A Management Model of theNorthwest African Cephalopod Fishery

W. E. GRANT, W. L. GRIFFIN, and J. P. WARREN

Figure 1.- FAO Major Fishing Area .'\4 and coastal countries of westernAfrica. Shaded areas represent main flshing grounds for cephalopods.

GUINEA BISSAU

"

,,I

/

Casablanca

34.1.1

Cape /Garnell

MAURITANIA

Nouakchott

SENEGAL

t::;--~--+-GA M BIA

oCanary Islands t?

",(/<::::) cJJc?

Dakar

34.1.2

34.3.1

34.1.3

o\)0 CAPE

VERDE

o

lOON

150 N

25°N

35°N

300 N

In 1967 the Food and Agriculture Or­ganization (FAO) of the United Nationsestablished the Fishery Committee forthe Eastern Central Atlantic (CECAF).The northwest African fishery, extendingfrom Morocco in the north to GuineaBissau in the south (FAO Major FishingArea 34, Fig. I), is within the jurisdic­tion of CECAF. This area is particularlyrich in fish resources and is fished inten­sively by both foreign and local fleets(FAO, 1976).

The total annual harvest of all speciesin the area is abou~ 2.5 million metric

ABSTRACT~ Two versions of a bioeco­nomic model of the northwest African ceph­alopod fishery, one assuming an instantane­ous natural mortality rate ofM = 1.25 on anannual basis and the other a rate arM = 2.0.predict the harvest of octopus. Octopus vul­garis; cuttlefish, Sepia spp.; and squid.Loligo spp. These predictions are comparedwith actual harvest data, the sensitivity ormodel behavior to changes in important bio­logical parameters is examined, and twomanaRement schemes for the fishery areevaluated.

Introduction

W. E. Grant is with the Department of Wildlifeand Fisheries Sciences and W. L. Griffin and J.P. Warren are with the Department of Agricul­tural Economics. Texas A&M University. Col­lege Station. TX 77843.

November /981. 43rllJ

Table 1. -Input data used in the simulation model.

agement-oriented bioeconomic modelsof other marine fisheries (810010 et al..Ili78: Grant and Griffin. 1979\.

Simulation Model Development

Most of the relevant biological infor­mation about the northwest Africancephalopod fishery has been reviewedrecently (FAO. In9l anu we have reliedheavily upon this information to set pa­rameters for the simulation model. Themajority of the information availablepertains to octopus. although some dataare available on cuttlefish. Virtually nodata have been reported for squiu. Eco­nomic information about the lishery hasbeen generated from a number of pub­lished and unpublished sources as dis­cussed elsewhere (footnote 2\.

The simulation model consists of a setof nonlinear difference equations repre­senting the dynamics of the system andhas been programmed in FORTRANfor use on a digital computer. The time­step for the model is I month: i.e.. thedifference equations are solved and thestate of the system is updated eachmonth of simulated time. Input datareljuired by the model are shown inTable I.

The basic dynamics of the model re­sult from changes in the number of or­ganisms in the fishery over time:

!:JV'INil (1+ 1) = Nil (I) + -61

(1)

Item

6, Parameters of von Ber­talanffy growth equationand length-weight con­version equation foreach species.

7 Natural mortality rateand proportion of thepopulation harvested byone real day fished,

8, Boundaries betweencommercial size classesand length of smallestorganisms harvested foreach species.

9. Economic data includ­ing prices of each spe­cies by size class, vari­able costs associatedwith fishing, and fixedcost of vessels by vesselclass,

Item

1 Number of months tobe simulated.

2. Number of species,number of cohorts peryear. and number ofcommercial size classesof organisms,

3. Number of vessel class­es. number of vessels ineach class. relative fish­ing power of each class.and number of nominaldays fished per monthby vessels in each class.

4, Initial number. length.and weight of organismsin model at beginning ofsimulation.

5. Magnitude and sea­sonal distribution of re­cruitment of organismsinto fishery

'Warren. J. P.. W. L. Cjriflin. and W. E. Grant.Regional flSh stuck management: A model fornorthwest Africa. lIn prep.l

Conceptual Modelof the Fishery

A simplifIed representation of themajor biological and economic aspectsof the northwest African cephalopodfIshery is presented in Figure 2. The bio­logical submodel represents the recruit­ment, growth. natural mortality, andharvest of octopus. Octopus vulgaris:cuttlefish, Sepia spp.; and squid, Loligospp. Interactions between these speciesare not well known and have not beenrepresented in the model. although thepotential importance of such interac­tions in the management of multispeciesfisheries is recognized (Gulland, 1974:May et al.. 1ny). Recruitment of indi­viduals of each species into the fishery isa function of environmental factors andis treated as a driving, or external. vari­able. Clear evidence of a stock- recruit­ment relationship is lacking (FAO, 1979)and recruitment is assumed to be inde­pendent of population size. Once re­cruited into the fIshery, individuals growand are subjected to both natural andfishing mortality. The latter is a functionof the fishing effort exerted within thefishery and is detennined in the harvest­ing sector of the economic submodel asa function of vessel characteristics anddays fished. Days fished are detenninedby the costs of fishing and the sellingprice of cephalopods. Selling price isdetennined by supply and demand inthe marketing sector. This general ap­proach has been used to construct man-

ate two management schemes for thefishery.

The ability of the mouel to distinguishbetween harvests predicted by alternatemanagement policies also is evaluatedwith regard to the effects of biased esti­mates of important biological parame­ters and in view of the inherent variabil­ity of the fishery. A companion paper2

discusses the economic and politicalimplications of the management schemesto countries of the region.

'Christy. F. T.. Jr. 1979. Economic benefits andarrangements with foreign fishing countries inthe northern subregion of CECAF: A prelimi­nary assessment. Draft report for FAO. Dakar.Senegal.

tons (t) valued at about US$<)OO million '.In tenns of both tonnage (about 200,000t annually) and commercial value, thecephalopod fIshery is the most impor­tant fIshery in the area and also is one ofthe most important cephalopod fIsher­ies in the world.

The main species harvested are octo­pus, Octopus vulgaris; cuttlefIsh, Sepiaofficinalis officinalis, S. officinalis hie,.­redda, and S. bertheloti; and squid,Loligo vulgaris and L. forbesi. Fleetsharvesting these species consist primari­ly of trawlers ranging in size from ISO to550 gross metric tons pulling bottomtrawls with mesh sizes ranging from JOto 70 mOl (FAO, 1979).

Historically, international fleets ex­ploited the waters of northwest Africawithout restriction. More recently therehas been increasing control of fIshingthrough extension of territorial watersand imposition of fIshing limits by coast­al countries. Of course, fIsh stocks arenot confmed within political boundaries,so fisheries management is complicatedby the need to coordinate planning ona regional scale. It is anticipated thatCECAF will provide the vehicle for re­gional planning in fisheries managementfor northwest Africa (Everett, 1976,1978).

In this regard, a number of researchand planning activities, including a planto simulate mathematically the majorbiological and economic processes in­volved in the northwest African fIshery,have begun (FAO, 1977). The initialeffort in this undertaking involved de­velopment of a bioeconomic simulationmodel of the regional cephalopod fish­ery (Griffin et aI., 1979). This paperreports on further development of themodel, which focuses upon the repre­sentation of important biological as­pects of the fIshery, the comparison ofmodel predictions of the harvest withactual harvest data, the examination ofthe sensitivity of model behavior tochanges in important biological param­eters, and the use of the model to evalu-

2 Marine Fisheries Reviell'

Other World

Production

...

1><] .....

"-\IIIIIIIIII

I/

/

MarketingSector

C....__S_U_PrrP_ly__)y,

Prices of Octopus,Cuttlefish, and Squid

$

Squid

Size 1

Siz.e 2

Siie n

ECONOM IC SUBMODEL

------

HARVEST(Number of individuals)

Octopus Cuttlefish

Size 1 Size 1Size 2 Si~e 2

Size n Size n

-----....--,.--Harvesting

Sector

BIOLOGICAL SUBMODEL

Figure 2.-Simplified representation of the major biological and economic aspects of the northwest African cephalopodfishery. Symbols follow Forrester (1961).

November /98/.4](11) o.>

where N" (t) = number of organisms ofthe ith species, jth co­hortJ present at time 1and

6N"-- = net change in number of61 organisms of the ith spe-

cies, jth cohort over thetime interval 1 to 1+ l.

where R" = number of individuals ofthe ith species,jth cohortrecruited into the fisheryduring the time intervaL

NM" = number of individuals ofthe ith species,jth cohortdying due to natural (non­fishing) causes during thetime interval, and

FM"k = numher of organisms ofthe ith species,jth cohortremoved by fishing duringthe time interval by typek vessels (m = numher ofvessel classes(

Recruitment of organisms into thefishery is represented as varying on aseasonal basis:

R" = RMAX, X 5, (3)

where RMAX,= maximum number of in­

dividuals of the ith spe­cies that can be recruitC'dinto the fishery duringone time interval and

5, = a seasonality factor. 0 S5, S 1. representing therelative magnitude of re­cruitment of the ith spe­cies into the fishery duringa given time interval: 5,values for each time in-

'All organisms of a given species that are intro­duced into the mude! in a given month are treat­ed as being identical in t-erms of size. growthrate. mortality rate. etc.. and are designated acohort.'Note that .'V.W" and F'VI" do not represent thenatural mortality coefficient "VI) and hshingmortality coefficient IFl. respectively. as de­fined by Gulland IJ9691 and others. If the timeinterval 1 to 1+ I is indefinitely small. thenNM" = MNdl as discussed by Gulland 11969:58!.

4

terval are specified as in­put data.

For octopus. recruitment peaks in thespring and again in the fall. whereascuttlefish recruitment peaks in the spring(FAO. 1979). Squid recruitment is as­sumed to be relatively high throughoutthe sumner. The absolute magnitude ofrecruitment and the specific representa­tion of the seasonality of recruitmentin the model have been determined bysimulation experiments. RMAX, and 5,have been adjusted such that I) modelbehavior is consistent with available in­formation about the dynamics of thefishery and 2) the model is a good pre­dictor of the actual harvests of eachspecies. Octopus are assumed to be re­cruited into the fishery at a mantle lengthof 6.43 cm. cuttlefish at 7.64 cm. andsquid at 8.64 cm. These recruitmentlengths are hased on assumptions relatedto the representation of growth discussedbelow.

Natural mortality is represented on aspecies-specific basis as a constant rateper month:

NM" = NMORT, X N" (4)

where NMORT, = proportion of thepopulation of the ithspecies dying due tonatural causes duringthe time interval.

Although information on natural mor­tality is sparse, an instantaneous rate ofM = 2.0 on a yearly basis has beensuggested for octopus in the northwestAfrican fishery (FAO, 1979) and rateshetween M = 1.00 and M = 1.50 forsquid (Loligo pealei and /IIex illecehro­sus) off the northeastern United States(Au, 1975). Other short-lived species(i.e .. capelin. smelt. and certain min­nows) also generally have M>1.0 (Bever­ton and Holt, 1959). Because of the un­certainty with which natural mortalityrates are estimated and the importanceof these rates in determining model he­havior we developed two versions of themodel. one using M = 1.25 (0.1042 on amonthly basis) for each of the threespecies and one using M = 2.0 (0.1667on a monthly basis). In addition to theseconstant mortality rates that are appliedindependent of age, an upper limit onage is imposed by removing octopus andcuttlefish after they have been exposed

to the fishery for 18 months and squidafter 12 months (FAO, 1979).

Fishing mortality is represented on aspecies- specifIc basis as a function ofthe abundance of organisms; the sus­ceptibility of organisms to harvest,which is represented as a constant pro­portion of the population harvested by 1real (standardized) day fished; and thelevel of fishing effort:

where FEk = fishing effort in real daysfished expended in thefIshery during the timeinterval by type k vesselsand

He, = proportion of the popula­tion of the ith speciesremoved by I real dayfished.

Fishing effort, in tum, is calculated asthe product of the relative fIshing powerof vessels in the fishery and the numberof nominal days fished (days at sea):

where NDFk = number of nominal daysfished by the "average"type k vessel during thetime interval,

NVE5k = number of type k vesselsin the bshery during thetime interval, and

RFPk = relative fishing power oftype k vessels5

•

Relative fishing power is calculated asthe ratio of catch per day fished by avessel in the kth vessel class to that ofa standard vessel. Relative fishing poweris based on 1975 landings data for allspecies aggregated.

In the model the susceptibility of or­ganisms to harvest is 1.4xlO 5 for allthree species. This value was chosensuch that the model simulated appro­priately the relationship between annualcatch and effort that has been observedsince 1969 in the northwest Africancephalopod fishery and approximatedthe appropriate size-class distributionin the harvest based on 1975 data fromthe fishery.

'Note that FEk does not represent the fIshingeffort exerted by a unit operation (j) as de­fined by Gulland (1969) and others. FEk /

NDFk = las discussed by Gulland (1969:45).

Marine Fisheries Review

Growth of organisms is representedon a species-specific basis by the vonBertalanffy equation:

I" (t) = L~" (1-e K"(I,, 'a") (7)

Table 2. - Values of parameters of the von Bertalanllyequation (I ~ L~ (1-e K(I- 10 1)) and of the length-weightconversion equation (w = aID) used In the simulaHonmodel. See text for symbol definitions.

Species L~ K to a b

Octopus 40.0 0.72 0.34 0.976 2.691Cuttlefish 45.8 0.75 0.34 0.147 2910Squid 400 140 034 0.229 2.290

Rent to the fishery obtained by a givenvessel class is the difference between thetotal revenue and total cost:

where w,! = weight of the ith species,jth cohort in grams.

i I

'In specifying parameter values for the twoversions of the model, RMAX; and 5 wereadjusted, in the manner described earlie;, inde­pendently for each version. Thus, the two ver­sions have identical estimates for all parametersexcept NMORT" RMAX

"and S;. However,

the behaVior of the two versions is not neces­sarily identical when values of NMORT;, or anyother parameter, are varied proportionally. Thetwo versions represent two somewhat differentsets of hypotheses concerning the dynamics ofthe lishery.

1/

P, = price of the ith species inU.S. dollars, and

TONS,. = metric tons of the ithspecies caught by vesselclass k.

Model Validation

Validation of the model consisted oftwo steps. In the fIrst step, values ofparameters in each version of the model(with M = 1.25 and M = 2.0) were speci­fIed such that they represented condi­tions in the northwest African cephalo­pod fIshery during 19756

. Comparisonof results of I-year baseline simulationruns under these conditions with actual1975 harvest data (FAG, 1979) indicatesthat each version of the model predictsthe total harvest and represents the gen­eral seasonal dynamics of the harvest ofeach species reasonably well. Each ver­sion predicts the general increase inlandings from January through Decem­ber, somewhat underestimating theactual harvest early in the year and over­estimating later in the year (Fig. 3). Es­timates of the annual harvest of eachspecies and of total cephalopods are allwithin 7 percent of actual values, butmodel predictions are less accurate withregard to the size-class distributions ofthe harvests (Table 3). Predicted har­vests of each species contain relativelytoo many middle-sized organisms andunderestimate the proportion of bothsmall and large organisms in the catch.

where FC. = fIxed cost of the k classvessels and

C2. = fIxed cost per vessel ofclass k.

Total cost for a given vessel class is thesum of the variable and fIxed costs:

where VC. = variable cost of a vesselof class k and

C1. = variable cost per dayfIshed per vessel of class k.

Fixed cost for a given class of vessel isthe product of the fIxed cost per vesseland the number of vessels:

I" = mantle length of the ithspecies,jth cohort in cen­timeters, and

a and b = parameters of the model.Length-weight relationships used werethose reported for octopus and cuttlefishin the northwest African fishery byGuerra (FAG, 1979) and for squid (Loltioforbesl) off the east coast of North Amer­ica by Holme (1974) (Table 2).

Economic considerations are linkedto the biological dynamics of the fIsherythrough fIshing effort and the harvest(Fig. 2). Amount of fishing effort is de­termined external to the model basedon historical levels of effort expended inthe fIshery (footnote 2) and is used as adriving variable. In the marketing sectorthe price of cephalopods is given foreach size-class of each species. Unitcosts of fIshing are taken from budgetsdeveloped by size-class of vessels (foot­note 2). The unit cost is defined as thesum of variable and fIxed costs per ves­sel per month. Variable cost for a givenclass of vessel is calculated as the prod­uct of variable cost per day fIshed, num­ber of days fished, and the number ofvessels:

(8)W'! = al"b

where I" (t) = mantle length in centi­meters of the ith species,jth cohort at time t,

L~" = asymptotic mantle lengthin centimeters of the ithspecies, jth cohort,

K,! = coefficient proportionalto rate of catabolismbased on mantle lengthin centimeters of the ithspecies, jth cohort,

t"

= age in years of the ith spe­cies,jth cohort, and

lo" = hypothetical age in yearsat which mantle length ofith species, jth cohort iszero.

All organisms of a given species have thesame initial size at recruitment, regard­less of the time of year that they enterthe fIshery. Parameters of the equationfor octopus in the northwest AfricanfIshery have been estimated by Guerra(FAG, 1979), however, estimates are notavailable for cuttlefIsh or squid. Initialparameter values for cuttlefIsh andsquid were assigned based upon theassumption that the growth of these or­ganisms was such that they entered thelargest commercial size class at 20 per­cent of their asymptotic weight, which isthe case for octopus; and upon informa­tion about their length of life, whichsuggests a lifespan of 2 years for octopusand cuttlefIsh and 1 year for squid (FAG,1979). For squid, these initial parametervalues were adjusted to increase growthrate consistent with qualitative informa­tion in FAG (1979) and with data on oneof the same species (Loligo forbesi) offthe east coast of North America (Holme,1974). Parameter values used in themodel are presented in Table 2.

The length-weight relationship usedin the model to convert number of or­ganisms in the harvest to metric tons inthe harvest is of the form:

November 1981, 4J(llj 5

75

77

·71

~l

SQUID

OCTOPUS

.69

140

130120110100908070

;:;- 60S; 50V) 40ZS 30',! 20"" 10~ 0+---=--==-=-=--=----------------~ 50 CUTTLEFISH .73

t:; 40

>: 30~ 20I 10

0+-------------------605040302010

0.l,3~0-40-5~0-60,-7~0-80.,....--:9-0-10...,.0~---,-,:12...,.0~-...,..,14...,.0~-...,..,16...,.0~-,1=80(baseline)

EFFORT (NOMINAL DAYS FISHED-10')

Figure 4.-Comparison of simulated (M = 1.25, dash rule;M = 2.0 dash/dot rule) and actual (indicated by year basedon FAO statistics for 1969 through 1977) annual harvests ofoctopus, cuttlebsh, and squid generated by different levelsof bshing effort.

-­#,#"'J'"_r-=-:.:I~'~~'''''-.

SQUID

CUTTLEFISH

;I_~_.I----- ..,..r.;~-.... =-~0+---'=-"==-'-----------------

10

8

6

4

2 =,=:...... ,,...,,...0.OJ.......;=~-M--A--M--J,--J-~A--,-~O-c:N---::D

MONTHS

Figure 3.-Comparison of simulated (M = 1.25,dash rule; M = 2.0, dash/dot rule) and actual(solid rule, based on FAO statistics for 1975)harvests by month of octopus, cuttlebsh, andsquid.

2624 OCTOPUS

22

20

18

1614

12

~lO

- 8Z 6 //o /,~ 4 /;;:/;:;;: 2 ~,/I- __.-.:;

~ 0+---'=-=------------------­-8....~ 6~ 4

~ 2

Table 3.-Comparison 01 simulated and actual (based onFAO statistics lor 1975) harvests by size class 01 octopus,cuttlefish, and squid. Table entries represent simulated mi·nus actual harvest in metric tons and (percent difference).

Species Size class M = 1.25 M = 2.0

Total cephalopods -10.046(-5) . ·9.734(-5)

Octopus <0.5 kg -21,386(-47) -14,757(-32)0.5-2.0 kg 17,730(33) 18,312(34)>2.0 kg -5.188(-16) -11,941(-38)Total -8.845(-7) -8,387( -6)

Cuttlefish <0.2 kg -1,545(-27) -302(-5)0.2-0.7 kg 861(6) 1.539(12)>0.7 kg -407(-4) 2.116(-23)Total -1.09O{-4) -880(-3)

Squid <0.1 kg -3,132(-38) -1.891(-23)0.1-0.4 kg 12,560(58) 12,468(57)>0.4 kg -9,533( -68) 11.037(-76)Total -104(-<1) -460(-1)

In the second validation step, severaladditional simulations in which the levelof nshing effort was adjusted from 20 to110 percent of baseline were run andthe annual harvests predicted by eachversion of the model at each effort levelwere compared with the actual annualharvests associated with similar levels ofeffort based on FAO historical data.Predictions of each version of the modelcompare favorably with actual harvests

from 1969 to 1977 (Fig. 4)'. Onedifficul­ty in estimating the actual effort curvesresults from the absence of data on thenshing effort exerted on each species.Effort figures reUect days fJshed for allcephalopods. while harvest data are re­ported by species. Thus, although ves­sels may be directing effort towardcertain types of cephalopods, there is nobasis for representing this in the analy­sis. For the present analysis it was as­sumed that effort was directed equallytoward all species.

Sensitivity Analysis

Each version (M -= 1.25 and M = 2.0)of the baseline model was subjected to asensitivity analysis (Smith, 1970) to de­termine the relative influence of differ­ent parameters on model predictions ofthe annual harvest of each species'.Parameters for which relatively good es­timates are available were increased, one

'Note that fishing effort in Figure 4 is expressedas nominal days fished because estimates of realdays fished are not available, except for 1975.8Sensitivity analysis focused on the biologicalparameters in the model. Economic parame-

at a time, by 10 percent of their baselinevalues and parameters for which littleinformation is available were increasedby 100 percent. Among the parametersfor which relatively good information isavailable. model predictions of annualharvests are most sensitive to changes inthe exponent of the length to weightconversion equation (b) (Table 4).Among the parameters for which littleinformation is available, model predic­tions are most sensitive to changes inrecruitment rate, but also are sensitiveto changes in natural mortality rate (M).Predicted annual harvest of each speciesresponds similarly to most parameterchanges.

lliustrative Use of the Model

Evaluation of AlternativeManagement Policies

To demonstrate the utility of the

tel'S, such as the market price of cephalopods,variable costs associated with fishing, and bxedcosts of vessels, were held constant during allsimulations.

6 Marine Fisheries Reviell'

Table 5.-Comparison of harvests by size class of octopus, cuttlefish. and squid with 1) an April-May closed season and2) a 40 percent reduction in the number of nominal days fished each month with harvest predicted under baselineconditions. Table entries represent harvest with a 1) closed season or 2) 40 percent reduction in effort minus baselineharvest in metric tons and (percent difference).

517376141

40% effort

40% effort

33,029( 17)

1',294( 36)1',929( 17)3,652(18)

-19.571(-16)

-1,988(-37)-2.794(-19)

779(11)- 4.003( 15)

2,562( 40)-7481(-22)

588(17)9455( '21)

M=2.0

676541135

M=20

April-May closure

April-May closure

631626

5

Baseline

percent reduced effort policy. revenueis reduced 15 percent (M = 1.25) or 18percent (M = 2.0), and cost is reduced.because fewer vessels are active in thefishery. 40 percent (both versions).

Robustness ofModel Predictions

The ability of each version of themodel to distinguish between harvestsunder alternate management schemes iforiginal estimates of important biologi­cal parameters actually are too high ortoo low also was evaluated. A series ofsimulations were run in which the point

535376159

-40% effort

40% effort

M 125

699541158

M= 1.25

April-May closure

April-May closure

629626

3

Baseline

Table 5.-Comparison of revenues, costs, and rents in millions of U.S. dollars obtained under 1) baseline conditions,2) an April-May closed season, and 3) a 40 percent reduction in the number of nominal days fished each month.

Revenue.cost, andrent

Speciesandsize class

Total cephalopods 24,455( 13) 26,217( 14) 15.893(8)

Octopus <05 kg -6.586( -27) ·8.846( 36) -8,419(-27)05-2.0 kg 12.810(18) 1','68( 16) 11.759(16)

>2.0 kg 12,243(46) 5,106(19) 9,078(46)Total 18467(15) . 14.908( 12) 12,418(10)

Cuttlefish <02 kg 1,113(-27) . 1.526( 37) -1,459(-27)02-07 kg 1,767( 12) . 2,581( 18) 1.730(12)

>0.7 kg 3,353(38) 1,048(12) 2,662(37)Total 4,007(15) --3,059( 11) 2.933(11)

Squid <0.1 kg 1.064( 21) 2.065( 40) . 1,320( 21)0.1-04 kg 818(2) -7.080( 21) 326(1)

>04 kg 2.227(44) 895(18) 1,536(44)Total 1,981(4) 8,250(- 18) 542(1)

RevenueCostRent

for each species is shifted toward largersized animals, and seasonal trends in theharvests of all three species parallelbaseline trends.

Comparison of economic aspects ofthe fIshery indicates a substantial in­crease in rent (=revenue-costs) relativeto baseline under each of the manage­ment policies (Table 6). Under the April­May closure policy, revenue is increased11 percent (M = 1.25 version) or 7 per­cent (M = 2.0 version), and cost is re­duced, because the same number ofvessels are fIshing fewer days per year.14 percent (both versions). Under the 40

Table 4.-Results of sensitivity analysis indicating percent error in predicted annual harvests of octopus, cuttlefish, andsquid resulting trom an overestimation of either 10 or 100 percent in the indicated parameter. Relative sensitivity,indicated parenthetically, is obtained from percent error by setting the largest error in a given column equal to one.

PercentM 1.25 M~2.0

Parameter change Octopus Cuttlefish Squid Octopus Cuttlefish Squid

L 10 291029) 32(026) 24(0.24) 29(0.29) 32(027) 24(0.24)K 10 23(0.23) 24(020) 16(016) 23(023) 25(021) 16(0.16)to 10 -15(-0.15) -15(-012) -12(-012) -16(-016) -16( 0.13) -14(-014)a 10 10(0.10) 10(008) 10(0.10) 10(010) 10(008) 10(0.10)b 10 99(1.00) 123(1.00) 97(0.98) 96(097) 120(100) 95(0.96)Relative

fishingpower 10 1(0.01) -1(-001) 2(002) 1(001) 1(0.01) 2(002)

Recruit-ment rate 100 98(099) 98(0.80) 99(1.00) 99(100) 98(0.82) 99(1.00)

M 100 -44(-044) -45(-036) -38(-0.38) -58(-0.58) -61(-051) -53( 053)HC 100 14( 014) 18(-015) 2(002) 4( 004) '10( 0.08) 10(010)Organisms

initiallyin model 100 2(002) 2(002) 1(0.01) 1(001) 1(001) 1(001)

model within a decision-making frame­work. the effects of two managementschemes on the harvest of cephalopodswere simulated using each version of themodel and compared with the baseline.or "present management." situation.Simulation of a management schemethat closes the cephalopod lishery forthe period of peak recruitment duringApril and May. hut does not alter flshingeffort during the 10- month open season.indicates increased annual harvests rel­ative to baseline for all three speciesITable 5). The version of the model withM = 1.25 predicts slightly larger in­creases than the version with M = 2.0.Harvesting efflciency in the fishery alsois increased: 1.68 1M = 1.25) or 1.61 1M= 2.0) t being caught per I real dayflshed compared with 1.16 Iboth ver­sions) under baseline conditions. Theincreased yield of each species resultsfrom a shift in the size-class distributionof the catch toward larger sized animals.The harvest of squid increases less thanthe harvests of octopus and cultleflshdue. at least in part. to the relationshipbetween periods of peak recruitmentand the period of closure. April andMay are the 2 months of highest recruit­ment for both octopus and cuttlefish.with only I other month exhibitingequally high recruitment (Septemberfor octopus and June for cuttlelJshL Incontrast. squid recruitment is highestfrom May through September. and Oc­tober recruitment equals April recruit­ment. Thus. squid are relatively less"protected" by the closure than are oc­topus and cuttlefish. Seasonal trends inthe harvests of all three species after theApril- May closure parallel the harvestsduring these months under the baselinesituation.

Simulation of a management schemethat reduces the number of nominaldays fished each month by 40 percent(achieved by limiting the number of ves­sels active in the flshery) indicates adecreased annual harvest relative tobaseline for each species (Table 51. Theversion of the model with M = J .25 pre­dicts slightly smaller decreases than theversion with M = 2.0. Harvesting effl­ciency is increased, however. from 1.16(both versions) to 1.56 (M = 1.25) or1.51 (M = 2.0) t caught per I real dayfished. As in the April- May closure case.the size-class distribution of the harvest

November 1981. 4](1/} 7

estimates for rates of recruitment. natu­ral mortality. and the proportion of thepopulation harvested by I real dayfIshed were adjusted. one at a time. overa relatively large range of values. Whenpoint estimates for rate of recruitmentare varied from 0.2 to 2 times the base­line value. total harvests predicted byboth versions of the model under theApril- May closure policy remain high­er. and total harvests predicted underthe 40 percent reduced effort policyremain lower. than predicteu baselineharvests over all test values (Fig. 51.

When natural mortality rates are var­ied from 0.2 to 10 times the baselinevalue. total harvests predictcd under thc40 percent reduced effort policy remainlower than baseline over all test values.but harvests predicted under the April­May closure policy are higher than base­line for the lower test values and lowerthan baseline for the higher test values(Fig. 51. Harvests predicted under April­May closure and baseline policies areequal at natural mortality rates approxi­mately:\ 1M ---01.25 version I or I.K (M =2.0 version) times higher than the ratesused in the original model.

The relationship of the three policieswith regard to total harvest varies as theproportion of the population harvestedby 1 real day fIshed. which is indicativcof fIshing mortality rate. is varied from0.2 to 10 times the baseline value (Fig.5). Although the shapes of the curvesrelating total harvest to flshing mortalityrate are similar. beth versions of themodel predict the largest harvest underthe April- May closure policy for lowertest values and under the 40 percentreduced effort policy for higher test val­ues. Predicted harvest under the baselinepolicy is larger than the 40 percent re­duced effort policy for lower test values.but smaller for higher test values.

Statistical Comparisons ofAJternative Management Policies

To enable statistical comparisons ofharvests under the different manage­ment policies, each version of the modelwas stochasticized by allowing the ratesof recruitment (RMAX" Equation (3))and natural mortality (NMORT" Equa­tion (4)) and the proportion of eachpopulation harvested by I real day fIshed(He" ELjuation (5)) to vary by ±50 per­cent of their deterministic values each

8

month. This was done by generating auniform random variable on the intervalo to I. adding 0.5 to the random vari­able. and multiplying the deterministicvalue of the rate to be stochasticized bythe resulting number. A new randomvariable was generated each time a ratewas stochasticized and the ranuomnum­bcr generator was seeded differently foreach of the threc values. recruitment.natural mortality. and proportion har­vested by I real day lished. for eachsimulation. Twenty-live simulationswere run rcpresenting each llf the threealternatives. The 2:'> total cephalopouharvests prcdicted under each manage­mcnt schcme formed a set of indepen­dent. identieally distributed. randomvariables. Results of 2-sample I tests(Snedecor and Cochran. 1%7) compar­ing the two hypothctical managementschemes with the baselinc situationindicate that the total harvest of cepha­lopods predicted by both versions of themodel is increased signitlcantly(P<O.OOI) under the April- May closurepolicy and decreased signitlcantly(P<O.OO I) under the 40 percent reducedeffort policy.

Summary and Discussion

The currcnt model of the northwestAfrican cephalopod lishery. as part ofthe initial research and planning activi­ties of FAO. is particularly useful in atleast three ways. First. sensitivity analy­sis of the model identilies those parame­ters to which model behavior is mostresponsive ITable 4) and helps to identi­fy. within a Ljuantiwtive framework. theareas where data crucial to regionalplanning decisions are lacking. This in­formation is useful not only in establish­ing future research priorities. but also indetermining how much confIdenceshould be placeu in model prcdictionsbased on the confidence with which themost influential parameters have beenestimated (Kowal. 1971). Forthe cepha­lopod fishery. additional data on rates ofrecruitmtnt appear particularly impor­tant. although. in terms of evaluatingalternate management policies. this in­formation may be somewhat less crueialthan suggesteu by sensitivity analysis (asdiscusseu bdow). New data on rate ofnatural mortality and on the amount oflishing effort directed toward each spe­cies also appear critical.

Second. as a result of model valida­tion procedures the dynamic relation­ship of the harvest to rates of recruitment.growth. natural mortality. and lishingmortality within the cephalopod lisheryis better understood. Reliable estimatesof all these rates are not available for thespecies under consideration here andsuch rates are known with conlidencefor very few. if any. commercially im­portant marine stocks. Although thepresent model accurately predicts totalharvest of cephalopods by species (Ta­ble J) anu reflects the general seasonaluynamics of the harvest IFig. :\1. oneapparent shortcoming is the lack of cor­respondence between the size-class dis­tributions of animals in the simulatedharvests and those of animals in theactual harvests ITable 31. This discrep­ancy results primarily because recruit­ment rates cannot be adjusted relativeto literature- based estimates of growth.natural mortality. and fJshing mortality.such that both I) size-class distributionsare appropriate and 2) catch/effort rela­tionships accurately represent historicalcatch/effort relationships over the rangeof effort levels for which data are avail­able (Fig. 4). The rapid rates of growthand relatively high natural mortalityrates that are suggested for cephalopodsin the northwest African lishery (FAO.IY7l}) imply that high lishing mortalityrates would be required to catch theproportions of small octopus. cuttlelish.and squid in the actual harvests. Whensuch high fishing mortality rates arcused in the model to obtain appropriatesize-class distributions in the harvests.the total simulated harvests are fargreater than the actual harvests. It issuggested that both natural and lishingmortality rates of cephalopods changewith age (FAO. 1979) and this representsa further rennement that might be in­corporated into the model as more in­formation becomes available.

Finally. use of the model to evaluatemanagement schemes suggests a gener­al type of management strategy for thecephalopod lishery that warrants fur­ther consideration and also providesinsight into the degree of uncertaintythat must accompany current decisionsregarding management alternatives. Ini­tial comparisons of the three policiessuggest that both harvesting efficiencyand rent in the tlshery are increased

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November /98/. 4](")

relative to baseline by uniformly reduc­ing nshing effort by 40 percent through­out the year or by closure of the nsheryduring April and May. However. 40 per­cent reduction of effort signincantlydecreases total harvest and revenue.whereas April- May closure signincantlyincreases total harvest and revenue. rel­ative to the baseline situation. Thesepredictions allow for a relatively highdegree of variability in rates of recruit­ment, natural mortality. and fIshingmortality within the fIshery. That is.confIdence in the predictions does notdepend upon correct representation ofthe true variability of these importantvariables unless we believe that theyvary by more than ±50 percent of theirestimated values each month due tochance; or. more strictly. due to pro­cesses or events not represented in themodel. Estimates of the variability in­herent in most biological processes ofimportance in marine nsheries are lack­ing. We have assumed that ± 50 percentin any given month is a liberal estimate.Of course, the ability of the model todistinguish between alternative manage­ment policies lessens as the amount ofvariability represented increases.

Also of interest when interpretingmodel results is the question of whetheroutcomes of the policy comparisons arechanged if estimates of important vari­ables are, in reality, either too high ortoo low. In this regard, the three policiesmaintain the same relationship to eachother concerning magnitude of totalharvest over a wide range of values forrecruitment rate (Fig. 5). Thus. althoughmodel behavior is sensitive to the esti­mate of recruitment, as indicated bysensitivity analysis (Table 4). ability torank the policies with regard to totalharvest is unaffected by the accuracy ofthis estimate unless the actual rate ofrecruitment is less than 20 percent ofthe original estimate. This is not the casefor estimates of rates of natural or f]sh­ing mortality.

Ability to rank the 40 percent reducedeffort and baseline policies with regardto total harvest is unaffected by the ac­curacy of the estimate of natural mortal­ity rate if the actual rate is between 20and 500 percent of the original estimate(Fig. 51. However, ranking of the April-

10

May closure and baseline policieschanges if the actual rate of naturalmortality is more than roughly 1.8 1M =2.0 version) or 3 L'vI = 1.25 version)times higher than the original estimate.Likewise. ability to rank the April- Mayclosure and baseline policies is unaf­fected by the accuracy of the estimate offJshing mortality rate if the actual rate isbetween 20 and 500 percent of the orig­inal estimate. although differences be­tween policies become negligible as theestimates become small. But ranking ofthe 40 percent reduced effort and base­line policies changes if the actual rate ofhshing mortality is more than roughly1.4 (M = 1.25 version) or 1.8 (M = 2.0version) times higher than the originalestimate.

In conclusion. it appears that man­agement schemes which reduce fJshingeffort on a seasonal basis have potentialfor increasing total harvest and harvest­ing efficiency. as well as revenue andrent. in the northwest African cephalo­pod fIshery. To the extent that a closedseason of 1.5- 2 months duration can betimed to coincide with the period ofpeak recruitment into the fIshery. in­creases will be maximized. ConfIdencein this prediction rests on assumptionsthat the actual recruitment rate into thefIshery and the actual fishing mortalityrate are both at least 20 percent of theestimated rates. that the actual naturalmortality rate is less than 1.8 times theestimated rate. and that actual rates ofrecruitment. natural mortality . and fish­ing mortality do not vary due to chanceby more than e- 50 percent of their esti­mated values each month.

Acknowledgments

This work was supported by the Foodand Agriculture Organization of theUnited Nations. George Y. Everett ofthe Fishery Committee for the EasternCentral Atlantic was particularly help­ful in assembling and providing informa­tion about the northwest African fishery.John H. Wormuth provided informationon the growth of squid. The manuscriptwas reviewed by Mark E. Chittenden. L.Joseph Folse. Kyle G. Isakson. F. JosephMargraf, Richard L. Noble. and twoanonymous reviewers. each of whomprovided valuable suggestions. All con-

elusions are those of the authors and donot necessarily reflect the views or poli­cies of the FAG or the National MarineFisheries Service. NOAA.

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Marine Fisheries Reviell'