assessmentofthespatialstructureandbiomassevaluationof...

ICES Journal of Marine Science, 55: 102–120. 1998

Assessment of the spatial structure and biomass evaluation ofNephrops norvegicus (L.) populations in the northwesternMediterranean by geostatistics

Francesc X. Maynou, Francisco Sarda, andGerard Y. Conan

Maynou, F. X., Sarda, F., and Conan, G. Y. 1998. Assessment of the spatial structureand biomass evaluation of Nephrops norvegicus (L.) populations in the northwesternMediterranean by geostatistics. – ICES Journal of Marine Science, 55: 102–120.

The spatial distribution and biomass of Nephrops norvegicus were assessed by trawlingover commercial fishing grounds (‘‘Serola’’, off Barcelona, Spain) during two surveys(spring and fall 1991), using geostatistical methods. The surveys were set 6 monthsapart, in order to analyse possible seasonal differences. In the present surveys, Norwaylobster was caught between 200 and 600 m depth, with peak abundance at about400 m. The analysis of the structure of spatial correlation by means of semivariogramsshowed that densities of Nephrops norvegicus were spatially autocorrelated and lobsterpopulations were distributed in high-density patches 6 to 9 km in diameter. No spatialsegregation per biological category (size or sex) was detected. The semivariogramswere consistent for all biological categories. A strong linear relationship between localmean and standard deviation (proportional effect) was modelled by the relativesemivariogram. Relative experimental semivariograms were fitted to a spherical model.The shape of the semivariogram, and the spatial autocorrelation structure of Norwaylobster populations, remained stable over the two surveys. The density of Nephropsnorvegicus available to the experimental gear was mapped by point kriging. High-density patches of different biological categories exactly conformed and remainedstable over the two surveys, showing a certain intra-annual stability. However, meandensities and overall abundance (computed by global kriging) decreased sharply inthe fall survey. This was accounted for by means of knowledge on the biology of thespecies for the same area. The biological characteristics of Nephrops populations in thearea studied are similar to those of other Mediterranean and Atlantic populations,hence our results are not restricted to the study area. We conclude that thegeostatistical analysis approach, which takes into consideration the spatial auto-correlation structure of the populations, is adequate for the direct biomass estimationand assessment of Nephrops harvestable stock.

? 1998 International Council for the Exploration of the Sea

Key words: Nephrops norvegicus, Mediterranean, semivariograms, kriging, evaluationof resources.

Received 13 September 1996; accepted 28 February 1997.

F. Maynou and F. Sarda: Institut de Ciencies del Mar, CSIC. Pg. Joan de Borbo s/n.,Barcelona E-08039, Spain. G. Y. Conan: Department of Fisheries and Oceans,Newfoundland Region Science Branch, P.O. Box 5667, St John’s, NF A1C 5X1,Canada.

Introduction

Norway lobster (Nephrops norvegicus) is the mostimportant species in the European crustacean fishery (interms of catch and economic value, FAO, 1992). Thebiology of the species is now well known and a summarycan be found in Sarda (1995). Fisheries data are con-tinuously evaluated by the ICES Nephrops WorkingGroup (ICES., 1992). Uncertainties about growth and

mortality coefficients of Nephrops norvegicus generatedifficulties for assessing stocks from data on landingsand cohort analysis (see Sarda and Lleonart, 1993 for anapplication). Alternative methods, such as direct assess-ments, have been recommended (Conan, 1985; ICES.,1989).Norway lobster populations show highly complex

aggregated patterns of spatial distribution. Fishermenand researchers indicate that sex ratio, size composition,

1054–3139/98/010102+19 $25.00/0/jm970236 ? 1998 International Council for the Exploration of the Sea

presence of berried females and overall abundance of thecatch may vary between localities in close proximity, aswell as seasonally (Sarda, 1991).Nephrops is found between 200 and 800 m depth on

the Catalan Sea slope off Barcelona (Spain, northwestMediterranean), which is deeper than for Bay ofBiscay and higher latitude northeast Atlantic stocks, butpublished information on the depth and geographicdistribution of the species in the area surveyed is stilllimited (Sarda and Abello, 1984; Sarda, 1991).It is important for the purpose of stock conservation

and profit optimization, to map and accurately forecastthe location and the spatial characteristics of theresource (Conan, 1985). Only a portion of the stock canbe harvested with profit. At locations and times at whichthe density of commercial quality Norway lobster is toolow, harvesting costs may be higher than the value of thecatch. It may be also worthwhile to protect certainfishing areas by setting annual or seasonal closures toprotect certain biological categories, such as berriedfemales or immature individuals.The presence of spatial patterns has not, until

recently, been taken into account for calculating bio-masses and setting confidence limits on these estimates,other than by using stratified random sampling. Conan(1985), Conan et al. (1988a, 1988b, 1992) and Conanand Wade (1989) have introduced techniques derivedfrom the geostatistical methodology, initially developedin Mining Geology (Matheron, 1971; Journel andHuijbregts, 1978), which are at present routinelyemployed for the assessment and management of snowcrab stocks in the Gulf of St Lawrence (Canada)and which are gaining interest in other species andareas (Simard et al., 1992; Petitgas, 1993; Farina et al.,1994).In order to map and assess the harvestable biomass of

Norway lobster on the fishing grounds, experimentaltrawl surveys and geostatistics were employed to opti-mize the evaluation of this spatially structured resource.We investigated the applicability of statistical methodol-ogy to directly assess Nephrops stocks on commercialfishing grounds located off Barcelona, Spain (northwestMediterranean) based on data from two experimentalcruises carried out during spring and fall 1991. Thesampling scheme for both cruises was specificallydesigned for the geostatistical application. The tech-nology available (Global Positioning System and anacoustic measuring device for the trawl, SCANMAR)allowed for highly accurate positioning and measuringof the area swept by trawl.The application of geostatistics for mapping and

estimating marine benthic harvestable resources is alsoreviewed and analysed. The need to adapt existinggeostatistical models to actual case studies (species) isstressed and a critical study of their use and scope ispresented, together with an application of the method-

ology to the commercial fishery of Nephrops norvegicusin the northwest Mediterranean area.

Material and methods

The sampling routine

Two surveys (GEOESC-I, spring 1991, and GEOESC-II, fall 1991) were specifically designed for the mappingand assessment of harvestable Nephrops resources off

northeast Spain. The survey site was chosen over muddybottoms with gentle slope and depth contours (100 to900 m) approximately parallel to the coast, limited bytwo submarine canyons (Fig. 1). A regular grid 1 by 2nautical miles was set parallel to the coast and a startlocation for each tow was randomly chosen within eachcell. Total area covered was 790 km2, comprising 115cells. Due to logistic and practical constraints only abouthalf of the cells could be sampled on both surveys (59trawl hauls in GEOESC-I and 51 in GEOESC-II).Mid-point position of hauls are shown in Figure 1aand b.The experimental fishing gear was a specially designed

otter trawl (‘‘Maireta System’’, Sarda et al., 1994)drawn by a single warp, to reach up to 2000 m depth.The codend stretched mesh was 12 mm in order toretain small individuals, not normally available to thecommercial fishing gear.The actual opening of the trawl was measured using a

SCANMAR acoustic system and stabilized at 14.0 mwidth by 2.0 m height. During the survey, tows weremade parallel to the depth contours. The duration ofeach tow was set to exactly 15 min (time of effectivetrawling). The towing speed varied between 2.3–2.6knots (mean 2.5 knots). Start and end locations foreach tow were measured by GPS. The actual surfacecovered by each tow was computed from the GPS andSCANMAR readings. Effective time of the surveys wasfrom 7.30 to 20.00 h each day.The total catch of Nephrops was counted, weighed and

measured and the presence of berried females was noted.The catch was sorted into biological categories for eachtow: juvenile males, juvenile females, adult males, adultfemales and berried females. A carapace length (CL) of26 mm was used as a knife-edge approximation to firstpresence of gonadal maturity for segregating juvenilefrom adult individuals, 32 mm (CL) size at 50% maturityto determine the percentage of ovigerous females (Sarda,1991).

Geostatistical methods

Basic to the linear geostatistical methodology is theassumption of second order stationarity, analogous tothe same concept in time series analysis. Let the densityof Norway lobster be a spatially referenced variable,

103Spatial distribution and biomass of Nephrops norvegicus

Z(x), where x is the position of a sampling point in Rn,n=2 for our purposes. Then Z(x) is called a regionalizedvariable (Matheron, 1971) if the value taken by Z at xonly depends on its geographical position.

Under the second order stationary hypothesis, themathematical expectation of the first moment (mean) ofZ(x) is assumed to be constant over the field of study, aswell as the variance. This strong stationarity hypothesis

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Figure 1. Location of the trawl hauls in (a) the spring and (b) the fall surveys.

104 F. Maynou et al.

can be relaxed to the intrinsic hypothesis (Matheron,1971) by the use of the semivariogram. The intrinsichypothesis requires only that the mean and variance ofthe increments Z(x)"Z(x+h) and not Z(x) be constantover the field which is more realistic when dealing withfisheries data.The experimental semivariogram, which is a form of

computing the variance of a population taking intoaccount the spatial position of the samples, is employedas a descriptor of the spatial structure of the density ofNorway lobster. The experimental semivariogram isgiven by (Matheron, 1971):

where,

N(h)=the number of pairs used to compute the exper-imental semivariogram at distance h.

h=vector of distances&a specified range or toler-ance

Z(xi)=the density of Nephrops at location xi.Z(xj)=the density of Nephrops at location xj which is

within distance h of location xi.

The spatial structure of the Z(x) is represented by aplot of ã(h) against h from which the parameters thatsummarize the structure of spatial dependence wereobtained.Most semivariograms show a regular increase of

ã(h) with h up to a certain distance a (range of the

semivariogram) where ã(h) stabilizes around c*+c0 (sillof the semivariogram). The range of the semivariogramcan be interpreted as the distance beyond which noeffects of spatial covariance among samples exists. In theabsence of spatial autocorrelation, the mathematical ex-pectation of the semivariogram is the sample varianceand the variogram appears flat (pure nugget effect).Many experimental semivariograms show a dis-

continuity at the origin, c0, called the nugget componentof the variance, which represents the microscale vari-ability of Z(x) at distances shorter than the smallestdistance among samples. It may also include samplingerror or white noise. The variability introduced by thenugget effect can considerably increase the variance ofthe kriging estimates, thus a correct modelling of c0 anda careful design of the sampling plan are central togeostatistics in order to produce precise estimates.We tested for departures from stationarity by

means of plots of Nephrops density vs. the geographicalcomponents (northing, easting), the time of day anddepth. We examined the relationship between localmean density and local standard deviation to correct fora possible proportional effect (Isaaks and Srivastava,1989). The presence of a proportional effect is wide-spread in fisheries data: locations which average highdensities show also a higher variability than low-densitylocations (s2 m2). We tested for such effect by moving a7#7 km window by discrete 3.5 km steps over the areasampled, and computing for each window the localmean and the local standard deviation.

Table 1. Descriptive statistics of Nephrops catch data for the spring (GEOESC-I) and fall (GEOESC-II) surveys. All densities inindividuals km"2, except total weight, in kg km"2.

GEOESC-IJuvenilemales

Juvenilefemales

Adultmales

Adultfemales

Totalnumber

Totalweight

Mean 118.02 190.27 312.70 313.00 936.12 18.87Standard error of the mean 31.28 40.94 52.97 59.03 167.47 3.331st Quartile 0.00 0.00 16.04 0.00 73.98 1.65Median 34.36 64.15 129.09 117.33 397.77 9.553rd Quartile 83.56 250.36 443.12 394.84 1251.51 24.94Maximum 1449.41 1389.91 1690.98 2084.87 5918.41 108.71Standard deviation 240.30 314.44 406.88 453.39 1286.35 25.55Count 59 59 59 59 59 59

Adult Adult Berried Total TotalGEOESC-II Juveniles males females females number weight

Mean 53.32 253.87 112.08 16.52 365.94 9.39Standard error of the mean 15.97 61.48 25.71 5.52 82.15 2.281st Quartile 0.00 0.00 29.33 0.00 24.99 0.14Median 0.00 70.39 0.00 0.00 145.64 3.753rd Quartile 65.25 352.96 137.80 0.00 472.75 10.64Maximum 599.55 2209.74 753.65 150.73 2599.70 94.24Standard deviation 114.07 439.07 183.59 39.41 586.67 16.25Count 51 51 51 51 51 51


In mining geostatistics the proportional effect hasbeen described (David, 1977; Isaaks and Srivastava,1989) and modelled by a relative semivariogram, whichre-scales the local semivariance by the local mean:

We used experimental semivariograms (Matheron,1971), relative experimental semivariograms (Isaaksand Srivastava, 1989) and their theoretical equivalent(Cressie, 1991), experimental semivariograms on log-transformed data, to describe the spatial autocorrelationstructure of Nephrops densities in the area surveyed, forthe biological categories established and for the twosurveys.For the purpose of mapping the resource we

employed the spatial estimation technique known aspoint kriging (Matheron, 1971) within the boundariesdefined by the presence of samples. In order to imple-ment the kriging technique, the experimental semi-variograms need to be fitted to a theoretical model.

Models which comply with certain mathematical con-ditions (Matheron, 1971) and suitable for kriging arewell-described in the literature (Journel and Huijbregts,1978; Cressie, 1991).To produce precise maps of the density of Nephrops in

the study area we used biological information and catchdata to restrict the area by means of an irregularpolygon bounded by the 200 and 800 m depth contoursand by adjacent submarine canyons. We estimated thedensity at the nodes (Z*) of a 276#249 regular grid(internodal distance 1/6 km) within the boundaries ofthe polygon using the linear estimator (Matheron, 1971):

where the Z(xi) are the observed densities and wi areweights obtained by the solution of the kriging system ofequations using the fitted semivariogram. The krigingvariance (ó2k) obtained when solving the kriging systemwas used as a precision index to help establish thearea within which reliable global estimates could be

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produced. When kriging with relative semivariograms,as will be the case here, the kriging variance needs to bere-scaled by the local mean in order to obtain a variancewhich is at the same scale as the data (Conan et al.,1992).Block kriging (Matheron, 1971) was used to produce

global estimates of average density and total (availableto the fishing gear) biomass over the surveyed area andto give confidence intervals for the biomass esti-mates. The global estimate of the quantity Zv over the(irregular) polygon V for point samples defined on v is:

Its estimation variance (ó2e) is given by:

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where ã(-,-) is the average of the fitted semivariogramover the areas or volumes in parentheses. Computingaverage semivariograms on two dimensions requires

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the computation of double integrals (see Journel andHuijbregts, 1978, for details). The computation of theaverage semivariogram can be achieved analytically onlywhen the polygon V is a simple geometric shape andmust be approximated by numerical integration in thegeneral case (Journel and Huijbregts, 1978). One of theauthors (G. Y. Conan) developed a numerical approxi-mation to integrate the semivariogram over an irregularcontour and to obtain estimates of the mean and globaldensities and their associated confidence intervals on thearea sampled.

For ease of comparison of the global estimates andtheir standard deviations produced by kriging, globalestimates and standard deviation of the mean were alsoproduced by the swept area method (Cochran, 1977;Sparre et al., 1989).

Results

Total abundance in number, weight and densities of thecatch in the spring survey were higher than in the fall

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survey (Table 1). Size frequency distribution rangedfrom 12 to 58 mm CL and the mode of the distributionwas 27 mm LC. Sex ratio (males/females) varied between0.75 in spring to 1.5 in fall. Juveniles (<26 mm LC) weremore abundant in spring (51%) than in fall (17%).Ovigerous females were present only in fall, representing74% of the total mature females. Biological assessment ofthe data showed that the populations under study havesimilar biological characteristics to other Mediterranean

and Atlantic populations. Depth distribution of thespecies in the area ranged between 216 and 584 m, witha peak abundance at about 400–450 m depth (Fig. 2a).An exploratory data analysis was conducted in order

to check for inconsistencies with the assumptions of themodel (spring survey (Fig. 2); the fall survey showedsimilar patterns, though at lower densities). Dispersiondiagrams of Nephrops density vs. depth did not showany obvious depth-related trend (Fig. 2a). The catch was

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Figure 3. Plots of local mean vs. local standard deviation of Nephrops categories for (a) spring and (b) fall using moving windowsof 7#7 km2. The moving windows analysis is repeated for other window sizes in (c) for total density in number (spring survey).


not related to the time of day (Fig. 2b) and no geo-graphical trend was observed in Nephrops density (Figs2c and 2d) in a northern or eastern direction. Hence, thebasic assumptions of the linear geostatistical methodwere not invalidated.Dispersion diagrams of local standard deviation vs.

local mean (Fig. 3a, spring survey; Fig. 3b, fall survey)showed a linear relationship between mean density and

standard deviation, revealing the existence of a propor-tional effect, and suggested, at this exploratory stage,that relative semivariograms were appropriate fordescribing the spatial covariance structure of thisspecies. The linear relationship between standard devi-ation and mean was also evident when using other‘‘window’’ sizes (in Fig. 3c results for ‘‘window’’ sizes of3#3 to 9#9 km2 are shown).

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Figure 4. Experimental semivariograms computed for juvenile males (left panel) and juvenile females (right panel) for the springsurvey. Top row: Matheron’s semivariogram. Middle row: Relative semivariogram. Bottom row: Matheron’s semivariogram onlog-transformed data. Spherical model fitted to relative semivariogram and the parameters of the model are shown. Left panel:C0=0.459; c*=3.974; a=5.9 km. Right panel: C0=1.331; c*=1.070; a=6.7 km.


For the spring cruise, experimental semivariogramscomputed for Nephrops categories are shown in Figures4, 5 and 6. Relative semivariograms (middle row inFigs 4, 5 and 6) described the structure of spatialdependence better than traditional (Matheron’s) semi-variograms (top row in Figs 4, 5 and 6) or traditionalsemivariograms on log-transformed data (bottom rowin Figs 4, 5 and 6). The formal equivalence betweenrelative semivariograms and semivariograms on log-transformed data (Cressie, 1991, pp. 64–66) was not

substantiated in our case study. Relative semivariogramsfor all categories were fitted by a spherical model (modeland parameters shown in Figs 4, 5 and 6, middle row).This was consistent for all the biological categories inwhich Nephrops catch was subdivided. The experimentalsemivariograms for the fall cruise showed similar results(only relative semivariograms are given, Fig. 7). Thus,the relative semivariogram better described thespatial structure of Nephrops populations in the area ofstudy.

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Figure 5. As in Figure 4, for adult males (left panel) and adult females (right panel). Left panel: C0=0.658; c*=1.144; a=8.3 km.Right panel: C0=0.745; c*=1.600; a=9.9 km.


Spring relative semivariograms showed a better fitthan fall relative semivariograms and with lower nuggetcomponents (variance unexplained by the spatialmodel). The c0 to total variance (c0+c*) ratio was 14.6%in spring and 20.1% in fall for total densities in number.This may represent a higher spatial variability forNephrops populations during the fall cruise, when catchwas also lower than in spring (Table 1).The structure of spatial dependence was very similar

among biological categories and across seasons (see also

Conan et al., 1992). Range of fitted relative semi-variograms varied from 5.9 to 9.9 km (mean 7 km),which is remarkably close considering the extent ofthe area surveyed (50 km approximately, in a W–Edirection).Presence of anisotropy (differential spatial con-

tinuity in a given geographical direction) could not bedemonstrated for any biological category or season(Conan et al., 1992). Hence, in the absence of ani-sotropy, the spatial structure of Nephrops populations in

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10 20 30 400

7

51

156

206

261

339161

130

147

9762

24

Var

1000

Lag

Sem

ivar

ian

ce 1

0–4 800

600

400

200

10 20 30 400

153

40

206252

328

151

130

21

Ave

144

94 6224

Var

0.5

1.5

43

206

1.5

21

43

Ave

7

43

126

Sem

ivar

ian

ce 1

0–4R

elat

ive

sem

ivar

ian

ce

8

21

10021

47

Figure 6. As in Figure 4, for total number (left panel) and total weight (right panel). Left panel: C0=0.299; c*=1.750; a=8.2 km.Right panel: C0=0.446; c*=1.596; a=8.9 km.


7

Lag

6

4

10 20 30 400

8

42

124

116197

259

107

156

30

72

14

57

Ave

Rel

ativ

e se

miv

aria

nce

52

(a)

3

2

1

5

Lag

4

10 20 30 400

842

107 116

197

259

124

15672

14

57

Ave

Rel

ativ

e se

miv

aria

nce

2

(b)

3

2

1

30

1440

4

Lag10 20 30 400

842

124

116197

259

107

156

30

72

1457

Ave

Rel

ativ

e se

miv

aria

nce

40

(c)

3

2

1

5

Lag

4

10 20 30 400

842

107 116

197

259

124

156

72

1457

Ave

Rel

ativ

e se

miv

aria

nce

2

(d)

3

2

1

30

40

60

Lag

40

10 20 30 400

11

42

124

116

197259

107

156

30

72

14

57

Ave

Sem

ivar

ian

ce 1

0–4 5021

(e)

30

20

10

10

Lag

4

10 20 30 400

1142

107116

197259

124 156

72 14

Ave

Sem

ivar

ian

ce

2

(f)

2

3014

5

Lag

4

10 20 30 400

8

42

124

116

197

259107 156

30

72

1457

Ave

Rel

ativ

e se

miv

aria

nce

2

(g)

3

2

1

2

14

14

2

188

Var 6

8

108

21

Var

40

14

14

Figure 7. Relative semivariograms (except e and f) for Nephrops categories, fall survey. Fitted spherical semivariograms and theparameters of the model are shown. Categories are: (a) juvenile (C0=2.552, c*=1.824, a=8.3 km); (b) adult males (C0=1.323,c*=1.726, a=8.7 km); (c) adult females (C0=1.871, c*=0.773, a=8.2 km); (d) total number (C0=0.516, c*=2.056, a=7.5 km); (e)Matheron’s semivariogram on total number; (f) Matheron’s semivariogram on total number log-transformed data; and (g) totalweight (C0=0.972, c*=2.051, a=7.9 km).

41°20' N

41°10'

(a)

200

400 60

0

800

2°10' 2°20' E

Juvenile males (ind./km2)< 200

200 – 400

400 – 600

600 – 800

800 – 1000

1000 – 1200

> 1200

41°20' N

41°10'

(b)

200

400 60

0

800

2°10' 2°20' E

Juvenile females (ind./km2)< 100

100 – 200

200 – 300

300 – 400

400 – 500

500 – 600

> 600

Figure 8. (a) and (b).


41°20' N

41°10'

(c)

200

400 60

0

800

2°10' 2°20' E

Adult females (ind./km2)> 200

200 – 400

400 – 600

600 – 800

800 – 1000

1000 – 1200

> 1200

41°20' N

41°10'

(d)

200

400 60

0

800

2°10' 2°20' E

Adult females (ind./km2)< 200

200 – 400

400 – 600

600 – 800

800 – 1000

1000 – 1200

> 1200

Figure 8. (c) and (d).


41°20' N

41°10'

(e)

200

400 60

0

800

2°10' 2°20' E

Total number (ind./km2)> 700

700 – 1400

1400 – 2100

2100 – 2800

2800 – 3500

3500 – 4200

> 4200

41°20' N

41°10'

(f)

200

400 60

0

800

2°10' 2°20' E

Total weight (ind./km2)< 10

10 – 20

20 – 30

30 – 40

40 – 50

50 – 60

> 60

Figure 8. (e) and (f).

Figure 8. High-resolution density maps for Nephrops categories, spring survey. (a) Juvenile males; (b) juvenile females; (c) adultmales; (d) adult females; (e) total number; and (f) total weight.


41°20' N

41°10'

(a)

200

400 60

0

800

2°10' 2°20' E

Juveniles (ind./km2)> 30

30 – 60

60 – 90

90 – 120

120 – 150

150 – 180

> 180

41°20' N

41°10'

(b)

200

400 60

0

800

2°10' 2°20' E

Males (ind./km2)> 200

200 – 400

400 – 600

600 – 800

800 – 1000

1000 – 1200

> 1200

Figure 9. (a) and (b).


41°20' N

41°10'

(c)

200

400 60

0

800

2°10' 2°20' E

Females (ind./km2)< 40

40 – 80

80 – 120

120 – 160

160 – 200

200 – 240

> 240

41°20' N

41°10'

(d)

200

400 60

0

800

2°10' 2°20' E

Total number (ind./km2)< 300

300 – 600

600 – 900

900 – 1200

1200 – 1500

1500 – 1800

> 1800

Figure 9. (c) and (d).

Figure 9. High-resolution density maps for Nephrops categories, fall survey. (a) Juveniles; (b) adult males; (c) adult females; (d)total number.


the northwest Mediterranean can be regarded as high-density patches 6–10 km in diameter.Density maps were generated by point kriging for all

categories and both cruises. The locations of high-density patches extensively overlapped for all biologicalcategories (Fig. 8, spring; Fig. 9, fall). The location ofhigh-density patches was fairly constant across seasons,indicating a certain stability in the population of struc-ture of Nephrops off Barcelona fishing grounds.Global biomass and average density were computed

by block kriging within the polygon over which Norwaylobster density was mapped. Table 2 shows the meandensity, the global estimate and their kriging standarddeviations. For comparison, Table 2 includes also meandensity, global estimates and standard deviation of themean computed by the swept area method.

DiscussionOne of the aims of fisheries biology is the study of spatialand temporal distribution patterns in relation to abun-dance. Within the ICES Working Group on Nephrops,studies in this direction have been recommended (ICES,1992). The geostatistical model built here has beenshown to be a useful step in that direction, as it directlyrevealed the spatial structure of Nephrops populations ata finer resolution than in the past.High-resolution mapping may be worthwhile in order

to optimize profit and to forecast accurately the locationand the spatial characteristics of the resource (Conan,1985). Also, density maps are useful for assessing theeconomical potential of the catch as well as for fisheriesmanagement.

Nephrops norvegicus is a benthic species of low mobil-ity at the scale of study, due in part to its burrowingbehaviour (Chapman, 1980). This makes the applicationof linear geostatistics ideal to this species, as well as toother crustaceans and molluscs which can be consideredsessile at the spatial and temporal scales of study.The applicability of geostatistical techniques was

enhanced by the availability of accurate technology(GPS, SCANMAR) and a careful design of the samplingscheme. A preliminary data analysis was necessary tocheck the validity of the geostatistical technique and tobuild a spatial model for our data sets.Average abundances obtained in this study (Table 2)

were similar to those found by authors working in thesame area (Sarda and Abello, 1984; Sarda and Lleonart,1993) and slightly lower than those reported for theAtlantic (Briggs, 1987; Hillis and Geary, 1990; Farinaet al., 1994). Population biology characteristics (seasonalvariations in abundance and sex ratio) of Catalan SeaNephrops populations show no marked differences withother areas (Sarda, 1995).The geostatistical analysis of the harvestable fraction

of the Nephrops populations over the slope off Barcelonashowed that these populations were spatially structuredin patches about 7 km in diameter. We also showed thatthe spatial dependence effects remained stable withinbiological categories (cf. Conan et al., 1988a for snowcrab in the Gulf of Saint Lawrence (Canada) where animportant spatial segregation by size and sex was dem-onstrated) and that there was no marked temporal(seasonal) variability in the location of high-densitypatches. Analysis of Nephrops stocks in northwest SpainAtlantic waters (Farina et al., 1994) at larger spatial

Table 2. Global kriging and swept area computations of mean and global abundances for Norway lobster categories, along withtheir standard deviations.

Global kriging Swept area

Z(B) óK ZG(B) óKG Xa sa XG sG

GEOESC-IJuvenile males 115 35 85 531 25 896 118 31 93 239 24 715Juvenile females 177 48 131 403 35 786 190 41 150 315 32 340Adult males 261 56 193 692 41 815 314 53 247 826 41 847Adult females 233 55 172 936 40 544 313 59 247 269 46 630Number 752 152 559 020 112 711 936 167 739 532 132 301Weight 14.7 3.1 10 903.0 2 284.6 18.9 3.3 14 906.6 2 628.1

GEOESC-IIJuveniles 50 19 36 985 14 277 53 16 42 119 12 618Adult males 246 75 183 017 55 636 254 61 200 555 48 570Adult females 108 34 80 086 24 987 112 26 88 541 20 309Number 341 68 253 484 50 233 366 82 289 096 64 899Weight 9.6 2.8 7 132.9 2 066.2 9.4 2.3 7 417.3 1 798.1

Z(B) is the mean density computed by global kriging, óK its standard deviation; ZG(B) is the total abundance computed byglobal kriging, óKG its standard deviation; Xa is the mean density computed by the area swept method, sa is the standard error ofthe mean; XG is the total abundance computed by the swept area method, sG is its standard error.Z(B) and Xa in individuals km

"2, except for weight, in kg km"2. ZG(B) and XG in individuals, except for weight, in kg.


scales revealed a spatial structure in larger (around100 km) patches, but our results are not directly com-parable to theirs due to the fact that the distancebetween stations in Farina et al. (1994) was larger thanthe range obtained here.In summary, the pattern of spatial structure for

northwest Mediterranean lobster populations has beendemonstrated. This spatial pattern remained fairly stablebetween spring and fall. Further research is needed toascertain the underlying causes of spatial patterning inNephrops norvegicus, although sedimentological factorscertainly require attention. It would be also interest-ing to further investigate the generality of this patternto Atlantic Nephrops fishing grounds, by means ofappropriate experimental surveys and the geostatisticalmethodology laid out in this work.

Acknowledgements

G. Y. Conan, senior research scientist from DFO,Canada, was sponsored by a personal award from theDireccion General de Investigacion Cientıfica y Tecnica,DGICYT (Spanish Ministry of Education and Science)during his work in Spain. The research work of F.Maynou was also supported by a grant of DGICYT.The authors also wish to acknowledge the assistanceduring the field work of J. B. Company and J. E. Cartes.Special thanks to the crew of the R/V Garcıa del Cid.The authors wish to acknowledge the suggestions andcomments of two anonymous referees, which helpedimprove the quality of the manuscript.

ReferencesBriggs, R. P. 1987. A review of the factors influencing landingsize in the Northern Ireland Nephrops fishery. ICES CM1987/K:34, 24 pp.

Chapman, C. J. 1980. Ecology of juvenile and adult Nephrops.In The biology and management of lobsters, pp. 143–178. Ed.by J. S. Cobb and B. F. Phillips. Academic Press, New York.

Cochran, W. G. 1977. Sampling techniques. John Wiley &Sons, New York.

Conan, G. Y. 1985. Assessment of shellfish stocks by geo-statistical techniques. ICES CM 1985/K:30, 24 pp.

Conan, G. Y. and Wade, E. 1989. Geostatistical analysis,mapping and global estimation of harvestable resources in afishery of the northern shrimp (Pandalus borealis). ICES CM1989/D:1, 29 pp.

Conan, G. Y., Maynou, F., and Sarda, F. 1992. Directassessment of the harvestable biomass from a stock ofNephrops norvegicus, seasonal and spatial variations. ICESCM 1992/K:22, 24 pp.

Conan, G. Y., Moriyasu, M., Wade, E., and Comeau, M.1988a. Abundance and spatial distribution surveys of snowcrab stocks by geostatistics. ICES CM 1988/K:10, 23 pp.

Conan, G. Y., Buerkle, E., Wade, E., Chadwick, M., andComeau, M. 1988b. Geostatistical analysis of spatial distri-bution in a school of herring. ICES CM 1988/D:25, 18 pp.

Cressie, N. 1991. Statistics for spatial data. Wiley Interscience,New York. 900 pp.

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Farina, A. C., Freire, J., and Gonzalez-Gurriaran, E. 1994.Nephrops norvegicus in the Galician continental shelf (NWSpain): abundance and distribution. Fisheries Research, 19:333–347.

Hillis, J. P. and Geary, M. 1990. The Irish fishery for Nephropson the Porcupine Bank. ICES CM 1990/K:22, 15 pp.

ICES. 1989. Report of the workshop on spatial statisticstechniques. ICES CM 1989/K:38, 42 pp.

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Isaaks, E. H. and Srivastava, M. R. 1989. Applied geostatistics.Oxford University Press, New York. 561 pp.

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Matheron, G. 1971. The theory of regionalized variables andits applications. Les Cahiers du Centre de MorphologieMathematique, fasc. 5. Ecole Nationale Superieure de Minesde Paris, Paris.

Petitgas, P. 1993. Geostatistics for fish stock assessments: areview and an acoustic application. ICES Journal of MarineScience, 50: 285–298.

Sarda, F. 1991. Reproduction and moult synchronism inNephrops norvegicus (L.) (Decapoda, Nephropidae) in theWestern Mediterranean: is spawning annual or biennial?Crustaceana, 60(2): 186–199.

Sarda, F. 1995. A review (1967–1990) of some aspects of thelife history of Nephrops norvegicus. ICES Marine ScienceSymposium, 199: 78–88.

Sarda, F. and Abello, P. 1984. Distribucion y abundancia deNephrops norvegicus (L.) en el mar Catalan. Seguimiento deuna poblacion. Actas do IVo simposio Iberico de Estudos doBenthos Marinho. Lisboa. III, 235–243.

Sarda, F. and Lleonart, J. 1993. Evaluation of the Norwaylobster (Nephrops norvegicus, L.) resource off the ‘‘Serola’’bank off Barcelona (western Mediterranean). ScientiaMarina, 57(2–3): 191–197.

Sarda, F., Cartes, J. E., and Norbis, W. 1994. Spatio–temporalstructure of the deep-sea shrimp Aristeus antennatus (Deca-poda: Aristeidae) population in the western Mediterranean.Fishery Bulletin, 92: 599–607.

Simard, Y., Legendre, P., Lavoie, G., and Marcotte, D. 1992.Mapping, estimating biomass, and optimizing samplingprograms for spatially autocorrelated data: case study of thenorthern shrimp (Pandalus borealis). Canadian Journal ofFisheries and Aquatic Science, 49(1): 32–45.

Sparre, P., Ursin, E., and Venema, S. C. 1989. Introductionto tropical fish stock assessment. Part 1 – Manual. FAOFisheries technical papers, 306/1: 1–337.


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