Stochastic Modeling of Biodiversity: f-diversity, self f-diversity and Marginal f-diversity

Abstract

The paper is devoted to stochastic modeling of biodiversities, that are presented as selected f-diversities frequently used in biology and medicine. The most often used in biology and medicine are f-diversities called Number Alles, Gini-Simpson diversity and Shannon diversity. We have introduced two new general concepts, named marginal f-diversity and self f-diversity. The statistical properties of sample estimates of the selected f-diversities are mentioned. Results of simulations of f-diversities, self f-diversities and marginal f-diversities for Number Alles, Gini-Simpson and Shannon type diversities on the example of three alleles with fixed probabilities of occurrence and several sample sizes used are presented