AGGREGATION OF SAMPLING UNITS - AN ANALYTICAL SOLUTION TO PREDICT VARIANCE

Geographical variables generally show spatially structured patterns co rresponding to intrinsic characteristics of the environment. The size of the sampling unit has a critical effect on our perception of phenom ena and is closely related to the variance and correlation structure o f the data. Geostatistical theory uses analytical relationships for ch ange of support (change of sampling unit size), allowing prediction of the variance and autocorrelation structure that would be observed if survey teas conducted using different sampling unit sizes. To check th e geostatistical predictions, we use a test case about tree density in the tropical rain forest of the Pasoh Reserve, Malaysia. This data se t contains exhaustive information about individual tree locations, so it allows us to simulate and compare various sampling designs. The ori ginal data set was reorganized to compute tree densities for 5 x 5-, 1 0 x 10-, and 20 x 20-meter quadrat sizes. Based upon the 5 x 5-meter d ata set, the spatial structure is modeled using a nugget effect (white noise) plus an exponential model. The change of support relationships , using within-quadrat variances inferred from the variogram model, pr edict the spatial autocorrelation structure and new variances correspo nding to 10 x 10-meter and 20 x 20-meter quadrats. The theoretical and empirical results agreed closely, whereas neglecting the autocorrelat ion structure would have led to largely underestimating the variance. As the quadrat size increases, the range of autocorrelation increases, while the variance and the proportion of noise in the data decrease.