Update: A non-parametric method for the measurement of size diversity, with emphasis on data standardization. The measurement of the size evenness

Abstract

A method for the measurement of the size diversity based on the classical Shannon–Wiener expression was proposed as a proxy of the shape of the size distribution. The summatory of probabilities of a discrete variable (such as species relative abundances) in the original Shannon–Wiener expression was substituted by an integral of the probability density function of a continuous variable (such as body size). Here, we propose an update of this method by including the measurement of the size e-evenness, just dividing the exponential of the size diversity by its possible maximum for a given size range. Assuming a domain of the size range of (0,∞), for a given logarithmic mean ( math formula) and a logarithmic standard deviation math formula, the distribution with the highest diversity is the Log-Normal. The size e-evenness ranges between 0 and 1 because of the division by the maximum exponential diversity. Size e-evenness is useful to discriminate whether variations in size diversity are due to changes in the shape of the size distribution or caused by differences in size dispersion