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

Abstract

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.

Feeding strategy of Menticirrhus americanus and Menticirrhus littoralis (Perciformes: Sciaenidae) juveniles in a sandy beach surf zone of southern Brazil

“…Until not long ago, little attention was given to the statistical properties of trophic overlap measurements, and overlap indexes were calculated without statistical significance (PETRAITIS 1979, RICKLEFS & LAU 1980, MAURER 1982, SMITH & ZARET 1982, MUELLER & ALTENBERG 1985. DIXON (2001) commented that it is easy to calculate such indexes but difficult to estimate their precision.…”

Measures of Niche Overlap, II

“…The function x(x) = (1 -x)i, for instance, allows much greater freedom of choice: we shall restrict ourselves to considering functions T from the family (1 -x) Vp 4. Modified form of Horn's index (Ricklefs and Lau, 1980),…”

“…MANY different indices are currently being used to quantify the notion of niche overlap (Ricklefs & Lau, 1980). In Schatzmann, Gerrard, and Barbour (1986) [Part I], a number of properties that a reasonable measure of overlap might be expected to possess are proposed in the form of axioms, and their motivations and consequences are discussed from a biological standpoint, with particular reference to the more commonly used measures.…”

“…This, in turn, makes it easy to construct new measures for applications in which existing measures may be inappropriate, and some examples of these are given. It is shown that four of the commonly used measures of overlap, those of Renkonen (1938), Matusita (1955), Horn (as modified in Ricklefs & Lau, 1980), and van Belle & Ahmad (1974), satisfy all the axioms.…”

Nonparametric estimation of a polarization measure

“…The de…nition can easily be extended to the multivariate x case, and indeed we treat this case below. This quantity has received a lot of attention in medical statistics, Mizuno, Yamaguchi, Fukushima, Matsuyama, and Ohashi (2005), and Ecology, where it is known as the overlap coe¢ cient or the coe¢ cient of community, see for example Ricklefs and Lau (1980). To provide a sense of the magnitude of we looked at the male-female height distributions from the National Health and Nutrition Survey of 1999 for the US age group 20-29.…”