The dynamic face of rarity: tracking species at risk beyond space

Abstract

Avoid extinction of rare species is critical for biodiversity conservation. Rabinowitz proposes rare species is pattern that emerge from combination of three parameters: geographical range, habitat specificity and population size. Several papers have been looked to improves this method over last years, but they often neglect the temporal dimension, crucial for understanding the extinction process. This study introduces a dynamic framework that model the three dimensions of rarity as a continuous three-dimensional space, integrating vector-based representations and an ecological vector field to quantify rarity, temporal dynamics, displacement and equilibrium. Derivative equations are used to describe the temporal evolution in that system which is integrate to account the shift in that space. This framework allows to reinterpret ecological change as a trajectory though space, where each axis corresponds to an ecological dimension. This multidimensional representation distinguishes intrinsic rarity from extinction risk and can identify demographic declines, habitat restriction, or range contraction. The method can be applied to a single species or a set of species, using short or long sampling time intervals. A test across freshwater fish, birds, amphibians, and terrestrial plants showed that rarity dimensions can change independently among species. By monitoring the shifts in this dimension simultaneity, we can plan the conservation by priority species that are shaking their dimensions over time. Unlike static assessments that already exist, this method provides a nuanced understanding of a rare species vulnerability as a dynamic representation of temporal changes. An R package and application guide are provided, helping conservation practitioners use this approach.