Relationship between plot size and the variance of the density estimator in West African savannas

The relationship between the variance of the density estimator and the plot size in forest inventories based on fixed area plots was characterized in West African savannas. Nine sites ranging from dry to moist savanna were surveyed, and the variance of the density estimator was assessed for varying sample plot sizes. An approximate theoretical expression of the variance was derived, taking into account the uncertainty on plot limits. In six sites, a Matern process was fitted to the spatial pattern of trees. The point process was used to generate spatial patterns, yielding simulated values of the variance. A power function was also fitted to observed and simulated data. The theoretical expression and simulations showed that the contribution of uncertain plot limits to the variability of the density estimator was negligible with respect to the contribution of the spatial pattern of trees. The theoretical expression matched the data for small areas, but was inaccurate for large areas. The power function provided better fits. Nevertheless, the theoretical expression did not require any statistical fit to data and established a clear link between the spatial pattern of trees and the variance of the density estimator, with interpretable parameters.