Assessing the performance of linear geostatistical tools applied to artificial fisheries data

Most marine species are spatially clustered and thus the analysis of their distribution with geostatistical techniques is becoming increasingly common in fisheries studies, as a way of producing continuous distribution maps, reducing estimated error and analysing species spatial behaviour. The use of geostatistics is coupled with an increased computation power and development of statistical methods, leading to a greater availability of those to fisheries scientists. Thus, after the application of parametric classical geostatistical models to fisheries, a range of methods is now available that possibly are more adequate to fisheries data, typically non-normal, highly skewed and restricted to a low number of samples. However, the use of such recently available methods is still minimal and had not been widely applied or tested for its potential in fisheries studies. In the current work, we use simulated catch data, generated with an underlying spherical covariance function, considering two types of distribution function (Gaussian and log-Gaussian) and three levels of nugget variability (0, 30 and 50%). Twenty to 200 samples were randomly redrawn from the simulated data. Thus, for each case (sampling number, nugget and distribution) first, we test the efficiency of Mantel statistic in detecting significant autocorrelation. Second, we study the extent to which the originally defined covariance structure (variogram model parameters: nugget, sill and range) is recovered by different fitting methods: based on least squares (weighted least squares and Cressie) and on maximum likelihood (ML and relative ML) methods and the performance of the classical and robust variogram estimators. Third, we determine the reliability of several goodness-of-fit criteria (Akaike's, cross-validation, ‘gof’ and minimising function) in detecting the original model type (between spherical, exponential, Gaussian or linear). Finally, the bias of the fitting methods was modelled, so it can be corrected in future studies. Mantel test was able to detect significant autocorrelation in 20–85% of the cases, with Pearson r correlation coefficient varying between 0.04 and 0.12. The test statistic gave the best results with Gaussian data, increasing number of samples (more than 100) and decreasing nugget. Still, overall its behaviour was poor in identifying spatial autocorrelation. All fitting methods analysed gave significantly correct estimates for more than 50–70 samples, even when using log-Gaussian data with 50% nugget. Both estimator types behaved similarly in the Gaussian case, although the robust estimator performed considerably worse for log-Gaussian data. Using the least square methods, both weighted least squares (WLS) and Cressie behaved similarly well, for more than 50 samples, even with 50% nugget. As expected, the precision and accuracy of the estimates increased with the sample size, except for the range, which even when only 20 samples where used the estimates were correct. While the nugget was underestimated for any of the methods tested, the sill was generally overestimated, particularly in the presence of nugget. With increasing nugget variability (from 0 to 50%), more samples were required to accurately estimate the parameters. The range of variograms was in general overestimated by all methods studied. No goodness-of-fit criterion was able to detect the correct spatial model in more than 60% of the cases. Still, Akaike's, ‘gof’ using weights as pairs and the minimising function gave the best results. In this assessment, there was little influence of sample size and amount of nugget. A geostatistical analysis in a fisheries context is often carried out at the border of acceptability from a theoretical point of view; however, the results of this simulation study show that the reliability of a structural analysis can be improved when appropriate tools are employed.