records, abundance indices (Figure 3-3) were estimated for each species listed in Table 3-2 using both the VMS and delta-GLM methods. Those that showed the

strongest degree of positive correlation and lowest OVLCorr (Table 3-5) included two species that were subject to high levels of directed targeting across a wide expanse of available fishing grounds, red snapper and gag grouper, as well as two species that are caught in association with them, gray triggerfish and black grouper, respectively. In general, most species showed some level of positive correlation, with both approaches revealing similar trends, though values of

OVLCorr were notably large. The greater the combined uncertainty between the two approaches, the higher the OVLCorr in the relationship even if the mean trajectories appeared to correlate visually, e.g., yellowtail snapper, hogfish, and mutton snapper. In these three cases, the delta-

GLM I indices all showed greater uncertainty than the VMS. All three of these species have relatively restricted spatial distributions of catch in an area of the Gulf of Mexico (SEGOM) that is subject to lower levels of fishing effort relative to the other regions. A delta-GLM approach attempting to standardize abundance at the Gulf-wide scale, like that currently used, could estimate higher levels of uncertainty due to fewer observations in spatial strata outside of the geographic core of the species catch distributions.

Two species were of particular concern, red porgy and mangrove snapper, as the two methods appeared to estimate inverse trends. This was corroborated by looking at the overall change in stock abundance inferred by each method for these two species as the OVLChange was zero for both. For both of these species the VMS method indicated an overall increase in stock abundance and the delta-GLM indicated an overall decrease. Additionally, there were 10 other species where the OVLChange indicated meaningful differences (OVLChange < 0.05) and/or inferred different patterns of stock abundance. Clearly, these conflicting results were driven by differences in how the data were standardized or how spatial information was handled. However,

without knowing the true trend, it was impossible to determine which method provided more accurate estimation. This issue demonstrated the need for our simulation study.

The simulation generated 100 sets of catch and effort data across eight scenarios. Using each simulated data set, five abundance indices (VMS and delta-GLMs I-IV) were created for each species within each scenario. Of the 15 species included in the simulation, the results for five of them are shown as representative of the diversity of patterns exhibited across all species.

Species 1-2 and 7-8 were characterized by broad spatial distributions, while species 9 had a very restricted spatial distribution. Additionally, species 7 and 9 were used in the target switching scenarios with effort switching on or off (respectively).

A clear pattern emerged in the simulated abundance indices (Figure 3-4). The VMS indices (dark blue) were consistently able to track the true abundance (white) for each species, across scenarios. Of the three factors manipulated to create the scenarios, abundance pattern and spatial targeting shifts both negatively affected performance of the simulated delta-GLM I indices (light red). As expected, changing the abundance pattern from global (scenarios 1-4) to local (scenarios 5-8) had a negative effect on the delta-GLM I performance, since that particular formulation was unable to account for asymmetrical changes in abundance at scales smaller than the considered strata. Introducing a shift in spatial targeting had a subtler effect on the delta-

GLM I indices. These indices appeared to be biased high for species in time periods when they were directly or indirectly targeted with greater effort. This effect is most clearly shown in scenarios 3 and 4 across all species. Effort targeting increased in the first three years for species

9, in year 4 for species 1 and 2, and in the last 3 years for species 7 and 8. Manipulating the effort distribution by restricting it within certain regions did not appear to alter the ability of either method to distinguish the true trend.

Accounting for additional delta-GLM formulations offered improvement but did not change the overall pattern that VMS indices more closely approximated the true trend (Figure 3-

5). As expected, the formulations using the smaller spatial strata provided an improvement in the delta-GLM indices. Allowing for models with spatial-temporal interaction terms to be included in the model selection process had mixed results. In most cases, including interactions resulted in a best model that either improved or did not meaningfully change the fit, even if inclusion of interaction terms were unwarranted (global abundance scenarios). However, there were cases where the unwarranted inclusion of interaction terms resulted in a diminished ability to estimate the true trend. In scenarios (Figure 3-4, scenarios 3-4 for species 9) where the species occupied a restricted spatial range, a spatial shift in targeting occurred, and small spatial strata were used in the delta-GLM; the AIC indicated a mis-specified model as the best performer, which resulted in poor estimation of the true trend.

In addition to evaluation of methods, the simulation study was also able to replicate the prediction of inverse trends first observed in the actual data (Figure 3-4, Species 8). A multivariate visualization (Figure 3-6) showed the particular abundance and effort characteristics associated with this observation. An abundance decline and range contraction occurred simultaneously with a shift in spatial targeting. This resulted in a case where simulated fishing effort became increasingly able to target “hot spots” of abundance even as the stock decreased in range and total abundance. The increased correlation between effort and abundance shown by the increasing trend in Lee’s L supported this. This dynamic was likely what proved problematic in the delta-GLM approaches, as effort was sampling non-randomly within the spatial strata considered, and thus introducing upward-biased catches into the analysis.

Accounting for in-year sequential depletion did not appear to make a meaningful difference in the method’s ability to estimate the true population trend. In-year decreases in abundance averaged -49.85 % (std. dev. = 5.94) across all 15 species and 100 sets of data.

Comparing the RMSD of the two methods (VMS and delta-GLM I) from scenario 6 to those from the depletion scenario (Figure 3-7) did not indicate deteriorations in either method, nor any change in their relative performances.

3.4 Discussion

This paper shows that in fisheries where non-transient species are easily targeted at fine spatial scales, spatial averaging of high resolution CPUE data provides a robust estimate of abundance trends. Even in simulated cases where there were pronounced shifts in both the spatial distributions of effort and abundance, the VMS indices could more closely track the true abundance pattern relative to the status-quo delta-GLM method. This may allow VMS indices to serve as a bridge across significant perturbing events that may alter the spatial targeting pattern of the fishery provided catchability has remained relatively constant during the transition.

Additionally, the pairing of high-resolution spatial data with catch rate information can also lead to the creation of region-specific indices of abundance, which can be used as input in spatial stock assessments (Booth 2000) and be an important layer (Babcock et al. 2005; St Martin and

Hall-Arber 2008) in the marine spatial planning process (Gilliland and Laffoley 2008).

Inferences on species trends targeted in the vertical line fishery for reef fish in the Gulf of

Mexico may be limited due to the unquantified impacts of changing management practices. The emergence of inverse trends in both the actual and simulated data indicates that a spatial shift may have occurred at either the species or fleet level and that the VMS index may more accurately reflect abundance. However, either method would be susceptible to bias if the implementation of an individual fishing quota system (IFQ) on the grouper-tilefish sector of the

fishery in 2010 (GMFMC 2008) resulted in a sudden shift in catchability due to quota consolidation among more efficient vessels (Yandle and Dewees 2008) or increased rates of discarding so that landings data became uncorrelated with abundance (Turner 1997). This issue could partially be addressed by crafting abundance indices from a reference fleet of vessels, with assumed constant efficiency, which fished before and after the implementation of the IFQ system. Improving knowledge of discarding behavior through mandatory reporting or increased observer coverage could also explain changes in catchability. In addition to the potential IFQ influences on catchability, the multi-species nature of the reef fish fishery in the Gulf of Mexico could also affect catchability as a result of substructure within the fleet. For example, there exist several sub-fleets within the fishery, including those targeting shallow-water grouper, red snapper, and deep-water species (Scott-Denton et al. 2011). Though all targeted species are susceptible to capture by vertical line gear, subtle differences in gear configuration among sub- fleets could result in differential species-specific catchabilities. If differences in catchabilities are large and sub-fleet distribution is non-random, spatial biases in catch rate could be introduced. A good understanding of vessel membership among sub-fleets would be critical to addressing this potential source of bias as abundance indices could be derived from the spatial CPUE distribution corresponding to each sub-fleet and then averaged together.

Though not explicitly accounted for, the VMS indices were robust to the simulated sources of variability in catchability in the form of trip-level uncertainty and regional trends.

This is likely a function of how the nominal spatial CPUE distributions used for the creation of those indices were defined. In defining spatial CPUE across all trips at the grid cell level, individual trip or vessel effects were averaged out provided there were a large number of unique samples within that cell. A limited number of trips in a given cell could reintroduce a bias in

catch rates due to trip or vessel effects. Imputing values for cells with limited numbers of trips using regression could diminish this source of bias in the spatial averaging process used to create the abundance indices.

Targeting species at spatial scales finer than what is modeled has the potential to introduce hyperstability due to sequential-depletion. The simulation used to explore the effects of sequential depletion was not exhaustive and it is possible that hyperstability occurred at the grid cell level, but was masked due to the variability in abundance across cells and/or across years.

Future work is needed to further examine the issue of sequential depletion and how aggregation scale affects our ability to observe fine scale processes. The high-resolution nature of VMS data makes it uniquely positioned to address this issue as it allows for aggregation at the same spatial scale that targeting is occurring.

Abundance indices derived from using the delta-GLM method were shown to be just as effective provided that the model was correctly specified to match the scale and dynamics of the underlying population. Improperly specifying the delta-GLM through the inclusion of unwarranted interaction terms or the use of inappropriately sized spatial strata led to decreased predictive ability. Earlier studies showed that AIC may select an overly complex model as best from a pool of candidate models (Carruthers et al. 2010; Kadane and Lazar 2004). This result arose in the simulation in some cases as interaction models were incorrectly selected when there was in fact only a global trend in abundance. In a worst case scenario, specifying a model with inappropriately large strata resulted in an inverse trend being predicted by the delta-GLM.

Further simulation of that scenario with smaller strata did improve the mean RMSD, though it still did not achieve the accuracy of the VMS-derived approach.

In scenarios where the two methods appeared to be equally effective in tracking the true abundance trend, determined by their overlapping RMSD distributions, there still existed visual differences in predicted trend. Particularly in scenarios where a spatial shift in targeting occurred, slight anomalies were introduced in species trends using the delta-GLM method. This difference between the two approaches could be meaningful in a stock assessment, particularly if it causes the abundance trend to conflict with other data sources. Issues with conflicting data are generally dealt with by either dropping the offending data source or reweighting it in the model

(Maunder and Piner 2017). Given the importance placed on maintaining a fit to the abundance trend during the data weighting process (Francis 2011; Francis 2017), changing the data weighting to better fit the anomalous time series could have a large impact on the assessment output (Maunder et al. 2017; Punt 2015).

One of the advantages of the VMS approach is comparative simplicity. The only major decision required is specifying the imputation rule for filling in unfished areas. Though not an overly complicated model structure, a delta-GLM requires a relatively large amount of expert knowledge of the fishery to correctly specify the sub-models. Some of the decisions required include choice of variables used for standardizing CPUE, the number and size of spatial strata, whether to include interaction terms, imputation method for unfished strata combinations, model selection criteria, model error structure, and model effects structure. Additionally, a precursor to the application of a delta-GLM model is to identify trips targeting the focal species using a method such as that of Stephens and MacCall (2004). Currently, there is no general guidance regarding how changing the selected trips affects the estimated abundance index or associated uncertainty. Averaging across a spatial catch rate distribution comprising all available catch records avoids this potential added source of uncertainty.

An extension of the delta-GLM, the spatiotemporal delta-generalized linear mixed model

(delta-GLMM) is growing in popularity, though it is limited to regions where commercial logbooks include high resolution spatial data at the individual fishing set or tow level (Thorson and Barnett 2017; Thorson et al. 2015). These models have shown the ability to accurately track abundance trends in multi-species fisheries where vessel targeting behaviors occur at multiple spatial scales (Thorson et al. 2016), provided the estimation model is correctly specified. Until the data requirements for this approach are met through observer coverage or electronic logbooks, creating indices from VMS-derived spatial CPUE data appears to be a suitable stepping stone from more commonly used delta-GLM approaches. Alternatively, the VMS- derived spatial CPUE could be used as input for the spatiotemporal delta-GLMM models.

This analysis demonstrates the utility of using high resolution CPUE distributions derived from VMS data to generate indices of abundance. The VMS method is comparatively simpler than delta-GLMs, and robust to changes in species and effort distributions. This approach shows much potential to incorporate high resolution spatial information about the fishery, and ultimately to improve stock assessments of non-transient species such as reef fishes in the Gulf of Mexico.

Table 3-1. Species occurring in the top 25 of catch by the vertical line fleet. The * indicates species in the Gulf of Mexico Reef Fish Management Plan, and the # indicates species removed from the analysis. Scientific Name Common Name Balistes capriscus Gray Triggerfish * Calamus leucosteus Whitebone Porgy Calamus nodosus Knobbed Porgy Caranx crysos Blue Runner Caranx ruber Bar Jack Epinephelus flavolimbatus Yellowedge Grouper * Epinephelus morio Red Grouper * Epinephelus nigritus Warsaw Grouper * Epinephelus niveatus Snowy Grouper * Lachnolaimus maximus Hogfish * Lutjanus analis Mutton Snapper * Lutjanus campechanus Red Snapper * Lutjanus griseus Mangrove Snapper * Lutjanus synagris Lane Snapper * Lutjanus vivanus Silk Snapper * Mycteroperca bonaci Black Grouper * Mycteroperca microlepis Gag Grouper * Mycteroperca phenax Scamp * Ocyurus chrysurus Yellowtail Snapper* Pagrus pagrus Red Porgy Rachycentron canadum Cobia # Rhomboplites aurorubens Vermilion Snapper * Scomberomorus cavalla King Mackerel # Seriola dumerili Greater Amberjack * Seriola rivoliana Almaco Jack *

Table 3-2. The 15 species used to inform the simulation and their approximate geographic distribution denoted as proportion of abundance in each region. Number Species WGOM NGOM NEGOM SEGOM 1 Red Grouper 0.00 0.03 0.52 0.45 2 Gag Grouper 0.07 0.12 0.60 0.21 3 Black Grouper 0.20 0.07 0.31 0.43 4 Warsaw Grouper 0.85 0.06 0.05 0.04 5 Snowy Grouper 0.26 0.21 0.18 0.35 6 Yellowedge Grouper 0.58 0.10 0.11 0.21 7 Red Snapper 0.83 0.14 0.02 0.01 8 Vermilion Snapper 0.65 0.29 0.05 0.01 9 Yellowtail Snapper 0.02 0.00 0.00 0.98 10 Mangrove Snapper 0.35 0.12 0.26 0.27 11 Mutton Snapper 0.00 0.01 0.00 0.97 12 Red Porgy 0.15 0.48 0.28 0.09 13 Gray Triggerfish 0.54 0.27 0.10 0.09 14 Whitebone Porgy 0.06 0.75 0.17 0.03 15 Hogfish 0.00 0.03 0.82 0.15

Table 3-3. Description of each scenario used in the simulation. Scenario Abundance Pattern Effort Distribution Targeting Shift 1 Global Restricted No 2 Global Unrestricted No 3 Global Restricted Yes 4 Global Unrestricted Yes 5 Local Restricted No 6 Local Unrestricted No 7 Local Restricted Yes 8 Local Unrestricted Yes

Table 3-4. Description of variables used in PCA Variable Description 1 - Species abundance trend The slope of the true trend in abundance. 2 - Species hotspot trend The slope of the trend in the annual number of cells that had abundance values greater than or equal to 2/3 of the maximum abundance value. 3 - Correlation with true trend The time series correlation between the estimated trend and the true trend as described in section 2.4. 4 - Pseudo-significance of correlation The pseudo-significance of correlation to the true trend as to the true trend described in section 2.4. 5 - Average annual Lee’s L correlation Lee’s L is a bivariate measure of the spatial correlation between the distributions of effort and between two distributions (Lee 2001). Lee’s L is bounded species abundance between -1 and 1 with values greater than 0 indicating a positive correlation. 6 - Trend in Lee’s L correlation The slope of the trend in the annual Lee’s L correlation between the distributions of effort and between the distributions of effort and species abundance. species abundance 7 - Abundance pattern A binary variable indicating either a global or local abundance pattern. 8 - Targeting shift A binary variable indicating the presence or absence of a spatial targeting shift. 9 – Root-mean-square deviation The RMSD between the estimated and true trend calculated as shown in Eq. 13.

Table 3-5. The metrics of agreement, mean correlation and mean inferred change in stock abundance, and their respective overlapping coefficients (OVLs) between the two estimated indices of abundance for each species arranged in order (highest to lowest) of proportion of fleet-wide catch.

Common Name Correlation OVLCorr ChangeVMS ChangeGLM OVLChange Red Snapper 0.85 0.05 2.23 1.53 0.04 Vermilion Snapper 0.41 0.34 -1.64 -0.30 0.00 Red Grouper 0.51 0.27 2.19 0.31 0.00 Gag Grouper 0.97 0.01 -1.75 -1.86 0.72 Yellowtail Snapper 0.44 0.73 -1.09 0.04 0.53 Greater Amberjack -0.03 0.92 -0.13 -1.30 0.43 Red Porgy -0.55 0.33 1.80 -2.08 0.00 Scamp 0.69 0.17 -1.02 -1.72 0.17 Mangrove Snapper -0.57 0.28 1.67 -1.00 0.00 Black Grouper 0.95 0.09 -1.85 -1.87 0.60 Lane Snapper 0.33 0.67 0.45 -0.60 0.38 Whitebone Porgy -0.14 0.69 -2.04 0.06 0.06 Gray Triggerfish 0.86 0.09 -2.22 -1.96 0.63 Warsaw Grouper 0.67 0.32 2.05 2.02 0.78 Snowy Grouper -0.25 0.75 1.80 -1.55 0.05 Yellowedge Grouper -0.28 0.70 1.84 -1.93 0.03 Almaco Jack 0.45 0.50 1.90 0.50 0.10 Silk Snapper -0.32 0.76 -0.17 0.47 0.70 Bar Jack 0.55 0.59 2.23 1.62 0.23 Hogfish 0.58 0.51 1.78 1.18 0.40 Knobbed Porgy -0.42 0.81 -1.38 1.50 0.20 Blue Runner 0.24 0.81 2.25 0.77 0.62 Mutton Snapper 0.57 0.68 2.30 1.11 0.40

Figure 3-1. The Gulf of Mexico EEZ with the spatial regions considered in the analysis. The colored areas denote the four main regions: western Gulf (WGOM), northern Gulf (NGOM), northeastern Gulf (NEGOM), and southeastern Gulf (SEGOM). The lines indicate the 10 subdivided regions for the smaller spatial strata considered.

Figure 3-2. Diagram explaining how to calculate the correlation between two indices (A). The uncertainty of the initial indices is shown by the shaded regions. For each index, a new index is created by resampling from the uncertainty of the initial index (B). A correlation is calculated between the two new indices and is shown in dark green. For each new index in B, an additional index is formed by rearranging the order (C). A correlation is calculated between the two rearranged indices and is shown in light orange. The process shown in panels B and C is repeated 10 000 times resulting in the two distributions of correlations (D). The time series correlation of the two initial indices is given by the mode of the distribution of correlations with order preserved (dark green). The overlapping coefficient (OVLCorr) is given by the overlap of the two distributions.

Figure 3-3. Indices of abundance with associated uncertainty constructed using the two methods. The dark blue corresponds to the VMS index with the median estimate and the 95% inter-quantile range shown. Light red corresponds to the delta-GLM index with the mean and the 95% confidence intervals shown.

Figure 3-4. Simulated abundance indices for five selected species, where each line represents a different prediction. The white line is the true abundance. Dark blue corresponds to the VMS-derived index and light red corresponds to the estimate from a delta-GLM I index. The scenario number is denoted in the top right corner of each panel.

Figure 3-5. Violin plots showing the RMSD between predicted and true abundance for five selected species. The black line inside each violin signifies the 95% inter-quantile range, the black bar the 50% inter-quantile range, and the white dot the median RMSD. Moving from left to right within each panel the violins correspond to each method: VMS, delta-GLM I, delta-GLM II, delta-GLM III, and delta-GLM IV. The scenario number is denoted in the top right corner of each panel.

Figure 3-6. Principal components biplot for six of the nine variables used in the analysis. The lines represent the different variables, and the colored dots represent each species- method-scenario combination. For the three trend variables, dark blue circles are decreasing, light red circles are increasing, and gray triangles are stationary. For the abundance pattern dark blue signifies global trends and light red signifies local trends. For the targeting pattern dark blue indicates no switch in spatial targeting and light red indicates a switch in spatial targeting. For the remaining variable, dark blue shows a low RMSD and light red shows a high RMSD. The large colored dots highlight scenarios 7 and 8 for species 8.

Figure 3-7. Violin plots showing the RMSD from Scenario 6 for two methods: VMS (dark blue) and delta-GLM I (light red). The pair on the left are without simulated sequential depletion, and the pair on the right (shaded region) are with simulated sequential depletion.

CHAPTER 4 SPATIAL CHARACTERIZATION OF THE COMMERCIAL VERTICAL LINE FISHERY FOR REEF FISH IN THE GULF OF MEXICO

4.1 Introduction

The sustainable management of exploited fish stocks is a complicated and challenging endeavor. Complicating factors include competing stakeholder groups, stock metapopulation structure, multi-species ecosystem interactions, and environmental stochasticity. These factors become compounded with spatial scale as heterogeneity increases across larger landscapes.

Typically, management boundaries line up with geopolitical boundaries that may or may not be representative of the underlying system (Stephenson 1999). Management frameworks like marine spatial planning or ecosystem-based management could help address these challenges to sustainable management. Spatially explicit fisheries management at small spatial scales, executed through marine spatial planning, can counter the commercial fleet’s ability to increasingly target patchy distributions of spatially distinct species assemblages (Wilen 2004).

Additionally, incorporating a spatially explicit ecosystem-based approach can account for interactions between species due to heterogeneity of habitat, patterns in population connectivity, trophic dynamics and environmental drivers (Crowder and Norse 2008). However, a necessary first step towards moving to more sophisticated management frameworks is identifying whether spatially explicit sub-fleets (or métiers) and species assemblages exist.

Identifying métiers and species assemblages boil down to a common problem: grouping observations such that within-group similarity and between-group dissimilarity are maximized.

Métier identification should group vessels or trips based on a combination of species encountered, gear fished, and area fished using input information (technical specifications of the gear/vessel recorded in the logbook or a priori interviews with fishers), output information (catch history from the logbook) or a combination of the two (Marchal 2008). Behavioral information

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from the individual vessel trajectories themselves have also been used to define métiers

(Bastardie et al. 2010; Russo et al. 2011b). For the purposes of spatially explicit management and marine spatial planning, the area fished by each métier should also be tied back to a coastal community or region (Douvere 2008). Multivariate techniques have typically been used for métier identification (Castro et al. 2010; Lewy and Vinther 1994; Pelletier and Ferraris 2000;

Tzanatos et al. 2005).

The presence of regional spatial species dynamics and species assemblages can be identified through a non-parametric analysis of species abundance time series. For instance, if regional spatial dynamics exist, then species abundance time series should exhibit greater similarity within the same region than between regions due to similar forcing. Therefore, when using non-parametric time series models to assess predictability between two indices, predictability should be higher within indices from the same region than between regions.

Empirical dynamic modeling (EDM) is a non-parametric, data driven approach for analyzing non-linear time series data (Sugihara 1994; Sugihara and May 1990). EDM methods can be used to assess the predictability between time series and are based on reconstructing the state space or attractor manifold that generated a series of observations. The attractor manifold can be reconstructed from the time series of each variable making up that particular dynamical system

(Packard et al. 1980). Unfortunately, in fisheries and other ecological systems, the variables making up the dynamical system are often unknown or impossible to measure. However, a topologically equivalent approximation of the true attractor manifold (shadow attractor) can be reconstructed from lags of a single variable belonging to the dynamical system (Takens 1981).

By reconstructing the attractor manifold that generated a time series of observations, EDM methods can be used to identify assemblages of dynamically equivalent species (Liu et al. 2012;

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Liu et al. 2014). More specifically, Convergent Cross Mapping (CCM) is an EDM method that estimates the ability of a time series X to cross predict another time series Y (Sugihara et al.

2012). If X is a good predictor of Y then it means that information from Y has left an imprint on X and that there is a connection between the two time series due to a shared forcing mechanism or causal relationship. Additionally, applying CCM between many pairs of species time series can identify assemblages of species with linked dynamics that all share similar forcing mechanisms

(fishing pressure or environmental drivers) or trophodynamics (Liu et al. 2012). These dynamically equivalent assemblages can be used to identify potential indicator species, as well as metapopulation structure if dynamics differ across spatial regions.

The Gulf of Mexico (GoM) is a large dynamic system, ~715,000 km2 within the US exclusive economic zone (EEZ), with multiple distinct habitat regions and a wide diversity of commercially encountered species. Coarsely, the eastern GoM is characterized by a broad, shallow continental shelf and the western GoM is characterized by deeper hard bottom habitat.

Commercially targeted communities are composed primarily of snappers (i.e. Lutjanus spp.) and groupers (i.e. Epinephelus spp.), though over 180 taxa have been observed as caught by the fleet

(Scott-Denton et al. 2011). There is evidence that vessels that fish different gears (bottom longline vs. vertical line) target different depths and regions in the GoM, resulting in spatially heterogeneous catch assemblages (Ducharme-Barth and Ahrens 2017; Scott-Denton et al. 2011).

Management and assessment of reef fish in the Gulf of Mexico is currently done in a single species, spatially indiscriminant manner. These regulations and single-species assessments make the implicit, simplifying assumption that a spatially homogenous fishery exists and targets species that are uniformly distributed within the GoM (i.e. exhibit the same dynamics across the

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entire system). Due to spatially distinct métier-species interactions it may not be valid to assume that regulations and regulatory changes have the same impact across the whole region.

Given the apparent diversity of the GoM, spatially indiscriminate management may not be appropriate and there has been growing pressure to assess and manage these stocks in a spatially explicit manner and/or to account for potential multispecies interactions. Before moving management towards either of these approaches there is a need to 1) characterize the spatial distributions of métiers within the vertical line fleet, 2) determine if spatial differences in species dynamics exist for reef fish species, and identify if assemblages of dynamically linked species exist within different spatial regions in the Gulf of Mexico. In this paper, we help provide a foundation for this move in a two-part analysis of the commercial vertical line fishery for reef fish in the GoM by analyzing the spatial structure of both the fleet and exploited stocks. In the first part of the analysis, we identified métiers, and the spatial regions that they operate in, within the vertical line fleet using a multivariate clustering analysis of commercial logbook (CLB) catch records and vessel locations from vessel monitoring systems (VMS) data. The second portion of the analysis used CCM to identify spatial differences in species dynamics for reef fish species and characterize spatially explicit assemblages of dynamically linked species. Previous species assemblage work targeting reef fish within the region identified community assemblages in the

GoM based off of fisheries dependent and fisheries independent catch records (Farmer et al.

2016) and co-occurrence from fisheries observer data (Pulver et al. 2016). Additional work focusing on a similar fishery and species group in the adjacent US south Atlantic identified differences across regions and years based off of CLB catch records (Shertzer and Williams

2008; Shertzer et al. 2009). This work represents the first holistic characterization of the commercial vertical line fishery for reef fish in the GoM and the first spatially-explicit

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characterization of reef fish species in the GoM based on the similarity of their temporal dynamics.

4.2 Methods

4.2.1 Study Frame

This research focused on the commercial vertical line fishery for all trips targeting reef fish in the GoM within the US EEZ (Figure 4-1) during the time period from 2007 to 2013. Trips were determined to have targeted reef fish if they reported having landed at least one species managed as a part of the GoM Reef Fish Fishery Management Plan (Table 4-1) within their CLB catch records. This corresponded to 31,643 vertical line fishing trips made by 888 unique vessels within the study frame. Vertical line gear is defined as fishing multiple baited hooks on lines deployed vertically from a stationary or slowly drifting vessel. These lines are most commonly retrieved using mechanical means (electric or hydraulic reels) though some vessels still retrieve lines using hand reels. This fleet is capable of achieving high resolution spatial targeting of the underlying habitat structure and associated species through multiple short, spatially distinct fishing sets (Pollack et al. 2013; Scott-Denton et al. 2011). As a part of this analysis, we included

23 reef fish species that made up the greatest proportion of the catch by weight during the study period (Table 4-2).

4.2.2 Data

In order to identify spatially distinct métiers and dynamically linked species assemblages, we used two data sets: CLB catch records corresponding to vessels within the study frame and

VMS-derived spatial catch-per-unit-of-effort (CPUE). Beginning in 2007, VMS was required for all vessels holding a commercial GoM Reef Fish Permit. Location data for each vessel was recorded at approximately 1-hour intervals at a spatial resolution of ~0.1 m. Since vessels were required to report their locations even when they were not engaged in fishing activity, we

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excluded VMS points that were outside of the study frame or were within 5 km of shore. This resulted in 2,769,857 vessel locations within the study period (excluding July and August 2010; these data were unavailable).

In order to create VMS-derived spatial abundance time series for the reef fish species within the study frame, catch values from the CLB had to be associated with VMS points corresponding to fishing activity to generate distributions of spatial CPUE. A two-part random forest classification algorithm was used to identify VMS points that corresponded to fishing activity (Ducharme-Barth and Ahrens 2017). Species-specific distributions of spatial CPUE were built on a 1/12th degree spatial grid at monthly time steps (82 monthly distributions; January

2007 – December 2013 minus the two missing months) where the CPUE in each grid cell was defined as the total catch weight across trips divided by the total effort across trips. Within each cell, effort was defined as the number of VMS points corresponding to fishing activity. Species- specific catch was defined in each cell as the total catch across all trips that took place within that month. The spatial allocation of catch occurred at the trip level. For every trip in the CLB, the species-specific total catch by weight for that trip was uniformly allocated to all VMS points associated with that trip that corresponded to fishing activity. The two-part classification algorithm used is capable of generating uncertainty in the spatial distributions of CPUE. For simplicity, the average distribution of spatial CPUE was used to create VMS-derived spatial abundance time series. Additional detail on the VMS classification process can be found in

Ducharme-Barth and Ahrens (2017).

VMS-derived abundance time series for each species were created within each spatial region (Figure 4-1) from the spatial distributions of CPUE (Ducharme-Barth et al. 2018). Within each region, 82 monthly CPUE distributions were created. For all cells within a region, temporal

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imputation was used to fill cells that were empty in one month but fished in another. Empty cells were filled with the average of the preceding two months with one exception. If a cell was empty at the beginning of the study period but fished in a later month, all months leading up to the first month fished were filled with the value from the first month fished. After all empty cells had been imputed, all cells corresponding to the specified region were averaged together to create a monthly abundance time series for that region. In the case of the two missing months (July and

August 2010), their monthly CPUE was taken as a linear interpolation from the two adjoining months (June and September 2010). For more details on the method used to create the monthly spatial abundance time series see Ducharme-Barth et al. (2018). Several species were subject to seasonal closures during the study period, cells within impacted months were assumed to be empty and imputed accordingly (Figure 4-2).

4.2.3 Métier Identification

A two-part multivariate analysis conducted in R 3.3.2 (R Core Team 2016) was used to identify métiers within the vertical line fishery as well as the regions that they operate in. The first part of the analysis used k-means clustering (Hartigan and Wong 1979) to identify species groups that are caught together by individual vessels within a week (vessel week). In total,

29,623 unique vessel weeks were identified and the vast majority of vessel weeks (93%) corresponded to catches coming from a single trip. Within each vessel week, the proportion of the total catch by weight made by a given vessel in a given week for each of the 23 species, as well as “other species”, was calculated. K-means clustering of the vessel weeks based on the proportion of total catch of each species was used to assign each vessel week to a species group.

The optimal number of clusters was determined using a scree plot.

A second k-means clustering analysis was used to group individual vessels based on characteristics summarizing their behavior. Vessels participated in the fishery with differing

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frequencies, and the proportion of total weeks (366 weeks from January 2007 – December 2013) that a vessel participated in the fishery or recorded catches was calculated. For each week that a vessel participated in the fishery, the species group that they caught the most of and the county group (Figure 4-1) where the majority of their catch was landed in was identified. For each vessel, the proportion of weeks (relative to weeks participating in the fishery) where each species group and each county group made up the greatest proportion of the catch was also calculated.

Lastly, the average latitude, longitude, and home range (area of minimum convex polygon containing VMS points) were calculated for each vessel from the VMS data. The average latitude and longitude were calculated using weighted averages of the VMS points. The weight associated with each VMS point corresponded to the likelihood that VMS point corresponded to fishing activity. K-means clustering of the vessel characteristics was used to assign each vessel to a métier. The optimal number of clusters was determined using a scree plot subject to the constraint that each métier had to account for at least 10% of total vessels in the fishery. The approximate region each métier operated in was taken as the minimum convex polygon containing the average latitude and longitudes of all vessels assigned to that métier.

4.2.4 Spatially-Explicit Characterization of Species Dynamics

Relative abundance time series for 23 reef fish species within 6 regions in the Gulf of

Mexico (regions shown in Figure 4-1 and time series shown in Figure 4-3) were used as inputs for an EDM analysis (using the rEDM package (Ye et al. 2017)) to identify if 1) spatial differences in species dynamics existed for reef fish species, and 2) dynamically linked assemblages existed within different spatial regions in the Gulf of Mexico. Additionally, the average proportion abundance of each species in each region was calculated from the VMS data.

For the purpose of the ensuing analysis, species-region combinations where the average proportion of total abundance was less than 5% were ignored since species may not have been

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encountered enough by the fleet in these regions to generate relative abundance time series that accurately reflect the true dynamics of the species within the region.

We used the degree of shared information between two time series (or lack thereof) as a basis to test for the presence of spatial differences in the species dynamics of reef fish species.

Information flow between two time series was defined as the predictability between the two time series using CCM. CCM is a predictive, non-parametric time series modeling approach that uses the reconstructed attractor manifold of one time series, X, to try and predict the dynamics of a second time series, Y. The performance of CCM is measured as the correlation between the predicted values (using X to train the model and predict on Y) and the observed values (Y). Since negative correlations have a meaningless interpretation for CCM analyses, they are truncated to a

0 – 1 scale. If the correlation 푋 → 푌 is high, then the interpretation is that X contains more information from Y, and conversely if the correlation is low, then the interpretation is that X does not contain as much information from Y. Prior to EDM analysis each time series had the seasonal trend removed, was rescaled to a Z-score (mean zero and standard deviation of 1), and first differenced to remove long term trend.

The existence of spatial differences in species dynamics were tested in two ways. Spatial dynamics were determined to exist if the calculated CCM correlations for within region-species time series were greater than between region-species time series. This implied that interactions between species or common external forcing within a region (environmental or fishery related) resulted in a greater degree of information sharing within a region than across regions. For the purposes of this test CCM correlations were only calculated between time series where the species were different. A one-tailed Mann-Whitney U test was used to test if the median CCM correlation within region was greater than between regions. A second test was used to test for

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spatial differences in the dynamics of time series of the same species. Spatial differences in dynamics were identified if the calculated CCM correlations of adjacent regions was greater than non-adjacent regions (i.e. CCM(western GoM gag grouper Mycteroperca microlepis, northern

GoM gag grouper) > CCM(western GoM gag grouper, southern Florida Shelf gag grouper)).

Again, a one-tailed Mann-Whitney U test was used to test if the median CCM correlation between adjacent regions was greater than between non-adjacent regions.

Dynamically linked assemblages were defined using CCM as groups of time series that showed evidence of shared information flow between them. These were identified from a hierarchical clustering based on dissimilarity matrices constructed by calculating the CCM correlation between all species time-series pairs within a region. The pvclust package (Suzuki and Shimodaira 2015) was used for clustering since it has a bootstrapping routine capable of calculating an approximately unbiased p-value (AU) for each cluster in the dendrogram using multiscale bootstrapping. The AU values for each cluster were calculated from 10,000 bootstraps of the data, are bounded between 0 – 100, and are indicative of how strongly the cluster is supported by the data. AU values greater than 95 indicate strong support from the data.

Dynamically linked assemblages were identified at the highest level, meaning that an assemblage with strong support from the data includes all species under the umbrella of an AU value of at least 95 (i.e. in Figure 4-9 – N. Gulf of Mexico there are two distinct assemblages with strong support: gag grouper and red porgy Pagrus pagrus; mangrove snapper Lutjanus griseus, bar jack

Caranx ruber, blue runner Caranx crysos, red snapper Lutjanus campechanus, and warsaw grouper Hyporthodus nigritus).

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4.3 Results

4.3.1 Métier Identification

The k-means cluster analysis of vessel week catch composition identified 6 different species groups that were landed by the fishery (Figure 4-4). Species catch groups tended to be dominated by high proportions of catches from a single species such as red grouper Epinephelus morio, red snapper, yellowtail snapper Ocyurus chrysurus, and vermilion snapper Rhomboplites aurorubens (respectively, groups 1, 2, 4, and 5). These species groupings appear to identify a trade-off between two sets of species: gag grouper – red grouper and red snapper – vermilion snapper. These two sets of species were typically landed together in the same vessel week, but if more of one species was caught less of the other was caught in that vessel week. This trade-off could be due to subtle differences in targeting between species due to their behavior and biology or also as a result of quota availability for each species. Red snapper, red grouper, and gag grouper are all managed under an individual fishing quota (IFQ) system. The clustering analysis also identified a generalist group (group 3) and a specialist group (group 4). The generalist group did not have particularly high proportions of any one particular species though red snapper, vermilion snapper, red grouper, and “other species” were most frequently landed. The specialist group tended to catch very high proportions of yellowtail snapper with occasional catches of mangrove snapper Lutjanus griseus, black grouper Mycteroperca bonaci, and red grouper.

The métier analysis using k-means clustering of vessel specific information characterizing their frequency of fishing, weekly catches of particular species groups, regions where their catch was landed, and locations fished identified 5 unique métiers within the GoM vertical line fishery targeting reef fish (Figure 4-5). These métiers fished primarily in 4 distinct spatial regions within the GoM (Figure 4-6). There were no meaningful differences in the proportion of weeks fished across métiers. There did appear to be slight differences in the

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average vessel home range (larger home ranges for métiers 1 and 2), however the most meaningful differences were due to differences in catch, region catch was landed in, and area fished in. Vessels in métier 1 are characterized as primarily fishing for red grouper and gag grouper in the eastern GoM and landing their catch in the central Florida region. This métier accounts for ~29% of all vessels in the fishery. The next largest métier, 5, accounts for ~26% of vessels and fishes primarily in the northern GoM. This métier primarily catches vermilion snapper and red snapper and lands its catch in the Florida panhandle and Mississippi/Alabama regions. Métier 3 accounts for ~18% of vessels and catches predominantly red grouper in the northeast GoM. Catches from this métier are primarily landed in the Big Bend region of Florida.

The fourth métier is composed of vessels that catch predominantly yellowtail snapper and red grouper in the southeast GoM. This métier is likely a blend of vessels that exclusively target yellowtail snapper, and those that more commonly target red grouper given the overlap in spatial range with métier 1. This métier represents 14% of all vessels and lands its catch in south

Florida. The smallest métier, accounting for only 11% of vessels, operates in the largest region.

Vessels in métier 2 fish primarily for red snapper in the western GoM and land their catch in

Louisiana and the upper Gulf region of Texas.

4.3.2 Characterization of Spatial Stock Dynamics

Reef fish in the GoM showed evidence of spatially explicit dynamics. Time series of reef fish showed greater median shared information within the same region than across regions (0.045

−5 > 0.027; n1 = 908 and n2 = 3348; p-value = 4.306 × 10 ). This test indicated that species time series dynamics were more similar to those of other species within their same region than across regions either due to interactions among species or shared drivers. Additionally, when considering CCM correlations between indices of the same species there was greater median shared information between adjacent regions than non-adjacent regions (0.108 > 0.062; n1 = 80

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−3 and n2 = 86; p-value = 4.315 × 10 ). These spatial differences in dynamics could be due to the spatial imbalance in the distribution of most species (Figure 4-7). Of the 23 reef fish species considered in this analysis only 4 species had at least 5% of the total Gulf-wide abundance in each of the 5 regions. Additionally, 10 species had all of their Gulf-wide abundance in 2 or fewer regions.

Looking specifically at the spatial dynamics of seven widely distributed (at least 5% abundance in 4 of 5 spatial regions) species (Figure 4-8) there is moderate support from the data to define a break between the regions around the northern GoM/northern Florida Shelf. This break in the dynamics roughly corresponds in location to two transitions within the fishery: a habitat transition zone between the deep-water hardbottom communities of the western GoM to the shallower lower-relief communities of the Florida Shelf, and a fishery transition from métiers predominantly targeting snapper species to métiers predominantly targeting shallow-water grouper. Either of these transition zones could be used to explain a break in the dynamics as a result of shared time series forcing. Additionally, biophysical and hydrodynamic modeling of larval dispersal shows those regions to be self-recruiting with limited mixing (Karnauskas et al.

2013) indicating that the break in dynamics could be supported by isolated oceanographic conditions.

Within each region, 2 sub-regions showed strong support for the presence of multiple dynamically linked species assemblages at an AU value of at least 95: the northern GoM, and southern Florida Shelf (Figure 4-9). In the northern GoM two dynamically linked assemblages were identified, including an assemblage headlined by red snapper. This region is fished primarily by vessels belonging to Metier 5; landing red snapper, and vermilion snapper. Given that these two species are not grouped together into the same assemblage; this analysis shows

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that they appear to exhibit differing dynamics. Although red snapper and vermilion snapper can be caught together within the same vessel week, the métier analysis indicated that vessels in

Metier 5 predominantly landed one or the other within a given vessel week. In combination with the EDM analysis, this is an indication of potential differential targeting or fishing pressure between the two species.

Moving to the Florida Shelf, two large assemblages were identified with strong support in the southern Florida Shelf region. The predominant species in each assemblage in terms of fisheries importance are red grouper and gag grouper in the first, and yellowtail snapper and greater amberjack in the second. These predominant species respectively mirror the landed species of the two métiers (1 and 4) operating in the region. Additionally, the two assemblages appear to be comprised of ecologically similar species. The first assemblage is composed of four grouper species (subfamily Epinephelinae) and a snapper (family Lutjanidae) associated with rocky, hard-bottom habitat. The second assemblage appears to be characterized by reef- associated species found at shallower depths and higher in the water column than those in the first assemblage. A notable exception to this is silk snapper Lutjanus vivanus which is typically associated with deeper reefs and hard-bottom habitat, though it does come to shallower waters at night (Allen 1985). These ecological similarities could explain the dynamic assemblages as a result of shared targeting and fishing pressure from the two métiers or environmental forcing.

At the Gulf-wide level, fewer species could be grouped together with shared dynamics.

Gag grouper and black grouper showed strong support for shared dynamics at the Gulf-wide level, as well as mangrove snapper and mutton snapper Lutjanus analis. The lack of multiple, well-defined assemblages at this scale is likely a function of aggregating across spatially imbalanced regions to create the Gulf-wide abundance indices. A well-defined association

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between multiple species at the regional level is lost at the Gulf-wide level as that association becomes contaminated by the dynamics occurring in the other spatial regions. This could also lead to potentially spurious associations at the Gulf-wide level such as the association between mangrove snapper and mutton snapper. Though Farmer et al. (2016) found a slight co-occurence between mangrove snapper and mutton snapper this was based predominantly off of their analysis of the National Marine Fisheries Service (NMFS) bottom longline survey, and their analysis of 5 other data sets did not show an association. In the only region where each species had at least 5% abundance (southern Florida Shelf), the dynamics of these two species are significantly different from each other. Furthermore, though these species both belong to the family Lutjanidae they do not appear have a great deal of biological similarity. Mangrove snapper are a shallow-water coastal species typically associated with near-shore reefs and habitats such as mangroves and estuaries along the Florida coast, as well as offshore reefs and artificial structures in the northern GoM. Mutton snapper usually occupy deeper reef habitat further out on the continental shelf. However, there is intuition for the association between gag grouper and black grouper at this scale. Both are shallow-water grouper species and as a result it is likely that they share similar fishery-related and environmental forcing factors. Additionally, in two of the five regions the data provides at least moderate support for dynamic similarity.

4.4 Discussion

This paper shows that analysis of fishery-dependent catch records augmented with high- resolution spatial information from VMS can be used to identify complex spatial dynamics within a fishery. The purpose of this study was to spatially characterize the commercial vertical line fishery for reef fish in the GoM by 1) identifying the presence of distinct spatial métiers using a multivariate analysis of fisheries-dependent catch records, and to 2) identify spatial differences in the dynamics of targeted reef fish stocks by modeling fisheries-dependent

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abundance indices. Our results show the presence of multiple spatial métiers which can be directly linked to coastal communities. Furthermore, we show that reef fish stocks have spatial abundance dynamics resulting from either regionally specific fishing pressure or environmental conditions. These results have ready practical applications. In the event of a catastrophic impact to the fishery, this spatial métier information can be used to direct disaster relief funds to the most likely impacted communities. Knowledge of the regional spatial structure in stock dynamics could improve assessment performance and management since ignoring the structural uncertainty with respect to spatial stock structure may lead to poor results (Punt and Donovan

2007). At a minimum, this paper extends the work of Ducharme-Barth et al. (2018) to create region and species specific fisheries dependent relative abundance indices which can be used to inform a spatially explicit modeling structure.

There is nothing novel about the idea that fishers and fish do not have spatially homogenous distributions. It has long been suspected that spatial heterogeneities in effort and abundance patterns existed (Paloheimo and Dickie 1964) yet these distributional patterns were often ignored (Booth 2000; Goethel et al. 2011) to simplify the stock assessment modeling, management of the exploited population or both. Using the commercial vertical line fishery for reef fish in the GoM as a model system this study confirms the existence of spatial heterogeneity in the composition of the fishing fleet, but more notably demonstrated the existence of spatial stock structure by finding regional differences in the temporal dynamics of reef fish stocks in addition to spatial patterns in their abundance. Identifying how species and métier interactions change spatially can lend insight into how perturbations to the system can cause spatially differential impacts.

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Red porgy is a broadly distributed, commercially marketed, unassessed and unregulated bycatch species (~100 metric tons/year sector of the fishery with ex-vessel value of

~$275,000/year over the past decade (NOAA 2017)) with a core distribution centered in the northern GoM. Moving away from the core region, the strength of information flow between regions deteriorates indicating that outlying portions of the distribution in the western GoM and

Florida Shelf are not interacting as strongly with the core region or are subject to different external drivers. Additionally, red porgy dynamics are more closely associated with different species (vermilion snapper vs. shallow-water groupers) and encountered by different métiers

(snapper-targeting vs. shallow-water grouper-targeting) in the western and eastern portions, respectively, of its range. Regulatory restrictions on the primary target species for either métier is likely to increase the bycatch interaction with red porgy, though this interaction is unlikely to be spatially homogenous given our improved understanding of the system. Future assessment and management, especially of predominantly bycatch species, should account for this spatial complexity in stock dynamics and fleet distribution where it exists.

Spatially complex stock structure can arise due to variable oceanographic conditions impacting larval settlement (Shulzitski et al. 2018), dispersal of adult individuals (Bowler and

Benton 2005), or spatially differential fishing pressure (Cope and Punt 2011; Denson et al.

2017). Though it was beyond the scope of this analysis to differentiate among the mechanisms responsible for spatial stock structure of reef fish in the GoM, others have repeatedly demonstrated that it is important to appropriately account for spatial stock structure in the management and assessment of exploited fish stocks regardless of its cause. Failing to account for the presence of heterogeneous structure can reduce the overall precision of the assessment model (Berger et al. 2012), and can produce biases in the estimation of management reference

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points (Goethel and Berger 2017). However, this is all predicated on the fact that spatial stock structure can be appropriately identified since improperly assessing a population as multiple stocks can also lead to poor model performance (Butterworth and Geromont 2001).

The existence of spatial stock structure can be identified in many ways. Unit stock boundaries and metapopulation structure have previously been defined with an array of methods including tagging data (Block et al. 2005), morphometrics (DeVries et al. 2002), and various markers (genetic (Cuellar-Pinzon et al. 2016), chemical (Tanner et al. 2016), and biological (van der Lingen et al. 2015)), with an interdisciplinary approach utilizing multiple methods increasing the probability of properly identifying the stock spatial structure (Cadrin and Secor 2009; Hohn

1997). However, the cost and data requirements for many of these analyses makes their application prohibitive in some cases. The EDM analysis described in this study represents a cost-effective method for testing the hypothesis of explicit spatial stock structure based on existing fisheries dependent data. This EDM approach can be applied to identify spatial stock structure preliminary to the methods listed above, especially for those commercially encountered species that lack direct research attention.

Aside from correctly identifying the stock structure, it is also important to consider the scale of the desired management recommendations when defining the spatial structure of the assessment model. Assessments that assume single area stock structure are able to adequately estimate population level depletion even when heterogeneous spatial structure is present (Cope and Punt 2011). These single area assessments break down when trying to estimate depletions at more localized scales. However, the restricted nature of the distributions for many of the GoM reef fish species considered in this analysis, i.e. yellowtail snapper, means that single area assessments are already able to provide localized, regional management recommendations. These

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single area assessments can be further refined by fitting to relative abundance indices created from data corresponding to vessels that belong to the spatial métier operating in the localized region. These indices are able to provide a better match of the effective effort targeting species within a region.

In addition to finding evidence for spatial stock structure in GoM reef fish, this analysis was able to corroborate several preexisting assemblages using EDM to assess the degree of shared information in their temporal dynamics. Originating in 1989 with Reef Fish Amendment

1 and continuing through the implementation of the individual fishing quota in 2010, management of grouper (subfamily Epinephelinae) in the GoM has been split between two categories: shallow-water (SWG) and deep-water groupers (DWG). No rationale was provided for why individual species were grouped into their respective categories though presumably species biology and depth of encounter were taken into account. At the regional level, this analysis provided some support for both of these groupings based on the species temporal dynamics. Within the three Florida Shelf regions where SWG species are most abundant, the four SWG species considered in this analysis (red grouper Epinephelus morio, gag grouper

Mycteroperca microlepis, scamp Mycteroperca phenax, and black grouper Mycteroperca bonaci) typically clustered together. Two of the three DWG species considered in this analysis

(snowy grouper Hyporthodus niveatus, and yellowedge grouper Hyporthodus flavolimbatus) clustered together in the two regions where they are most abundant. This pairing is the same as the one found in two previous studies based on observed fishing set co-occurrence (Pulver et al.

2016) and fisheries-dependent and fisheries-independent catch records (Farmer et al. 2016).

Furthermore, this analysis also supported, at the gulf-wide level, two additional pairings found in

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those studies: yellowtail snapper – hogfish (Lachnolaimus maximus) and almaco jack (Seriola rivoliana) – greater amberjack (Seriola dumerili).

Time series of fisheries data lend themselves well to non-linear, non-parametric time series analysis using EDM since these data are often non-linear (Anderson et al. 2008; Sugihara et al. 2011) and influenced by a variety of environmental drivers (Hsieh et al. 2005a; Liu et al.

2014) and fishing pressure (Glaser et al. 2014a; Klein et al. 2016). In a review of 18 studies applying EDM techniques to fisheries data these analyses focused on quantifying the non- linearity and dynamics of populations, assessing the impact of fishing pressure on temporal dynamics, identifying the causal influence of environmental variables (Harford et al. 2014;

Nakayama et al. 2018), predicting recruitment and its causal drivers (Harford et al. 2017; Pierre et al. 2017), predicting CPUE (Glaser et al. 2011; Glaser et al. 2014b), identifying species with similar dynamics (Liu et al. 2012), and creating species-interaction networks (Frossard et al.

2018). To the best of our knowledge, we are the first to apply EDM techniques, and more specifically CCM, to explicitly test for and characterize stock spatial structure based on their temporal dynamics. An earlier study with similar design (Hsieh et al. 2005b) did test for differences within and between groupings of taxa in the California current ecosystem-based on depth strata, habitat preference, and coarse geographic region. However, they utilized pairwise correlations of time series to assess differences between groups.

As evidenced by the previous paragraph, the application of EDM analyses to fisheries problems has spread rapidly around the globe. However, there still exists a research gap with applying this type of analysis to the GoM region (two previous studies) and reef fish in general

(one previous study). Liu et al. (2017) utilized simplex projection (Sugihara and May 1990) to quantify the dimensionality of red snapper dynamics in the eastern GoM and western GoM

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(using the Mississippi River mouth as the divide). Based on differences within region in dimensionality and predictive ability as well as regional differences in simplex co-predictability

(Liu et al. 2014) with environmental variables, they found evidence for regionally distinct red snapper sub-populations in the GoM. Using our red snapper indices from the western GoM and northern GoM, the divide between these regions corresponds to the one used in their analysis, we did not detect a large difference in dimensionality between the two regions using simplex projection. However, a test for non-linearity using s-maps (Sugihara 1994) found statistically significant time series non-linearity in the western GoM and not in the northern GoM.

Additionally, our CCM analysis showed an asymmetric flow of information between the dynamics of the two regions with the northern GoM having an almost order of magnitude greater influence on the western GoM than vice-versa. Though not a direct comparison due to differences in the time series analyzed, [Liu et al. (2017) considered 4 annual indices within each region spanning a 30-40 year period: 2 recreational fisheries dependent indices and two fisheries independent trawl surveys that typically catch individuals too small to have recruited to the fishery], we were able to find additional evidence supporting regionally distinct sub-populations of red snapper in the GoM.

Though we were able to find statistically significant differences in CCM correlation at both the regional and species level, overall these correlations were quite low. EDM analyses can struggle to identify meaningful signals if the time series are too short (< 20 observations, (Hsieh et al. 2008)) or too noisy, and are most effective in the analysis of longer time series data (Giron-

Nava et al. 2017; Sugihara et al. 2012). Though we considered time series with 84 monthly observations in this analysis, if the dominant signal in the data occurred at an annual interval it may be difficult to identify anything except for strong trends in the data (White 2017). However,

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utilizing multiple spatial replicates has been shown to improve prediction and detection of non- linearity in the analysis of short time series (Clark et al. 2015; Hsieh et al. 2008). Given that the indices considered in this analysis were derived from data with a high spatial resolution, it could be possible to further subdivide the regions into multiple spatial replicates in order to improve signal detection.

One of the shortcomings of this analysis is that vessel participation in a particular métier is based on a vessel’s average behavior over a seven-year period. Though inspection of individual vessel behaviors showed that the majority of vessels maintained small home ranges

(<3% GoM Exclusive Economic Zone) and consistently caught the same species group throughout the duration of the study period, our analysis did not account for the possibility that métier participation is dynamic and that vessels may have switched groups during the study period as a result of a large perturbation to the system such as the change to a grouper IFQ or the

Deepwater Horizon oil spill. Future analysis should account for this potential dynamic by determining métier participation at shorter time intervals and tracking how vessels may switch between groups.

This analysis successfully utilized fisheries dependent catch records along with high resolution spatial data to define the spatial dynamics of the commercial vertical line fleet in the

GoM as well as characterizing the spatial stock structure for a suite of targeted reef fish species.

Using CCM to identify the presence of spatial stock structure can be a cost-effective first step and provide justification for the application of additional methods to define spatial stock structure. This analysis provides a first look at how to spatially partition the vertical line fleet and targeted reef fish stocks for assessment and management in the GoM.

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Table 4-1. Species included in the Gulf of Mexico FMP. Scientific Name Common Name Balistes capriscus Gray Triggerfish Caulolatilus chrysops Goldface Tilefish Caulolatilus cyanops Blackline Tilefish Caulolatilus intermedius Anchor Tilefish Caulolatilus microps Blueline Tilefish Diplectrum bivittatum Dwarf Sand Perch Diplectrum formosum Sand Perch Epinephelus adscensionis Rock Hind Epinephelus drummondhayi Speckled Hind Epinephelus guttatus Red Hind Epinephelus itajara Goliath Grouper Epinephelus morio Red Grouper Epinephelus striatus Nassau Grouper Hyporthodus flavolimbatus Yellowedge Grouper Hyporthodus mystacinus Misty Grouper Hyporthodus nigritus Warsaw Grouper Hyporthodus niveatus Snowy Grouper Etelis oculatus Queen Snapper Lachnolaimus maximus Hogfish Lopholatilus chamaeleonticeps Tilefish Lutjanus analis Mutton Snapper Lutjanus apodus Schoolmaster Snapper Lutjanus buccanella Blackfin Snapper Lutjanus campechanus Red Snapper Lutjanus cyanopterus Cubera Snapper Lutjanus griseus Mangrove Snapper Lutjanus jocu Dog Snapper Lutjanus mahogoni Mahogony Snapper Lutjanus synagris Lane Snapper Lutjanus vivanus Silk Snapper Mycteroperca bonaci Black Grouper Mycteroperca interstitialis Yellowmouth Grouper Mycteroperca microlepis Gag Grouper Mycteroperca phenax Scamp Mycteroperca venenosa Yellowfin Grouper Ocyurus chrysurus Yellowtail Snapper Pristipomoides aquilonaris Wenchman Rhomboplites aurorubens Vermilion Snapper Seriola dumerili Greater Amberjack Seriola fasciata Lesser Amberjack Seriola rivoliana Almaco Jack Seriola zonata Banded Rudderfish

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Table 4-2. Species retained for the analysis. The * indicates species in the Gulf of Mexico Reef Fish Management Plan. Scientific Name Common Name Balistes capriscus Gray Triggerfish * Calamus leucosteus Whitebone Porgy Calamus nodosus Knobbed Porgy Caranx crysos Blue Runner Caranx ruber Bar Jack Epinephelus morio Red Grouper * Hyporthodus flavolimbatus Yellowedge Grouper * Hyporthodus nigritus Warsaw Grouper * Hyporthodus niveatus Snowy Grouper * Lachnolaimus maximus Hogfish * Lutjanus analis Mutton Snapper * Lutjanus campechanus Red Snapper * Lutjanus griseus Mangrove Snapper * Lutjanus synagris Lane Snapper * Lutjanus vivanus Silk Snapper * Mycteroperca bonaci Black Grouper * Mycteroperca microlepis Gag Grouper * Mycteroperca phenax Scamp * Ocyurus chrysurus Yellowtail Snapper* Pagrus pagrus Red Porgy Rhomboplites aurorubens Vermilion Snapper * Seriola dumerili Greater Amberjack * Seriola rivoliana Almaco Jack *

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Figure 4-1. Delineation of the 5 sub regions within the Gulf of Mexico and their relation to the 10 different county groups that catches were landed in. The sub-regions were created from 1-degree hexagonal cells that contained on average at least 0.05% of monthly fishing points from the VMS data. Hexagonal cells that met this criterion were merged to form sub-regions that mirrored the spatial métier distribution. The 200m isobath is shown on the figure for reference.

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Figure 4-2. Colored hexagons indicate months where a temporal closure impacted the fishery for a particular species. Like colors correspond to species in the same taxonomic family or regulatory grouping.

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Figure 4-3. Abundance time series for each of the 23 reef fish species and each of the 6 regions (5 sub-regions and 1 Gulf of Mexico).

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Figure 4-4. Radar plot of the mean proportion of the total catch for each species (from the vessel weeks) for each species group. The species groups clustered principally around 5 species, all other species in the analysis were grouped in the “Other” category. The number of vessel weeks identified in each catch group is listed at the bottom of the figure.

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Figure 4-5. Radar plot of the mean proportion of species group and county group variables defining each métier. The number of vessels in each métier is listed at the bottom of the figure. The species groups in the non-shaded region correspond to those in Figure 4-4 and the county groups in the shaded region correspond to those in Figure 4-1.

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Figure 4-6. This figure denotes the spatial regions typically fished by each métier along with the county group that their catch is predominantly landed in.

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Figure 4-7. The proportion of abundance contained in each region for each species. Empty hexagons indicate species-region combinations with less than 5% abundance.

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Figure 4-8. Co-prediction dendrograms within species and across regions using Convergent Cross Mapping. The number above each split in the dendrogram is the AU value associated with that cluster.

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Figure 4-9. Co-prediction dendrograms within regions and across species using Convergent Cross Mapping. The number above each split in the dendrogram is the AU value associated with that cluster.

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CHAPTER 5 CONCLUSION

This research was successful in leveraging the high-resolution spatial information contained in VMS data to gain a better understanding of the spatiotemporal dynamics in the vertical line fishery for reef fish in the GoM at both the fleet and species level. These developments hinged on creating a routine for classifying vertical line VMS data and incorporating uncertainty in the resultant spatial distributions (Chapter 2). This process allowed for the spatial analysis of vertical line fisheries and provided information on how the fishery may have changed within the study period given two significant perturbing events that occurred in

2010 (Deepwater Horizon and the grouper-tilefish IFQ). Additionally, being able to attribute fishing effort, catch, and CPUE at high spatial resolutions is a useful tool for a range of management tasks. The accurate tracking of spatial effort and catch improves our understanding for how effort shifts across areas and species and greatly facilitates science based spatial management for this fishery. Understanding these pathways can ease the transition from a single stock management framework to ecosystem-based fisheries management (Hilborn 2011).

Furthermore, increasing the capacity for spatial analysis of fishing effort and CPUE can permit the estimation of gradual changes within the fishery (Walters and Bonfil 1999; Walters and

Martell 2004).

The research presented in Chapter 2 took a broad view in examining how the fishery changed within the study period. More significantly however, this research developed a framework for propagating the uncertainty in the spatial distributions through to the creation of time series and other higher order data products. This was a critical component as without it there would be limited potential for including time series of effort and species CPUE (quantities that are of interest to managers and assessment scientists) produced by this research into regional

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stock assessments. Additionally, this analysis laid the foundation for the two subsequent chapters and future work investigating fishermen behavior with respect to their targeted stocks and fleet dynamics in GoM vertical line fisheries.

In Chapter 3 the research showed that in fisheries where the fleet is able to target non- transient species at fine spatial scales, simple imputation and temporal averaging of high resolution spatial CPUE data provided a robust estimate of abundance trends. Utilizing this approach to derive indices of abundance from VMS data was comparatively simpler than properly setting up a delta-GLM standardization model and more closely tracked abundance across all simulated effort and abundance scenarios. Incorporating high resolution spatial information from the fishery in this way shows much potential for improving stock assessments of reef fishes in the GoM. The fact that the VMS approach outperformed the status-quo method even in simulations where extreme shifts in spatial targeting occurred showed that VMS indices may be able to bridge the gap across events that significantly alter the spatial distribution of effort. Furthermore, pairing the catch rate information with the VMS data in this way can also lead to the creation of region specific indices of abundance as seen in Chapter 4. These regional indices can be used as input in spatial stock assessments (Booth 2000) and be an important layer

(Babcock et al. 2005; St Martin and Hall-Arber 2008) in the marine spatial planning process

(Gilliland and Laffoley 2008).

The setup work in the previous two chapters paved the way for Chapter 4 which showed that analyzing fishery-dependent catch records augmented with fine scale spatial information from VMS can be used to identify complex spatiotemporal dynamics within a fishery. The results of this analysis showed 5 distinct spatial métiers which were directly linked to coastal communities. Additionally, the spatial CCM analysis of the regional abundance time series

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indicated the presence of spatial abundance dynamics for reef fish in the GoM as a result of regionally specific fishing pressure or environmental conditions. Characterizing the spatial stock structure of reef fish species in this way can be a cost-effective first step and provide justification for additional methods to define spatial stock structure.

It has been known for a long time that fish and fishers have heterogeneous spatial distributions (Paloheimo and Dickie 1964) however these patterns were often ignored (Booth

2000; Goethel et al. 2011) to simplify the assessment or management process. This study confirmed the existence of spatial heterogeneity in the fishing fleet and more notably showed the existence of regional differences in the temporal dynamics of reef fish stocks as well as spatial patterns in their abundance. The results from this chapter have ready practical applications.

Identifying how species and métier interactions change spatially can lend insight into how perturbations to the system can cause spatially differential impacts; in the event of a catastrophic impact to the fishery, the spatial métier information can be used to direct disaster relief funds to the most likely impacted communities. Furthermore, since ignoring the structural uncertainty with respect to spatial stock structure may result in poor assessment results (Punt and Donovan

2007) incorporating this new knowledge of the regional spatial structure in stock dynamics could improve assessment and management performance. This analysis provided a first look at how to spatially partition the vertical line fleet and targeted reef fish stocks for assessment and management in the GoM.

This research only scratched the surface of potential applications with this data set, and opened the door for broader, more interdisciplinary research. Revisiting the initial classification of VMS locations as fishing or non-fishing given the research from Chapter 4 showing the presence of multiple spatial métiers, it may have been a bit naïve at the time to assume that all

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vertical line vessels exhibited the same fishing signature. Utilizing a unique random forest model to classify the VMS data for each métier-associated region could improve upon the classification performance. Additionally, this research could have benefited tremendously from extensive social science (either through interviews with commercial vertical line vessel and fish house operators or through direct observation of fishing behavior) work at the onset of the project.

There is only so much that can be gained through data analytics and using interviews to identify factors that influence site choice could have aided in the development of a random forest model with more informative covariates. Regardless, any future work building on the current research that seeks to evaluate how fishing effort redistributes across species and areas as a result of external perturbations to the system should rely on stakeholder interviews to inform those behavioral models.

The work presented in Chapter 3 showed that simple temporal imputation and spatial averaging of high-resolution data fisheries-dependent CPUE data can produce reliable indices of abundance provided the fishery was able to fully sample the underlying spatiotemporal distribution of the stock. However, in many cases, the spatiotemporal sample from fisheries dependent data is incomplete generating “holes” in the distribution, or areas that are fished in one time period but not in another. In fisheries dependent data, these holes can arise for many reasons including preferential sampling by the fishery, changes in spatial targeting, range shifts and contractions of the underlying stock, as well impeded access to fishing grounds due to regulations or economic factors. As a result, the decision on how to fill these spatiotemporal holes in CPUE distributions can result in different relative abundance time series when using the same data. Future simulation work should compare multiple, more statistically-rigorous methods

(Cressie and Wikle 2011; Thorson and Barnett 2017) for filling spatiotemporal holes and

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evaluate how these imputation methods impact the ability of the derived index to track the true abundance trend under extreme effort and abundance scenarios. This research would more appropriately identify under what circumstances different imputation techniques should be used when creating abundance indices from high-resolution fisheries dependent data.

Any future analysis based on the métier analysis in Chapter 4 to try to predict fisher site choice or how fishing effort distributions may change under management scenarios is likely going to be incomplete unless species IFQ availability is accounted for. Previous work has shown that in multi-species fisheries, lack of species quota results in avoidance of limiting species (Branch and Hilborn 2008; Walters and Bonfil 1999). Given the presence of two separate

IFQ systems for reef fish in the GoM, one for red snapper implemented in 2007 (GMFMC 2006) and the other for the grouper-tilefish complex implemented in 2010 (GMFMC 2008); it is highly probable that species quota availability affects fisher site choice. Additionally, existing research on the social networks surrounding the transfer of red snapper IFQ in the GoM found distinct trading communities and regional differences in quota pricing (Ropicki and Larkin 2014).

Revisiting the métier analysis with information regarding quota availability and membership within distinct quota trading networks would result in more realistic métier identification and enhance the ability to track regulatory cascades within the fishery.

With the addition of National Standard 8 into the Magnuson-Stevens Fishery

Conservation and Management Act (USG 2011), managers are required by law to take into account the effect of regulatory changes on fishing communities. As a result, fisheries anthropologists with NOAA-Fisheries have used a combination of socio-economic indicators

(e.g. population composition, poverty, flood risk, etc.) to quantify the social vulnerability, gentrification pressure, sea-level rise risk, and reliance on fishing activities (Colburn and Jepson

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2012; Colburn et al. 2016; Jepson and Colburn 2013). Taken together, these indices are used to measure the long-term vulnerability of fishing communities as well as their acute vulnerability to perturbing events. There is a lot that could be gained from pairing a métier analysis done at the community level, similar to the one described in Chapter 4, to the estimated community vulnerability metrics. This would allow managers to directly link the fishing grounds and target species connected to the most vulnerable communities and identify how specific regulations or spatial closures would likely impact these communities. Highly vulnerable communities that are overly reliant on a limited number of target species could also be identified as candidates for portfolio diversification in an effort to mitigate their risk (Cline et al. 2017). This type of integrated analysis to identify relationships at multiple levels of the fishery system could be used to inform the development of the GoM Integrated Ecosystem Assessment program (Schirripa et al. 2012), given the growing pressure to move towards ecosystem-based management in the

GoM (Gruss et al. 2017).

Given the utility of incorporating high-resolution fisheries dependent data derived from

VMS analyses into the existing management and stock assessment frameworks, there is a need to create a data integration plan for the continued analysis of VMS data linked to the vertical line fishery for reef fish in the GoM. The current research spans the start of the VMS program in

2007 and runs through 2013. Further efforts need to be taken to update the analysis through 2018 before a real-time data integration plan, based on the research in Chapter 2, can be implemented.

At that point, on monthly or annual intervals, the current VMS data can be queried and classified according to an updated random forest classification model informed by the newest GoM reef fish observer program data. Subsequently, these current fishing locations can be linked to their respective commercial logbook catch records and uncertainty in the spatial distributions of catch,

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effort, and CPUE can be calculated. At this point these data can be used to update any of the analyses described in Chapters 2-4 so that they can be used as inputs into current assessments and management frameworks.

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APPENDIX CHAPTER 2 – SUPPLEMENTARY MATERIAL

A.1 Variables Used in Random Forest Classification

Variables were included in the RF model if they contributed to an increase in the PPV.

These included calculated variables that characterized vessel movement (Time_from_previous,

Distance_from_previous, Speed_from_previous, FIRST_NN, SECOND_NN, and

BEARING_DIFF), timing of fishing activity (FRACTION_DAY, JULIAN_DATE,

REL_TRIP_TIME, TOTAL_TRIP_TIME, and LunarPhase), or location choice (DEPTH and

DEPTH_DIFF). Recorded variables (variables that were not calculated) were also included to account for variability related to vessel characteristics. Since the first two nearest neighbor distances were highly correlated, additional nearest neighbor distances were not included in the model. Distributions of the variables can be shown in Figure A-1. For the two most important variables to the classification, FRACTION_DAY and REL_TRIP_TIME there is a clear difference in the distribution between fishing points and non-fishing points.

It is easy to imagine the following sequences of splits being used to identify fishing points within one of the 500 trees used in the model: FRACTION_DAY > 0.3 followed by

FRACTION_DAY < 0.8 at a later split or REL_TRIP_TIME > 0.1 followed by

REL_TRIP_TIME < 0.9. In the first example described, FRACTION_DAY is likely a proxy variable for daylight hours. Since the Gulf of Mexico is relatively close to the equator, the

FRACTION_DAY representing daylight hours is likely to be fairly constant throughout the year.

However, it could be used in combination with JULIAN_DATE to account for seasonal differences in daylight.

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A.2 Selection of Classification Threshold

A classification threshold value was used to classify the output of the RF model as fishing or non-fishing. The output from the RF model is a decimal value bounded from 0 to 1.

Values above the classification threshold are classified as fishing, and values below the threshold are classified as non-fishing. This classification threshold value (0.43) was selected using a receiver operating characteristic (ROC) type plot. The model PPV, NPV, sensitivity and specificity were plotted for different threshold values. PPV was selected as a metric of interest because, given an entry was classified as fishing, the probability that a vessel was actually fishing could be calculated. A high PPV increases confidence that predicted fishing points are actually what they claim to be. The threshold value of 0.43 was selected as it maximized the combination of PPV, NPV, sensitivity and specificity subject to the constraint that PPV remained above 0.6. Maximizing solely the PPV would have resulted in high numbers of observed fishing points being incorrectly classified as non-fishing. Reducing the threshold would have reduced the PPV to undesirable levels as it would increase the number of observed non-fishing points classified as fishing.

A.3 Lee’s L and Bounded Permutation

A bivariate spatial association metric, Lee’s L, was used to assess the spatial correlation between the paired distributions. This metric retains the direction and some of the magnitude of the bivariate point-to-point association, Pearson’s correlation, between the two distributions as well as incorporating the degree of spatial association between the distributions using an extension of a univariate measure of spatial autocorrelation, Moran’s I (Lee 2001). This metric is bounded on the interval -1 to 1, with positive values indicating a positive point-to-point

Pearson’s correlation. A bounded permutation, where the point-to-point correlation between the

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two distributions remains constant, is used to determine if there is a significant spatial association between the two distributions (Lee 2001; Lee 2004).

The bivariate measure of spatial association, Lee’s L, is described in Eq. A - 1 for two distributions X and Y who have the same dimensions (i = j).

∑푖[(∑푗 푤푖푗(푥푗 − 푥̅ )) ⋅ (∑푗 푤푖푗(푦푗 − 푦̅ ))] 퐿푋,푌 = (퐴 − 1) 2 2 √∑푖(푥푖 − 푥̅ ) √∑푖(푦푖 − 푦̅ )

The 푤푖푗 is an element from a row standardized binary adjacency matrix. Values of 1 in the adjacency matrix indicate that corresponding cells in the distribution are contiguous, while values of 0 indicate that they are not. To ensure the comparison of two distributions with the same dimensions, cells that held a value in one distribution but not in the other were filled with 0 in the distribution that initially held no value for that cell. Cells that were empty in both distributions were ignored in the calculation. Prior to calculation of Lee’s L both distributions were scaled relative to their respective mean’s and standard deviation’s. The 95% quantile around the point-estimate of Lee’s L was determined from 1,000 bounded permutations. If the point estimate fell outside this interval the bivariate spatial correlation between the two distributions was assumed to be significant at the 95% confidence level (Lee 2001).

A.4 Comparison to Null Model

The performance of the classification algorithm was evaluated through a comparison with a null model trained only on "Speed_from_previous" and which effectively classifies entries at random. The Matthews Correlation coefficient curve and receiver operating characteristic (ROC) curve (Figure A-2) were calculated for both the RF model used and the comparative null model.

The Matthews Correlation coefficient is a useful measure for describing classification performance particularly in unbalanced data sets as it accounts for the correct classification of both positive and negative entries (Baldi et al. 2000; Matthews 1975). The interpretation of the

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Matthews Correlation coefficient is similar to that of a Pearson Correlation coefficient where 1 indicates perfect classification, 0 random classification, and -1 completely wrong classification

(Powers 2011).

Keeping in mind that the OBS data set was unbalanced in terms of fishing and non- fishing points, a random classifier would have a PPV of ~22%. The RF model used correctly classifies fishing points at a rate 3x better than random. This can be more clearly shown in a comparison with a null model. In each metric the RF model used in the analysis surpassed the null model. A perfect classification model would have a Matthews Correlation coefficient and

AUC (Area under the ROC curve) of 1. Additionally, even in cases when the model classifies something incorrectly it is not incorrect in a way that is likely to make much of a difference in terms of identifying where fishing actually takes place (Figure A-3).

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Figure A-1. The density distributions for 12 of the 13 (SECOND_NN was omitted from the figure as it was visually identical to the FIRST_NN) continuous variables used in the classification model. The black line represents OBS data for fishing points and the red line represents OBS data for non-fishing points.

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Figure A-2. Diagnostic plots for the classification model used. The gold point represents the classification threshold considered in the analysis, and the bold line segment indicates threshold values that would result in a PPV greater than 60%. The blue represents a null model trained only on “Speed_from_previous” that is used for comparison.

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Figure A-3. The trajectories from 4 randomly selected trips from the OBS data. Black (a and c) represents not fishing, and blue (b and d) represents fishing. The a and b panels represent the observed values. The c and d are the predicted values. Most of the differences between observed and predicted occur in the tight clusters of both fishing and non-fishing points.

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Figure A-4. The spatial residuals by activity type, Fishing and Non-Fishing, from the classification model denoted as the proportion of entries in a given cell classified correctly.

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BIOGRAPHICAL SKETCH

Nicholas David Ducharme-Barth majored in fisheries and aquatic sciences and completed his Doctor of Philosophy in the summer of 2018 while completing a Graduate Certificate in quantitative fisheries science in August 2016. Prior to arriving at the University of Florida, he completed a Bachelor of Science in mathematics in May 2013 at the College of William and

Mary in Virginia.

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