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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.: EPPI0004002000 Task Order No. 5Subcontract No.: EPPI0504002000WCSPeriod 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 fisheryindependent data set ....................................... 7Abundance trends from the LAMP fisheryindependent data set ....................................... 8
Bayesian DeLury statespace 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 fisheryindependent data set ..........................13
Estimates of total abundance and fishing mortality from depletion analysis ........13Bayesian DeLury statespace 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 Longterm 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 rightsbased access and marketdriven 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 transboundary watershed areas andseven key focal species. The four transboundary regions are the Gulf of Honduras, the
Moskitia Coast, CahuitaGandocaBocas 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 rightsbased legislation andprograms, establishment of managed protected areas and notake 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 agebased 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 MesoAmerican 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 selfsustaining
population. Instead, we used lengthbased indicators and depletion methods to estimatethe abundance and fishing mortality of postrecruitment 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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GLOVERS REEF ANNUAL REPORT 3
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 20022004; 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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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(1exp(K(tt0)))], 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 20042005 than in 20062010.
From 2006 to 20010, the majority of the lobsters (61%) were taken in the central lagoon
north of the conservation zone (areas G5G7). 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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GLOVERS REEF ANNUAL REPORT 7
(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 logCPUE 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 logCPUE.
Abundance trends from the LAMP fisheryindependent 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.
Abundance trends from the LAMP fisheryindependent data set
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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GLOVERS REEF ANNUAL REPORT 9
(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 statespace model fitted to catch
We assumed that all recruitment occurred between fishing seasons, so that no lobsterswould grow from sublegal 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 (20022009). The fishing mortality rate in each
monthly time step was approximated asFt=log(1Ct/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 noninformative 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 logmean and logstandard 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 multiyear 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 tradeoff
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 multiyear models
(model E).
The prior distributions of the estimated parameters (Table 1b) were noninformative ,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
burnin of 50,000 iterations, and a thin rate of 10. With these settings, all the models
converged adequately according to the GelmanRubin 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 reran 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) 7896% of the catch was mature individuals; (2) 15%were near the optimal length; and (3) 4% were megaspawners. 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 logCPUE data (Figure 4) appear to show a downward trend in log
CPUE with time within most fishing seasons. LogCPUE 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 2wayinteractions 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.
Abundance trends from the LAMP fisheryindependent data set
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 qqnormal 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 vesselday 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 1020% 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 statespace 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
multiyear 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 multiyear 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 timevarying 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 nonlinear
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 nonhierarchical 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
multiyear 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 nonhierarchical multiyear model with timevarying 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
byyear 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 5575% 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 multiyear models than for the year byyear models. Because the multiyear 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 statespace 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 statespace 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 statespace 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 freediving 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 notake 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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Lo, N. C. H., L. D. Jacobson, and J. L. Squire. 1992. Indices of relative abundance from
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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) 10001.0E7
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
nonhierarchical models
0
10001.0E7
qj Catchability for abundance indexj log(qj)=Normal(=0, =0.01) 1.0E71.0
j Observation error variance forabundance indexj
1/ j =Gamma(0.01,0.01) 0.001100
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
fishermanhour, 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 20052009 then in 20022004WCS 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 7080 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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GLOVERS REEF ANNUAL REPORT 23
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 logCPUE (in kg) data summary, showing the trend in logCPUE (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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24 GLOVERS REEF ANNUAL REPORT
Figure 5. Residuals versus fitted values, and qq normal plot, for the AIC best fit
mixed effects model (Table 3.2b) for lobster logCPUE.
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 QQ 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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GLOVERS REEF ANNUAL REPORT 25
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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26 GLOVERS REEF ANNUAL REPORT
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
logcount
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)
logcount
5 10 15
10
5
0
5
Depth
Depth(m)
logcount
8 10 12 14 16
8
4
0
2
4Start time
Time
logcount
prC10AB prC1AB prC3AB prC6AB prC8AB
6
4
2
0
2
Site
logcount
2 1 0 1 2 3
8
4
0
4
Distance from conservation zone
Distance (km)
logcount
CZ Line GUZ
6
4
2
02
Management zone
logcount
0 5 10 15 20 25 30
4
2
0
2
4
6Days from full moon
Day
logcount
1 2
6
4
2
02
Fishing season
fishseason
logcount
Figure 10. Residuals and qqnormal 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
Theoretical Quantiles
Std
.dev
ianceres
id.
Normal QQ6
5718
(b) Positive loglobsters 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
Theoretical Quantiles
Std
.dev
iance
res
id.
Normal QQ
29
38
183

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GLOVERS REEF ANNUAL REPORT 27
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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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

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Figure 13. CPUE data points from the Cooperative data (by vesseltrip) and from
the WCS catch and effort data (by fishermanhour), 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

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30 GLOVERS REEF ANNUAL REPORT
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

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Figure 16. Catchability (q) and error variance by year for the non hierarchical
models with and without timevarying 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) logCPUE 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)

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32 GLOVERS REEF ANNUAL REPORT
Figure 18. Fishing mortality rates estimated from Glovers Reef data (methods on
yaxis), 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 F2009FmaxF0.1M
Figure 19. Expected catches with a F0.1harvest strategy, applied to the biomass
estimates from the models specified in the yaxis.
 
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
C2
002
C2
003
C2
004
C2
005
C2
006
C2
007
C2
008
C2
009

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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.