Diversity Measures and Coarse-graining in Data Analysis with an Application Involving Plant Species on the Galapagos Islands

Abstract

In a numerical entity-characteristic incidence matrix we can use simple or multiple regression and calculate correlations between pairs of characteristics. However, in order to detect similarities/dissimilarities, interdependence, and multiple probabilistic causality among the characteristics we have to group the entities in classes. The number of uniform classes obtained by coding the given values of these characteristics depends on the balance between the class uncertainty and class ambiguity. The similarity, interdependence, and multiple probabilistic causality among characteristics are analyzed. When a set of entities and the abundance of their components are given, the average within-entity diversity and the average between-entity diversity are studied. The results are applied to the number of endemic and immigrant plant species in the Galapagos Islands.

Keywords

• Endemic And Immigrant Plant Species
• Probabilistic Causality
• Class Uncertainty And Ambiguity
• Similarity
• Interdependence
• Diversity Measure
• Uniform Coding
• Galapagos Archipelago