Approaches to assessing stocks of Loligo gahi around the Falkland Islands

Ž .Fisheries Research 35 1998 155–169

Approaches to assessing stocks of Loligo gahi around theFalkland Islands

D.J. Agnew a,), R. Baranowski a, J.R. Beddington a, S. des Clers a, C.P. Nolan b

a Renewable Resources Assessment Group, Imperial College, London SW7 1NA, UKb Falkland Islands Fisheries Department, Stanley, MalÕinas

Received 2 September 1997; accepted 21 December 1997

Abstract

Management of the Falkland Islands Loligo gahi fishery is by a combination of effort control and in-season assessmentof the state of the stock in relation to biological reference points. There are two fishing seasons, from February to May andfrom August to October inclusive. There appear to be at least two, and sometimes three cohorts that recruit to the fisheryover a year, in January, AprilrMay and October. The fishing seasons therefore do not directly coincide with the separatecohorts; the second cohort is caught in both the first and second seasons. Assessments of the cohorts were made using aDelury depletion model. In situations when a Delury could not be fitted satisfactorily, an extension was developed in whichannual trends in catchability coefficients were used together with individual vessel CPUE data to estimate stock size. TheDelury and its extension enabled both first and second cohorts to be assessed for all years from 1987 to 1996. Resultsindicated that the cohorts have different dynamics and should be considered as separate stocks. Both cohorts have beendeclining in size over the last several years. The significance of a transition between two distinct stocks in a single fishingseason is discussed in the context of real-time management of this fishery. q 1998 Elsevier Science B.V. All rights reserved.

Keywords: Loligo gahi; Squid; Stock assessment; Delury; Southwest Atlantic; Falkland Islands

1. Introduction

Loligo gahi, the Patagonian longfin squid, hasbeen the subject of a major trawl fishery since theearly 1980s. Since 1987 the stock around the Falk-land Islands has been managed by the Falkland

Ž .Islands Fisheries Department FIFD and assess-ments of the stock have been performed on behalf ofthe FIFD by the Renewable Resources AssessmentGroup at Imperial College, London.

) Corresponding author.

In common with other Loligo species, L. gahiŽhas an annual life cycle Patterson, 1988; Hatfield,

.1991 . It is thought to spawn in shallow water,juveniles migrating offshore into deeper water to

Žfeed and returning to shallow water to breed Hat-.field et al., 1990; Hatfield and Rodhouse, 1994 .

Squid size is therefore stratified by depth, and thefishery takes place on feeding aggregations of adultsquid in water deeper than 100 m.

When the Falkland Islands fisheries managementregime was set up in 1987 the year was divided intotwo fishing seasons of 6 months duration each.

0165-7836r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.Ž .PII S0165-7836 98 00083-6

( )D.J. Agnew et al.rFisheries Research 35 1998 155–169156

Ž .Fig. 1. Catches of L. gahi around the Falkland Islands, 1984–1996. The fishery started in 1982. Csirke 1987 provides data for the first twoyears for the whole southwest Atlantic, but they are un-separated by month so are not plotted on the figure. Assuming all catches except

Ž .those by Argentina came from around the Falkland Islands, Falkland catches in these years were 18190 tonnes 1982 and 38013 tonnesŽ . Ž .1983 . Data for 1984–1986 were estimated from surveillance data by MRAG 1986 , but their report is incomplete, lacking any data after

Ž .June 1986. Data from 1987 to 1996 are from the Falkland Islands Fisheries Department FIFD, 1997 .

Although these were set up for largely administrativereasons, it was also considered that the two peaks in

Ž .catch seen in the fishery Fig. 1 corresponded to twostocks which should be managed separately. Theseasons now run from February to May inclusive andAugust to October inclusive, although they wereslightly longer in the early years. The fishery isconcentrated to the east and south of the Falkland

Ž .Islands Fig. 2 , with some L. gahi being taken asbycatch in other Falkland Island fisheries to the west

Ž .and north of the Islands Patterson, 1988 .It is generally accepted that the stocks on the

Falkland fishing grounds are local although it hasbeen speculated that there may be exchanges with L.gahi stocks spawning close to the Argentinian coastŽ . Ž .Wysokinski, 1996 . Early work by Patterson 1988suggested that there were two periods of recruitmentcorresponding to the two fishing seasons—in Jan-uary and in MarchrApril. Although the fishery is onfeeding aggregations of squid, pre-spawning animalsare usually found in MarchrApril and in Septem-

Ž .berrOctober Patterson, 1988; Hatfield, 1991 . It isthought that these animals leave the fishery in lateautumn and spring respectively for the spawninggrounds. Extensive spawning beds have not beenfound, but mated squid have been found in thefishery in October and small numbers of egg massesresembling those of loliginids have been found by a

SCUBA survey around the east and north coast ofŽ .the islands George and Hatfield, 1995 . More recent

Ž .work by Hatfield 1996 has confirmed the Januaryand AprilrMay recruitment pulses and indicated thatthere may be a further recruitment event in October.

The first stock assessments for L. gahi wereŽ .reported in FIFD 1989 . Assessments were under-

taken separately for each of the two seasons usingŽ .the modified Delury depletion methodology of

Ž .Rosenberg et al. 1990 which is used successfullyfor assessing the Southwest Atlantic Illex argentinus

Ž .stock Basson et al., 1994 . However, subsequentassessments of both seasons have met with difficul-ties because the recruitment pulses reported by Hat-

Ž .field 1996 often cause CPUE to rise towards theend of the season. A depletion model cannot be fittedto such a CPUE pattern. One solution is to fit thedepletion model to the early season decline, thenassume that the late season recruitment is to thesame population and examine the immigration thatwould have been required to produce it. The funda-mental problem with this method is that while CPUEcontinues to rise the estimated size of the stock alsocontinues to rise, and a stable stock assessment isnever reached. Another solution to this problem de-

Ž .veloped by Brodziak and Rosenberg 1993 is toconsider the pulses to be separate cohorts of a singlepopulation and to account for immigration within the

( )D.J. Agnew et al.rFisheries Research 35 1998 155–169 157

Fig. 2. Relative position of all catches 1987–1996, showing the sample area used for this paper. The irregular area is the Falkland IslandLoligo management area. 100, 200 and 500 m depth contours are shown.

Delury model. Such an approach requires an inde-pendent measure of immigration, such as an adjacent

Ž .fished area Brodziak and Rosenberg, 1993 , whichis not available for the Falklands fishery.

The fishery is currently regulated by effort controlŽ .FIFD, 1997 with the target that proportional es-capement 1 should not fall below 40%. This is anarbitrary figure, based on experience in the I. ar-

Ž .gentinus fishery Beddington et al., 1990 . The con-

1 The ratio of the numbers of animals surviving to the end ofthe season against the numbers that would have survived in theabsence of fishing.

tinuing problems with the assessment of L. gahihave frustrated attempts to derive empirical biologi-cal reference points such as minimum levels ofspawning stock biomass. Although effort is set at thestart of each season, because it is an annual speciesreal-time assessment of the Loligo fishery is re-quired to ensure the escapement target is met.

This paper presents an alternative approach toassessments of L. gahi around the Falkland Islands.Firstly, we demonstrate the difficulties that arisewhen applying a Delury depletion model assumingthat each fishing season represents a separate stock.Secondly, we use the available biological and fish-eries information to postulate the occurrence of anumber of cohorts of L. gahi, and determine their


contributions to the fishery. Finally, we present anapproach which uses information on trends in catch-ability coefficients to provide estimates of stock sizein the absence of satisfactory Delury estimates.

2. Methods

Detailed daily catch and effort data have beenŽcollected by FIFD from the fishery since 1987 FIFD,

Ž . Ž .Fig. 3. L. gahi CPUE thousandsrh, left axis, solid line , the percentage of immature animals right axis, grey line and mean weightŽ .grammes, right axis, dashed line around the Falkland Islands. The percentage immaturity is the percentage of animals of both sexes having

Ž .Lipinski’s maturity of 1–2 Lipinski, 1979 . Transition periods identified from length frequency data are shown on the x axis, which is inweeks.


.1997 . FIFD has also implemented a comprehensiveobserver programme, which has collected biologicaldata from the fishery during each fishing seasonsince 1987. Data from the pre-1987 fishery are avail-

Žable from a number of sources MRAG, 1986; Csirke,.1987; Patterson, 1988 , but are not as comprehensive

as the FIFD data and were not used in this study.Although catches of L. gahi have been made

from all around the Falkland Islands, since 1987 over98% have been taken within a box defined by 508S–

X Ž .53830 S and 568E–618E Fig. 2 . This is the area thatcontains the current licensed fishery. In order toeliminate data that may have originated from otherstocks on the Patagonian shelf, all analysis wasrestricted to this box.

Units of time were periods of 7 days followingthe 1st of January. Thus March begins in week 9,May begins in week 18, August begins in week 31and October in week 40. Weekly length frequency

data were used in combination with land-based mea-surements of the length-weight relationship for aparticular season to calculate mean weight at week.Where sampling was inadequate, mean weight atweek was interpolated from adjacent weeks.

Catch per unit effort was calculated as tonnes perhour for 7 defined fleets. The largest single fleet hasalways been the Spanish fleet, from which a numberof vessels have re-registered to the Falkland Islandsin recent years. Consequently, preliminary Deluryanalyses indicated that the catchabilities of Spanishand Falklands fleets were very similar, and that largevessels have higher catchabilities than small onesŽ .FIFD, 1989 . Therefore the first set of fleets was

Ž .defined as SpanishrFalkland ESrFK - 1000Ž .tonnes GRT gross registered tonnage , 1000–2000 t

GRT and )2000 t GRT. Most other vessels havebeen European, Eastern European or South Ameri-

Ž .can, and were grouped into Other OTH -1000 t,

Table 1Delury assessment of L. gahi assuming one population per season

Ž . Ž .First week Last week N at start of first week millions Biomass at start of first Biomass at end of last Escapement %Ž . Ž .with standard error in parenthesis week ’000 tonnes week ’000 tonnes

1st cohortŽ .1987 1 25 5281 96 106 1.2 5.3Ž .1988 1 25 3335 351 138 11 35Ž .1989 1 23 7135 234 171 18 26Ž .1990 1 23 7791 809 288 29 47Ž .1991 1 22 2033 y 77 0.042 0.2Ž .1992 1 22 4171 670 125 12 25Ž .1993 1 22 1432 72 57 5 27

1994 y y y y y yŽ .1995 1 22 3958 324 170 23 43

1996 y y y y y y

2nd cohortŽ .1987 27 44 2903 828 99 36 72Ž .1988 27 44 156 18 8 1 26

1989 y y y y y y1990 y y y y y y

Ž .1991 27 44 1409 347 51 12 48Ž .1992 27 44 3630 935 182 30 67

1993 27 44 y y y yŽ .1994 27 44 1141 61 50 4 20Ž .1995 27 44 1549 145 72 17 38Ž .1996 27 44 850 57 46 8 36

Where CPUE started to rise at the end of a season, the Delury was fitted only to the declining part of the CPUE curve although projectionscontinued until the end of the season. For the first season in 1991, however, this would have produced a final population of 42 tonnes, so theassessment was stopped week 12. Dashes indicate failures to fit a Delury assessment. Escapement is the ratio of the numbers at the end ofthe last week to the numbers that would have been present in the absence of fishing.


1000–2000 t and )2000 t fleets. Finally, the veryfew large Japanese vessels involved in the fisheryappear to have very different fishing strategies fromthe other vessels, and have been separated into a

Ž .Japanese JP )2000 t fleet.CPUE was calculated only for vessels in these

fleets licensed to fish for L. gahi, since it could beassumed that these vessels were targeting squid. Inthe early years, 1987–1989, these vessels accountedfor about 70% of the total catch in the box, rising toover 90% after 1990. Total catch was derived fromall vessels fishing in the box, irrespective of licencetype.

Delury assessments were performed usingMSQUID, a computer program developed at theRenewable Resources Assessment Group, Imperial

Ž .College, by Holden et al. 1990 . This program fits amodified Delury as described in Rosenberg et al.Ž .1990 to observed catch and effort data from anumber of fleets. A maximum likelihood method isused to estimate starting population numbers.

In a study of I. argentinus in the southwestŽ .Atlantic, Beddington et al. 1990 estimated natural

Ž .mortality M as 0.06 per week. Although it growsto a larger size, I. argentinus, like L. gahi, is anannual squid species occurring in the waters aroundthe Falkland Islands. Natural mortality for L. gahiwas therefore assumed to be the same as for I.argentinus, 0.06 per week, which is in any caselikely to be an adequate approximation so long it isused consistently throughout the assessment process.Tests confirmed that the maximum likelihood func-tion is insensitive to the level of M used.

3. The two-season approach

Fig. 3 presents CPUE, weight and maturity datafor the years 1987–1996. There are periods of de-clining CPUE in the first season of all years, and in

Žmost of the second seasons first seasons are weeks.1–26, second seasons are weeks 27–44 . Treating

the data as representing two populations, one in eachseason, application of the MSQUID model producedthe assessments presented in Table 1.

For five out of the 20 seasons, the assessmentsfailed; that is, a Delury model could not be fitted tothe data on CPUE and cumulative catch. In a number

of other cases the Delury model fit was poor, produc-ing skewed likelihood functions. There are various

Ž .reasons for these failures refer to Fig. 3 . In the firstseasons of 1993 and 1996, two peaks can be identi-fied and a Delury model could not be fitted to theCPUE and cumulative catch data. In the 1989 and1990 second seasons, no decline in CPUE was ap-parent in the data. And in the second season 1993 thedecline at the start of the period was too rapid. Thiswas also a problem with the first season in 1992, buta Delury model could be fitted if the peak at week10 was omitted. In 1991, considering the first seasonto be a single population was clearly inappropriate,and resulted in a biomass at the end of week 22 ofonly 42 tonnes. This was because although the Delurywas fitted to only the declining part of the CPUE

Ž .series, catches taken after this point week 12 im-plied an effective depletion of the population to verylow levels.

4. The multiple cohort approach

It is clear that considering each season as exploit-ing a single population is inappropriate. We nowhypothesise that the scheme proposed by HatfieldŽ .1996 is a more appropriate description of this L.gahi population; that is,1. that there are at least two cohorts in a year, which

recruit to the fishery in January and AprilrMay;and

2. that there may be a further period of recruitmentin SeptemberrOctober.The evidence for this hypothesis can be seen in

Fig. 3. At the start of the first season, the populationis dominated by small immature animals. As theseason progresses the proportion of immature ani-mals decreases and their mean size increases, as onewould expect of a resident, maturing population.Such a population is effectively closed, and could beassessed using a Delury depletion approach. At some

Žpoint in the first season, usually AprilrMay weeks.14–20 , the proportion of immature animals starts to

rise again, and mean weight drops. This pattern isconfirmed by examination of length frequency distri-butions, and although these are not presented herefor reasons of space the transition periods suggestedby them are shown on Fig. 3.


The increase in proportion of immature animals inearly May is obviously either due to emigratingmature animals or immigrating young animalsŽ .Patterson, 1988 . It indicates that the cohort that hasbeen resident on the fishing grounds up to the end ofApril is being replaced by a new cohort, which willbecome resident once it has fully recruited. Thechange in the proportion of immature animals issometimes coincident with a change from decliningCPUE to increasing CPUE, but more often it isoffset slightly. For example, in 1991, 1992 and 1994the first season change seems to occur after thetrough in CPUE. In 1990 and 1995 it occurs beforethe trough in CPUE. Where the proportion of imma-ture animals starts to rise as CPUE declines, theimplication is that emigration of mature animalsexceeds immigration of immature animals. On theother hand, if the proportion of immature animalsstarts to rise as CPUE troughs or starts to increase,then immigration of immature animals exceeds emi-gration of mature animals.

It seems fairly clear that the cohort that recruits to

the fishery in April or May forms the main target ofthe second season fishery. Despite the break in sam-pling occasioned by the closed season in June andJuly, the size of animals at the end of the first seasonand the start of the second is comparable. Further-more, CPUE patterns are similar between the end of

Žthe first season and the start of the second correla-tion coefficient 0.761, ns10 for CPUE either side

.of the mid-season break shown in Fig. 3 .In contrast to the first season, transitions between

Žcohorts in the second season i.e., when the second.cohort is replaced by a third are not always seen.

For instance, a biological transition involving de-creasing mean length and increasing proportion ofjuvenile animals is seen in 1989, 1990, 1992 and1993. In only 1990 is there a corresponding increasein CPUE. On the other hand, a peak in CPUE is seenafter week 39 in 1987 and 1991 without biologicalindications of a change in cohort. These transitions

Ž .are around week 40 late Septemberrearly October .The other years show neither biological nor CPUEindications of a third cohort coming into the fishery.

Table 2Results of the cohort model Delury assessment

Ž . Ž .First week Last week N at start of first week millions Biomass at start of first Biomass at end of last Escapement %Ž . Ž .with standard error in parenthesis week 000 tonnes week 000 tonnes

1st cohortŽ .1987 1 18 2471 38 101 3.5 8.3Ž .1988 1 17 2802 283 115 24 51Ž .1989 1 20 6873 241 165 30 32Ž .1990 1 15 5566 671 206 37 51Ž .1991 1 12 1392 136 53 10 41Ž .1992 1 16 3233 324 97 20 42Ž .1993 1 18 1163 72 47 9 35Ž .1994 1 16 1702 201 55 5 20Ž .1995 1 19 4534 631 195 47 55Ž .1996 1 16 727 y 31 0.042 0.2

2nd cohortŽ .1987 19 39 4745 1337 202 40 73Ž .1988 18 40 777 82 39 6 38Ž .1989 21 40 1062 115 46 4 24

1990 16 40 y y y yŽ .1991 13 40 3811 745 146 16 51Ž .1992 17 43 7336 1900 264 46 64

1993 19 41 y y y yŽ .1994 17 40 2377 111 116 8 25Ž .1995 20 40 2422 222 141 18 37Ž .1996 17 41 1950 123 130 12 34


It may be that the cohort usually recruits to thefishing grounds to feed after the fishery has finished,and it is only when this cohort arrives early that it isseen.

It is beyond the scope of this paper to fullyexplore the periods of transition between one cohortand the next. Instead, we adopted the pragmaticapproach of assuming a knife-edge transition fromone cohort to another. For the purposes of re-runningthe Delury assessments, this point was identifiedfollowing consideration of the biological and CPUEindices shown in Fig. 3 and weekly length frequencydata from the fishery. Since catches at these timesare generally low, and the Delury is only fitted to theearlier strongly declining part of the CPUE series,the simplistic assumption of a knife edge transition islikely to have relatively little impact on the results.For those years where a second season transitioncould be identified we chose week 40 for the point atwhich the second cohort gave way to the thirdcohort. For the other years, the second cohort wasassumed to run to the end of the fishing season.However, in no years were there sufficient data to fita Delury model to the third cohort.

The results of the cohort Delury analysis aregiven in Table 2. The approach enabled more cohortsto be assessed than with the two-season approach.However, for those that had been assessed previ-ously, especially those from the second season, therewas generally little improvement to the fit of themodel. In other words, the previously identified

CPUE decline was the only one that could be mod-elled. A number of the assessments were still unsat-isfactory, with skewed likelihood functions or ex-

Žtremely low final biomass such as the first cohort.3500 tonnes in 1987 or the 42 tonnes in 1996 .

One major consequence of the multiple-cohortapproach was the increase in the estimated size of allsecond cohorts. This is because whereas before, the

Žsize of these cohorts was estimated at week 27 1.July , in the new analysis it was estimated at the time

that they enter the fishery, at about week 18.Ž .Trends in q catchability coefficient derived from

the Delury assessments are shown in Fig. 4. For thefirst season, there appear to be two types of year,those producing low q and those producing high q.

ŽThe higher values of q seen in 1987, 1991 and.1993 do not seem to be a result of high stock levels.

Although there is a generally decreasing trend of qwith stock size, the two are not significantly corre-

Žlated Pearsons correlation coefficient: y0.479, ns10 for the first cohort, and y0.515, ns8 for the

.second cohort . Loligo assessments performed usingŽ .depletion models by Augustyn et al. 1993 and

Ž .Brodziak and Rosenberg 1993 have similarly failedto find a relationship between stock size and q.Explanations for the existence of two types of yearare at present speculative. High q years could beproduced when there is a large immigration eventtaking place, or when animals are easier to catch,perhaps a result of different aggregation character-istics. There is, however, no evidence from Fig. 3

y5 ŽFig. 4. Catchability coefficients arising from the Delury analysis of cohorts. Values are in 10 i.e., 5 on the figure is actually.5Ey5s0.00005 . ES-FK is the SpanishrFalkland fleet, JP is the Japanese fleet and OTH is other vessels, and the numbers following

these abbreviations indicate the Gross Registered Tonnage class of the fleet.


that more emigration is taking place in these yearsthan in others having low q values.

The low q values from the first cohort are slightlyhigher than those seen in the second cohort. Thiscould be caused by differences in the behaviour ofthe fleet or squid in the first and second seasons. For

Žinstance, the long term mean hours per day is 8.5 sd. Ž .3.78 for the first season and 13.3 sd 5.41 for the

second. Both first and the second cohort qs exhibittrends to increasing catchability with time. The trendsare not directly linear or always increasing, but couldbe explained by fleet learning behaviour.

5. Delury extension

Although Table 2 shows that fitting a Delurymodel was successful for the majority of cohorts,there were occasions when either a fit could not beobtained or the likelihood function was markedlyskewed. Further, it is not sufficient to manage annualLoligo cohorts simply with post-season assessmentsŽ .Brodziak and Macy, 1994 . In-season, real-timemanagement is required. It would be useful to have asupplementary method for assessing cohort size ei-ther in the absence of a successful Delury assessmentor early in the season before a depletion event towhich a Delury could be fitted has fully developed.

Obviously, in such circumstances the character-istics of the fishery are not completely unknown.

Delury assessments of earlier and later seasons pro-vide information about the likely values of catchabil-ity coefficients. In a Bayesian-style approach, theseq values are priors which could be used to provideestimates of current biomass and cohort size in theabsence of a Delury. Without developing a fullBayesian analysis, the following demonstrates how qvalues arising from successful Delury assessmentscan provide information about otherwise unknowncohorts.

Q values arising from the successful Delury as-sessments of individual cohorts are presented in Fig.4. Three groups of catchability coefficients were

Ž .recognised, the high qs in cohort one group 1 , theŽ .low qs in cohort 1 group 2 and the qs for cohort 2

Ž .group 3 . An expected q value for each year wasderived from 3-point moving averages of these q

Ž .values Table 3 . Cohort size was then estimatedfrom the combination of the expected q with CPUEdata.

Each vessel in each fleet was considered to be anindependent sampler of the stock biomass in eachweek. In other words, an estimate of the stock

ˆnumbers at time t calculated using vessel Õ, N , ist,Õ

N̂ sC rE rq where C and E are the catch int,Õ t,Õ t,Õ f

numbers and effort in hours by vessel Õ at week t,and q is the expected q value of the fleet to whichf

vessel Õ belongs. An estimated stock size at week t,N̂ , was calculated as the mean of all N , weightedt t,Õ

by the number of days fished per vessel. Because the

Table 3Methods used to calculate expected q from the observed qs shown in Fig. 5

Catchability group

Fleet Group 1 Group 2 Group 3

ESyFK-1000 mean of years 1987, 1991, 1993 3-point moving average 3-point moving averageESyFK)2000 mean of years 1987, 1991, 1994 3-point moving average 3-point moving averageESyFK 1000–2000 mean of years 1987, 1991, 1995 3-point moving average 3-point moving averageJP)2000 mean of years 1987, 1991, 1996 3-point moving average equal to ES-FK)2000q10%OTH-1000 equal to ES-FK-1000 equal to ES-FK-1000 equal to ES-FK-1000OTH)2000 mean of years 1987, 1991, 1996 3-point moving average equal to ES-FK)2000OTH 1000–2000 mean of years 1987, 1991, 1996 3-point moving average 3-point moving average

Expected qs were used in the Delury extension analysis. Q group 1 is years 1987, 1991 and 1993 in the first cohort; group 2 is all otheryears in the first cohort; and group 3 is all years in the second cohort. There appeared to be trends of q with time for groups 2 and 3 sothree-point moving averages were used to calculate the model qs. For group 1 there were insufficient data points to indicate a trend. TheOTH-1000 fleet was not represented in enough Delury assessments to calculate moving averages of observed q, and so model q was set toequal the ES-FK-1000 fleet qs. The same was true of OTH)2000 in the second cohort and JP)2000. For the latter fleet, qs weremodelled as being 10% higher than the largest ES-FK fleet.


week was the unit of sampling, only data from weekswhere a vessel had fished for more than two dayswere used.

Next, we calculated the starting population whichwould have been required to give each week’s esti-

ˆmate of population size, N , taking into account thet

Ž . Ž . Ž .Fig. 5. Number of recruits millions"2 SE of the first thick line and second thin line cohorts estimated using the Delury extension.These numbers apply to the first week for the cohort, given in Table 3. The weeks used for the calculation of mean estimated recruits areshown along the x-axis.


Table 4Results of the Delury extension analysis

Ž . Ž .First week Last week N at start of first week millions Biomass at start of first Biomass at end of last Escapement %Ž . Ž .with standard error in parenthesis week 000 tonnes week 000 tonnes

1st cohortŽ .1987 1 18 2820 34 116 9 20Ž .1988 1 17 2264 72 93 15 39Ž .1989 1 20 8554 167 205 53 45Ž .1990 1 15 5262 174 195 33 48Ž .1991 1 12 1347 46 51 9 39Ž .1992 1 16 3720 120 112 28 50Ž .1993 1 18 1322 14 53 12 43Ž .1994 1 16 2070 45 66 11 34Ž .1995 1 19 4935 106 212 54 58Ž .1996 1 16 2280 35 98 45 68

2nd cohortŽ .1987 19 39 3198 154 137 22 60Ž .1988 18 40 836 44 41 7 42Ž .1989 21 40 1328 43 58 9 40Ž .1990 16 40 3407 116 104 20 57Ž .1991 13 40 5488 209 210 30 66Ž .1992 17 43 7575 223 272 48 65Ž .1993 19 41 1682 37 90 10 27Ž .1994 17 40 2721 39 133 13 34Ž .1995 20 40 2648 52 155 22 43Ž .1996 17 41 1866 64 124 10 31

catches up to that point. There are two componentsto this calculation: estimating the number of recruitsthat would have given rise to the current estimate ofpopulation size, and calculating the number of re-cruits that would have given rise to the cumulativecatches taken from the fishery.

The week that the cohort recruited to the fisheryis termed the start week, s. Projecting the estimate ofN̂ back to the start week is a straightforward multi-t

plication by emŽ tysq0.5., where m is the weeklynatural mortality. The 0.5 term is necessary becauseN̂ is assumed to relate to the middle of a week,t

whereas we want recruits at the start of week s.Projecting the catch in numbers at week t back tothe start week is similarly straightforward. The num-ber of recruits represented by a catch C at week t isC PemŽ tysq0.5.. The number of recruits that wouldt

have given rise to all catches up to the present week,P , is therefore P sÝt C =emŽ iysq0.5.. Sincet t iss i

catches are known, P is not an estimate. Combiningt

these two calculations, the full equation for estimat-ing the number of recruits, R, made at week t is

tmŽ iysq0.5. mŽ tysq0.5.ˆ ˆRs C =e qN e 1Ž .Ý i t

iss

where C is the catch in numbers at week i, m isiŽweekly natural mortality, s is the start week week

ˆ.of first recruitment and N is the estimate of popula-t

tion size at week t.For the first cohort, s was assumed to be week 1

Ž .1 January . For the second cohort, the start weekwas taken to be the same as in Table 2. Using Eq.

ˆŽ .1 , we calculated R for each week of the fishery.tˆAs would be expected, plots of R generally showedt

a rise in estimates of starting population size as acohort recruited, followed by a period of relatively

2 ˆThese periods of constant R would be expected since qt

values were originally derived from Delury assessments.


ˆ Ž .constant R Fig. 5 when the cohort was resident ont

the fishing grounds. 2 Since they represent stableestimates of population size, the constant periodsidentified in Fig. 5 were used in the calculation of ay

ˆmean of estimates, R. Although the identification ofthese periods may seem somewhat subjective, thesechoices also have to be made when fitting a Delurymodel—both Delury and Delury extension ap-proaches rely on there being identifiable periodswhen the population is closed and being depleted aty

ˆa constant rate by fishing. From R, the starting andfinal cohort biomass, and the escapement, could beobtained after taking into account removals by natu-ral mortality and fishing. The results are given inTable 4.

As would be expected, the estimates of startingpopulation size derived using this method comparedwell with the results of the original Delury assess-

Ž .ments Fig. 6 . Confidence intervals shown on thisFigure were derived from the maximum likelihoodestimates of the Delury and the normal variance of

ˆestimates of R . This latter variance decreases witht

increasing t because more of the estimate is com-posed of cumulative catch, P , which has no vari-t

ance. Significant differences between estimates, madeby comparing 95% confidence intervals, were seenonly in the first seasons of 1987, 1989 and 1996. Theestimates for 1987 are significantly different only atthe 95% level, not at the 99% level. The reason forthe discrepancy in 1989 is that 3-year moving aver-age q values for 1989 are lower than the q values

derived from the Delury. This arises because of thedomed shape of Fig. 4 in the years 1988, 1989 and1990. For 1996, the Delury estimate of startingpopulation is unreliable: the highly skewed confi-dence interval shown by the Delury estimate in Fig.6 reflects a highly skewed likelihood function, andthe lower confidence interval is in fact the minimumpopulation that could have produced the observedcatches.

6. Discussion

The occurrence of two cohorts is common inother Loligo fisheries, but not universal. Grist and

Ž .des Clers 1997 have presented theoretical workbased on models of growth and maturation and theirrelationship with water temperature cycles whichsuggests that annual squid species may be morelikely to stabilise with 2- and 3- populations orcohort pulses a year than one. The L. pealei fisheryoff Cape Cod has two cohorts, which spawn in late

Žspring and early autumn Brodziak and Rosenberg,.1993 . L. Õulgaris reynaudii off South Africa usu-

ally has one peak in late spring and sometimes oneŽ .in the autumn Augustyn et al., 1992, 1993 . These

two fisheries are on spawning rather than feedingaggregations. Other two-peaked fisheries are the Por-

Žtuguese fishery for L. Õulgaris and L. forbesi da.Cunha and Moreno, 1994 and the Azores fishery for

Ž .L. forbesi Porteiro, 1994 , both of which have strong

Fig. 6. Estimates of starting population size for the first and second cohorts, determined by the Delury assessments and the Deluryextension. Numbers in millions with 95% confidence limits, solid line is the Delury, dotted line is the Delury extension.


autumn and weaker late spring peaks. The Catalo-Ž .nian fishery for L. Õulgaris Guerra et al., 1994 and

Ž .the UK fishery for L. forbesi Pierce et al., 1994Ž .only seem to have single peaks. Mohamed 1996

also reports a single winter peak in the Mangalorefishery for Loligo duÕauceli, but notes that monsoonconditions prevent fishing and therefore observationsin the summer.

The presence of a third cohort has not yet beennoted in any other Loligo fishery, but its occurrencefalls within the ranges of theoretical possibilities

Ž .predicted by Grist and des Clers 1997 . We have notassessed it in this paper because we do not havesufficient information from the fishery to determinewhether the late spring peak is a separate cohort, partof the second cohort or indeed an advance guard ofthe next year’s first cohort.

As methods for arriving at an assessment of L.gahi, the Delury depletion method and the extensionoutlined here are complementary. There are certainlytimes when a very poor fit is obtained from theDelury model or a Delury cannot be fitted at all,especially early in a fishing season. In these situa-tions, an approach based on knowledge of historicaltrends in fleet catchabilities can provide supplemen-tary information on current stock size, projected finalstock biomass and escapement.

One major difficulty with using the Delury exten-sion to provide real-time estimates of Falkland Island

L. gahi stock size in the first season is that it is notclear why there should be two groups of qs. At themoment it would not be possible to tell in advancewhether a cohort fell into the low-q or high-q groups.Under these circumstances, use of the expected highq values would always provide a conservative esti-mate of first cohort size, but a Delury model wouldhave to be fitted to provide a final assessment. Thisproblem is being addressed by continuing research atImperial College. For instance, it is possible that a

ŽBayesian approach e.g., McAllister and Kirkwood,.1997 or additional early season sampling might

facilitate identification of the type of q that is appli-cable. For the second cohort, on the other hand,where q appears to be more consistent, the Deluryextension is more applicable. Indeed, for those yearswhere a Delury cannot be fitted to second cohortdata, the Delury extension provides the only estimateof stock size. Other methods of calculating expectedcatchability, such as a mean q over all seasons or aregression of q on time, might be more appropriatewith other Loligo stocks.

7. Management

Fig. 6 demonstrates that the two cohorts haveseparate dynamics. The first cohort peaked in 1989,and has been in decline since then with the exception

Ž . Ž .Fig. 7. Stock-recruit data for L. gahi estimated using the Delury a; taken from Table 2 and Delury extension b; taken from Table 4 .Stock is the biomass of animals at the end of the last week of the assessment, assumed to be equal to spawning stock. Recruits is the numberof animals recruiting to the following season’s cohort. Solid squares are the first cohort, open squares are the second cohort.


of 1995. The second cohort had a peak slightly later,in 1991 and 1992, and may also have been decliningslowly since then. Catches from the two seasons also

Ž .show these changes Fig. 1 . Catchability coeffi-cients are different for the two cohorts, those fromthe second cohort being smaller than from the first.Recruitment to the fishery appears to be much morerapid for the first than the second cohort, whichrarely develops CPUE peaks as high as the firstcohort. The second cohort is generally composed oflarger animals, and the differences in q values couldbe explained in terms of their having a more diffusefeeding distribution than the first cohort. It is there-fore appropriate that the cohorts should be consid-ered to be two populations, and be managed sepa-rately, even though a study by Carvalho and PitcherŽ .1989 failed to detect genetic differences betweenany Falkland Islands Loligo stocks.

The current situation of two management seasonsalmost coincides with the cohorts, but importantlyfishing in the first season usually targets the recruit-ing second cohort as well as the first cohort. There isa danger that the second cohort could be depleted byheavy fishing in the first season while it is recruiting,or that the two cohorts could be confused in thisseason leading to inappropriate assessments andmanagement in subsequent years. These dangerscould be avoided by regular in-season assessmentsleading to temporary fishery closures when manage-

Ž .ment reference points such as absolute escapementare reached. Once a new cohort starts recruiting thefishery could be re-opened.

Although L. gahi stocks are nominally managedon an arbitrary target escapement of 40%, the fisheryhas never been closed early even when escapementhas apparently declined below this level. This isbecause of uncertainty about the meaning of propor-tional escapement in terms of subsequent recruit-ment. There is a need to establish an appropriatelevel of absolute escapement in terms of spawningstock biomass. Stock-recruit data are shown in Fig.7. With only 10 years data for each cohort, it isdifficult to identify stock recruit relationships withany confidence. It is interesting that the first andsecond cohorts appear to have similar ranges ofstock and recruitment, which could lead to the adop-tion of similar target escapement levels for eachcohort.

The identification of transition periods betweencohorts remains unsatisfactory, and the significanceof the occasional third cohort is unknown. A usefuldevelopment would be a model including immigra-tion, such as that described by Brodziak and Rosen-

Ž .berg 1993 . One of the biggest difficulties that isencountered in separating the cohorts is the lack ofdata from the fishery or from observers in June andJuly, between the seasons. In this paper we havetaken the simplest approach, and assumed that thecohort that recruits in AprilrMay continues into thesecond season, but it is possible that a fourth cohortmay sometimes recruit in the mid-season period.Fishing and sampling from the period between thefirst and second seasons would provide much valu-able data and increase our confidence in assessmentsof this species.

Acknowledgements

We would like to acknowledge all FIFD observerswho work to ensure good biological informationfrom the fishery is available for analyses such asthis. We also acknowledge the work of all past andpresent members of the Falklands Group at RRAG,especially the work done on the database by L.Purchase, J. Crombie and S. Holden. M. McAllister,E. Hatfield, L. Purchase and the reviewers providedmany constructive comments on the draft for whichwe are very grateful.

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Approaches to assessing stocks of Loligo gahi around the Falkland Islands

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