Both the ordination of taxonomic tables and the measurements of species diversity aim to capture the prominent features of the species composition of a community. However, interrelations between ordination techniques and diversity measurements are seldom explicated and are mainly ignored by many field ecologists. This paper starts from the notion of the species occurrence table, which provides a unifying formulation for different kinds of taxonomic data. Here it is demonstrated that alternative species weightings can be used to equate the total inertia of a centered-by-species occurrence table with common diversity indices, such as species richness, Simpson diversity, or Shannon information. Such an equation defines two main ordination strategies related to two different but consistent measures of species diversity. The first places emphasis on scarce species and is based on Correspondence Analysis and species richness (CA-richness strategy). The second, in which abundant species are prominent, relies on Non-Symmetric Correspondence Analysis and Simpson diversity (NSCA-Simpson strategy). Both strategies are suitable for measuring ? and ? diversity by analyzing the centered-by-species occurrence table with respect to external environmental or instrumental variables. In this paper, these two strategies are applied to ecological data obtained in a Neotropical rainforest plot. The results are then discussed with respect to the intrinsic characteristics of the community under analysis, and also to the broad classes of floro-faunistic data used in ecology (i.e., data gathered from museum or herbarium collections, exhaustive inventories in a reference plot, or enumeration through species-by-relevés tables). The approach encompasses several well-known techniques such as Correspondence Analysis, Non-Symmetric Correspondence Analysis, Canonical Correspondence Analysis, and Redundancy Analysis, and provides greater insight into interrelations between ordination methods and diversity studies.