TDV-optimization: A novel numerical method for phytosociological tabulation

I present the Total Differential Value (TDV), an index designed for vegetation analysis based on the operational concept of differential species, as classically illustrated by Heinz Ellenberg and Dieter Mueller-Dombois. Given a phytosociological table and a grouping of its relevés, TDV is obtained by averaging the Differential Value (DiffVal) for each species in the table. DiffVal, grounded in combinatorial-discrete mathematics, quantifies the differential power of a species. The novelty of this approach lies in its distinction between two types of species absences: (i) absences from some relevés within a group and (ii) absences from all relevés representing a group. By leveraging the distribution of species absences among groups, this method effectively quantifies the differential power and distinguishes differential from non-differential species. I illustrate the computation of DiffVal and TDV and show that, because only differential species contribute to TDV, it reflects the strength of the differential species patterns in a classified table. TDV can be optimized (TDV-optimization), providing partitions of relevés. I demonstrate TDV-optimization using both an artificial and a well-known real-world data set. Key features of this method include its ability to identify patterns very closely resembling manual phytosociological tabulation and to detect reticulate patterns. TDV-optimization may lead to partitions where outlier or extreme relevés are isolated in groups; however, enforcing a minimum group size can highlight partitions with more balanced group sizes. An R package is now available, implementing DiffVal and TDV calculation as well as TDV-optimization. Abbreviations: DiffVal = Differential Value; EllPar = Ellenberg’s partition into three groups; NDR = number of discrepant relevés; NSS = number of significant species; TDV = Total Differential Value.