A Biogeographic Assessment of the Stellwagen Bank National Marine Sanctuary - Kriged Predictive Map of Zooplankton Samples

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To examine the spatial and temporal patterns of zooplankton abundance and distribution the data were divided into three-year seasonal bins. Yearly bins included 1977-79, 1980-82, 1983-85, 1986-88 and seasons include: spring-March, April, May; summer-June, July, August; fall-September, October, November; and, winter-December, January, February. These binned data were separately mapped in a GIS and interpolated to create a predictive surface of zooplankton abundance throughout the Gulf of Maine. Prior to interpolation, all data were tested for spatial autocorrelation. Spatial autocorrelation is frequently encountered in ecological data, and many ecological theories and models assume an underlying spatial pattern in the distributions of organisms and their environment (Legendre and Fortin, 1989). Typically, species abundance is positively autocorrelated, such that nearby points have similar values than distant points. Moran's I and Geary's C statistics were calculated for all the data to identify significant autocorrelation (Levine, 2002). Detrending was done to standardize estimates across the analysis extent, and is a prerequisite for the interpolation used here. Empirical variograms show the decrease in relatedness between pairs of points as a function of distance. Chapter 1 page 38A Biogeographic Assessment of the Stellwagen Bank National Marine Sanctuary AnalysisSample sizeLag SizeNumber of LagsCross Validation Prediction Map -r2Cross Validation Probability Map -r2Neighbors (total, minimum)spring 77-7936420120.020.035, 2spring 80-8235220120.020.025, 2spring 83-8539120120.580.265, 2spring 86-8832020120.270.265, 2spring all1,22320120.140.145, 2summer 77-7923120120.360.325, 2summer 80-8229820120.300.255, 2summer 83-8536720120.370.395, 2summer 86-8834630120.580.535, 2summer all1,02930120.360.325, 2fall 77-7944620120.360.235, 2fall 80-8232020120.390.315, 2fall 83-8540220120.580.505, 2fall 86-8846320120.550.475, 2fall all1,35220120.470.395, 2winter 77-7917530120.240.195, 2winter 80-8215220120.360.355, 2winter 83-8514720120.540.455, 2winter 86-8822530120.580.555, 2winter all44520120.450.405, 2Table 1.7.1. Summary statistics for NEFSC MARMAP zooplankton ordinary and indicator kriging. In order to calculate the empirical variogram, pairs of points must be binned by distance and an average value calculated for all pairs in a given bin. The size of the bin is called the lag size. A variogram model is fit to the empirical variogram and its parameters are later used in the interpolation. Empirical variograms were calculated using the default lag size and number of lags, as well as for 10, 15, 20 and 30 km lag sizes. The appropriate lag size and number of lags were chosen to optimize variogram coherence. The interpolation method used is termed ordinary kriging. Kriging is a linear interpretation method that allow predictions of unknown values of a random function from observations at known locations (Kaluzny et al., 1998). Ordinary kriging is the method generally used for interpolation of a single continuous variable of unknown mean. Kriging is a preferred method because weights are based on the data's spatial structure (the variogram) and has been shown to outperform other interpolation techniques, such as inverse distance weighting and triangulated irregular networking (Guan et al., 1999). (continued)

(continued from above) Trend analysis was conducted using JMP statistical software (SAS Institute), while detrending, variogram modeling, and kriging were conducted using ArcMap Geostatistical Analyst Extension (ESRI, Inc.).In addition to creating predictive maps, probability maps were developed using indicator kriging. Indicator kriging is a technique used to identify areas or values that exceed a certain threshold (Isaaks and Srivastava, 1989). Through indicator kriging, data values are transformed into binary indicator values (1 or 0), values which exceed a chosen threshold are coded 1, those below coded 0. These indicators are then analyzed to determine their spatial direction variability with a series of variograms. By inspection of these variograms, orientations of greatest and least spatial continuity are determined. Variogram models are fit to the experimental variograms corresponding to the directional continuity. Then the indicator data are kriged using the variogram models to determine the probability of exceeding the threshold value in a spatial extent. For this analysis, the spatial mean of the zooplankton data was used as the threshold to compare predicted estimates and to also identify areas of high zooplankton abundance.The kriging neighborhood was set to the nearest 5 neighbors with a minimum of 2 to capture small scale variability(NCCOS, 2002). Cross validation was conducted to assess model accuracy by regressing observed versus predicted values (See modeling statistics Table 1.7.1). Maps of the kriging standard error were also generated and used to exclude poorly interpolated areas within the analysis extent. The lowest 50% of standard error was clipped from the interpolated map to depict the areas of strongest interpolation. (end continuation)