Report on spiny lobster abundance and fishing mortality and preliminary analysis of existing fisheries data at Glover’s reef research station

8/13/2019 Report on spiny lobster abundance and fishing mortality and preliminary analysis of existing fisheries data at Glov

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March 2011

This publication was produced for review by the United States Agency for InternationalDevelopment. It was prepared by Dr. Elizabeth Babcock and Dr. Robin Coleman; WildlifeConservation Society

GLOVERS REEFANNUAL REPORTREPORT ON SPINY LOBSTER ABUNDANCE AND FISHINGMORTALITY AND PRELIMINARY ANALYSIS OF EXISTINGFISHERIES DATA AT GLOVERS REEF RESEARCH STATION


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The authors views expressed in this publication do not necessarily reflect the views of the UnitedStates Agency for International Development or the United States Government.

GLOVERS REEF

ANNUAL REPORTREPORT ON SPINY LOBSTER ABUNDANCE AND FISHINGMORTALITY AND PRELIMINARY ANALYSIS OF EXISTINGFISHERIES DATA AT GLOVERS REEF RESEARCH STATION

Contract No.: EPP-I-00-04-0020-00 Task Order No. 5Subcontract No.: EPP-I-05-04-0020-00-WCSPeriod of Performance: November 24, 2010 to September 15, 2014


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The authors views expressed in this publication do not necessarily reflect the views of the UnitedStates Agency for International Development or the United States Government.


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vi GLOVERS REEF ANNUAL REPORT

CONTENTS

List of Acronyms and Abbreviations ............................................................................... iiiv

Preface................................................................................................................................ ix

Introduction .........................................................................................................................1

Part I: Spiny Lobster Abundance and Fishing Mortality at Glovers Reef Marine Reserve

Abstract ................................................................................................................................3

Method ........................................................................................................................................... 3Length based metrics of fishing pressure ........................................................................ 3Abundance trends from the WCS catch per unit effort data set .......................................... 5Abundance trends from the LAMP fishery-independent data set ....................................... 7Abundance trends from the LAMP fishery-independent data set ....................................... 8

Bayesian DeLury state-space model fitted to catch.9

Bayesian DeLury regression model based on effort..10

Results ...............................................................................................................................11

Length - based metrics of fishing pressure ............................................................11

Abundance trends from the WCS catch per unit effort data set ............................12

Abundance trends from the LAMP fishery-independent data set ..........................13

Estimates of total abundance and fishing mortality from depletion analysis ........13Bayesian DeLury state-space model fitted to catch ....................................14

Bayesian DeLury regression model based on effort ...................................15

Discussion ..........................................................................................................................15

References ..........................................................................................................................18

Table and Figures ...............................................................................................................20

PART II: Preliminary Analysis of Existing Fisheries Data at Glovers Reef Marine

Reserve

Abstract ..............................................................................................................................33

Methods..............................................................................................................................33WCS Catch and Effort Data ...................................................................................33

LAMP data .............................................................................................................35

Catch and Effort from Fisheries .............................................................................36


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GLOVERS REEF ANNUAL REPORT vii

Results ................................................................................................................................36

WCS Catch and Effort Data ...................................................................................36LAMP Data ............................................................................................................37

Fisheries Data.........................................................................................................38

Discussion ..........................................................................................................................38

References ..........................................................................................................................39

Tables and Figures .............................................................................................................41


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viii GLOVERS REEF ANNUAL REPORT

LIST OF ACRONYMS AND ABBREVIATIONS

AIC Akaike information criterion

BIC Bayesian information criterion

CITES Convention on International Trade in Endangered Species of Wild Fauna

and FloraCL Carapace Length

CPUE Catch Per Unit Effort

CZ Conservation ZoneDIC Deviance Information Criterion

F0.1 Fishing mortality rate that corresponds to a slope of the yield per recruit

function 10% of its level for an unexploited stockFAO Food and Agriculture Organization of the United Nations

Fmax Fishing mortality rate that maximizes yield per recruit

GLM Generalized Linear ModelGLMM Generalized Linear Mixed Model

GUZ General Use ZoneLAMP Long-term Atoll Monitoring Program

Lopt Length that Optimizes Yield per RecruitMCMC Markov Chain Monte Carlo

MSY Maximum Sustainable Yield

SL Shell LengthTL Total LengthWCS Wildlife Conservation Society


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GLOVERS REEF ANNUAL REPORT ix

PREFACE

The Management of Aquatic Resources and Economic Alternatives program, financed by

the United States Agency for International Development (USAID) and implemented by

Chemonics International, with the Wildlife Conservation Society as a subcontractor,

builds on previous projects in Central America to support and promote marine andcoastal conservation through rights-based access and market-driven mechanisms in

concert with local partners from both the private and public sectors. The USAID program

will achieve these goals with a focus on four key trans-boundary watershed areas andseven key focal species. The four trans-boundary regions are the Gulf of Honduras, the

Moskitia Coast, Cahuita-Gandoca-Bocas del Toro, and the Gulf of Fonseca. The focal

species for the USAID program are divided into species with commercial importance:mangrove cockles, queen conch, grouper, snapper, and spiny lobsters; as well as two

groups of endangered species: sharks and sea turtles.

The USAID program will employ multiple strategies to positively affect its target species

within its regional points of focus including the promotion of rights-based legislation andprograms, establishment of managed protected areas and no-take reserves, promoting

specific protections and management regimes for threatened species and by providingeconomic alternatives to local communities where resource extraction threatens marine

and coastal natural resources.

This Glovers Reef Annual Report provides long term analysis of spiny lobster and

queen conch fishery independent surveys and catch per unit effort surveys to provide

stock and catch information necessary to implement and manage an ecosystem approachto rights based fisheries at Glovers Reef.


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GLOVERS REEF ANNUAL REPORT 1

INTRODUCTION

Caribbean spiny lobster (Panulirus argus) is the most economically important species in

the fisheries of Belize. According to an age-based stock assessment of spiny lobster in

Belize (Gongora 2010), the spawning stock biomass declined by 8.7% between 1999 and

2009 and fishing mortality increased 46% to 1.3, because of increasing fishing effort.Although the biomass appears to be fairly stable in recent years, the fishing mortality rate

is higher than the optimal level. According to yield per recruit analysis, the fishing

mortality rate that would maximize yield (Fmax) is 0.85, while the more precautionaryF0.1reference point is 0.49 (Gongora 2010). A reduction in fishing mortality nationwide

would be required to achieve either of these targets.

Lobsters are also the most important fishery at Glovers Reef Marine Reserve. Conch are

also an important fishery at the marine reserve (Acosta 2006). At Glovers Reef, WCS,

with the support of USAID Program, has been interviewing fishermen to collect data onlobster and conch length, weight, catches and fishing effort from 2004 through the

present (Grant 2004). The WCS LAMP data set, from a fishery independent underwatercensus focusing on conch, lobster and select finfish, was also available from 2004

through the present, including length and abundance of lobsters and conch at fixed sitesin both the Conservation Zone and the General Use Zone. The National and Northern

fisheries Cooperatives also report catches of spiny lobsters and conch to the Fisheries

Department by month for the Glovers Reef region (Region 3); these data were availablefrom 2002 through the present.

Queen conch (Strombus gigas) is the second only to lobster as an economically importantspecies in the fisheries of Belize. Queen conch are depleted throughout the Caribbean

and are listed on Appendix II of CITES (FAO 2007). In Belize, conch production has

increased over the last decade but is still below the national total allowable catch quota,and recent assessments have shown in increase in the population (Belize national reportin FAO 2007, Carcamo 2008).

The objectives of this paper are to evaluate the available data on size and abundance ofspiny lobsters at Glovers Reef and to determine the level of fishing mortality, population

size and trends in population size. It is not known what fraction of the lobsters recruiting

at Glovers Reef are offspring of the local spawning stock and what fraction come fromelsewhere in the Meso-American Barrier Reef system. Therefore, we did not apply stock

assessment methods that assume a relationship between spawning stock and recruitment,

as such models would require the assumption that Glovers Reef is a self-sustaining

population. Instead, we used length-based indicators and depletion methods to estimatethe abundance and fishing mortality of post-recruitment lobsters at Glovers Reef. Given

this information, an appropriate sustainable catch level at Glovers Reef could be

determined by applying the national target fishing mortality rate (Gongora 2010) to thelobsters at Glovers Reef. Another objective is to evaluate the available data on size and

abundance of conch at Glovers Reef and to determine whether these data will be useful

in estimating the level of fishing mortality, population size and trends in population size.


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PART I: SPINY LOBSTER ABUNDANCE AND FISHINGMORTALITY AT GLOVERS REEF MARINE RESERVE

ABSTRACT

Data available on spiny lobsters at Glovers Reef Marine Reserve include the reportedcatch and fishing effort from the fishing Cooperatives, data on sizes, catches and fishingeffort collected from fishermen at Glovers Reef, and a fishery independent visual survey

(LAMP). Most of the harvested lobsters at Glovers Reef were above the size at

maturity, but many were below the optimal size for harvest. The fishing mortality rateestimated from the length frequencies was less than the current national fishing mortality

rate. The abundance data from the LAMP survey shows a generally increasing abundance

trend across the time series, which combined with the fact that the LAMP survey foundthat lobsters tend to be bigger and more abundant inside the Conservation Zone,

demonstrates that the Conservation Zone provides significant protection for lobsters.

The catch per vessel day (from the Cooperative data) and the catch per fisherman hour

showed a decline in relative abundance during the fishing season in most years. TheWCS CPUE trend appeared to decline across years, while there was no clear trend in the

Cooperative CPUE. Catches at Glovers Reef (those reported as region 3 by the National

and Northern Cooperatives) were lower in recent years than in 2002-2004; however, it isunknown what fraction of catch from Glovers is inaccurately reported as catch from

other regions. Delury population depletion models fitted to the CPUE data, combined

with either catch or effort data from the Cooperatives gave extremely variable resultsdepending on the model formulation and whether catch or effort data were used. More

reliable catch and effort data would be needed to use these methods to estimate stock

status and reference points. Recommendations are made for the improvement of data

collection under new licensing scheme.

METHOD

Length based metrics of fishing pressure

Froese (2004) proposed three simple indictors to determine whether a population was

being harvested in a sustainable fashion, based on the length distribution of fish in the

catch. To avoid recruitment overfishing, he suggested that the fraction of fish in thecatch that are above the length of maturity (Lm) should be high, preferably 100%, so that

each individual has a chance to spawn at least once before being harvested. To prevent

growth overfishing, all or most of the fish caught should be within plus or minus 10% ofthe optimal length of harvest (Lopt) based on yield per recruit analysis. The optimallength is the length at which the number of fish in a year class multiplied by their average

weight is maximized; allowing the fish to grow to this size before harvesting them

maximizes the weight of fish that can be caught. The third indicator proposed by Froese(2004), is the number of mega spawners which he defined as fish that are more than

10% aboveLopt. A fishery management plan that included a maximum size limit and so

avoided capturing any of these mega spawners would be ideal because the large fish are a


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4 GLOVERS REEF ANNUAL REPORT

critical source of fecundity. In the absence of a maximum size limit in the fishery, the

fraction of mega spawners in the population should be greater than 20%, consistent

with a population with a healthy age distribution (Froese 2004).

To calculate the Froese (2004) indicators for spiny lobster, we assumed the size at

maturity was 70 to 80 mm carapace length (CL, FAO 2000). The minimum legal size forlobsters in Belize is 3 inches CL (76 mm), which is around the age at maturity, so that we

expect most lobsters caught to be above this length. The optimal length (Lopt) was

calculated as the length at which the numbers at age (assuming only natural mortality)multiplied by the weight at age reached a maximum using the von Bertalaffy growth

curve [L=L(1-exp(-K(t-t0)))], using parameter values from Gongora (2010), a weight

length relationship from FAO (2001) (W = 0.00460 CL ^2.630) and exponential decline

in numbers, with a natural mortality rate of 0.34.

Average length data can also be used to estimate total mortality (Z) based on average

length and life history parameters taken from the literature, using the method of Beverton

and Holt (1957) as modified by Ehrhardt and Ault (1992) and Ault et al. (2008, 2005).The original Beverton and Holt (1957) method makes the following assumptions:

recruitment has been relatively constant in recent years; fish growth follows the von Bertalanffy growth model, with parameters K (growth

rate) and L (asymptotic length);

the total mortality rate (Z) is relatively constant over time and fish ages; and there is knife edge recruitment into the fishery at length Lc, and all fish above this

size are equally likely to be captured.

Given these assumptions, the total mortality can be calculated as:

(1))()(

cLLLLKZ

=

Ehrhardt and Ault (1992) showed that this method can be biased if the fishery does not

exploit all older age classes of fish (for example if older individuals move into deeperwater). They proposed the following formulation that also includes a maximum size of

capture (

L ) assumed to be less than L.

(2))()(

)()(

LLKLLZ

LLKLLZ

LL

LL cK

Z

c +

+=

Given these estimates of total mortality (Z) for each species, we calculated fishing

mortality rate (F) by subtracting the natural mortality rate (M) taken from the literature.Any population for which F is much larger than M has probably experienced overfishing

in its recent history. The method of Ehrhardt and Ault (1992) has previously been applied

to spiny lobsters in the Caribbean (FAO 2001).


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Lengths were reported in mm carapace length (CL) in both the LAMP data and the WCS

catch data. The catch data also included tail length (TL) and second segment width

(SW). Both TL and SW were recorded more often than CL in the WCS catch data setbecause the data recorders often had no access to lobster tails before they were processed

by the fishermen. Nevertheless, the available life history data and the LAMP data used

CL, so we used CL for all calculations, converting TL to CL using the linear relationbetween CL and TL calculated from the lobsters for which both lengths were available.

There are many published growth curves for spiny lobster. We used a von Bertalanffygrowth curve, with values ofL=183 mm CL,K= 0.24, and t0=0.44, consistent with the

most recent national assessment (Gongora 2010). We estimated total mortality from the

WCS CPUE data set, as well as the LAMP visual survey data both in the General Use

Zone and in the Conservation Zone.

Abundance trends from the WCS catch per unit effort data set

WCS researchers collected data on the number and size of lobsters caught fromfishermen on the fishing grounds at Glovers Reef between 2004 and the present. For

each fisherman, we calculated catch per unit of effort (CPUE) in whole weight of lobsters

caught per fisherman hour. For more than 60% of the lobsters that were observed in thecatch data set, whole weights were recorded. For lobsters for which tail weights had been

recorded, we converted to whole weight using the conversion of tail weight to total

weight from FAO (2001) (WTotal=2.97Wtail - 0.000327 in kg for females, WTotal=3.38Wtail- 0.0238 for males). For individual lobsters for which no weights were

recorded, we converted carapace length (WTotal= 0.00460CL2.630

) to total weight using

relationships from FAO (2001).

It was necessary to exclude data for which the fishermans name was not recorded

because it was not possible to determine how many lobsters had been captured by each

individual fisherman. There were 641 unique combinations of fisherman, boat and datefor which these data were collected. For each of these, we calculated CPUE as the weight

of Caribbean spiny lobsters caught per hour fishing. There were a few cases (10 out of

641) in which the individual fisherman were interviewed twice in one day; we calculatedonly one value of the CPUE in this case, counting all the lobsters they had caught that

day and using the largest reported value for hours fished.

Lobster CPUE is expected to be proportional to abundance. However, catch rates can alsovary depending on fishing location, environmental conditions and the relative

effectiveness of different fishermen. Provided that data are available, a generalized

linear model (GLM) can be used to estimate the impact of environmental conditions andother explanatory variables on the catch rates so that these effects can be removed from

the estimated temporal trend. The GLM estimated trend should reflect only changes in

abundance over time without being biased by any of the confounding factors (Maunderand Punt 2004).

The data collected along with the lobster catches, biological data and hours fishing

include the name of the boat, the name of the fisherman, the location, date, time and


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depth fished. We classified the data into fishing seasons, assuming that lobster season

started on June 15 and ended February 14 of every year, so that, for example, fishing

season 2005 would begin on June 15, 2005, and include all fishing through the followingFebruary. Month within each fishing season was included in the model as a factor, so

that the change in abundance during each fishing season could be tracked. We also

included the moon phase (full: within 4 days of full, new: within 4 days of new, mid:otherwise) as a factor in case moon phase influenced catch rates.

We did not include time of day in the analysis because most fishermen reported fishingsix hours or more, so that the time each individual lobster was captured was not precisely

known. Also, most data were collected between noon and 3:00 PM, so that the fishermen

were all fishing around the same time of day (morning and early afternoon). We also

did not include depth in the analysis because, although the fishermen were asked to reportthe depth range at which they were fishing, most had fished for 6 hours or more, so that it

seemed unlikely that they had stayed within one depth zone.

Of the 18 boats for which lobster catch and effort data were recorded, only 12 weresampled on 3 or more days. For the models in which boat name was included as a factor,

we included only the 12 boats that had been sampled on three or more occasions.Locations were described with different categories in 2004-2005 than in 2006-2010.

From 2006 to 20010, the majority of the lobsters (61%) were taken in the central lagoon

north of the conservation zone (areas G5-G7). It was not possible to include both boat

and location in the model, because most combinations of boat and location contained zerodata points. Because there appeared to be more variability between boats than between

locations, we chose to include boat in the model and ignore location.

Using only data from the 12 boats with multiple samples, for the 2005through 2010

fishing seasons, the number of CPUE records was 641. There were no zero observations

because the data recorder did not fill out a data sheet for fishermen who did not catch anylobsters. The lack of zero observations may introduce a bias into the estimated time trend

of abundance because fishermen are more likely to catch zero lobsters when lobster

abundance is low.

The GLM model was:

(3) lkjikjilkji wayVMTCPUE ,,,,,, 2)log( ++++=

where Tiis the effect of fishing year and month (i) for the 37 months between June, 2005

and July, 2010 for which data were collected,Mjis the effect of moon phase (j=full, midor new), and Vkis the effect of individual boat (k= boat 1 through 12), and lkji ,,, is a

normally distributed error term. All of the second order interactions between the termsare included.

To determine which of these factors and their interaction significantly improve themodel, we used Akaikes Information Criterion (AIC, Akaike 1974):


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(4) AIC=-2log(L)+2n

where log(L) is the natural log of the likelihood of the model and n is the number ofparameters. The model with the lowest AIC thus optimizes the tradeoff between

achieving a good fit between the GLM model and the CPUE data, and minimizing the

number of parameters. We allowed the stepAIC function in the MASS library for R tochoose the model that minimized AIC (Venables and Ripley 2002). In the case where

boat or any of the two way interactions with boat were included in the AIC best model,

we treated these parameters as random effects, using the functionglmerin R (Bates 2010,Ortiz and Arocha 2004, R Development Core Team 2010). The AIC and the BIC

(Bayesian information criterion; Bates 2010) were used to choose the best model with

random effects.

The time period (year and month) effect calculated by the mixed model was used to

predict the log-CPUE for month and year and the predicted values and their standard

errors were transformed from normal to lognormal to extract the temporal trend in

abundance.

Finally, to determine whether there was a significant decreasing trend in abundancewithin each fishing season, we repeated the GLM model with day within fishing season

as a numerical variable to estimate the linear regression between day and CPUE within

season:

(5) lkjikjiilkji wayVMDYCPUE ,,,,,, 2)log( +++++=

where Yiis the effect of fishing year i, andDiis the slope of the linear relationship

between day since the beginning of fishing season iand log-CPUE.

Abundance trends from the LAMP fishery-independent data set

For lobster observations in the fishery independent LAMP data set, we used a similar

generalized linear modeling approach. In the LAMP case, the sampling unit was onedive, so that the number of lobsters seen per dive is assumed to be an index of lobster

abundance. For each lobster seen, the divers recorded the date, site, carapace length

(CL), sex, whether eggs were visible, start time, number of minutes spent searching,depth, visibility and other physical variables.

The LAMP data were collected at 11 fixed sampling locations that were either inside theconservation zone or in the general use zone near the boundary between zones. To testfor an effect of management zone on lobster abundance, we included distance from the

Conservation Zone boundary as a numerical variable (with negative values inside the

Conservation Zone). An alternative formulation included management zone as factorwith three levels: (1) general use zone more than 500 m from the conservation zone, (2)

general use zone less than 500 m from the conservation zone, and (3) in the conservation


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zone, in case the relationship between management zone and lobster abundance was non-

linear.

Of the 207 dives in the dataset, 40% recorded zero lobsters. Therefore, we used a delta

lognormal modeling approach, in which the number of lobsters in dives in which lobsters

were seen was modeled as lognormal, while presence or absence was modeled as abinomial process (Ortiz and Arocha 2004).

As in the fisheries CPUE analysis, we included potential explanatory variables in themodel, to remove any effects of environmental conditions that may influence the count of

lobsters. The potential explanatory variables we considered were the time period (year

and month), the linear effect of distance from the management zone boundary, moon

phase (full, new or mid), and the linear effects of time of day, visibility and depth.

The GLM models were:

(6) kjijikji waydtvZMTC ,,,, 2)log(

+++++++=

for positive sets, and :

(7) waydtvZMTP jikji 2)(logit ,, ++++++=

for presence or absence (P), where Tiis the effect of time period i,Mjis the effect of

moon phase (j=full, new or mid), Z is the linear effect of distance from the Conservation

Zone boundary (km), v is the linear effect of visibility (m), tis the effect time of day (in

decimal 24 hour time), dis the linear effect of depth (m) and kji ,, is a normally

distributed error term. Some 2 way interaction terms were also included, although it wasnot possible to include all interactions given the relatively small sample sizes.

To determine which of these factors significantly improve the model, we used AkaikesInformation Criterion (AIC, Akaike 1974). The index of abundance was calculated by

multiplying the inverse logit of the time period effect from the binomial model by the

exponent of the time period effect from the lognormal model (with bias correction).

Standard errors were calculated using the method of Lo et al. (1992). All factors weretreated as fixed effects.


Catches and fishing effort (in vessel days) for region 3 (Glovers Reef) were provided by

the Belize Fisheries Department by month, as reported by the National and Northern

Cooperatives. The catches were reported as lobster tail weight and lobster head weight.We calculated total weights from tail weight as WTotal= 3.175 Wtail- 0.01206 (FAO 2001).

The CPUE in lobster weight per fishing vessel day appeared to decline during mostfishing seasons. Therefore we used several modifications of the DeLury depletion model


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(Robert et al. 2010, Quinn and Deriso 1999, Bataille and Quinn 2006) to estimate the

biomass of lobsters in the open area at the beginning of each fishing season, using a

Bayesian method to estimate the parameters of each model.Bayesian DeLury state-space model fitted to catch

We assumed that all recruitment occurred between fishing seasons, so that no lobsterswould grow from sub-legal to legal size during the fishing season. During each month ofthe fishing season, the number of lobsters can be calculated as (Robert et al. 2010):

(8) 2412,1, ,MNM

titi eCeNN ti

+ =

whereNi,t is number of legal sized lobsters in the General Use Zone at the beginning ofmonth t in fishing season i, C

Ni,tis the catch in numbers during month tassumed to take

place in the middle of the month,Mis the instantaneous natural mortality rate, assumed

to constant across years;Mis in annual terms, so it is divided by 12 for a monthly timestep in Equation 8. Assuming that the average weight of lobsters is constant, so that

biomass is proportional to numbers:

(9) 2412,1, ,MM

titi eCeBB ti

+ =

whereBi,t is biomass of legal sized lobsters in the General Use Zone and Citis catch inweight. We used Equation 9 rather than Equation 8 because the catch data were available

in weight not numbers. Bi,1, the biomass at the beginning of the fishing season i, is a

parameter that must be estimated; biomass in each subsequent month can be calculatedfrom the starting biomass, natural mortality rates and catches using Equation 9.

To estimate the model parameters, the predicted abundance trend from Equation 9 wasfitted to catch per unit of effort as an index of abundance. The abundance indices used

were the CPUE index derived from the Cooperative data (i.e. the average of the weight of

lobster caught per vessel day in each month), and the standardized index of abundance

derived above for the WCS catch and effort data described above. The standardizeLAMP series could also be used as an index of abundance, but it was only available for

two or three months in every year, so the we did not use it for the depletion model.

The catch per unit effort from either the fishing Cooperative data or the WCS CPUE data

was assumed to be proportional to abundance in the middle of the month, approximated

by the average of abundance at the beginning and end of the month:

(10) eBB

qI titi

jtij

+= +

2

1,,

,,

where Ij,i,tis the value of thejth

CPUE index of abundance in month tof fishing season i,

qjis the constant of proportionality for abundance indexjand is a normally distributed

error (with variance j2). Both qjand j

2are assumed to be constant across months within

a year; we ran some model formulations where they varied by year and some where they


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were constant across all eight years (2002-2009). The fishing mortality rate in each

monthly time step was approximated asFt=-log(1-Ct/Bt), and the annual fishing mortality

rate was the sum of the monthly rates.

We used a Bayesian method to estimate the model parameters, implemented in the

WinBUGS software (Sturtz et al. 2010, Lunn et al. 2000), which uses a Markov ChainMonte Carlo (MCMC) algorithm to approximate the posterior distributions of the

parameters. Several alternative model structures were used (Table 1a). For models A

through D, we fit the two abundance series for all eight years simultaneously. In modelsA and B, the model estimated a common catchability and variance across years for each

series and a common natural mortality rate, along with the starting biomasses in each

year. Models C and D allowed the model to estimate a different catchability and variance

in each year for each series. The models also differed in how the starting biomass ineach season (i= 2002 to 2009) was estimated. In models A and C, each years starting

biomass was given an independent non-informative prior (Table 1). In models B and D a

Bayesian hierarchical modeling framework was used, so that the starting biomasses in

each fishing season was assumed to be randomly drawn from a lognormal distribution,with log-mean and log-standard deviation estimated by the model (Table 1a and b). This

hierarchical structure allows the data from multiple years to inform the estimate ofstarting biomass in each year, thus increasing the precision of the estimates for each year

(Royle and Dorazio 2008).

The four multi-year models (A through D) were compared using the DevianceInformation Criterion (DIC, Royle and Dorazio 2008), which is the equivalent of the AIC

for Bayesian models, and allows us to pick the model that optimizes the trade-off

between the number of parameters and goodness of fit to the CPUE data. Note that thehierarchical models have a lower number of effective parameters than do the non-

hierarchical models, because there is a correlation between starting biomasses in each

year. As an additional sensitivity analysis, we fit the model to the CPUE data to eachseries in each year independently, using the same priors as in the multi-year models

(model E).

The prior distributions of the estimated parameters (Table 1b) were non-informative ,except for the prior forM, which was normally distributed with a mean of 0.34, and

standard deviation of 0.04 (Gongora 2010, FAO 2001). This prior distribution

constrained the value ofMto be within a biologically plausible range. To ensureadequate convergence of the MCMC, we ran three chains, with 450,000 iterations after a

burn-in of 50,000 iterations, and a thin rate of 10. With these settings, all the models

converged adequately according to the Gelman-Rubin diagnostic (Lunn et al. 2000).

Bayesian DeLury regression model based on effort

The decline in abundance during a fishing season can also be modeled using effort ratherthan catch:

(11)tqUM

titi eNN

+ = ,1,


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where Utis the effort in montht. Therefore, the log of the abundance index (I) in each

time period can be modeled as:

(12) ttt qEtMqBI += )5.0()log()log( 1

whereEtis cumulative effort up to the middle of month tand is a normally distributederror term (Quinn and Deriso 1999, Battaile and Quinn 2006). This is the classical

DeLury regression method, with the addition of natural mortality. The model was fitted

to the average CPUE per vessel trip from the Cooperative data and the Cooperative effort

data in vessel days. We used a Bayesian method to estimate the parameters for thismodel, with the same priors forM, qand the error variance that were used in the state-

space model (Table 1). The prior for qonly allowed positive values of this parameter; we

also re-ran the model with an unrestricted prior for qto determine whether the datasupport a relationship between cumulative effort and CPUE (i.e. whether the value of q

was positive and significant). The annual fishing mortality rate was calculated asF=qEt

at the end of the season.

RESULTS

Length - based metrics of fishing pressure

Of the 3309 lobsters recorded in the WCS catch dataset, TL was measured for all, but CL

was measured for only 2113. For the 2089 lobsters for which both CL and TL data were

measured and the two values were consistent with each other, the regression wasCL=14.6+0.54TL (R

2=0.47). We used this equation to convert TL to CL. The optimal

length (Lopt) was 119 mm CL, corresponding to an age of 4.8 years. The values of theFroese (2004) indicators were: (1) 78-96% of the catch was mature individuals; (2) 15%were near the optimal length; and (3) 4% were mega-spawners. These values indicate

that there is some potential to harvest a higher yield of lobsters from Glovers Reef if

they were allowed to grow somewhat bigger before they are harvested.

In general, the average sizes within the size range most commonly taken in the fishery

(between 89 and 180 cm CL) were slightly higher in the conservation zone LAMP data

than in the general use zone LAMP data, and both were larger than in the fisheries data(Table 2, Figure 1). The distribution of sizes for male and female lobsters was fairly

similar to each other in each data set (Figure 1). Because of the difference in average

size, the estimated fishing mortality rate was higher for the fishery data than for theLAMP data in the fished zone, which was higher than the estimate in the unfished zone.

The estimated value of F from the fishery data was 0.88, which is considerably lower

than the national average fishing mortality rate of 1.3, but higher than the Fmaxof 0.85(Gongora 2010). The higher average size in the LAMP data may be in part explained by

spillover from the marine reserve. The size distribution of lobsters seen in the LAMP

survey more than 500 m from the Conservation Zone (Figure 1b) is similar to the length


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distribution in the fishery (Figure 1a), while there are many more lobsters greater than

100mm CL within 500 m of the boundary (Figure 1c).

The annual average size of individuals above the minimum size in the LAMP data appear

to have increased and then decreased again between 2002 and 2009 (Figure 2), while the

average size in the fisheries data seems to be fairly constant. The lack of change inaverage size between years is consistent with relatively stable recruitment and relatively

similar fishing mortality rates in each year. Within the fisheries data, the average sizes are

fairly constant across months in most years (Figure 3), the exception being a decline inaverage size in 2006 and an increase in 2005.

Abundance trends from the WCS catch per unit effort data set

The unstandardized log-CPUE data (Figure 4) appear to show a downward trend in log-

CPUE with time within most fishing seasons. Log-CPUE also appears to be lower in the

new moon, and variable between fishing boats. Fishing location shows no obvious

patterns in the raw data.

In the GLM, all of the direct effects of time period, boat and moon phase were highly

significant (Table 3a). The interactions between boat and moon phase and boat and timeperiod were also included in the AIC best fit model with fixed effects. This model

explained about 47% of the variability in the log CPUE data. The diagnostics showed a

good fit between the model and the data (Figure 5). When boat and the 2-wayinteractions were treated as random effects, both the BIC and the AIC found that the best

model was the one that included the three main effects plus the time period x boat and

time period x moon phase interactions (Table 3b). This model was used to calculate the

standardized CPUE trend.

The standardized CPUE by month (Figure 6) is highest in the first month of the season

for all seasons, while the last month of each season has the lowest CPUE. If the fishingmortality remained at a sustainable level, we would expect CPUE to decline during the

fishing season, and increase again at the beginning of the next season. While the CPUE

at the beginning of each season is higher than that at the end of the first season, there alsoappears to be a declining trend across the entire time series. When a linear trend was

estimated for CPUE across days within the fishing season (rather than including month asa factor), there was a decline in CPUE during every fishing seasons except 2006.

Unfortunately, the data set includes catch and effort from only fishermen who caught

lobster; fishermen who went out looking for lobsters and did not find any on the day

when they were interviewed are not included in the dataset (i.e. no zero data arerecorded). A histogram of the count of lobsters caught per fishermen in the dataset

(Figure 7) shows that it is quite common for fishermen to catch only one or two lobsters;

thus, it is probably common for fishermen to catch zero lobsters. This lack of zeroobservations can introduce bias into the use of CPUE as an index of abundance. For

example, if low abundance of lobster causes fishermen to spend more time searching for

lobsters without finding any, the lack of zero observations in the data would cause the


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CPUE method to overestimate abundance at times when abundance was low, thus

reducing the estimated change in abundance.


In the LAMP data set, about 39% of dives recorded zero spiny lobsters, although somereported as many as twenty (Figure 8). A total of 579 lobsters were observed, of which

67% were above the legal size. The natural log of lobsters seen per dive appeared to vary

by time period, visibility, depth, time of day, sampling site, management zone, moon

phase and whether lobster season is open (Figure 9). Estimating the impact of thesevariables on the number of lobsters seen would thus improve the estimate of changes in

abundance over time.

For both GLM of the log of positive CPUE and the presence/absence GLM, the AIC best

fit models (Table 4, Figure 10) included time period and distance from the Conservation

Zone. The best model also included visibility and depth for the presence/absence model.

The interaction between distance from the Conservation Zone and time period was notsignificant and was not included in the AIC best model; implying that the temporal trend

in abundance was the same both inside and outside of the Conservation Zone. In both

models, distance from the Conservation Zone had a negative effect on abundance,although the effect was only significant in presence/absence model.

These models explained 24% of the deviance in the presence/absence data and 71% ofthe deviance in the abundance if present. The diagnostics (Figure 10) showed a good fit

to the positive CPUE model (Figure 10b), although the qq-normal plot of the

presence/absence GLM (Figure 10a) shows some departure from normality.

When an abundance index was calculated as the product of the predicted fraction of divesto see a lobster, times the expected number of lobsters, from the AIC best fit models, theabundance of lobsters is quite variable but shows a generally increasing trend (Figure 11).

Despite the fact that more lobsters are seen in the Conservation Zone than the General

Use Zone (Figure 9), the temporal trend is the same both inside and outside the

Conservation Zone. There is also a tendency for abundance to be higher around thebeginning of lobster season in most years (Figure 11).

Estimates of total abundance and fishing mortality from depletion analysis

The reported catch of spiny lobster at Glovers Reef, from the Northern and Central

Cooperatives, has been lower in 2005 through 2009 than in 2002 through 2004; reportedcatches also declined between the beginning and end of the lobster season in most years(Figure 12). The CPUE (i.e. average of catch per vessel-day as reported to the

Cooperatives) also declined during the first few months of the lobster season every year

(Figure 12b), although there are also some high CPUE values late in the year in 2004 andespecially 2008. The low reported catches in recent years are not consistent with the

WCS data (Figure 12c). Although WCS has consistently been sampling on 10-20% of

the days in each month, there are some months when WCS sampled a larger catch than


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was reported to the cooperatives (fraction of catch greater than 1 in Figure 12c). This

implies that some of the decline in Glovers Reef catches reported to the cooperatives is

likely an error, perhaps caused by incorrect allocation of catches from area 3 (GloversReef) to other regions.

Bayesian DeLury state-space model fitted to catch

The Bayesian depletion models, whether fitted to data from only one year, or to all years

simultaneously were able to fit the declining trends in CPUE during each year (Figure13). For the single year models in 2008, the trend estimated with the only the

Cooperative CPUE data was different from that estimated with only the WCS CPUE

data, because in that year, the WCS data showed a decline while the Cooperative data

showed an increase in CPUE throughout the fishing season. The multiyear models andthe single year models produced similar trends every year except 2009. In 2009, the

multi-year models showed very little decline throughout the fishing season while the

single year model showed a decline.

The posterior distributions of the biomass at the beginning of the fishing season (Figure

14) implied that the biomass was very poorly estimated in most years. Although therewas a distinct peak in the posterior distribution at biomass levels on the order of 100 t in

most years, implying that values in this range were the most likely, the posterior

distribution had a long tail to the right, implying that even very high biomass levels had

posterior probabilities greater than zero.

Of the four multi-year models, the DIC preferred the models with separately estimated

variances and catchabilities in each year over the models with fixed catchability andvariance (Table 5). The DIC best model was the one with time-varying qand variance

and without hierarchical structure in the starting biomasses in each year (Model C, Table

5). Model C estimated an increase in both catchability and variance in the Cooperativeseries; both catchability and variance were variable but decreasing for the WCS series

(Figure 16). The reason for these estimated trends in catches is not clear. The

catchability for the Cooperative CPUE series, based on catches per vessel day, could

change between years if trip length or number of fishermen per boat changed, or if therewere changes in how data are recorded. Catchability may be more constant between

years in the WCS series based on catch per fishermen hour, if fishing methodologies have

not changed. It is also possible that catchability changes over time within fishing season,for example if lobsters are easier to find earlier in the season or that there is non-linear

relationship between catch rates and abundance.

The hierarchical models across all years (B and D) gave a more precise estimate of the

starting year biomass than the non-hierarchical models (A and C), and models that

allowed variance and catchability to vary across years (C and D) were more precise thanthose with catchability and variance fixed across years (A and B) (Figure 15). All of the

multi-year models except model D give more precise results than did the single year

models (Figure 14, Figure 15a). Model D, which allowed q and variance and starting

year biomass to vary freely between years was, as expected, nearly identical to the results


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obtained by fitting data from each year separately. The hierarchical models, as expected,

estimated more similar abundance levels in each year than did the year by year models.

Interestingly, the non-hierarchical multi-year model with time-varying qand variance(model C) also gave more similar starting biomass estimates across years than did the

single year models, implying that whether or not catchability and error variance are

allowed to vary across time periods has a significant influence on the results. The yearby year models give a reasonably precise estimate of the starting year biomass in years

when the CPUE appeared to decline exponentially over the course of the season (e.g.

2002 for the Cooperative series, 2007 for the WCS series). For years in which the CPUEincreased during the fishing season (e.g. 2008 for the Cooperative data series), the year-

by-year model estimated an extremely broad credibility interval for starting year biomass.

The models estimated starting biomass levels from about 20 to 200 t live weight oflobsters in the General Use Zone (Figure 15a). The lobster biomass was depleted to

about 55-75% of starting biomass in each fishing year (Figure 13). The fishing mortality

rates estimated by the models ranged from 0.05 to 0.5 (Figure 15b). Like the biomass

estimates, theFestimates are more precise for the multi-year models than for the year byyear models. Because the multi-year models (except for model D) estimate relatively

constant starting biomasses across the year, they estimate a declining trend in fishingmortality rate. The year to year trend in biomass and fishing mortality also varies with

model structure.

Bayesian DeLury regression model based on effort

The Leslie regression methods were able to estimate beginning year biomass levels from

the Cooperative effort data in every year (Figure 17, Figure 15). Because of the

informative prior forM, and the fact thatqand was constrained to be positive, the modelestimated a declining trend in each year, even when CPUE appeared to increase with

cumulative effort in 2008. An alternative run in which negative qwas allowed estimated

a negative starting biomass in 2008, but produced identical results in every other year.

The regression methods generally estimated a starting biomass in each season in the

lower range of the posterior distribution estimated by the Bayesian models and alsoestimated that starting biomass declined between 2002 through 2009 (Figure 15a).

Because of the decline in biomass, these models implied an increase in fishing mortalityrate between 2002 and 2009 (Figure 15b), and the estimated fishing mortality rates were

much lower than those estimated by the state-space models.

DISCUSSION

The analysis presented here provides a somewhat complex picture of the status and trendsin abundance of spiny lobsters at Glovers Reef marine reserve (Table 6). According to

the size based indicators, most of the harvested lobsters at Glovers Reef are above the

size at maturity, but many are below the optimal size for harvest. The fishing mortalityrate based on the length data from the fisheries (F=0.88) is just above Fmax, and well


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above both F0.1 and M; it is also less than the current national fishing mortality rate

(F=1.3) (Figure 18). There are no obvious trends in average length over time, which

would indicate a change in fishing mortality rate.

The abundance data from the LAMP survey shows a generally increasing trend across the

time series, although abundance seems to be higher around the beginning of the lobsterseason than it is later in the season. This increase in abundance, combined with the fact

that the LAMP survey found that lobsters tend to be bigger and more abundant inside the

Conservation Zone is consistent with the Conservation Zone providing significantprotection for lobsters. All but two of the LAMP survey sites for lobster are either inside

the Conservation Zone or within 500 m of the boundary, so that it is to be expected that

the LAMP survey trend would be dominated by the Conservation Zone where lobsters

are more abundant.

The two CPUE indices of abundance (from the Cooperative data and from the WCS data)

show a decline in relative abundance during the fishing season in most years, and no

obvious trend between years except a slight decline in the WCS data. The CPUE in catchper fisherman hour (the WCS data) is more likely to be an accurate measure of

abundance than the catch per vessel day (the Cooperative data), because effort ismeasured more precisely. The CPUE in terms of vessel day can be biased if, for

example, the number of fishermen associated with a vessel changes, or if the vessel loses

a days fishing due to weather.

Some measure of catch (or effort) is necessary to estimate sustainable catch levels.

Unfortunately, the region 3 catches reported by the National and Northern Cooperatives

do not appear to include a significant fraction of catches from Glovers Reef, particularlyafter 2005. In part because the catch and effort data are inconsistent with the CPUE data,

the results of the Bayesian depletion estimates are quite variable. The state-space model

(using catch data) estimated very low fishing mortality rates, ranging from 0.05 to 0.5depending on the structure of the model (Figure 18). These mortality rates are quite low

compared to the current national averaging fishing mortality rate of 1.3 (Gongora 2010).

On the other hand, the regression model fitted to the effort time series estimated fishing

mortality rates very similar to those from Gongora (2010), with a current (2009) medianFof 1.5. Which of these two sets of estimates is more accurate is difficult to say; both

are based on the same CPUE indices of abundance, but the regression method uses effort

data while the state-space method uses catch data. Also, the different model structuresimply different error structures, which can influence the results. It would be worthwhile

to determine what fraction of Glovers Reef lobster catch is reported at the National and

Northern Cooperatives. If fishermen sell some of their catch elsewhere, especially if thefraction of catch sold elsewhere has changed over time, the catch and effort data may be

very misleading.

It should also be noted that, because these analyses are based on data from lobsters that

were caught by fishermen, the estimated biomass at the beginning of the season is only

the biomass that is available to the fishery, corresponding to the biomass of legal sized

lobsters in the General Use Zone within free-diving depths at the beginning of the lobster


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season. Spillover of lobsters from the Conservation Zone during the lobster season

would be interpreted by the models as lower fishing mortality rates, because such

spillover would prevent the CPUE indices from declining as rapidly as they wouldotherwise. Also, the models assume that no lobsters grow to the legal size during the

fishing season; such growth would be interpreted as lower fishing mortality by the model.

Assuming that the National and Northern Cooperative data capture all or most of the

lobsters taken from Glovers Reef, it would be possible to set a total allowable catch

(TAC) for Glovers Reef based on these data. For example, using F0.1as a target fishingmortality rate, and using the biomass estimates from the same models shown in Figure

18, the appropriate target catches range from much lower than the current catch, to as

high as catches used to be in 2002 through 2004 (Figure 19). Given the uncertainty of the

catch and effort data, these values should probably not be used. Alternatively, an ad hocmanagement system could be developed using the indicators that we have calculated, for

example using a decision tree in which the population is considered overfished if several

indicators show a negative trend (e.g. Prince 2008). Finally, relative densities inside and

outside the no-take zone could be used to determine an appropriate level of harvest. Forany management strategy, it is critical to be able to document the total catch and/or total

effort at Glovers Reef, either by improving the reliability of the area designations in theCooperative data, or by gathering complete catch and effort data from the fishermen

while they are at Glovers Reef.


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Automatic Control. 19:716 723

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Ault, J. S. S. G. Smith, J. Luo, M. E. Monaco and R. S. Appeldoorn. 2008. Length-based

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Battaile, B. C. and T. J. Quinn. 2006. A Delury depletion estimator for walleye pollock

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Management, and Ecosystem Science 1:118, 2009

Ehrhardt, N.M. & Ault, J.S. 1992. Analysis of two length-based mortality models appliedto bounded catch length frequencies. Transactions of the American FisheriesSociety 121: 115122.

FAO. 2001. Report on the FAO/DANIDA/CFRAMP/WECAFC Regional Workshops onthe Assessment of the Caribbean Spiny lobster (Panulirus argus). FAO Fisheries

Report No. 619.

Froese, R. 2004. Keep it simple: three indicators to deal with overfishing. Journal of FishBiology 56: 758773.

Gongora, M. 2010. Assessment of the spiny lobster (Panulirus argus) of Belize based onfishery-dependent data. Belize Fisheries Department. March, 2010.

Grant, S. 2004. Glovers Reef Marine Reserve Fisheries Boat Census 2004 (Part 1).Wildlife Conservation Society.


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of catch rates of non-target species from a pelagic longline fishery: billfish speciesin the Venezuelan tuna longline fishery. Fisheries Research 70: 275297.

Prince, J. D., H. Peeters, H. Gorfinec and R. W Dayc. 2008. The novel use of harvest

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TABLES AND FIGURES

Table 1. Parameters and their prior distributions for the Bayesian depletion models.

(a) Model parameters

Model configuration Parameters

A. All years, both series, constant qand 2 M q1, q2 12, 2

2 Bi,1 for 8 years

B. Same, but hierarchical model ofBi,1 M q1, q2 12, 2

2 Bi,1for 8 years B, B

2

C. All years, both series, variable qand 2 M q1- q12 12- 12

2 Bi,1for 8 years

D. Same, but hierarchical model ofBi,1 M q1- q12 12- 12

2 Bi,1for 8 years B, B

2

E. Each individual series (12 runs) M q 2 B1

(b) Priors for the model parameters

Parameter Description Prior Range

M Natural mortality rate M=Normal(=0.34, =0.04) - -

B Average across years of startingbiomass

log(B)=Normal(=0, =1000) 1000-1.0E7

B Variance between years of startingbiomass

1/ B2=Gamma(0.01,0.01) 0-

Bi,1 Exploitable biomass of lobsters atthe beginning of the lobsterseason i

log(Bi,1)=Normal(= B, = B) for the

hierarchical models,

log(Bi,1)=Normal(= 0, =1000) for

non-hierarchical models

0-

1000-1.0E7

qj Catchability for abundance indexj log(qj)=Normal(=0, =0.01) 1.0E-7-1.0

j Observation error variance forabundance indexj

1/ j =Gamma(0.01,0.01) 0.001-100

Table 2. Fishing mortality rate estimated from average length using the method of

Ehrhardt and Ault (1992).

Data source n Lc n in range L se Z M F

Catch data 3293 90 1859 105.3 0.33 1.22 0.34 0.88

LAMP general use zone 228 90 89 117.8 2.51 0.56 0.34 0.22LAMP conservation zone 341 90 214 120.3 1.69 0.49 0.34 0.15

Table 3. GLM of lobster log CPUE in whole weight of legal sized lobsters per

fisherman-hour, as a function of time period (T), boat (B) and moon phase (M), for

(a) the AIC best model with fixed effects, and (b) random effects models with all


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possible second order interactions. The best random effects model according to the

AIC and the BIC is in bold.

(a) For AIC best model with fixed effects

Df DevianceResid.Df

Resid.Dev F Pr(>F) % deviance

NULL 614 558.3

T 36 155.4 578 402.9 7.63 0.0000 0.28

B 11 29.4 567 373.5 4.72 0.0000 0.05

M 2 5.0 565 368.5 4.40 0.0128 0.01

T x B 38 47.1 527 321.4 2.19 0.0001 0.08

T x M 8 17.8 519 303.6 3.94 0.0002 0.03

B x M 2 11.2 517 292.5 9.86 0.0001 0.02

(b) With random effects.

Model AIC BIC deviance

T+M+B 1590.25 1771.53 1463.39T+M+B+TxB 1577.84 1763.55 1477.21

T+M+B+TxM 1581.12 1766.83 1507.77

T+M+B+BxM 1591.67 1777.38 1465.41

T+M+B+TxB+TxM 1572.01 1762.14 1502.30

T+M+B+TxB+BxM 1579.82 1769.95 1477.59

T+M+B+TxM+BxM 1581.42 1771.55 1509.36

T+M+B+TxB+TxM+BxM 1573.29 1767.84 1504.66

Table 4. Analysis of deviance table for AIC best fit model of log of the count of

lobsters per dive in the LAMP survey (T=time period[month and year], Z=distance

from conservation zone boundary, v=visibility and d=depth).(a) presence/absence

Df Deviance Resid. Df Resid. Dev P(>|Chi|) % deviance

NULL 220 305

T 20 43.4 200 261.6 0.0018 0.14

v 1 11 199 250.6 0.0009 0.04

d 1 9.4 198 241.2 0.0022 0.03

Z 1 9.5 197 231.7 0.0021 0.03

(b) log count of lobsters for positive dives.

Df DevianceResid.Df

Resid.Dev F Pr(>F)

%deviance

NULL 133 248.6

T 20 176.7 113 71.9 14.04 0 0.71

Z 1 1.5 112 70.5 2.31 0.1314 0.01


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Table 5. DIC results for the Bayesian state space models. Model C (catchability and

variance different in each year, no hierarchical structure for starting biomass) has

the lowest DIC.

Model Dbar Dhat pD DIC Delta DIC

A 144.20 134.84 9.36 153.56 36.27B 144.76 137.68 7.08 151.84 34.56

C 100.25 83.21 17.04 117.28 0.00

D 99.99 73.50 26.50 126.49 9.21

Table 6. Summary of results for spiny lobster

Analysis Status

Froese indicators Most are mature, but too few large lobsters

F from ave. length F above F0.1 and close to Fmax

Catches Lower in 2005-2009 then in 2002-2004WCS CPUE Declines during season, between years

CPUE from Coop Declines during season, no trend between years

LAMP abundance Decrease during seasons, increase between years

B from depletion models Stable or decreasing depending on model

F from depletion models Increasing or decreasing depending on model

Figure 1. Length frequency distributions of spiny lobster in the LAMP and WCS

catch data. Lobsters mature at 70-80 mm CL (Gongora 2010), and the legal

minimum size is 78 mm CL.

0 20 40 60 80 100 130 160 190 220 250

Female

MaleUnknown

Coun

t

0

200

400

600

(a) Fishery

0 20 40 60 80 100 130 160 190 220 250

0

2

4

6

8

10

(b) LAMP General Use Zone far from boundary

0 20 40 60 80 100 130 160 190 220 250

Carapace length (mm)

C

oun

t

0

5

10

15

20

(c) LAMP General Use Zone near boundary

0 20 40 60 80 100 130 160 190 220 250

Carapace length (mm)

0

10

20

30

40

(d) LAMP Conservation Zone


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Figure 2. Average lengths plus or minus one standard error for the LAMP data in

both unfished and fished zones and for the WCS fisheries data, for all lobsters for

which carapace length (CL) was greater than the minimum size limit.

2004 2005 2006 2007 2008 2009

0

50

100

150

Year

CL(mm

)

(a) LAMP Conservation Zone

2004 2005 2006 2007 2008 2009

0

50

100

1

50

Year

CL(mm

)

(b) LAMP General Use Zone

2004 2005 2006 2007 2008 2009

0

20

40

60

80

100

1

20

Year

CL(mm

)

(c) Catch CL

Figure 3. Average lengths by months within years, in WCS catch data set.

2 4 6 8 10 12

0

50

100

150

Month

CL(mm)

20042005

20062007

20082009

Figure 4. Raw log-CPUE (in kg) data summary, showing the trend in log-CPUE (a)

by month within each fishing season (i.e. 2005.01 means the first month in the 2005

fishing season),(b) by moon phase, (c) by boat and (d) by location.

5

6

7

8

9

log

CPUE

2005

.01

2005

.02

2005

.03

2005

.04

2005

.07

2005

.08

2006

.01

2006

.03

2006

.04

2006

.05

2006

.06

2006

.08

2007

.01

2007

.02

2007

.03

2007

.04

2007

.05

2007

.06

2007

.07

2007

.08

2008

.01

2008

.02

2008

.03

2008

.04

2008

.06

2008

.07

2008

.08

2009

.01

2009

.02

2009

.03

2009

.04

2009

.05

2009

.06

2009

.08

2009

.09

2010

.01

2010

.02

(a) Month in season

5

6

7

8

9

log

CPUE

0 1 2 3 4 5 6 7 8 910

11

12

13

14

15

16

17

18

19

20

21

23

24

25

26

27

28

29

(b) Days after full moon

1 2 3 4 5 6 7 8 9 10 11 12

5

6

7

8

9

log

CPUE

(c) Boat

Eastern Reef G3 G4 G5 G6 G7 G8 North Point

5

6

7

8

9

log

CPUE

(d) Location


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Figure 5. Residuals versus fitted values, and qq normal plot, for the AIC best fit

mixed effects model (Table 3.2b) for lobster log-CPUE.

5.0 5.5 6.0 6.5 7.0 7.5 8.0

-2

-1

0

1

2

Residuals versus fitted

Predicted values

Res

idua

ls

-3 -2 -1 0 1 2 3

-2

-1

0

1

2

Normal Q-Q Plot

Theoretical Quantiles

Samp

leQuan

tiles

Figure 6. Trend in CPUE (solid line) during each fishing season from the AIC best

fit model (Table 3.2), plus and minus one standard error (dashed line), along with

unstandardized CPUE values (points).

2005 2006 2007 2008 2009 2010

0

1

2

3

4

Year

CPUE


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Figure 7. Histogram of number of lobsters caught per fisherman in the WCS catch

data.

Lobsters per fisherman

Coun

t

0

10

20

30

40

50

60

70

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45

Figure 8. Histogram of lobsters observed per dive in the LAMP data set.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Legal

All sizes

Number of lobsters

Num

bero

fdives

0

20

40

60

80

100


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Figure 9. Log number of lobsters observed per dive [log(Count+0.01)] in the LAMP

data, by month, visibility, depth, time of day, sampling site, distance from the

conservation zone boundary, management zone, days from full moon and whether

lobster season is open, including dives for which no lobsters were observed.

-6

-4

-2

0

2

Time period

log-count

2004.0

8

2004.1

0

2005.0

3

2005.0

5

2005.1

1

2006.0

3

2006.0

7

2006.0

9

2007.0

2

2007.0

5

2007.0

8

2007.1

1

2008.0

2

2008.0

5

2008.0

8

2008.1

1

2009.0

2

2009.0

6

2009.0

8

2010.0

55 10 15 20

-4

0

2

4

68

Visisbility

Visibility(m)

log-count

5 10 15

-10

-5

0

5

Depth

Depth(m)

log-count

8 10 12 14 16

-8

-4

0

2

4Start time

Time

log-count

prC10AB prC1AB prC3AB prC6AB prC8AB

-6

-4

-2

0

2

Site

log-count

-2 -1 0 1 2 3

-8

-4

0

4

Distance from conservation zone

Distance (km)

log-count

CZ Line GUZ

-6

-4

-2

02

Management zone

log-count

0 5 10 15 20 25 30

-4

-2

0

2

4

6Days from full moon

Day

log-count

1 2

-6

-4

-2

02

Fishing season

fishseason

log-count

Figure 10. Residuals and qq-normal plot of the AIC best fit model of (a) presence or

absence of lobsters and (b) log lobster sightings per minute in the LAMP

observations for dives in which lobsters were seen.

(a) Presence/absence

-4 -2 0 2 4

-2

-1

0

1

2

3

Predicted values

Res

idua

ls

Residuals vs Fitted6

5765

-3 -2 -1 0 1 2 3

-2

-1

0

1

2

3


Std

.dev

ianceres

id.

Normal Q-Q6

5718

(b) Positive log-lobsters per dive

0.5 1.0 1.5

-2

-1

0

1

Predicted values

Res

iduals

Residuals vs Fitted

2938

183

-2 -1 0 1 2

-2

-1

0

1

2


Std

.dev

iance

res

id.

Normal Q-Q

29

38

183


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Figure 11. LAMP lobster standardized trend (liness), plus and minus one standard

error, from the AIC best fit models (Table 4). The CPUE abundance index is the

product of the predicted fraction of dives seeing a lobster times the predicted

number of lobsters seen given that any were seen. Unstandardized average count

for sites in the General Use Zone is also shown (points). The index and the raw data

have been divided by their means. Vertical lines indicate the beginning (at the tickmark) and end of the fishing season.

2004 2005 2006 2007 2008 2009 2010

0

1

2

3

4

5

6

Fishing season

Lo

bster

abun

dance

index

Figure 12. Lobster (a) catches and (b) catch per unit of effort from area 3 (Glovers

Reef) from the Belize fisheries data set by month, for Northern and National

Cooperatives combined, and (c) comparison between catch and effort sampled byWCS and catch and effort reported to the cooperatives.

(a)

Who

lewe

ight(kg

)

0

5000

10000

2002 2003 2004 2005 2006 2007 2008 2009


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28

GLOVERSREEFANNUALREPORT

Year

(c)

Fractionofcatchsampled

Fractionofdayssampled

0.0 0.2 0.4 0.6 0.8 1.0

2004.04

2005.01

2005.02

2005.03

2005.04

2005.07

2006.01

2006.03

2006.04

2006.05

2006.06

2007.01

2007.02

2007.03

2007.04

2007.05

2007.06

2007.07

2008.01

2008.02

2008.03

2008.04

2008.06

2008.07

2009.01

2009.02

2009.03

2009.04

2009.05

2009.06


39/58


Figure 13. CPUE data points from the Cooperative data (by vessel-trip) and from

the WCS catch and effort data (by fisherman-hour), along with the median values of

the fitted biomass trends from the depletion model fitted to the data from each year

separately (fitted to each index independently and to the two together), as well as the

biomass trend from the models fitted to data from all years simultaneously.

0.0

0.5

1.0

1.5

2.0

2.5

3.0 2002 2003 2004

0.0

0.5

1.0

1.5

2.0

2.5

3.0 2005 2006 2007

0.0

0.5

1.0

1.5

2.0

2.5

3.0

2 4 6 8 10 12

2008

2 4 6 8 10

2009

Coop CPUE

WCS CPUE

Trend Coop 1 yr

Trend WCS 1 yr

Trend Both 1 yr

Trend multiyear

2 4 6 8 10

Month

CPUE

Figure 14. Posterior distributions of starting exploitable biomass of lobsters at

Glovers Reef, from the Bayesian depletion model with catchability and variance

different in each year (Model C), compared to the models fit to data from one year

at a time.

2002

0.0

0.1

0.2

0.3

0.4 2003 2004

2005

0.0

0.1

0.2

0.3

0.4 2006 2007

2008

0.0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000

2009

0 200 400 600 800 1000

All years: Model C

By year, Coop

By year, WCS

By year, both

0 200 400 600 800 1000

Biomass (t)

Probability


40/58


Figure 15. Comparison of depletion model results for the Bayesian state space

models described in Table 1, and the DeLury regression model fitted to effort.

(a) Starting biomass

- --

- - --

-

2002 2003 2004 2005 2006 2007 2008 2009

0

200

400

600

800

1000

Year

Start

ing

biomass

(t)

- --

- -- -

-

- - - - - - - -

--

-

- -

--

-

- - - - - - - -- --

- - - - -- -

-

- - - - -

-

-

-

-

-

-

-- -

-

- - - - -- - - -- - -

--

-

-

-

-

-

-

-

-

-

-

-

-

-

- - - - - - - -- - - - - - - -

All years:AAll years:B

All years:CAll years:D

By year:CoopBy year:WCS

By year:Both

Regression

(b) Fishing mortality rate

- - - - - - - -

2002 2003 2004 2005 2006 2007 2008 2009

0.0

0.5

1.0

1.5

2.0

Year

Fishingmorta

lityra

te

-

--

- - -- -- - - - - - - -

-

--

- --

- -

--

-

- - -- -

--

-

--

--

--

- - - - - - -

-

- --

- --

-

-

- - - - - - -- - - -- - - -

-

- --

- --

-

- --

-

-

--

-

-- -

-

-

-

-

-

--

- -

-

-

-

-All years:AAll years:BAll years:CAll years:D

By year:CoopBy year:WCS

By year:BothRegression


41/58


Figure 16. Catchability (q) and error variance by year for the non hierarchical

models with and without time-varying q and variance (Table 1, models A andC).

2002 2003 2004 2005 2006 2007 2008 2009

0.0

0

0.0

4

0.08

0.1

2

Year

q(*1000)

(a) q for Coop series

2005.0 2005.5 2006.0 2006.5 2007.0 2007.5 2008.0

0.0

0

0.0

2

0.04

0.0

6

Year

q(*1000)

(b) q for WCS series

2002 2003 2004 2005 2006 2007 2008 2009

0.0

0.2

0.4

0.6

Year

V

ariance

(c) Variance for Coop series

2005.0 2005.5 2006.0 2006.5 2007.0 2007.5 2008.0

0

200

400

600

800

Year

V

ariance

(d) Variance for WCS series

Figure 17. Observed (points) and predicted (lines) log-CPUE from the Cooperative

data versus cumulative effort from the Cooperative data, from the Delury

regression.

2002

0

1

2

3

4

2003 2004

2005

0

1

2

3

4

2006 2007

2008

0

1

2

3

4

100 200 300 400 500

2009

0 200 400 600 800 0 200 400 600 800

Cumulative effort (vessel days)

Log

(CPUE)


42/58


Figure 18. Fishing mortality rates estimated from Glovers Reef data (methods on

y-axis), compared to the values computed for the whole of Belize in 2009, and Fmax

and F0.1(Gongora 2010). The value of M is also shown for comparison.

| | |

0.0 0.5 1.0 1.5 2.0

Fishing mortality

X

| | |

| | |

| | |

| | |

| | |

Model A, all years

Model A, 2009

Model C, all years

Model C, 2009

Regression, all years

Regression, 2009

From ave. length

Belize F-2009FmaxF0.1M

Figure 19. Expected catches with a F0.1harvest strategy, applied to the biomass

estimates from the models specified in the y-axis.

| |

0 10000 20000 30000 40000 50000 60000

Catch (kg live wt)

| |

| |

| | |

| | |

|||

Model A, all years

Model A, 2009

Model C, all years

Model C, 2009

Regression, all years

Regression, 2009

C-2

002

C-2

003

C-2

004

C-2

005

C-2

006

C-2

007

C-2

008

C-2

009


43/58


44/58


included as a numerical variable instead of months, to test for a linear trend within each

fishing season.

We did not include time of day or depth in the analysis because most fishermen reported

fishing six hours or more, so that the time and depth at which each conch was captured

was not precisely known. Of the 26 boats for which conch catch and effort data wererecorded, 19 were sampled on 3 or more days and were included in the analysis. There

was much less variability in catch rates between locations than there was between boats,

so we included boat as a factor in the model but not location.

Documents

Report on spiny lobster abundance and fishing mortality and preliminary analysis of existing fisheries data at Glover’s reef research station