Towards A New Prokaryotic Biodiversity Assessment: The Pasta Index

We assume that the distribution of "biological objects" (species, family, phyla,) inside a "set" (community, assemblage, etc.) is at random. Although similar assumptions have been put forward by others (see text), our treatment is basically different. Based on a simple algorithm describing the random partition of a set, we obtain the resulting statistical laws characterizing the partition (that is to say: probability density, repartition function and moments). The theoretical results are supported by mathematical simulations of thousands random drawings. Assuming that the reduced variable characterizing a biological object is analogous to a probability, we adjust curves of rank / relative abundance type (like non-log plots Witthaker type, Fisher plots,) with probabilities calculated through our statistical functions. The results are compelling both for eukaryotes (not shown) and for prokaryotes. The sole fitting parameter is the partition order, M (number of parts of the set). As a rule, this number is an integer. Nevertheless, we are discussing the possibility that this variable can be considered as a simple index and may have non-integer values. This index, which we call the PASTA index (from the French Partition STAtistiques) is defined as a biodiversity estimate and characterizes what we call the bioclusters number of the assemblage. We take as true that this index can be applied to characterize structural, genetic biodiversities and thus applies to various levels of description of an assemblage.