Performance of two fixed‐area (quadrat) sampling estimators in ecological surveys

Many ecological surveys are conducted to collect information about organisms and environmental conditions dispersed across a continuous surface. In most situations, there is no natural division of the population into a finite collection of sampling units. Therefore, the sample is determined by randomly locating a series of m plots within the boundaries of the population and collecting information about one or more attributes that fall within the plots. These plots are usually referred to as fixed‐area plots in the forestry and sample survey literature and quadrats in the ecological literature. One method for determining the total number of organisms is to view the population as the realization of a point process and estimate the intensity, λ, which is the number of points per unit area. Then the estimator of the total number of organisms is given by $\hat{\lambda} |A|$ , where $|A|$ is the area over which the organisms are dispersed. For the m plots there are two distinctly different estimators for $\hat{\lambda}$ , which are the ratio‐of‐means and mean‐of‐ratios estimators. This article compares these estimators and gives the most basic conditions under which the estimator is expected to be model‐unbiased. It also shows that both estimators can exhibit very large biases when the population is subject to an edge‐effect, which is when conditions along the boundary of the population differ from those found in the interior. The ratio‐of‐means estimator also suffers from a poorly performing variance estimator, which required sample sizes of nearly 100 plots before the estimator was nearly unbiased regardless of the plot size. Results for these estimators are derived and the effects of plot size and the spatial arrangement of the population are discussed. Copyright © 2001 John Wiley & Sons, Ltd.