Non parametric tests and confidence regions for intrinsic diversity profiles of biological populations

Evaluation of diversity profiles is useful for ecologists to quantify the diversity of biological communities. Measures of diversity profile can be expressed as a function of the unknown abundance vector. Thus, the estimators and related confidence regions and tests of hypotheses involve aspects of multivariate analysis. In this setting, using a suitable sampling design, inference is developed assuming an asymptotic specific distribution of the profile estimator. However, in a biological framework, ecologists work with small sample sizes, and the use of any probability distribution is hazardous. Assuming that a sample belongs to the family of replicated sampling design, we show that the diversity profile estimator can be expressed as a linear combination of the ranked abundance vector estimators. Hence we are able to develop a non-parametric approach based on a bootstrap in order to build balanced simultaneous confidence sets and tests of hypotheses for diversity profiles. Finally, the proposed procedure is applied on the avian populations of four parks in Milan, Italy. Copyright # 2003 John Wiley & Sons, Ltd