Multivariate measures of similarity and niche overlap

Niche overlap measures are used to assess the similarity in resource use by two species. Recently researchers have used niche overlap measures as summary measures and for making inferences, typically about competition for resources. The problem of estimating niche overlap when the niches are multivariate normal distributions with equal covariance matrices has previously been studied. In this work, the assumption of equal covariance matrices is relaxed. Two general measures of similarity are evaluated assuming general multivariate normal distributions. Commonly used measures of overlap are given as special cases of these two general measures. The question of bias in estimating these measures is discussed and shown to be a potential problem, especially when there are many redundant variables or if sample sizes are small.