ICES Journal of Marine Science: Journal du Conseil Advance Access published online on April 15, 2008
ICES Journal of Marine Science: Journal du Conseil, doi:10.1093/icesjms/fsn053
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Geostatistical comparison of two independent video surveys of sea scallop abundance in the Elephant Trunk Closed Area, USA
School for Marine Science and Technology, University of Massachusetts Dartmouth, 706 South Rodney French Boulevard, New Bedford, MA 02744-1221, USA
Correspondence to C. F. Adams: tel: +1 508 910 6386; fax: +1 508 910 6396; e-mail: cadams{at}umassd.edu
Adams, C. F., Harris, B. P., and Stokesbury, K. D. E. 2008. Geostatistical comparison of two independent video surveys of sea scallop abundance in the Elephant Trunk Closed Area, USA. – ICES Journal of Marine Science.Geostatistical prediction at unsampled locations is done by kriging, an interpolation technique that minimizes the error variance. Our goal was to verify the technique by comparing kriged abundance estimates with observed counts from an area containing the highest densities of sea scallop (Placopecten magellanicus) offshore of the northeastern USA. In 2006, two independent video surveys of scallop abundance were made in the Elephant Trunk Closed Area, one using a 5.6 x 5.6-km sampling grid and the other with a 2.2 x 2.2-km sampling grid. We generated kriged surfaces of scallop abundance with the 5.6-km grid data, using different combinations of variograms and theoretical models, then tested the null hypothesis of no difference between the predicted and assumed true values (i.e. the 2.2-km grid data). There were significant differences between predicted and true values for three out of four combinations of variogram–model fits to untransformed data, assuming isotropy. In contrast, there was no significant difference between kriged and true values for any combination of variogram–model fits to log-transformed, detrended, anisotropy-corrected data. Classical and robust variograms performed equally well. Kriging can be used to generate accurate maps of scallop abundance if the assumptions of geostatistics are met.
Keywords: geostatistics, kriging, Placopecten magellanicus, sea scallop, variogram
Received 11 October 2007; accepted 7 March 2008.
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Introduction |
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Geostatistics is a branch of spatial statistics that was developed by Matheron (1963, 1971) for the mining industry. The technique describes the spatial structure of a natural resource and can be used to predict values at unsampled locations. The strength of geostatistics is that it exploits the spatial correlation inherent in natural resource data through the variogram. Geostatistics is now considered an important tool for estimating the distribution and abundance of fish stocks (Petitgas, 1993; Rivoirard et al., 2000).
Geostatistical prediction at unsampled locations is done by kriging. The distinguishing feature of kriging, when compared with other interpolation techniques, is that it minimizes the error variance (Isaaks and Srivastava, 1989). Although simulation studies have examined the effect of methodological choices on kriging results (e.g. Rivoirard et al., 2000; Rufino et al., 2006), we wanted to verify the technique by comparing kriged abundance estimates with actual counts from an area containing the highest densities of sea scallop (Placopecten magellanicus) offshore of the northeastern USA (Stokesbury et al., 2004). Kriging has been used to generate estimates of sea scallop abundance (Conan, 1985; Ecker and Heltshe, 1994; Warren, 1998; Walter et al., 2007), as well as to estimate scallop dredge efficiency (Gedamke et al., 2005; Walter et al., 2007).
The School for Marine Science and Technology (SMAST), University of Massachusetts Dartmouth, in cooperation with members of the US commercial sea scallop industry, developed a video survey to assess sea scallop abundance offshore of the northeastern USA. Since 2003, 7200 quadrat samples covering ca. 60 000 km2 of continental shelf, including Georges Bank and the mid-Atlantic, have been examined annually using a 5.6 x 5.6-km sampling grid (Stokesbury et al., 2004). In 2006, an additional, independent video survey of sea scallop abundance was carried out in the Elephant Trunk Closed Area using a 2.2 x 2.2-km sampling grid (Figure 1), to provide a precise estimate of scallop abundance before reopening the area to harvest in 2007.
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We tested the null hypothesis of no difference between the mean predicted and assumed true scallop counts by generating a kriged surface of sea scallop abundance using the 5.6-km grid data, then comparing these predicted values with actual scallop counts at the 2.2-km grid stations. This analysis complements previous simulation studies by providing insights into the effects of methodological choices on kriging results. As spatial models and spatially explicit management strategies, such as time–area closures and marine protected areas, are increasingly being used to manage fisheries (Jensen and Miller, 2005), our work offers some guidelines for the use of kriging in these important management decisions.
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Material and methods |
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Study area and field sampling
The Elephant Trunk Closed Area (Figure 1) is ca. 5400 km2 of continental shelf that was closed to commercial fishing for sea scallops in 2004 as part of an area-rotation management plan, with a scheduled reopening in 2007 (NMFS, 2006). Sea scallop densities in the Elephant Trunk vary widely, ranging from areas with no scallops to areas with the highest densities of scallops offshore of the northeastern USA (Stokesbury et al., 2004).
The 5.6-km grid survey of the Elephant Trunk Closed Area was conducted from 25 June to 18 July 2006, and the 2.2-km grid survey from 24 to 31 August 2006. Grid resolution for each survey was determined by balancing the logistics of covering the study area with maintaining low coefficients of variation, assuming a random or negative binomial distribution (Stokesbury et al., 2004). A centric systematic design (Krebs, 1999) was used to position the stations. As a random starting point was selected for each survey, the design is equivalent to systematic random sampling in the fisheries geostatistics literature (Simmonds and Fryer, 1996; Rivoirard et al., 2000).
Both surveys used the SMAST video survey pyramid. Sampling was done with a live-feed downward-looking S-VHS underwater video camera viewing a 3.235-m2 quadrat. Four replicate quadrats were sampled at each station (Stokesbury et al., 2004). Pooling the four replicates increases the sampled view area to 12.94 m2, to allow detection of densities as low as 0.08 scallops m–2, which corresponds to minimum commercially viable levels (Brand, 1991; KDES, unpublished data). After each cruise, technicians reviewed the footage to verify the scallop counts recorded during the survey (Stokesbury et al., 2004).
Data preparation
Geographical referencing was done by setting the southwest corner of the Elephant Trunk Closed Area as (0, 0) and converting all coordinates to kilometres (Rivoirard et al., 2000). The midpoint of the latitude in the study area (38.5°N) was used to convert longitude.
Geostatistical analysis was done on summed sea scallop counts for each station. Values can be expressed in density (scallops m–2) simply by dividing the counts by the station sampled view area (12.94 m2).
Normality of the 5.6-km grid data (n = 154) was assessed using the Kolmogorov–Smirnov test, with critical values recomputed for tests of normality (Stephens, 1974). This test is more robust in the presence of autocorrelation than other tests of normality (Dutilleul and Legendre, 1992; Legendre and Legendre, 1998). There was a significant departure from normality (D = 0.29, p < 0.01) that improved somewhat with log-transformation (D = 0.13, p < 0.01). Although normality is not a requirement for kriging, the procedure works best when the distribution is close to normal (Isaaks and Srivastava, 1989).
Post-plots with row and column means (Webster and Oliver, 2001) suggested the presence of a slight longitudinal and/or latitudinal trend in the data (Figure 2) that, unless removed, would violate the assumption of intrinsic stationarity (i.e. constant mean and variance throughout the sampling space). However, the mean kriged estimate using the untransformed 5.6-km grid data, assuming isotropic conditions, was close to the mean for the 2.2-km grid data. Therefore, we performed two concurrent geostatistical analyses (Figure 3): one using the actual 5.6-km grid scallop counts, assuming isotropic conditions (AB); and the other using the residuals of the log-transformed 5.6-km grid scallop counts, corrected for anisotropy (RE).
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After log-transformation, the RE data were fitted with a locally weighted regression (span = 0.4), or loess (Cleveland and Devlin, 1988), using easting and northing as predictor variables (depth was dropped from the final equation because of lower multiple R2 values). Next, this trend was subtracted from the data, and the geostatistical analysis was performed on the residuals (Kaluzny et al., 1998; Lo et al., 2001; Giannoulaki et al., 2003; Mello and Rose, 2005). Finally, directional variograms revealed a constant sill with differing ranges, indicating a geometric anisotropy in the residuals. This was corrected by determining the direction of maximum spatial continuity, calculating the ellipse ratio, then rotating and rescaling the data (Isaaks and Srivastava, 1989). Note that the trend was added back to the kriged values before calculating summary statistics.
Geostatistics
We constructed omnidirectional empirical variograms for the AB and RE data using the classical estimator of Matheron (1963) and the robust estimator of Cressie and Hawkins (1980). Data were binned at 5.6-km intervals, because the grid spacing is the appropriate lag-spacing for data sampled on a grid (Isaaks and Srivastava, 1989). The maximum distance between pairs of points in the 5.6-km grid data was 100 km, so we initially calculated variograms with a maximum distance of 50 km, because only half the total distance measured in any direction may be legitimately represented in a variogram (Rossi et al., 1992). Erratic behaviour was observed in the last lag, so the maximum distance was decreased to 44 km for all subsequent analysis.
We fitted spherical and exponential models (Isaaks and Srivastava, 1989) to all empirical variograms using the method of weighted least squares (Cressie, 1985). The Gaussian model was not used because it can lead to unstable kriging equations in the absence of a nugget effect (Chilés and Delfiner, 1999), and some authors discourage the use of this function altogether (Webster and Oliver, 2001).
Theoretical model fits yielded nugget, sill, and range estimates. The nugget C0 is a discontinuity from the origin at distance h = 0. It describes measurement error and/or microscale variation, the latter resulting from small-scale variation not detected with the sampling grid. The sill is the asymptote of the variogram that occurs at range a. The sill consists of the nugget and the partial sill C, the latter describing the spatial component of the semi-variance 
. The range describes the extent of spatial correlation in the data (Isaaks and Srivastava, 1989) and the average patch diameter (Webster and Oliver, 2001).
Spatial correlation and patch diameter were also examined visually using standardized variograms and correlograms (Rossi et al., 1992). Standardized variograms were calculated for both 5.6- and 2.2-km grids to determine whether a finer scale sampling grid would reveal different spatial structures. Correlograms, which are a plot of correlation coefficients by lag, were calculated to verify the standardized variogram range estimates. Correlograms filter the lag means and variances, so providing alternative range estimates for cases where the assumption of intrinsic stationarity might not be tenable.
Ordinary kriging (Isaaks and Srivastava, 1989) was used to generate predicted scallop counts at 2.2-km grid stations (n = 852).
Comparison of kriged vs. true values
The null hypothesis H0 of no difference between the predicted and the assumed true values was assessed qualitatively by comparing the predicted values 
with the observed scallop counts z at the 2.2-km grid stations using methods outlined in Isaaks and Srivastava (1989). Summary statistics were compared for and z, with the expectation that the distribution of should be similar to that of z. The univariate distribution of the error –z was also examined, with the expectation that the mean, median, and standard deviation would all be as close to 0 as possible. Two additional statistics that incorporate both the bias and the spread of the error distribution are the mean absolute error:
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A formal test of H0 was done with the normal approximation to the Wilcoxon paired-sample test by ranks (Zar, 1999), because the errors –z were not normally distributed (Table 1). This non-parametric alternative to the paired t-test was used after we verified that the errors were symmetrical around the median (Table 1). We note that, although the paired test accounts for the correlation between i–zi at location i (Zar, 1999), it does not account for the spatial correlation between i–zi and j–zj (Legendre and Legendre, 1998). Also, we did not normalize the errors –z by dividing by s.e.{} (Ecker and Heltshe, 1994), because the loess fit is not independent of the kriging fit to the RE data. Therefore, we ran the paired test mindful of the increased risk of committing a type I error (Legendre and Legendre, 1998; Zar, 1999).
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Quantile–quantile plots (Wilk and Gnanadesikan, 1968) were used to compare the distributions of the kriged vs. the true values.
We plotted colour-scale maps of predicted values without contouring to avoid the additional interpolation that is introduced with the latter process, to permit a more accurate comparison of kriged vs. true maps. Colour-scale values were chosen to reflect minimum commercial densities, as well as departures from the 45° line = z observed in the quantile–quantile plots. Note that the predicted values for the RE data were back-transformed to the original units.
All analyses were done using S+ and the module S+SpatialStats (Insightful Corporation, Seattle, WA, USA), except for the Kolmogorov–Smirnov tests of normality, which were done in PROC UNIVARIATE (SAS Institute, Cary, NC, USA).
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Results |
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Geostatistics
The standardized variogram and correlogram for the 5.6-km data gave range estimates of ca. 17.2 km (Figure 4). Similarly, the apparent range in the standardized variogram for the 2.2-km data was between 15.7 and 17.8 km. In contrast to these three plots, however, was the correlogram for the 2.2-km data, which showed an asymptote between 20.0 and 24.6 km. Another noteworthy trend in Figure 4 is the smoothness of the correlogram asymptotes relative to those observed in the standardized variograms. This confirmed the geographic trend suggested in Figure 2, and that the assumption of intrinsic stationarity was questionable.
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The spherical model gave the best fit to the AB data, whereas the exponential model gave the best fit to the RE data (Table 2). For the AB data, spherical fits to the classical and robust variograms gave range estimates of 17.9 and 18.7 km, respectively. For the RE data, exponential fits to the classical and robust variograms gave range estimates of 21.0 and 20.0 km, respectively.
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Comparison of kriged and true values
For the AB data, the closest estimate of the true mean was given by a spherical fit to the classical variogram; the robust–spherical gave the closest approximation of the true median, maximum value, and
; and the classical–exponential gave the minimum value closest to 0 (Table 3). For the RE data, the closest estimate of the true mean and median was given by the classical–exponential; the robust–exponential gave the closest approximation of the maximum value and ; and the classical–spherical gave the minimum value closest to 0. Although no combination of variogram–model gave consistently better estimates of the true distribution for either the AB or RE data, two general trends were apparent: classical variograms always gave estimates of the true mean and minimum values closest to 0, whereas robust variograms gave the best approximations of the maximum value and .
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Error distributions for the AB data were generally best with the classical–spherical, which gave a mean, maximum,
, MAE, and MSE closest to 0 (Table 4). The robust variogram yielded a minimum and median closest to 0 using an exponential and spherical model, respectively. Error distributions for the RE data were better for the classical–exponential, which gave , MAE, and MSE closest to 0, but there was no consistent pattern for the other statistics.
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The null hypothesis of no difference between the predicted and the true values was rejected for the AB data with the exception of the robust–spherical, which was barely non-significant (Table 5). In contrast, H0 was not rejected for any combination of variogram–model with the RE data.
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Quantile–quantile plots for the AB data showed three general trends (Figure 5): negative estimates for 0 true values (particularly for spherical models), a close fit to the 45° line
= z for the majority of true values, and an underestimation of the highest values. The classical–spherical began to underestimate true values at ca. 35 scallops. It should be noted that these underestimates consisted of only 39 of n = 852 true values, or 4.6% of the total number of predictions. Similarly, the other three combinations of variogram–model began to underestimate true values at ca. 60 scallops, or just 0.9% of the total number of predictions.
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Quantile–quantile plots for the RE data revealed two additional trends (Figure 6). One was the range of predictions for log(0+1), log(1+1), etc., true scallops. Second, once the range of predictions began to smooth ca. 1.1 log(true) scallops, estimates resulting from the robust variograms were closer to the 45° line
= z than those from the classical variogram.
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Colour-scale maps of kriged values for the AB data were less patchy than the distribution of true scallops (Figure 7). Among the kriged maps themselves, two trends were apparent. One, the classical–exponential, had the fewest negative predictions (8), whereas the robust–spherical had the most (74). However, it should be noted that 171 of n = 852 true values were zeroes: if the negative and 0–0.9 predictions are taken together, then the robust–spherical was actually the most realistic, with 163 predictions <1 scallop. The other trend is that the number of true values
60 was nine, which was matched only by the robust–spherical, which also had nine values 60.
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Colour-scale maps of kriged values for the RE data were also less patchy than the distribution of true scallops (Figure 8). In this case, the classical–spherical had the fewest negative predictions (1), and the robust–exponential matched the true values exactly (171) when negative and 0–0.9 predictions were taken together. As for values
60, the best approximation of the true values (9) was given by the robust–exponential (5).
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A comparison of Figures 7 and 8 revealed a smoothing of the spatial structure in the latter along 48° (the direction of maximum spatial continuity) attributable to detrending and correcting for anisotropy. There were also fewer negative and
60 values in the RE maps. |
Discussion |
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Geostatistics
The range estimates in Table 2, and the apparent ranges in Figure 4, show that data from stations within 15.7–24.6 km of each other are correlated. Although this means that classical statistical tests on these data would have an increased probability of committing a type I error, parameter estimates would be unbiased, because each point has the same probability of being included in the sample. Only the variance will increase if the distribution is patchy (Legendre and Legendre, 1998).
Our range estimates were greater than the 4.8 km reported for scallops in the Northumberland Strait off eastern Canada (Conan, 1985), as well as the ca. 9.5 km for scallops in Georges Bank Closed Area II (Gedamke et al., 2005; Walter et al., 2007). In contrast, our range estimates were much smaller than the 1° (i.e. 127.8 km) reported for scallops in the New York Bight (Ecker and Heltshe, 1994). These large differences are likely due to geographic variation in scallop populations. If useful inferences are to be made regarding patch size, then what is clearly needed is a large-scale geostatistical analysis of sea scallop populations for both Georges Bank and the mid-Atlantic.
The apparent range in the 2.2-km correlogram warrants further discussion. At first glance this appears to suggest that the 2.2-km grid would more accurately describe the spatial structure than the 5.6-km grid, once local means and variance have been filtered with a correlogram. However, this is not the case. The parameters in Table 2 show that, in general, the RE data gave range estimates comparable to the apparent range in the 2.2-km correlogram. This is to be expected because the RE data were detrended and corrected for anisotropy to meet the assumption of intrinsic stationarity. In other words, the 5.6-km grid data can be used to describe the spatial structure, provided the data are properly detrended.
Comparison of kriged vs. true values
Weighted least squares suggested that the classical–spherical would give the best results for the AB data, and that the classical–exponential would give the best results for the RE data. This was indeed the case in terms of the mean for the AB data, as well as the mean and median for the RE data, but not for other summary statistics. It is important to note that the seemingly small differences in the means reported in Table 3 would translate to tremendous differences in abundance when extrapolated to the entire study area. For example, the difference between the mean of the classical–spherical and –exponential for the AB data is 0.1, which works out to a difference of ca. 42 million scallops over the entire Elephant Trunk Closed Area.
The standard deviations for the kriged estimates reported in Table 3 are lower than the standard deviation for the 2.2-km grid data. This is to be expected: as more samples are incorporated in a weighted linear combination, the resulting estimates generally become less variable (Isaaks and Srivastava, 1989).
A formal test of the null hypothesis of no difference between predicted and true values suggested that the robust–spherical was the only combination of variogram–model for the AB data that was not significantly different, when compared with the true mean. However, the test result (p = 0.051) was very close to the significance level (
= 0.05), indicating that additional analysis is needed before making any definitive statements about this combination of variogram–model (Zar, 1999). In any case, this result does indicate that, at the very least, the robust–spherical performed better with the AB data than the other three combinations of variogram–model. This result was not anticipated by the least-squares fits or the mean predicted value. However, other summary statistics, such as the median, maximum, and , indicated that the robust–spherical most closely approximated the true distribution. The median was the only summary statistic indicating that the robust–spherical had the best error distribution. Quantile–quantile plots for the AB data indicated poorest performance for the classical–spherical, but there was nothing to suggest that the robust–spherical was superior to either exponential fits. A tally of the number of cells <1 and 60 in the kriged maps would have suggested that the robust–spherical predictions would not have been significantly different from the true values. In short, there was no clear, consistent pattern indicating that the robust–spherical would have performed best for the AB data.
The null hypothesis was not rejected for any combination of variogram–model fit to the RE data. Test results were nowhere near the rejection region, which is strong evidence that, on average, predictions were not biased. The highest p-value was given by the robust–exponential. Similar to the results for the AB data, this result would not have been anticipated by the least-squares fit or the predicted mean, but it was predicted by the summary statistics maximum value and . Quantile–quantile plots indicated that the robust–exponential would perform best, as did the number of cells <1 and 60 in the kriged maps. As with the AB data, there was no consistent pattern, but the quantile–quantile plots were an additional tool that predicted that the robust–exponential would have performed best for the RE data.
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Conclusions |
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At first sight our results might seem to suggest that a spherical fit to a classical variogram on untransformed data would be a quick way to approximate the mean, or that an exponential fit to a robust variogram would be the best way to test hypotheses on log-transformed, detrended data. Such an interpretation would be incorrect: just because a particular combination of variogram–model performs better with one dataset does not mean the combination will always perform better with all fisheries datasets (Davis, 1987). Nevertheless, our analysis reveals some general guidelines for the typical application where the true values are not known.
The method of weighted least squares proposed by Cressie (1985) should be used with caution, particularly when working with robust variograms. This agrees with recent work that Cressie’s least-squares method should be considered a compromise solution, best used in conjunction with the classical variogram (Rufino et al., 2006).
Recent work with simulated fisheries data has suggested that the classical variogram is superior to the robust variogram (Rufino et al., 2006). Our results indicate that this is not the case. Indeed, the robust variogram has been applied successfully to a variety of other fisheries datasets (e.g. Sullivan, 1991; Maravelias et al., 1996; Lo et al., 2001; Páramo and Roa, 2003; Jensen and Miller, 2005; Mello and Rose, 2005; Walter et al., 2007).
Recent work has also suggested the removal of outliers to help uncover the spatial structure of a stock (Rufino et al., 2005). We did not employ this approach because the SMAST video survey is an absolute estimate and all scallop counts are known to be legitimate. Points should only be removed from a geostatistical analysis for valid physical or ecological reasons, such as an erroneous measurement or an unusually large concentration of food (Rossi et al., 1992; Rivoirard et al., 2000).
Finally, our results illustrate the importance of checking the assumptions of geostatistics. The most accurate reflection of the true values at unsampled locations was obtained with the data that were corrected for non-normality, trend, and anisotropy. This underscores theory presented in the standard geostatistical texts (e.g. Cressie, 1993; Rivoirard et al., 2000).
The objective of this study was to generate kriged estimates of sea scallop abundance using data from a 5.6-km systematic grid, then to compare these predicted values with the actual scallop counts observed at a finer-scale 2.2-km grid. There was no significant difference between kriged and true values for any combination of variogram–model fit to log-transformed, detrended, anisotropy-corrected data. In contrast, significant differences were found for three out of four combinations of variogram–model fit to untransformed data, assuming isotropy. These empirical findings confirm the utility of the kriging technique to predict scallop abundance accurately at unsampled locations when the assumptions of geostatistics are met. We also found that the classical and robust variograms performed equally well. The Elephant Trunk Closed Area contains the widest range of sea scallop densities (0–40 scallops m–2) offshore of the northeastern USA (Stokesbury et al., 2004), so kriging of SMAST video data for other areas will be robust. The advantage of geostatistics over other statistical techniques is that it exploits the spatial correlation inherent in ecological datasets. These strengths will become increasingly important as the delineation of marine protected areas, ecosystem-based, and other management strategies require spatially explicit interpretation of ecological data.
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Acknowledgements |
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We thank Brian Rothschild for his support and guidance, and the owners, Captains and crews who sailed with us. P. Christopher, D. Frie, R. Silva, and L. Gavlin provided the Letters of Authorization. Aid was provided by SMAST, the Massachusetts Division of Marine Fisheries, NOAA award NA07NMF4540031, and the sea scallop fishery and supporting industries.
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References |
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Brand A. R. Scallop ecology: distributions and behavior. In: Scallops: Biology, Ecology and Aquaculture—Shumway S. E., ed. (1991) Amsterdam: Elsevier. 517–584. 1095 pp.
Chilés J-P., Delfiner P. Geostatistics: Modeling Spatial Uncertainty. (1999) New York: Wiley–Interscience. 695.
Cleveland W. S., Devlin S. J. Locally weighted regression: an approach to regression analysis by local fitting. Journal of the American Statistical Association (1988) 83:596–610.[CrossRef][Web of Science]
Conan G. Y. Assessment of shellfish stocks by geostatistical techniques. ICES Document CM 1985/K: 30 (1985) 24.
Cressie N. Fitting variogram models by weighted least squares. Mathematical Geology (1985) 17:563–586.[CrossRef]
Cressie N., Hawkins D. M. Robust estimation of the variogram: I. Mathematical Geology (1980) 12:115–125.[CrossRef]
Cressie N. A. C. Statistics for Spatial Data, revised edn. (1993) New York: Wiley–Interscience. 900.
Davis B. M. Uses and abuses of cross-validation in geostatistics. Mathematical Geology (1987) 19:241–248.[CrossRef][Web of Science]
Dutilleul P., Legendre P. Lack of robustness in two tests of normality against autocorrelation in sample data. Journal of Statistical Computation and Simulation (1992) 42:79–91.[CrossRef]
Ecker M. D., Heltshe J. F. Geostatistical estimates of scallop abundance. In: Case Studies in Biometry—Lange N., Ryan L., Billard L., Brillinger D., Conquest L., Greenhouse J., eds. (1994) New York: John Wiley. 107–124. 529 pp.
Gedamke T., DuPaul W. D., Hoenig J. M. Index-removal estimates of dredge efficiency for sea scallops on Georges Bank. North American Journal of Fisheries Management (2005) 25:1122–1129.[CrossRef][Web of Science]
Giannoulaki M., Machias A., Koutsikopoulos C., Haralabous J., Somarakis S., Tsimenides N. Effect of coastal topography on the spatial structure of the populations of small pelagic fish. Marine Ecology Progress Series (2003) 265:243–253.[CrossRef][Web of Science]
Isaaks E. H., Srivastava R. M. An Introduction to Applied Geostatistics (1989) Oxford: Oxford University Press. 561.
Jensen O. P., Miller T. J. Geostatistical analysis of the abundance and winter distribution patterns of the blue crab Callinectes sapidus in Chesapeake Bay. Transactions of the American Fisheries Society (2005) 134:1582–1598.[CrossRef]
Kaluzny S. P., Vega S. C., Cardoso T. P., Shelly A. A. S+SpatialStats: User’s Manual for Windows® and UNIX®. (1998) New York: Springer. 327.
Krebs C. J. Ecological Methodology (1999) 2nd edn. Massachusetts: Addison Wesley Longman, Reading. 620.
Legendre P., Legendre L. Numerical Ecology. (1998) 2nd edn. Amsterdam: Elsevier. 853.
Lo N. C. H., Hunter J. R., Charter R. Use of a continuous egg sampler for ichthyoplankton surveys: application to the estimation of daily egg production of Pacific sardine (Sardinops sagax) off California. Fishery Bulletin US (2001) 99:554–571.
Maravelias C. D., Reid D. G., Simmonds E. J., Haralabous J. Spatial analysis and mapping of acoustic survey data in the presence of high local variability: geostatistical application to North Sea herring (Clupea harengus). Canadian Journal of Fisheries and Aquatic Sciences (1996) 53:1497–1505.
Matheron G. Principles of geostatistics. Economic Geology (1963) 58:1246–1266.
Matheron G. The theory of regionalized variables and its applications. In: Les Cahiers du Centre de Morphologie Mathématique 5 (1971) Fontainebleau: École Nationale Superieure des Mines de Paris. 211.
Mello L. G. S., Rose G. A. Using geostatistics to quantify seasonal distribution and aggregation patterns of fish: an example of Atlantic cod (Gadus morhua). Canadian Journal of Fisheries and Aquatic Sciences (2005) 62:659–670.
NMFS (National Marine Fisheries Service). Fisheries of the Northeastern United States; Atlantic Sea Scallop Fishery; Framework 18. Federal Register US (2006) 71:33211–33235.
Páramo J., Roa R. Acoustic-geostatistical assessment and habitat-abundance relations of small pelagic fish from the Colombian Caribbean. Fisheries Research US (2003) 60:309–319.[CrossRef]
Petitgas P. Geostatistics for fish stock assessments: a review and acoustic application. ICES Journal of Marine Science (1993) 50:285–298.
Rivoirard J., Simmonds J., Foote K. G., Fernandes P., Bez N. Geostatistics for Estimating Fish Abundance (2000) Oxford: Blackwell Science. 206.
Rossi R. E., Mulla D. J., Journel A. G., Franz E. H. Geostatistical tools for modeling and interpreting spatial dependence. Ecological Monographs (1992) 62:277–314.[CrossRef][Web of Science]
Rufino M. M., Maynou F., Abelló P., Gil de Sola L., Yule A. B. The effect of methodological options on geostatistical modelling of animal distribution: a case study with Liocarcinus depurator (Crustacea: Brachyura) trawl survey data. Fisheries Research (2005) 76:252–265.[CrossRef][Web of Science]
Rufino M. M., Stelzenmüller V., Maynou F., Zauke P. Assessing the performance of linear geostatistical tools applied to artificial fisheries data. Fisheries Research (2006) 82:263–279.[CrossRef][Web of Science]
Simmonds E. J., Fryer R. J. Which are better, random or systematic acoustic surveys? A simulation using North Sea herring as an example. ICES Journal of Marine Science (1996) 53:39–50.
Stephens M. A. EDF statistics for goodness of fit and some comparisons. Journal of the American Statistical Association (1974) 69:730–737.[CrossRef][Web of Science]
Stokesbury K. D. E., Harris B. P., Marino M. C., Nogueira J. I. Estimation of sea scallop abundance using a video survey in off-shore US waters. Journal of Shellfish Research (2004) 23:33–40.[Web of Science]
Sullivan P. J. Stock abundance estimation using depth-dependent trends and spatially correlated variation. Canadian Journal of Fisheries and Aquatic Sciences (1991) 48:1691–1703.
Walter J. F., Hoenig J. M., Gedamke T. Correcting for effective area fished in fishery-dependent depletion estimates of abundance and capture efficiency. ICES Journal of Marine Science (2007) 64:1760–1771.
Warren W. G. Spatial analysis for marine populations: factors to be considered. In: Proceedings of the North Pacific Symposium on Invertebrate Stock Assessment and Management—Jamieson G. S., Campbell A., eds. (1998) Canadian Special Publication of Fisheries and Aquatic Sciences, 125. 21–28. 462 pp.
Webster R., Oliver M. A. Geostatistics for Environmental Scientists. (2001) London: John Wiley. 271.
Wilk M. B., Gnanadesikan R. Probability plotting methods for the analysis of data. Biometrika (1968) 55:1–17.
Zar J. H. Biostatistical Analysis (1999) 4th edn. Upper Saddle River, New Jersey: Prentice Hall. 663.
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