Variance and spatial scales in a tropical rain forest: changing the size of sampling units

Abstract

The size of a sampling unit has a critical effect on our perception of ecological phenomena; it influences the variance and correlation structure estimates of the data. Classical statistical theory works well to predict the changes in variance when there is no autocorrelation structure, but it is not applicable when the data are spatially autocorrelated. Geostatistical theory, on the other hand, uses analytical relationships to predict the variance and autocorrelation structure that would be observed if a survey was conducted using sampling units of a different size. To test the geostatistical predictions, we used information about individual tree locations in the tropical rain forest of the Pasoh Reserve, Malaysia. This allowed us to simulate and compare various sampling designs. The original data were reorganised into three artificial data sets, computing tree densities (number of trees per square meter in each quadrat) corresponding to three quadrat sizes (5×5, 10×10 and 20×20 m⁽²⁾). Based upon the 5×5 m⁽²⁾ data set, the spatial structure was modelled using a random component (nugget effect) plus an exponential model for the spatially structured component. Using the within-quadrat variances inferred from the variogram model, the change of support relationships predicted the spatial autocorrelation structure and new variances corresponding to 10×10 m⁽²⁾ and 20×20 m⁽²⁾ quadrats. The theoretical and empirical results agreed closely, while the classical approach would have largely underestimated the variance. As quadrat size increases, the range of the autocorrelation model increases, while the variance and proportion of noise in the data decrease. Large quadrats filter out the spatial variation occurring at scales smaller than the size of their sampling units, thus increasing the proportion of spatially structured component with range larger than the size of the sampling units.