New indices regarding the dominance and diversity of communities, derived from sample variance and standard deviation

Dominance and diversity are important characteristics for the description of communities. The most commonly used indices are Simpson's dominance indexand Shannon's and Simpson's indices of diversity. This paper uses the basic concepts of statistics as applied to community analysis to develop new dominance and diversity indices that will enable scientists to establish correlations among various indices. The present study proves that the variance of the number of individuals of different species in a sample can be used to calculateSimpson's dominance and diversity indices. New indices have been developed from the ratios ofthe variance to number of species, and the mean number of individuals per species in a quadrat. A wide range of data, varying from high dominance to high evenness, was simulated for 25 quadrats, with each quadrat having ten species and 100 individuals in different combinations. Variance and standard deviation-based indices were computed using the simulated data and were found to be highly correlated with Simpson's and Shannon's indices. The proposed indices will give both the dominance and diversity of a community on the same scale based on the same statistic. Another important contribution of the present study relates to the variance of a sample consisting of a single value. It has been proved that the variance of a sample having only one value is equal to the square of that value. The paper establishes a new link between diversity studies and statistics.