A GEOSTATISTICAL APPROACH TO THE ASSESSMENT OF THE SPATIAL DISTRIBUTION OF PARAPENAEUS LONGIROSTRIS (LUCAS, 1846) IN THE CENTRAL-SOUTHERN TYRRHENIAN SEA
Identifieur interne : 001A03 ( Istex/Corpus ); précédent : 001A02; suivant : 001A04A GEOSTATISTICAL APPROACH TO THE ASSESSMENT OF THE SPATIAL DISTRIBUTION OF PARAPENAEUS LONGIROSTRIS (LUCAS, 1846) IN THE CENTRAL-SOUTHERN TYRRHENIAN SEA
Auteurs : Pierluigi Carbonara ; Teresa Silecchia ; Maria Spedicato ; Alessandra Acrivulis ; Giuseppe LemboSource :
- Crustaceana [ 0011-216X ] ; 1999.
English descriptors
- Teeft :
- Abundance, Abundance distribution, Abundance index, Abundance indices, Abundance levels, Average values, Canadian journ, Cape bonifati, Cape suvero, Central mediterranean, Cokriging, Cokriging estimation, Cokriging method, Cokriging technique, Deviation maps, Different years, Estimation, Estimation error, Experimental values, Experimental variograms, Fisheries research, Garigliano river, Geographical allocation, Geographical coordinates, Geostatistical, Geostatistical approach, Geostatistical techniques, Geostatistics, Giuseppe lembo, Higher abundance, Huijbregts, Isaaks, Isaaks srivastava, Italian seas, Journel, Journel huijbregts, Kriging, Kriging estimation, Lembo, Linear system, Long data series, Longirostris, Lucas, Mathematical geology, Mesh size, Minimum estimation variance, Omnidirectional model, Ordinary cokriging estimation, Ordinary kriging, Ordinary kriging estimation, Parapenaeus, Parapenaeus longirostris, Random function, Rouhani myers, Same time, Several variables, Shing effort, Shrimp parapenaeus longirostris, Similar pattern, Small scale level, Spatial, Spatial continuity, Spatial dimension, Spatial distribution, Spatial structure, Spherical model, Srivastava, Standard deviation, Stock assessment, Temporal dimension, Temporal persistence, Trawl surveys, Tropical sheries, Unsampled location, Variance, Variant application, Variogram models, Whole area.
Url:
DOI: 10.1163/156854099504040
Links to Exploration step
ISTEX:6FD36D5348C6A3B6E6BD764876AC0024DA2E7881Le document en format XML
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<p>A GEOSTATISTICAL APPROACH TO THE ASSESSMENT OF THE SPATIAL DISTRIBUTION OF PARAPENAEUS LONGIROSTRIS (LUCAS, 1846) IN THE CENTRAL-SOUTHERN TYRRHENIAN SEA 1 ) BY GIUSEPPE LEMBO, TERESA SILECCHIA, PIERLUIGI CARBONARA, ALESSANDRA ACRIVULIS and MARIA T. SPEDICATO COISPA Tecnologia & Ricerca, C.P. 62, I-70042 Mola di Bari (Ba), Italy ABSTRACT The spatial distribution of the abundance indices of the deep-water rose shrimp Parapenaeus longirostris was investigated applying geostatistical techniques on data collected in the central- southern Tyrrhenian Sea from bottom trawl surveys carried out in the autumn since 1994. Experi- mental variograms (auto and cross) were constructed on the variable “ abundance index ” , expressed in kg/km 2 , and those variogram models best describing the spatial continuity were detected and validated by the jackknife technique. The spatial structure of the “ abundance index ” , exhibiting a similar pattern throughout the surveys, was described by a spherical model and characterized by a spatial continuity at a small scale level in the whole area. The linear geostatistical approach was applied by different kriging techniques and the estimates extended to the spatio-temporal dimen- sion, in this case adopting the co-regionalized models and applying the cokriging technique. This method applied to the spatial dimension (abundance index and depth). Also, linking the spatial and temporal dimension of the abundance indices, measured in two different years, contributed to represent a more accurate picture of the abundance distribution, and allowed the detection of a temporal persistence of the localization of areas with higher abundance, reducing the standard deviation of the estimation error. This information, if coupled with an analysis of the geographical allocation of the shing effort, could be of importance in stock assessment, allowing some variant application of the composite surplus production models. R ´ ESUM ´ E La distribution spatiale des indices d ’ abondance de la crevette rose d ’ eau profonde Parapenaeus longirostris a ´ et ´ e ´ etudi ´ ee en appliquant les techniques de la g ´ eostatistique aux donn ´ ees collect ´ ees dans le centre-sud de la mer Tyrrh´enienne au cours des campagnes de chalutage d ´ emersal r´ealis´ees pendant l ’ automne, depuis 1994. Les variogrammes exp ´ erimentaux (auto et cross) ont ´ et ´ e con- struits sur la variable “ indice d ’ abondance ” , exprim ´ ee en kg/km 2 , et les mod ³ eles de variogramme d´ecrivants le mieux la continuit´e spatiale ont ´ et´e d´etermin´es et valid´es par la technique du “ jack- knife ” . La structure spatiale de l ’ indice d ’ abondance a pr ´ esent ´ e le m ^ eme aspect pour tous les 1 ) This paper was presented at the Fourth International Crustacean Congress, Amsterdam, 1998. Ó Koninklijke Brill NV, Leiden, 1999 Crustaceana 72 (9)</p>
<p>1094 GIUSEPPE LEMBO ET AL. ´ echantillonages; elle a ´ et ´ e d ´ ecrite au moyen d ’ un mod ³ ele sph ´ erique et caract ´ eris ´ ee par une con- tinuit ´ e spatiale ³ a petite ´ echelle dans toute la zone. La g ´ eostatistique lineaire a ´ et ´ e appliqu ´ ee en utilisant diff´erentes techniques du krigeage, et les estimations ont ´ et´e ´ etendues ³ a la dimension spatio-temporelle en appliquant les mod ³ eles cor ´ egionalis ´ es et la technique du cokrigeage. Cette m´ethode, appliqu´ee soit dans la dimension spatiale (indice d ’ abondance et profondeur), soit dans la dimension spatio-temporelle en consid´erant l ’ indice d ’ abondance ´ echantillonn´e en deux ann´ees diff ´ erentes, a contribu ´ e ³ a repr ´ esenter une image plus pr ´ ecise de la distribution de l ’ abondance, et a permis de d´etecter une persistance temporelle de la localisation des aires ³ a plus grande abondance, en r´eduisant l ’ ´ ecart type de l ’ erreur d ’ estimation. Cette information, avec l ’ analyse de l ’ alloca- tion g ´ eogra que de l ’ effort de p ^ eche, pourrait ^ etre importante dans l ’´ evaluation des stocks, en permettant l ’ application, avec quelques variantes, des mod ³ eles composites de production. INTRODUCTION The deep-water rose shrimp Parapenaeus longirostris (Lucas, 1846) has a very wide geographical distribution, from the eastern Atlantic to the Mediter- ranean and Marmara Sea (P ´ erez Farfante, 1982). In Italian waters this species is particularly abundant in the Strait of Sicily (Bombace, 1972; Froglia, 1982; Levi et al., 1995), in the northern Tyrrhenian Sea (Mori et al., 1986) and in the whole central-southern Tyrrhenian Sea, where it represents one of the most important resources of the epibathyal bottom (Ardizzone et al., 1990; Spedicato et al., 1996). In the Mediterranean basin, the distribution of P. longirostris is reported be- tween 20 and 700 m, though it is more common between 70 and 400 m (Holthuis, 1987). Along the central-southern Tyrrhenian coasts (from the Garigliano River to Cape Suvero) this species was caught between 61 and 587 m, but the higher abundance indices, measured as kg/km 2 , have been observed from 200 to 450 m (Spedicato et al., 1996). The main objective of this paper is to estimate the spatial and temporal dis- tribution of the deep-water rose shrimp by geostatistics, which provide a set of probabilistic techniques to analyse the spatial (or spatio-temporal) variability and to predict values of a variable distributed in space or time. Moreover, the geosta- tistical approach allows assessment of variables without restrictive assumptions on their probability distribution (Matheron, 1965). This method, therefore, has been applied for elaborating data on marine resources and assessing variables not normally distributed, as an abundance index (Smith, 1988), in many contexts (Conan, 1985; Petitgas & Poulard, 1989; VV. AA., 1990; Lembo et al., 1990; Fari ~ na et al., 1994; Maynou et al., 1996). Furthermore, by geostatistics it is also possible to link the spatial and temporal dimension of the variable, using the cokriging techniques (Myers, 1982, 1988; Rouhani & Myers, 1990). In fact, when the data are more numerous in the spatial than in the time dimension,</p>
<p>SPATIAL DISTRIBUTION OF PARAPENAEUS LONGIROSTRIS 1095 the spatio-temporal series can be interpreted as a single realization of several correlated random functions. However, while the technique of ordinary kriging has been widely applied to estimate the spatial distribution and abundance of shery resources (e.g., Pelletier & Parma, 1994), the potentiality of the cokrig- ing method has not yet been adequately exploited in such context (Lembo et al., 1998). MATERIALS AND METHODS Data collection The data were collected during three trawl-surveys carried out in October of 1995, 1996, and 1997 in the central-southern Tyrrhenian Sea from the Garigliano River to Cape Suvero, at a depth range between 15 and 700 m (study area 10,637 km 2 ). The duration of each survey was from a minimum of 8 days (1995) to a maximum of 20 days (1997). A commercial 64 tons, gross tonnage vessel with 600 HP engine was used. It was equipped with a nylon otter-trawl net with 37 mm stretched mesh size in the cod-end. A total of 34 hauls was carried out during the survey of 1995, while 68 hauls were performed during the survey of 1996 as well as during the survey of 1997. A strati ed random sampling design was adopted with allocation of hauls proportional to the area of the strata (e.g., Cochran, 1963; Fogarty, 1985). Fishing was restricted to daylight hours and the hauls lasted one hour each. The vessel speed, measured by using GPS, was maintained at 2.5-3.0 knots (approx. 4.5-5.5 km ¢ h 1 ), according to the depth. The horizontal net opening was measured by means of the SCANMAR sonar system (Fiorentini et al., 1994) and the “ swept area ” estimated according to the wing spread of the net and the speed of the vessel (Pauly, 1983). The weight of all the Parapenaeus longirostris caught was measured for each haul. Geostatistical techniques In this work, the spatio-temporal variable Z ( x ) investigated was the “ abun- dance index ” of P. longirostris , expressed as kg/km 2 . In geostatistics, both the random and structured aspects of the regionalized variable are expressed by a random function Z ( x ) , which can be seen as a set of correlated random variables Z ( x i ) de ned at each point x i of the investigated area (Matheron, 1971; Journel & Huijbregts, 1978). Under the intrinsic hypothesis of the random function Z ( x ) (Journel & Huij- bregts, 1978):</p>
<p>1096 GIUSEPPE LEMBO ET AL. a) the mathematical expectation exists and does not depend on the point x : E [ Z ( x )] = m ; 8 x ; b) for all vectorial distances h the increment [ Z ( x + h ) Z ( x )] has a nite variance which does not depend on x : VAR [ Z ( x + h ) Z ( x )] = E f [ Z ( x + h ) Z ( x )] 2 g = 2 ® ( h ) ; 8 x: ® ( h ) is the variogram function, i.e., the tool of the structural analysis for char- acterizing the structure of the spatial distribution of the variable under consider- ation. The concept of variogram can be generalized to spatial coregionalization of several variables when not only the primary variable, but also one (or more) secondary variables is/are known. In this case, and if a secondary variable(s) is spatially (or spatio-temporally) cross-correlated with the primary one, it gives useful information about the primary variable (Isaaks & Srivastava, 1989). The cross-variogram function: 2 ® 12 ( h ) = E f [ Z 1 ( x + h ) Z 1 ( x )][ Z 2 ( x + h ) Z 2 ( x )] g ; 8 x; was used to characterize the spatial correlation between the primary variable Z 1 ( x ) “ abundance index ” and the secondary variable Z 2 ( x ) “ depth ” at the same time, as well as to describe the spatio-temporal correlation of the abundance index sampled in two different surveys. The auto-variogram function is always positive, conversely the cross-variogram one can take negative values. The variogram (auto- and cross-) estimator was (Journel & Huijbregts, 1978): ® ¤ 12 ( h ) = 1 2 n ( h ) n ( h ) X k = 1 ( z 1 ( x k + h ) z 1 ( x k ))( z 2 ( x k + h ) z 2 ( x k )) ; where z 1 ( x k ) , z 1 ( x k + h ) and z 2 ( x k ) , z 2 ( x k + h ) are the experimental values, in the locations x k and ( x k + h ) separated by the vector h , (1) of the abundance index and depth at the same time t , when the depth was used as secondary variable; (2) of the abundance index in two different times t and t 0 , respectively; n ( h ) is the number of experimental pairs of data separated by the vector h . The spatial structure was decomposed along different directions to reveal dif- ferent behaviour of the variable (anisotropy). Modelling of the experimental variograms was performed using valid theoret- ical models, characterized by the parameters: nugget, range, and sill. The cross-validation allowed choosing the variogram models more consistent with the available data and the jackknife method (Miller, 1974) was used adopting</p>
<p>SPATIAL DISTRIBUTION OF PARAPENAEUS LONGIROSTRIS 1097 the two criteria that the mean error between the observed and estimated values should be close to 0 and the variance of the standardized error should be close to 1. A grid with a mesh size of 1 km was de ned on the investigated area. The estimate of the studied variable was obtained in each crossing point by linear geostatistics techniques. The Ordinary Kriging method was applied to estimate the value of the variable “ abundance index ” z ( x ) in each unsampled location x 0 within the studied area, using a linear combination of the experimental values f z ( x i ) ; i = 1 to n g (Isaaks & Srivastava, 1989; Journel & Huijbregts, 1978): ^ z ( x 0 ) = n X i = 1 a i z ( x i ) : The weighting coef cients a i are determined by imposing on the estimator the constraints of non-bias and minimum estimation variance. The Ordinary Cokriging method was applied both to estimate, in the spatial dimension, the value of the variable “ abundance index ” z 1 ( x ) (primary) observed in n locations, using the auxiliary cross-correlated information of the “ depth ” variable z 2 ( x ) (secondary) known in m locations, and to estimate, in the spatio- temporal dimension, the “ abundance index ” variable at time t , using the more abundant sample data of the same variable at the time t 0 . The cokriging method minimizes the variance of the estimation error by exploiting the information on the cross-correlation between several variables contained in the cross-variogram. The addition of cross-correlated information should help in reducing the variance of the estimation error (Isaaks & Srivastava, 1989). The linear cokriging estimator, in each unsampled location x 0 , is: ^ z 1 ( x 0 ) = n X i = 1 a i z 1 ( x 1 i ) + m X j = 1 b j z 2 ( x 2 j ) ; where the weights a i and b j are determined by imposing on the estimator the constraints of non-bias and minimum estimation variance (Isaaks & Srivastava, 1989; Journel & Huijbregts, 1978). The minimum kriging estimation variance was obtained from (Isaaks & Sri- vastava, 1989; Journel & Huijbregts, 1978): s 2 K ( x 0 ) = · + n X i = 1 a i ® ( x i x 0 ) ; and the minimum cokriging estimation variance from (Isaaks & Srivastava, 1989; Journel & Huijbregts, 1978):</p>
<p>1098 GIUSEPPE LEMBO ET AL. s 2 C K ( x 0 ) = · 1 + n X i = 1 a i ® 11 ( x 1 i x 0 ) + m X j = 1 b j ® 21 ( x 2 j x 0 ) ; where · and · 1 are the Lagrange multipliers. RESULTS Variography The analysis of the survey ’ s data always allowed to describe the spatial or the spatio-temporal structure of the variable “ abundance index ” , also when a secondary variable, like depth, was considered. In g. 1 the auto-variogram model of the abundance index (kg/km 2 ) of the 1997 survey is represented, while g. 2 contains the cross-variogram model of the abundance index (primary variable) and depth (secondary variable) obtained for the same survey. In both cases a spherical model was tted, describing a good level of spatial continuity, but the ranges were rather different and equal to 10.69 and 30.83 km, respectively. Thus, in the case of the cross-variogram, the spatial cross-correlation of the two variables contributed to increase the estimate of the continuity range of the abundance index, suggesting that the maximum distance at which the data are related is higher than 10.69 km. Fig. 1. Omnidirectional auto-variogram model of the variable “ abundance index ” (kg/km 2 ) of Parapenaeus longirostris (Lucas, 1846). Survey of 1997.</p>
<p>SPATIAL DISTRIBUTION OF PARAPENAEUS LONGIROSTRIS 1099 Fig. 2. Omnidirectional cross-variogram model of the primary variable “ abundance index ” (kg/km 2 ) of Parapenaeus longirostris (Lucas, 1846), and the secondary variable, depth. Survey of 1997. All variograms calculated along the directions 0 ¯ , 45 ¯ , 90 ¯ , and 135 ¯ showed differences in the distance-dependent correlation according to the changes in the spatial orientation. The data along the direction 135 ¯ were more continuous than along 45 ¯ , with an anisotropy ratio equal to 1.78 (auto-variogram 1997) and 1.9 (cross-variogram 1997). In g. 3 the auto-variogram model of the abundance index (kg/km 2 ) of the 1995 survey is reported, while g. 4 shows the cross-variogram model obtained considering the abundance index of the 1995 survey as the primary variable, and the abundance index of the 1996 survey as the secondary one. In both cases, a spherical model was tted whose very similar ranges (17.42 and 17.05 km, re- spectively) suggested a spatial structure with aggregation pattern of a short radius. Estimate The maps in gs. 5 and 6 represent the spatial distribution of the abundance index (kg/km 2 ) of Parapenaeus longirostris estimated by ordinary kriging and by cokriging, respectively (survey of 1997). Aggregations with higher abundance were generally localized at between 100 and 400 m depth, but the patches in the Gulf of Naples and on its northernmost side were characterized by the maximum estimates, reaching about 33 kg/km 2 (see table I). Other nuclei, though with a</p>
<p>1100 GIUSEPPE LEMBO ET AL. Fig. 3. Omnidirectional auto-variogram model of the variable “ abundance index ” (kg/km 2 ) of Parapenaeus longirostris (Lucas, 1846), in the survey of 1995. Fig. 4. Omnidirectional cross-variogram model of the primary variable “ abundance index ” (kg/km 2 ) of Parapenaeus longirostris (Lucas, 1846) in the survey of 1995, and of the secondary variable “ abundance index ” (kg/km 2 ) of Parapenaeus longirostris in the survey of 1996.</p>
<p>SPATIAL DISTRIBUTION OF PARAPENAEUS LONGIROSTRIS 1101 T ABLE I Kriging and cokriging estimates of the minimum, maximum and average values of the variable “ abundance index ” (kg/km 2 ) of Parapenaeus longirostris (Lucas, 1846) Methods of estimate Abundance index (kg/km 2 ) Minimum Maximum Average Kriging estimation 1995 0.00 22.11 3.18 Kriging Std. Dev. 1995 0.73 6.33 5.74 Cokriging estimation 1995 0.00 33.71 3.17 Cokriging Std. Dev. 1995 0.72 6.06 5.41 Kriging estimation 1996 0.00 37.52 4.19 Kriging Std. Dev. 1996 0.89 7.88 6.49 Kriging estimation 1997 0.00 32.31 7.12 Kriging Std. Dev. 1997 1.57 10.24 9.51 Cokriging estimation 1997 0.00 33.04 5.83 Cokriging Std. Dev. 1997 1.08 10.86 8.73 lower density, were localized in the Gulf of Salerno and along the coasts between the Capes of Licosa and Bonifati. However, some inconsistencies in the kriging estimates ( g. 5), concerning the abundance levels in the deeper waters (beyond 400 m depth), were observed. Analysis of the spatial cross-correlation between the abundance index and depth allowed appraisal of a density distribution closer to the known pattern. Further- more, an increase in reliability of the estimates was obtained, as can be observed both from the comparison of estimation standard deviation maps ( gs. 5 and 6), and from the average values of the estimation standard deviation (table I), which were 9.51 and 8.73 for the kriging standard deviation of 1997 and for the co- kriging standard deviation of 1997, respectively. Fig. 7 shows the spatial distribution of the abundance index estimated by kriging on the data from the 1995 survey, while g. 8 shows the estimates obtained by cokriging on the same data, using the information from the survey of 1996 as a secondary variable. These maps show that the patch in the Gulf of Naples, as well as the aggregations in the Gulf of Salerno and along Cape Bonifati were already present, though the former was displaced in the offshore direction and to a greater depth, compared with the map of 1997. The maximum estimate of abundance index (33.71 kg/km 2 ; see table I) ob- tained for 1995 by co-kriging was higher than that from kriging (22.11 kg/km 2 ; see table I), as it was in uenced by the information originating from the survey of 1996, in which the maximum estimated value was 37.52 kg/km 2 . Furthermore, also in this case, an improvement in reliability of the estimates was obtained by applying the co-kriging technique, as can be observed from comparing the estimation standard deviation maps ( g. 7 and 8).</p>
<p>1102 GIUSEPPE LEMBO ET AL. Fig. 5. Ordinary kriging estimation map of the variable “ abundance index ” (kg/km 2 ) of Parape- naeus longirostris (Lucas, 1846). Survey of 1997. Kriging standard deviation map in the window. The geographical coordinates on the axis are expressed in the linear system (km). DISCUSSION The study of the spatial distribution on Parapenaeus longirostris ’ abundance index was carried out under the implicit assumption of geostatistics that the structure of the investigated variable was stable in time, at least for the duration of each survey. This hypothesis seems to be realistic, considering the greater speed of the survey with respect to some possible biomass displacements. Moreover, catchability was not structured through space (Simard et al., 1992), as the daylight sampling guaranteed that the catches were not affected by vertical migratory movements.</p>
<p>SPATIAL DISTRIBUTION OF PARAPENAEUS LONGIROSTRIS 1103 Fig. 6. Ordinary cokriging estimation map of abundance index (kg/km 2 ) of Parapenaeus lon- girostris (Lucas, 1846). Survey of 1997. Primary variable: abundance index, secondary variable: depth. Cokriging standard deviation map in the window. The geographical coordinates on the axis are expressed in the linear system (km). Under these implicit assumptions, the spatial structure of the variable “ abun- dance index ” (kg/km 2 ) presented a similar pattern throughout the surveys, de- scribed by a spherical model and characterized by a spatial continuity at a small scale level in the whole area. Such behaviour was modi ed when a different variable, spatially cross-correlated, like depth, was considered in the analysis, which resulted in an increase of the spatial continuity of the variable under in- vestigation, and such in the extension of the aggregation radius. In this case, the adoption of the co-regionalized model and the cokriging technique (Rouhani & Wackernagel, 1990; Bourgault & Marcotte, 1991), applied to the spatial di-</p>
<p>1104 GIUSEPPE LEMBO ET AL. Fig. 7. Ordinary kriging estimation map of the variable “ abundance index ” (kg/km 2 ) of Parape- naeus longirostris (Lucas, 1846). Survey of 1995. Kriging standard deviation map in the window. The geographical coordinates on the axis are expressed in the linear system (km). mension (abundance index and depth), contributed to represent a more accurate picture of the abundance distribution, excluding the deepest waters, and to reduce the standard deviation of estimation (Isaaks & Srivastava, 1989). Furthermore, application of the cokriging technique, by linking the spatial and temporal dimension of the variable (Rouhani & Myers, 1990), measured in two different years, allowed detection of a temporal persistence of the localization of areas with higher abundance and to slightly reduce the standard deviation of the estimation.</p>
<p>SPATIAL DISTRIBUTION OF PARAPENAEUS LONGIROSTRIS 1105 Fig. 8. Ordinary cokriging estimation map of abundance index (kg/km 2 ) of Parapenaeus lon- girostris (Lucas, 1846). Survey of 1995. Primary variable: abundance index of 1995, secondary variable: abundance index of 1996. Cokriging standard deviation map in the window. The geo- graphical coordinates on the axis are expressed in the linear system (km). In the present study, though with some differences in abundance levels among the years (table I), three sub-areas with higher density of P. longirostris were detected by the analysis: the two most important ones, located in the Gulf of Naples and along the Calabrian coasts in the vicinity of Cape Bonifati, and a third one, with a relatively lower abundance, in the Gulf of Salerno. The geographical areas characterized by a higher level of abundance were mainly localized at depths ranging from 100 to 200 m, with some intrusions in the deeper levels. Such distribution of the abundance of P. longirostris might indicate a catch composition in which small sized shrimps were prevailing in some sub-</p>
<p>1106 GIUSEPPE LEMBO ET AL. areas, as can be argued by the knowledge on the bathymetrical partitioning of the different fractions (juveniles and adults) of the P. longirostris population in the same basin (Ardizzone et al., 1990; Spedicato et al., 1996). Information on the spatial distribution of abundance indices, if coupled with analysis of the geographical allocation of the shing effort, could be of impor- tance in stock assessment, allowing some variant application of the composite surplus production models (e.g., Munro, 1980; Caddy & Garcia, 1982). Such an approach may help evaluating the status of resources exploitation along the Ital- ian coasts, as in other Mediterranean regions, where abundance data have been collected since many years (Relini & Piccinetti, 1996; Bertrand et al., 1997) and no long data series of catch and effort data are available. Another kind of result that can be derived from cokriging applications, con- cerns the possibility of using data sets with different sample sizes, where the more numerous (secondary) variable can contribute to enhance the estimates to be obtained from the less numerous (primary) variable. This kind of outcome suggests also that, in the context of limited resources, the sampling effort in the realization of trawl surveys could be changed throughout the years, but calibrated so that a high coverage of the area is followed by a reduced number of sampling stations. ACKNOWLEDGEMENTS The data presented in this paper were collected within the GRU.N.D. Re- search program (Evaluation of Demersal Resources in the Italian Seas) funded by the Italian Ministry of Agricultural Policy, General Directorate of Fisheries and Aquaculture (National Law 41/82). REFERENCES A RDIZZONE , G. D., M. F. G RAVINA , A. B ELLUSCIO & P. S CHINTU , 1990. Depth-size distribution pattern of Parapenaeus longirostris (Lucas, 1846) (Decapoda) in the central Mediterranean Sea. Journal of Crustacean Biology, 10 (1): 139-147. B ERTRAND , J., L. G IL DE S OLA , C. P APACONSTANTINOU & G. R ELINI , 1997. An international bottom trawl survey in the Mediterranean: the Medits programme. ICES Annual Science Conference, CM, 1997/Y:03 : 1-7. B OMBACE , G., 1972. Considerazioni sulla distribuzione delle popolazioni di livello batiale con particolare riferimento a quelle bentonectoniche. Quad. Lab. Tecnol. Pesca, 1 (4): 65-82. B OURGAULT , G. & D. M ARCOTTE , 1991. Multivariable variogram and its application to the linear model of coregionalization. Mathematical Geology, 23 (7): 899-927. C ADDY , J. F. & S. G ARCIA , 1982. Production modelling without long data series. FAO Fish. Rep., 238 : 309-313. C OCHRAN , W. G., 1963. Sampling techniques: 1-413. (John Wiley & Sons, New York).</p>
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<p>1108 GIUSEPPE LEMBO ET AL. P ETITGAS , P. & J. C. P OULARD , 1989. Applying stationary geostatistics to sheries: a study on hake in the Bay of Biscay. ICES Demersal Fish. Comm. C.M./G., 62 : 1-21. R ELINI , G. & C. P ICCINETTI , 1996. Ten years of trawl surveys in Italian seas (1985-1995). FAO Fisheries Report, 533 : 21-41. R OUHANI , S. & D. M YERS , 1990. Problems in space-time kriging of geohydrological data. Math- ematical Geology, 22 (5): 611-638. R OUHANI , S. & H. W ACKERNAGEL , 1990. Multivariate geostatistical approach to space-time data analysis. Water Resources Researches, 26 (4): 585-591. S IMARD , Y., P. L EGENDRE , G. L AVOIE & D. M ARCOTTE , 1992. Mapping, estimating biomass, and optimizing sampling programs for spatially autocorrelated data: case study of the northern shrimp ( Pandalus borealis ). Canadian Journ. Fish. aquat. Sci., 49 : 32-45. S MITH , S. J., 1988. Evaluating the ef ciency of the D -distribution mean estimator. Biometrics, 44 : 485-493. S PEDICATO , M. T., G. L EMBO , T. S ILECCHIA & P. C ARBONARA , 1996. Distribuzione e biologia di Parapenaeus longirostris nel Tirreno Centro-Meridionale. Biol. Mar. Mediterranea, 3 (1): 579-581. VV. AA., 1990. Report of the working group on methods of sh stock assessment. Nantes, France, 10-17 November 1989. CM 1990/Assess., 15 : 1-95. First received 1 September 1998. Final version accepted 30 March 1999.</p>
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