Bias and Dispersion of Overlap Indices: Results of Some Monte Carlo Simulations

We have used computer simulations to determine the sampling distributions of four indices of overlap or similarity: the coefficient of community, Morisita's index, Horn's information theory index, and Euclidean distance. Estimates of overlap were systematically biased downward when sample size was small and when expected values were close to 1. The standard deviations of samples of indices were greatest when expected values were intermediate between 0 and 1, and sample sizes were small. In studies having sample sizes of 25, 50, or 100, one could expect the standard error of an estimated index of similarity to fall between 0.05 and 0.10, provided that samples were truly drawn from homogeneous populations. We suggest that simulations be used to estimate confidence limits on similarity and overlap indices where hypothesis testing is required. In addition, efforts should be made to develop indices of overlap for which statistical measures of dispersion and bias can be derived analytically.