Year: 2023
Type: article
Abstract: The measurement of diversity is a central component of studies in ecology and evolution, with broad uses spanning multiple biological scales. Studies of diversity conducted in population genetics and ecology make use of analogous concepts and even employ equivalent mathematical formulas. For the Shannon entropy statistic, recent developments in the mathematics of diversity in population genetics have produced mathematical constraints on the statistic in relation to the frequency of the most frequent allele. These results have characterized the ways in which standard measures depend on the highest-frequency class in a discrete probability distribution. Here, we extend mathematical constraints on the Shannon entropy in relation to entries in specific positions in a vector of species abundances, listed in decreasing order. We illustrate the new mathematical results using abundance data from examples involving coral reefs and sponge microbiomes. The new results update the understanding of the relationship of a standard measure to the abundance vectors from which it is calculated, potentially contributing to improved interpretation of numerical measurements of biodiversity.
Source: Journal of Mathematical Biology
Authors: Maike L. Morrison, Noah A. Rosenberg
Institution: Stanford University
Language: English
Subfield: Nature and Landscape Conservation
Field: Environmental Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,790
Awards: G4755611226, G9000145930
OpenAlex ID: W4387954766