Fisheries Research xxx (2005) xxx–xxx

Bioeconomic modelling and risk assessment of the Cubanfishery for spiny lobsterPanulirus argus

3

4

Rafael Pugaa,∗, Sergio Hern´andez Vazquezb,Juana L´opez Martinezc, Marıa E. de Le´ona

5

6

a Centro de Investigaciones Pesqueras, 5a Avenida y Calle 246, Barlovento, Sta. Fe, Playa,Apartado Postal 11300, Ciudad de la Habana, Cuba

7

8b Centro de Investigaciones Biol´ogicas del Noroeste, S.C. Apartado Postal 128, La Paz, B.C.S. 23000, Mexico9

c Centro de Investigaciones Biol´ogicas del Noroeste, S.C. Unidad Guaymas, Apartado Postal 349, Guaymas 85465, Sonora, Mexico10

Received 14 December 2003; received in revised form 21 February 2005; accepted 23 March 2005; online 17 June 2005

11

Abstract12

Spiny lobster (Panulirus argus), the most valuable fishery resource in Cuba, is subject to a state property regime and to alimited-access system. Managers need to be advised on the consequences of choosing different methods for managing the fishery.An age-structured bioeconomic model was developed to simulate the population dynamics of the stock allowing short-term andlong-term (equilibrium) predictions on catch, biomass, egg production, revenue, cost and profit, due to changes in the fishingeffort. The equilibrium version of the model can be used to estimate a number of bioeconomic reference points, such as thefishing effort for the maximum sustainable yield per recruit, or the maximum economic yield per recruit. The stochastic andd ment, takingi ds

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oral32

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was34

00235

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urce37

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FISH 1906 1–15

ynamic version can be used to assess every year the risk of exceeding common benchmarks used in fishery managento account uncertainty in parameters, such as catchability and recruitment. It was found that the recruitment has decreaseince 1988 and that the effort should be limited at the level of maximum economic yield.2005 Published by Elsevier B.V.

eywords: Panulirus argus; Population dynamics; Fishery assessment; Stock and recruitment

. Introduction

In Cuba, spiny lobsterPanulirus arguscan be foundll round the country, but it is most common around theouth coast where the main fishery occurs, especiallyn the Gulf of Bataban´o (Fig. 1), where 60% of the

∗ Corresponding author. Tel.: +53 7 2088638; fax: +53 7 2049827.E-mail address:rpuga@cip.telemar.cu (R. Puga).

total national catch is harvested. The Gulf of Batabois a reef lagoon with an area of 20,850 km2, 6 m meandepth, surrounded by a number of small keys and creefs and many sea grass beds (Paez and Revilla, 1991),an ideal habitat for spiny lobster. The average catch7034 t between 1978 and 1989, but from 1990 to 2this decreased to 5005 t.

Spiny lobster is the most valuable fishery resoin Cuba and many studies have been made on

165-7836/$ – see front matter © 2005 Published by Elsevier B.V.oi:10.1016/j.fishres.2005.03.014

2 R. Puga et al. / Fisheries Research xxx (2005) xxx–xxx

Fig. 1. Map showing fishing areas for spiny lobster in Cuban archipelago.

species. A review of the main aspects of the biology,39

fishery and management was reported byBaisre and40

Cruz (1994). About 70% of the catch is comprised of41

lobsters between 70 and 100 mm carapace length. More42

than 60% of the catch is processed as pre-cooked whole43

lobsters and exported to Japan, France, Spain, Italy and44

Canada, with an average price of US$ 12 kg−1.45

At present, there are 117 boats in the Gulf of Bata-46

bano fishery, which operate two kinds of fishing gears,47

artificial shelters and trap-like nets. There are about48

143,000 artificial shelters made of tree trunks and49

fibercement plates, and about 12,200 rectangular trap-50

like nets made of chicken wire with large leader nets51

(about 40 m long) attached at the two front corners52

in a V-pattern. The fishing gears used in the fish-53

ery are well described byBaisre and Cruz (1994)54

andCruz and Phillips (1994). The fishery is currently55

managed with input and biological controls which56

include a state property regime; limited entry; territorial57

rights to fishery enterprises; gear restrictions; a 105-58

day closed season from March to May; closed areas59

to protect juveniles and spawners; a minimum legal60

size of 69 mm carapace length (CL) and a prohibition61

on taking berried females. A detailed data-collecting62

system on the fishery has been established. The biolog-63

ical and fishery information are analysed at the Fish-64

eries Research Centre. The management regulations65

are annually revised by a Fisheries Management Com-66

mittee which comprises managers, decision-makers,67

users and scientists, and the final decisions are enforced68

b69

270

Historically, assessments of the spiny lobster71

resource in Cuba have been based on virtual population72

analysis (Puga et al., 1996), yield per recruit analy- 73

sis (Puga et al., 1995) and surplus production models 74

(Puga et al., 2003). Managers currently require advice 75

on the economic consequences of choosing from a76

number of alternative options for managing the fishery.77

The objectives of the present research were to apply78

a bioeconomic model to the fishery in the Gulf of79

Bataban´o, to explore some reference points and to per-80

form a risk assessment on the probability of achieving81

or exceeding them. Bioeconomic models have been82

applied to other spiny or rock lobster fisheries, such83

as New Zealand, Hawaiian, Archipelago and Mexico84

(Breen et al., 1994; Clarke et al., 1992; Seijo et al.,85

1991). General bioeconomic models forP. argusfish- 86

eries in Cuba, Brazil and Isla Mujeres (Mexico) were87

developed bySeijo et al. (2001). 88

2. Methods 89

2.1. Data sources 90

Catch, effort, proportions of exported products91

(fixed and variable), cost and spiny lobster price data92

were obtained from compulsory records from the fish-93

ing, processing and exporting enterprises. Effort data94

as boat fishing days are available since 1983 and catch95

data are available since 1928. The stock assessment96

w 02,97

b only98

y a Fisheries Inspection Unit (Puga and de Le´on,003).

FISH 1906 1–15

as performed with data for the period 1974–20ecause length frequency of landings is available

R. Puga et al. / Fisheries Research xxx (2005) xxx–xxx 3

since 1974. These length frequencies are converted99

from monthly landings by export size categories in the100

processing plants, as described byAlfonso et al. (1995).101

Mean values of proportions of different products cate-102

gories, costs and prices were estimated with statistics103

from 1999 to 2001.104

2.2. Parameters105

Natural mortality rate was assumed to be the same106

for all the age groups. It was estimated asM= 0.34107

using the growth parameters estimated byLeon108

et al. (1995), considered to be the most reliable for109

the species in its distribution area (Arce and de Le´on,110

2001), and a mean water temperature of 27◦C, using111

an empirical equation developed byCruz et al. (1981)112

for lobsters, similar to Pauly’s equation used for finfish113

(Pauly, 1980). There is also an estimate from Turks and114

Caicos Islands ofM= 0.36 using catch and effort data115

(Medley and Ninnes, 1997).116

The egg production was computed through size117

(age)-specific maturity and fecundity relations from118

previous studies (Cruz and de Le´on, 1991). Multi-119

ple spawning was modelled by assuming that females120

larger than 80 mm CL have two broods per year121

(Lipcius, 1985).122

Conversions between size (age) and weight were123

made with the length–weight relationship presented by124

Cruz et al. (1981).125

om-126

m n127

( s128

f nce129

and crew salary. Fixed cost comprises depreciation of130

boats, engines and fishing gears, administrative salary131

and opportunity cost on capital. Opportunity cost is132

defined bySeijo et al. (1998)as the net benefits that133

could have been achieved in the next best economic134

alternative of investment. Following the recommen-135

dation ofSparre and Willman (1993)andSeijo et al. 136

(1998), opportunity cost was estimated as a rate of the137

capital invested in the fishery and processing sectors,138

taking into account the real average interest rate of 11%139

from the Cuban banking sector. Opportunity cost of140

capital was calculated byBreen et al. (1994)using an 141

interest rate of 10% in the New Zealand fishery for142

Jasus edwarsii. Processing cost comprises transport,143

packing material, power and water, repair and mainte-144

nance, salary, depreciation of equipments and export145

tax. 146

All parameters used in the stock assessment and147

in the population dynamics model are presented in148

Tables 1–4. 149

2.3. Stock assessment 150

Length frequency of landings was converted to age151

structure of catches in numbers by a slicing method152

(Sparre andVenema, 1997) with the growth parameters 153

obtained byLeon et al. (1995). Sequential popula- 154

tion analysis (SPA) with the ADAPT framework was155

applied to the 1974–2002 matrix of catch-at-age groups156

f d 157

M in 158

n d the159

s mate160

TW

A ggs pe 3

>

W 981). Ega ork.

Economic parameters were computed as recended byAnderson (1986), Sparre and Willma

1993)andSeijo et al. (1998). Variable cost compriseuel and lubricants, food, ice, repair and maintena

able 1eight, egg production, selectivity and stock size at age

ge (year) Weight (kg) Egg production (efemale per year)

1 0.014 02 0.139 03 0.412 29614 0.781 353555 1.196 2290506 1.615 3795057 2.014 5069758 2.376 6229309 3.172 754359

eight estimates from length–weight relationship byCruz et al. (1nd de Le´on (1991). Selectivity and stock size from SPA in this w

FISH 1906 1–15

rom 1 to >9, using an Excel spreadsheet (Lassen anedley, 2000). The catch-per-unit effort (CPUE)umber was used as an index of abundance, antock sizes by age and year were used to esti

r Selectivity (relative toage 8 years)

Stock size in 198(thousands)

0.001 40836.40.385 27928.81.429 15874.22.149 6616.72.344 2257.81.867 736.81.600 289.51.000 122.40.500 109.8

g production estimates from maturity and fecundity results byCruz

4 R. Puga et al. / Fisheries Research xxx (2005) xxx–xxx

Table 2Set of biological parameters of the spiny lobster in the Gulf of Bataban´o fishery

Parameter Description Value Source

L∞ (males) (mm CL) Maximum asymptotic length 185 Leon et al. (1995)L∞ (females) (mm CL) 155 Leon et al. (1995)K (males) (year−1) Growth rate 0.23 Leon et al. (1995)K (females) (year−1) 0.19 Leon et al. (1995)t0 (males) (year) 0.44 Leon et al. (1995)t0 (females) (year) 0.37 Leon et al. (1995)M (year−1) Natural mortality rate 0.34q8 Catchability at age 8 years 1.16× 10−5 SPA in this workα Parameter of the Ricker stock–recruit relation 0.22226 SPA in this workβ Parameter of the Ricker stock–recruit relation −0.00214 SPA in this work

Table 3Economic parameters for the Gulf of Bataban´o lobster fishery, cal-culated from compulsory records from the fishing and processingenterprises between 1999 and 2001

Parameters Value Unit

Variable cost 171 US$/boat fishing dayFixed cost 24840 US$/boatProcessing cost 687 US$/t raw spiny lobsterFishing days per boat 173

logarithmic values of catchabilities (coefficients of pro-161

portionality between indices of abundance and absolute162

abundance) by age and year. Residuals from the matrix163

of catchabilities and the mean values by age were used164

to compute the minimum of the least-squares sum of165

residuals as the objective function, fitting the terminal166

fishing mortality rate for age group 8 years. Fishing167

mortality rates for ages 1–7 years in year 2002 were168

relative to age 8 years, on the assumption that the169

selectivity pattern remained stable during the period170

1997–2000.171

A Ricker (1954)stock–recruitment relationship was172

estimated from a non-linear fit to spawning and recruit-173

ment outputs from SPA. The spawning index used was174

the egg production at yeart, and the recruitment index 175

was the number of 1-year-old lobsters at yeart+ 1. 176

2.4. Population dynamics model 177

The model was developed on MS Excel spread-178

sheets. An age-based version of the Ricker yield per179

recruit model was used to generate long-term (equilib-180

rium) predictions on yield per recruit, profit per recruit181

and spawning per recruit, as a function of changes in182

the fishing effort. A dynamic age-structured version of183

the model was used for short-term predictions of catch,184

profit and egg production as responses to different lev-185

els of effort by year. 186

The dynamic model represents the flow of lobsters187

by age through the years, starting from the age structure188

in 1983 obtained from SPA. 189

Recruitment is determined by: 190

N1,t+1 = αSt e−βSt191

whereN1,t+1 is the number of individuals with age 1192

year at the start of the yeart+ 1,α andβ are the param- 193

eters from Ricker stock–recruitment relation andSt is 194

Table 4Industrial parameters for the Gulf of Bataban´o lobster fishery calculated from compulsory records from the processing and exporting enterprisesbetween 1999 and 2001

Proportion of differentproducts categories

Conversion factors from raw Price (US$ kg−1)

Pre-cooked whole lobster 0.621Frozen tails 0.309Frozen whole 0.049Alive 0.022

FISH 1906 1–15

material to products categories

0.926 12.120.320 27.870.980 12.24

1.000 12.32

R. Puga et al. / Fisheries Research xxx (2005) xxx–xxx 5

the egg production index at yeart.195

St =∑

NFa,tPEFa196

where NFa,t is the number of females with agea at the197

start of yeart and PEFa is the production of eggs per198

female per year by agea.199

The equations that describe the basic dynamics of200

the lobster fishery are:201

Na+1,t+1 = Na,t e−(Fa,t+M)202

whereNa,t is the number of individuals with agea at203

the start of yeart,Fa,t the age-specific fishing mortality204

rate at yeart andM is the natural mortality rate.205

Fishing mortality is calculated by age and time as206

follows:207

Fa,t = Sa/8F8,t208

whereSa/8 is the selectivity pattern by agea relative to209

age 8 years andF8,t is the fishing mortality rate at age210

8 years at yeart.211

F8,t = ftq8212

where ft is the fishing effort at yeart and q8 is the213

catchability coefficient at age 8 years.214

Catch is estimated on the assumption that it is taken215

instantaneously at the middle of the year:216

Ct =∑ (

(Na,t − Na+1,t+1)

(Fa,t

Fa,t + M

))Wa217

w218

2219

220

T221

w s222

o n223

f es224

a uct225

c lity226

o the227

l228

229

T230

where VC/f is the variable cost per unit of effort,ft the 231

fishing effort at yeart, FC/b the fixed cost per boat,bt 232

the number of boats at yeart, PCt raw the processing 233

cost per tonne of raw material andCt is the catch at 234

year t. The number of boats by year is estimated by235

means of the annual number of boat fishing days and236

the average figure of 173 fishing days per boat. 237

Total profits by year are then calculated as238

TPt = TRt −TCt, and the present value of profit over239

time was estimated taking into account a discount rate240

of 10%. 241

In a similar way, in the New Zealand fishery forJ. 242

edwarsii.Variable cost were assumed to depend on fish-243

ing mortality rate and fixed cost on the capital invested244

(Breen et al., 1994). They also used a discount rate245

of 10% to calculate the present value of profit over246

time. 247

2.6. Uncertainty and risk analysis 248

The deterministic equilibrium version of the model249

allows estimating some reference points usable for250

fishery management, while the stochastic dynamics251

version allows for uncertainties in input parameters252

and can evaluate the probabilities of achieving and253

exceeding reference points through Monte Carlo sim-254

ulation. Monte Carlo simulation is a convenient and255

extended tool to assess a model’s output given differ-256

ent types and levels of error in the model’s inputs as257

n n 258

( 259

s ses260

d ity261

f , 262

2 263

sti-264

m 265

266

er267

268

er269

270

sur-271

as272

273

rt 274

275

hereWa is the mean weight by age.

.5. Economic model

Total revenues are calculated according to:

Rt = Ct

∑PCpCFpPRp

hereCt is the catch at yeart, PCp the proportionf different product categoriesp, CFp the conversio

actors from raw material to each product categoripnd PRp are the prices per unit of weight by prodategoriesp. It should be noted that almost the totaf products are exported, so the consumption in

ocal market is irrelevant.Total costs are computed as:

Ct = VC

fft + FC

bbt + PCt rawCt

FISH 1906 1–15

oted byRestrepo et al. (1992), Francis and Shotto1997)andSeijo and Caddy (2000). The Monte Carloimulation approach is well suited for such analyue to the explicit control over the probability dens

unctions for uncertain input parameters (Legault et al.002).

In this work, the following reference points are eated:

fcurrent: average effort for the period 2000–2002;fmey/r: effort associated with maximum profit precruit;fmsy/r: effort associated with maximum yield precruit;fmed: effort associated with the observed medianvival ratio (N1/S) in a replacement line analysisexamined byMace and Sissenwine (1993);fhigh: a level of effort similar to the maximum effoobserved in the fishery.

6 R. Puga et al. / Fisheries Research xxx (2005) xxx–xxx

In the risk assessment performed byHobday and276

Punt (2001), about the Victorian southern rock lobster,277

J. edwarsiithe values for the parameters that determine278

age, natural mortality, egg production and selectivity279

were all assumed to be known exactly, and the future280

recruitment was determined by random sampling from281

the recruitments for the last 10 years of the assessment282

period.283

Simpfendorfer et al. (2000)assessed the status of the284

whiskery shark stock in southwestern Australia using285

an age-structured model. They conducted a risk analy-286

sis to determine the impact of future harvest strategies287

on biomass targets, and recruitment variability was288

assumed to be described by a normal distribution with289

CV = 20%.290

In the stochastic version of the CubanP. argus291

model, the values for the parameters that determine292

age, natural mortality and egg production were all293

assumed to be known exactly, while catchability and294

recruitment were considered as input parameters with295

uncertainty specified as log-normally distributed ran-296

dom variables. Since coefficients of variation from SPA297

were CV = 9.8% for catchability and CV = 18.4% for298

recruitment, coefficients of variation were assigned as299

10 and 20%, respectively, for both input parameters300

during Monte Carlo simulations.301

Each time the stochastic model was used, 2000 runs302

were made starting in the 1983 situation and projecting303

the population forward with the observed fishing effort304

during 1983–2002 and with three alternative levels of305

e306

the307

p han308

1 no309

fi cor-310

r rved311

m ysis312

( ple313

e lcu-314

l n be315

c -316

t For317

a hat318

c aight319

l s320

a321

r322

R f323

which can then be translated back to the SPR scale324

(Mace and Sissenwine, 1993). The replacement line is 325

defined as the line with a slope equal to the observed326

average survival ratio.Sissenwine and Shepherd (1987)327

referred to the fishing mortality rate that corresponds to328

the average survival ratio asF-replacement They pro- 329

posed estimating it from the median survival ratio, in330

which case it may be referred to, by the symbol,Fmed 331

(F-median). 332

3. Results 333

3.1. Stock assessment 334

An index of the “goodness of fit” of the SPA shows335

a high coefficient of determination (r2 = 0.79,p< 0.05) 336

between fishing mortality rate and effort for the period337

1983–2002 (Fig. 2). The equation describing the rela-338

tionship between both variables can be represented339

as:F=qf, whereq= 0.0000153/boat fishing day is the340

average catchability coefficient. 341

The exploitation rate (E) for the whole period under 342

study (Fig. 3) shows the highest values with a decreas-343

ing trend from 1974 to 1988, when it was higher than344

50%, while the fishing effort remained over 22,000 boat345

fishing days.After minimum values of exploitation rate346

in 1990 (39.6%) and fishing effort in 1992 (15,532 boat347

fishing days), increasing trends occurs from 1993 to348

r 99.349

D ita-350

t low351

l ). 352

F riod1

ffort for the subsequent period 2003–2010.The risk analysis was conducted by computing

robability that spawning per recruit was less t4.3% of the level that would occur if there whereshing. In this case, the value of SPR (%) = 14.3esponds with the effort associated with the obseedian survival ratio in the replacement line analfmed). Spawning per recruit (SPR) analysis is a simxtension of the dynamic pool model used to ca

ate yield per recruit. A standard SPR analysis caombined with spawning–recruitment (S–R) observaions to generate reference fishing mortality rates.ny constantF, there is a corresponding SPR level tan be inverted and used as the slope of a strine through the origin of theS–R scatterplot. Pointlong the line represent the average survival ratio (S/R)equired to support that particular constantF. Observed/Scan therefore be used to define target levels oF,

FISH 1906 1–15

eachE values slightly higher than 50% in 1998–19uring the current situation (2000–2002), the explo

ion rate remains under the 50% associated withevel of effort (average of 18,315 boat fishing days

ig. 2. Relationship between fishing mortality rate and effort, pe983–2002.

FISH 1906 1–15

R. Puga et al. / Fisheries Research xxx (2005) xxx–xxx 7

Fig. 3. Annual time series of exploitation rate (solid line) and effort(dotted solid line) in the spiny lobster fishery of the Gulf of Bataban´o.

The egg production shows an increasing trend from353

562× 109 eggs in 1980 to 1191× 109 eggs in 1992354

(Fig. 4) and a subsequent decline to 666× 109 eggs in355

2000. The level of recruitment (N1) decreased in 33%356

during the period 1988–1998 related the maximum357

level observed during 1977–1987. Maximum recruit-358

ment occurred in 1983 (40.8× 106) and minimum in359

1993 (23.9× 106). A recruitment recovery seems to360

have occurred since 1998. This variation matches quite361

well with a juvenile abundance index from nursery362

areas and with a puerulus settlement index (Fig. 5)363

recorded byCruz et al. (1995).364

The Ricker stock–recruitment fit (Fig. 6) produced a365

dome-shaped curve that suggests a density-dependence366

effect between adults and juveniles. The maximum367

number of recruits is determined by the total fecundity368

of the parent stock, and the actual number of recruits369

depends on the destiny of the eggs produced by the370

F andr

Fig. 5. Annual anomalies of recruitment (solid line), juvenile abun-dance index (dashed line) and puerulus settlement index (dotted solidline).

Fig. 6. The fit of the Ricker stock–recruitment relationship with eggproduction and recruitment lagged 1 year.

spawning stock. This relationship allows predicting371

recruitment by means of the egg production during the372

previous year, with an acceptable coefficient of deter-373

minationr2 = 0.68 (p< 0.05). 374

The annual economic results of this fishery for 2002375

indicate that the spiny lobster fishery is a very profitable376

activity, which produces a profit equivalent to the 83%377

of the total revenue (Table 5). The mayor source of cost 378

Table 5Economic results for year 2002

US$ year−1 (millions)

Revenues 55.87Variable cost 2.93Fixed cost 2.91Processing cost 3.63Total cost 9.46Profit 46.41

ig. 4. Annual time series of egg production (dashed line)ecruitment (solid line).

8 R. Puga et al. / Fisheries Research xxx (2005) xxx–xxx

Fig. 7. Equilibrium curve of profit per recruit as a function of effortshowing some reference points. Closed circle,fcurrent; left dashedline, fmey/r; solid line,fmed; right dashed line,fhigh.

is the processing cost, which comprises 38% of the total379

cost, while variable and fixed cost represent 31% each380

one.381

3.2. Reference points382

The corresponding bioeconomic indicators pro-383

duced by the deterministic equilibrium version of the384

model are displayed inTable 6.385

The current status of the fishery and three levels of386

effort (fmey/r, fmed and fhigh) were chosen to be rep-387

resented in the equilibrium curve of profit per recruit388

(Fig. 7). According to this model, the long-term maxi-389

mum profit will be obtained with a higher fishing effort390

(24,016 boat fishing days) than the current one (aver-391

age of 18,315 boat fishing days in 2000–2002). On392

the other hand, bothfmed= 26,814 boat fishing days393

andfhigh = 30,000 boat fishing days, will produce lower394

profits, will reduce the spawning stock and will increase395

the exploitation rate over 50%.396

3.3. Predictions397

The ability of the model to fit the data was examined398

by comparing the observed data with the model pre-399

diction corresponding to the 50th percentile of Monte400

Carlo simulations (Fig. 8). From 2003 to 2010, the401

projections were based on the current level of effort.402

The model generally captures the changes over time in403

t als,404

w ari-405

a iated406

t407

Fig. 8. Observed catch (closed circles) for the period 1983–2002,50% percentile of predictions (solid line), and upper and lower 80%percentiles (dashed lines) from the dynamic model. From 2003 to2010, the projections are based on the current level of effort.

Three different levels of fishing effort for the period408

2003–2010 were chosen to show short-term predictions409

in an economic indicator, such as present value of profit410

(Fig. 9) and a biological one, such as SPR (%) (Fig. 10). 411

The three possible decisions suppose gradual incre-412

ments of effort to reach the specific reference points413

(fcurrent, fmey/r andfhigh) in year 2006. It can be noted414

that predictions for both variables, like the model pre-415

dictions for the catch, reflect interannual changes likely416

associated to variations in recruitment and therefore in417

the stock structure. 418

3.4. Risk analysis 419

The purpose of the risk analysis is to examine420

the implications of alternative levels of fishing effort421

Fig. 9. Short-term prediction of present value of profit from thedd

he catch, with acceptable 80% probability intervhile the projections for 2003–2010 show similar vtions than the observed in the past, likely assoc

o changes in recruitment.

FISH 1906 1–15

ynamic model for three scenarios of effort. Solid line,fcurrent; dottedashed line,fmey/r; dashed line,fhigh.

R. Puga et al. / Fisheries Research xxx (2005) xxx–xxx 9

Table 6Reference points and some bioeconomic results

Effort (boat fishing days) F (year−1) E (%) Y/R (g/R) Profit/R (US$/R) SPR (%)

fcurrent 18315 0.266 43.9 193.90 1.6950 24.5fmey/r 24016 0.349 50.6 199.62 1.7306 17.0fmsy/r 26405 0.384 53.0 200.02 1.7260 14.7fmed 26814 0.390 53.4 200.01 1.7244 14.3fhigh 30000 0.436 56.2 199.34 1.7050 11.9

Fig. 10. Short-term prediction of spawning per recruit from thedynamic model for three scenarios of effort. Solid line,fcurrent; dotteddashed line,fmey/r; dashed line,fhigh.

for the future status of the resource over an 8-year422

period. The implications of the different management423

actions are summarized by changes over time in the424

SPR (%).Fig. 11shows the annual probabilities that425

the egg production will be less than the replacement426

SPR (%) = 14.3 as a function of the three levels of427

Fig. 11. Annual probabilities that the egg production to be less thanthe replacement SPR (%) for three scenarios of effort. Solid line,fcurrent; dotted dashed line,fmey/r; dashed line,fhigh.

effort. Whit fcurrent the probability will never exceed 428

the 25%, butfmey/r will produce probabilities of (SPR 429

(%) < 14.3%) greater than 50% between 2008 and430

2010. The risk of exceeding (SPR (%) < 14.3%) is con-431

siderably higher forfhigh, with probabilities over 70% 432

since 2006. 433

4. Discussion 434

4.1. Stock assessment 435

The average catchability coefficient ofq= 436

0.0000153/boat fishing day is similar to the value437

of q= 0.0000124/trip in the FloridaP. argusfishery, 438

estimated with data fromMuller et al. (1997). The 439

exploitation rate ranged between 40 and 65% for the440

whole period, analogous to the case of FloridaP. argus 441

fishery, with exploitation rates between 41 and 60%.442

The fishing effort and the exploitation rate reached443

the highest values before 1989 (Fig. 3). The exploita- 444

tion rate was particularly high between 1974 and445

1978 when the closed season was reduced to 45 days446

and large quantities of undersized individuals were447

landed causing a growth overfishing during this period448

(Baisre and Cruz, 1994). Since 1979, the closed sea-449

son was lengthened to 90 days and the minimum450

legal size was strictly enforced, and landings gradu-451

ally increased to 8125 t in 1985. Fishing effort and452

therefore exploitation rate remain at low levels from453

1 ban454

e 455

or 456

p - 457

c by458

h , 459

1 sed460

s also461

FISH 1906 1–15

991 to 1994 because of bad conditions in the Cuconomy.

In 1990, the catch dropped (Fig. 8) because a porevious recruitment (Puga et al., 1991) probably assoiated with a high mortality of juveniles causedurricane Gilbert in September 1988 (Baisre and Cruz994) and with a large catch during the 1989 cloeason. The poor catches in 2000 and 2001 are

10 R. Puga et al. / Fisheries Research xxx (2005) xxx–xxx

likely related to high landings during the 1999–2000462

closed seasons.463

The hypothesis of a stock–recruitment model seems464

reasonable taking into account that phyllosoma larvae465

distribution and abundance (Alfonso et al., 1991) cou-466

pled quite well with water circulation patterns deter-467

mined byGarcıa et al. (1991a)in the oceanic waters468

off the Gulf of Bataban´o.Hernandez and Pi˜neiro (2003)469

also studied the sea surface water transport, turbulence,470

depth of the top of the thermocline, sea surface temper-471

ature and vertical stability in the same region. They472

concluded that downwelling and upwelling move-473

ments produce a so-called “cascade effect” that main-474

tains nutrients suspended, and they suggested that this475

effect contributes with larvae retention in the region.476

Roberts (1997)characterized South Cuba as an impor-477

tant downstream reef area, with a high likelihood of a478

larva finding a site on which to settle and live.Lindeman479

et al. (2001)reported new information on current pat-480

terns off southwest Cuba based on satellite-tracker481

drifter paths from 10 m depths. They found that four482

drifters spent 1, 3, 5 and 8 months, respectively, in483

various eddies off the Gulf of Bataban´o, suggesting484

possible larval retention, taking into account that lar-485

vae remain about 6–8 months in the ocean (Alfonso486

et al., 1991).Yeung et al. (2001)also concluded that in487

the Florida Keys, a retention pathway of 6–8 months is488

possible forP. arguslocal larvae, because of the circu-489

lation mechanisms determined by eddies and counter-490

current systems.491

le492

o fects493

o ob-494

s the495

f ther496

m ove-497

m al-498

i )499

d500

u ity-501

d stud-502

i tal503

c vel504

o 3)505

r een506

r of507

a the508

s uit-509

ment is large, and the overall stock abundance trends510

are fundamentally governed by recruitment changes.511

In Cuba, the construction of dams in numerous rivers512

flowing into south coast has surely reduced the nutrients513

discharge into the coastal zone, as has the drastic reduc-514

tion of fertilizers used in agriculture (Baisre, 2000). 515

Between 1986 and 2000, dam capacity increased by516

50%, while fertilizer utilization decreased by 80%.517

Large-scale hydrological alterations on land, such as518

river damming, could cause reduction of nutrient inputs519

to the sea (Jickells, 1998; Ittekkot et al., 2000), while 520

the reduction of nutrient runoff may actually reduce521

productivity of shellfish stocks (Caddy and Defeo, 522

2003). On the other hand, between 1996 and 2002 the523

fishing area has been affected by five hurricanes and524

one tropical storm. The consequences of these phe-525

nomenons for the decline of recruitment since 1988526

need to be examined. 527

A shown inTable 5, the spiny lobster fishery is very 528

profitable in Cuba, with profits about 80% of the total529

revenue, in contrast to the New Zealand fishery for red530

rock lobster (J. edwarsii) which was overcapitalized 531

and had to be rebuilt (Breen et al., 1994). 532

4.2. Reference points 533

Because of the decreasing trend of the recruitment534

and the uncertainty for it variation in the future, the535

reference points were estimated on a per recruit pre-536

cautory basis instead on an absolute basis. 537

been538

d SPR539

a s 540

o d 541

S s 542

a ent543

o ed544

a n 545

F 546

M 547

fi 548

g high549

r ent550

S ment551

P ions552

b sh-553

e the554

U shed555

It is a matter of high priority to investigate the rof density-dependent and density-independent efn the variations of recruitment in Cuban spiny lter stock. Density dependence could result fromeeding rate being reduced by the presence of oembers of the same population and also from ments due to habitat limiting both in quantity and qu

ty (Rose et al., 2001). InAustralia,Morgan et al. (1982escribed a stock–recruitment relationship forPan-lirus cygnusand believed that after settlement densependent relationships dominated. More recent

es (Caputi et al., 2001) have shown that environmenonditions could be the factor controlling the lef puerulus settlement.Ehrhardt and Sobreira (200eported a density-dependent relationship betwecruitment success and parent stock abundanceP.rgus in northeastern Brazil. They concluded thatignificance of the environmental signals on recr

FISH 1906 1–15

Reference points based on SPR (%) haveefined based on the relationship betweennd the survival ratiosR/S obtained from pairf stock–recruitment observations.Sissenwine anhepherd (1987)proposed thatFmed could be used abiological reference point for defining recruitm

verfishing. More recently,Fmed has been considers a limit reference point since atF levels higher thamed stocks can be expected to decline (Caddy andahon, 1995). After a survey of 91 sets ofS–Rdata for

sheries resources,Mace and Sissenwine (1993)sug-ested that high fecundity may be associated withesilience and therefore with low values of replacemPR (%). They reported that the Fisheries Managelans developed in the U.S. use overfishing definitased on threshold levels of SPR for 60% of the firies stocks. The definition of overfishing used in.S. stated that the resource is recruitment overfi

R. Puga et al. / Fisheries Research xxx (2005) xxx–xxx 11

when the egg production is below 10% of a non-fished556

population forHomarus americanusand 5% forP.557

argus(Addison, 1997).558

In their analysis about reference points for fisheries559

management,Caddy and Mahon (1995)remarked that560

the fisheries economic theory holds that there is an eco-561

nomic target reference point, the maximum economic562

yield (MEY), which occurs at the effort level yield-563

ing the greatest margin of revenue over cost from the564

resource. SinceFmey occurs at lower levels of effort565

thanFmsy, the use of this economic target reference566

point is less likely to result in biological overfishing567

tan the use ofFmsy. Results inTable 6show that fish-568

ing effort is lower and SPR (%) is higher forFmey than569

Fmsy.570

In this case,Fmedalso exceedsFmey/r, so it does not571

make sense to apply a fishing mortality rate ofFmed572

since it will produce less profit per recruit. On the other573

hand,Fmed is tied to the observed history and will be574

risky if the fishery is around the depleted situation.575

Helser et al. (2002)stated that the Delaware Bay576

blue crab stock is not currently being overfished, since577

Fcurrent is belowFmed with 80% confidence.578

An economic tool is essential in fisheries manage-579

ment, and maximizing the net present value over an580

indefinite time horizon, must be made the primary581

goal of management (Hannesson, 2001), where eco-582

nomic efficiency is the over-riding policy objective.583

Therefore, to keep the exploitation around theFmey/r584

level must be a priority for the lobster fishery in585

C586

4587

for588

1 effi-589

c e-590

s ory591

o was592

l ictly593

e -594

t nd595

1 ugh596

t h597

l his598

i599

K .600

(601

In the Cuban fishery for spiny lobster, the fishing602

effort does not follow the model proposed bySmith 603

(1969) because a Fisheries Management Committee604

controls the effort under a limited-entry regime. Sim-605

ulations for three levels of effort show that predictions606

of catch and present value of profit are similar for607

fhigh andfmey/r with increases till 2005, and with sub-608

sequent declines followed by recovery in 2009. For609

fcurrent, the predictions of catch and present value of610

profit show lower levels with increases to 2004 and pos-611

terior declines.Fig. 11illustrates howfhigh will reduce 612

the egg production below the replacement SPR (%)613

since 2007 and f mey/r will also exceed this reference614

point in years 2009 and 2010. 615

Mace and Sissenwine (1993)andCaddy and Mahon 616

(1995)pointed out that SPR decreases monotonically617

as fishing intensity increases, whileBreen et al. (1994) 618

concluded that the economic performance in the New619

Zealand fishery for red rock lobster can vary widely 620

with recruitment. 621

4.4. Uncertainty and risk analysis 622

The reasons for risk analysis are related to the need623

of better ways to advise fishery managers and to the624

adoption of the precautionary approach (Francis and 625

Shotton, 1997). One stage in dealing with risk is the626

way fishery managers take uncertainty into account in627

making decisions. In this paper, a risk assessment is628

conducted in the context of the formulation of advice629

f of630

t 631

vari-632

a een633

s 634

S 635

ta,636

s red.637

N og-638

n ent639

r od-640

e that641

e ely642

d ort643

o risk644

a tion645

p nder-646

t of 647

uba.

.3. Predictions

The model predicts the observed catch983–2002 with an acceptable determination coient of r2 = 0.72 (p< 0.05). The main outliers corrpond to 1985 with the maximum catch in the histf the fishery after a period when the closed season

engthened and the minimum legal size was strnforced (Baisre and Cruz, 1994), 1990 with a dras

ic decline after the Hurricane Gilbert in 1988 a999 when the tropical storm Irene crossed thro

he Gulf of Bataban´o in October and provoked higandings during the mass autumnal migration. Ts a typical phenomenon described byHerrkind andanciruk (1978)and studied in Cuba byGarcıa et al

1991b).

FISH 1906 1–15

or fishery managers, in the form of an evaluationhe expected effects of alternative levels of effort.

One of the most fundamental sources of naturalbility in marine resources is the relationship betwpawning stock size and recruitment (Mace andissenwine, 2002).Due to the complexity of stock–recruitment da

tock–recruitment relationships were largely ignoowadays, recruitment overfishing is widely recized as a reality and consequently, stock–recruitmelationships are a primary focus of uncertainty mlling. In particular for lobsters, scientists agreelucidating stock–recruitment relationship is extremifficult, but it is suggested that defining some sf stock–recruitment relationship is essential ifnalysis of the consequences of different exploitaatterns and management strategies is to be u

aken (Addison, 1997). Another important source

12 R. Puga et al. / Fisheries Research xxx (2005) xxx–xxx

uncertainty associated with human activities includes648

changes in catchability (Mace and Sissenwine, 2002).649

Although simple models may be biased, they tend650

to be more statiscally stable than more complex mod-651

els. And even in complex models, there is a possibility652

that some important aspect of the dynamics of the sys-653

tem will be excluded or misrepresented (Mace and654

Sissenwine, 2002). In this paper, uncertainty in the655

model is based on recruitment and catchability histor-656

ical variations on the assumption that the parameters657

that determine age, natural mortality and egg produc-658

tion were known exactly.Allowing for uncertainty in all659

of these parameters is beyond the scope of the current660

study, although any such allowance would probably661

have led to wider probability intervals in the predic-662

tions.663

Variability in the projections during the assessment664

of king and Spanish mackerel is derived from the future665

recruitment values and the future natural mortality rate666

(Legault et al., 2002). Future recruitment is generated667

from a log-normal distribution with mean and variance668

set at the values from the historical recruitments esti-669

mated by the ADAPT framework.670

Because of the fluctuation of recruitment and catch-671

ability, the annual risk to achieve or exceed a reference672

point for fishery management could vary between years673

for the same level of effort in the Cuban spiny lobster674

fishery. Shepherd (2002)used an age-based popula-675

tion model in the stock assessment of the Atlantic676

striped bass. The incoming annual recruitment was ran-677

d bu-678

t rate679

t also680

f sen681

b the682

s ly683

d684

il-685

i s in686

c be687

b688

5689

ore690

d hery691

t lable692

from the monitoring program. Although the model is693

simple in form, it allows biological and economic indi-694

cators of interest to managers to be estimated, together695

with the uncertainty associated with the predictions.696

Future research should be conducted to develop a more697

complex model, taking into account environmental698

effects and fluctuations over time in parameters, such699

as growth and natural mortality rates. 700

Exploitation of spiny lobster in Cuba is a very prof-701

itable activity. If the main aim of the fishery is to702

maximize profits in a sustainable way, the effort must703

be limited at the level of maximum economic yield.704

Nevertheless, the status of the resource and the risk of705

reducing SPR below the replacement SPR (%) need to706

be updated regularly. 707

The annual exploitation rate of the limited-entry708

rock lobster fishery of Western Australia (P. cygnus) 709

is controlled by constraining the total allowable effort.710

The model developed byHall (1997)allows the eval- 711

uation of alternative levels of fishing effort within the712

management zone, providing managers and industry713

with a tool to explore alternative harvest strategies. 714

Mackerel assessments in the Gulf of Mexico are715

conducted annually such that the following year the716

total acceptable catch, or quota, can be chosen by the717

management councils (Legault et al., 2002). Taking 718

into account the results of this paper, the assessment of719

the Cuban fishery for lobster should be updated annu-720

ally, the annual fishing effort needs to be planned in721

consequence by the Fisheries Management Commit-722

t the723

F ved724

b by725

b self726

c lems727

( ds728

t ene-729

fi into730

a r the731

fi , 732

2 733

A 734

aid735

o p 736

h s on737

omly chosen from log-normal recruitment distriions bounded by the levels occurring under modeo high levels of spawning stock biomass. Theyound that the probabilities of exceeding the choenchmark level were different between years forame targetF during a 10-year projection period, likeue to variations in the abundance-at-age values.

Maximizing catch, minimizing depletion probabty and limiting the range of year-to-year changeatch limits, are three conflicting aims that have toalanced (Holt, 1998).

. Conclusions

The proposed model provides a tool for metailed analyses of the Cuban spiny lobster fis

hrough the use of fishery statistics and data avai

FISH 1906 1–15

ee, and the final decisions must be enforced byisheries Inspection Unit. It could be easily achiey assigning a maximum number of fishing daysoat in each fishing enterprise. Limited entry by itannot be expected to solve all management probCharles, 2002). The permitted effort in a year neeo be determined with care so as to optimize the bts from the resource in a sustainable way, takingccount the status of the resource, the objectives foshery and the needs of the interest groups (Cochrane002).

cknowledgments

This work has been made possible with thef FAO-DANIDA through a Bioeconomic Workshoeld in Cuba, 1995, and the Regional Workshop

R. Puga et al. / Fisheries Research xxx (2005) xxx–xxx 13

Management of the Spiny Lobster Fisheries in the738

WECAFC area held in Belize, 1997, and Mexico, 1998.739

The first author is a Ph.D. student in Centra de Inves-740

tigaciones Biol´ogicas del Noroeste (CIBNOR) and he741

has a grant (#182872) of Consejo Nacional de Cien-742

cia y Tecnolog´ıa (CONACYT) of Mexico. Funding743

by Ministerio de la Industria Pesquera (MIP) of Cuba744

during this project is also greatly appreciated.We grate-745

fully acknowledge Dr. Juan Carlos Seijo (CINVES-746

TAV, Mexico) for his assistance in bioeconomic mod-747

elling, Dr.Victor Restrepo (ICCAT, Spain) and Dr. Paul748

Medley (UK) for their assistance in stock assessment749

methods. We also thank Dr. Silvia Salas (CINVES-750

TAV, Mexico), Dr. Nick Caputi (Western Australian751

Marine Research Laboratories) and the two anony-752

mous reviewers, for their valuable revisions of the753

manuscript.754

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