Use of the kriging method for the stock assessment of oysters in the Chesapeake Bay

The krlging technique Is now employed ln more and more fields: mlnlng (Journel. 1977), hydrology (Delhomme, 197B; Shamsi et al" 1988; Dingman et al" 1988), fishery (Conan, 1989) and ecology (Robertson, 1987; Schotzko and O'Keeffe, 1989, 1990). Recent developments of the mathematlcal theory tend to extend the number of applications where Il may be used. Baslcally defined for the case of a statlonary spatial process, It now encompasses more general processes assuming less and less strong hypotheses (Intrinsic hypothesls, Intrlnsic generalised hypothesis, disjunctive krlglng). In its most general formulation, it allows to study the spatial structure of a process including large scale or local trends. The basic idea remains to take Into account the spatial structure ln order to estimate the mean and the variance of the sampled variable either over a given area, either at a point. In the one dimensional case, it may be applied to time series (Ibanez, 1985; Robertson, 1987). Delails and malhematlcal formulations may be found in the references cited above and will not be recalled in this report. It is just necessary to know that the IInear krlglng estlmator of a process is the best linear unbiased estimator and that the estimation consists in computing the weights of the estimator from the spatial slructure, so that observed points closed to the point to estimate have a greater Influence than observed points whlch are far from it. Systematlc sampllng was applled to the study of the oyster populations ln some oyster bars of the Chesapeake Bay. Some of the resulls were chosen ln order to evaluate the advantages and drawbacks of the krlglng method compared to more classlcal ones (random sampling). We are faced with the following problems : - does the use of a regular grid yield to an Interesling resull (feasability, good precision)? ln that case, the sampling points are not randomly drawn, so that the estimators used for random sampling do not work. That means that we must use more efficient techniques for the stock assessment. Consequently, the kriging method was chosen. - Is It possible to make some proposals for a global survey of the bay? ln other words, is the previous method efficient enough to be Incorporated Into a global strategy. It appears that this question is linked to at least two more points: -- the cholce of units and subunits of the sampling schemes and of the method to draw these units. -- the comparlson of the cost (number of polnls) and tIhe precision (variance) obtained for the few examples that were analysed