Unveiling the size scaling of extinction and extremal abundance in marine phytoplankton

Introduction The intricacies of population collapse and the occurrence of extreme population abundances in nature present considerable challenges to a straightforward understanding. Developing a framework based on scaling approaches to define the boundaries of population abundance is crucial to understand population collapses and fluctuations. Methods Here, we derived specific predictions on the size scaling of population abundance for species-rich communities by combining a general Lotka-Volterra model with Allee effect and the size scaling of biological rates. Model predictions were contrasted with data from 1183 microbial communities sampled weekly during 28 years at the English Channel L4 station. Results We found that the scaling of the upper limit to abundance (α theo =-1 to -1.3) is related to the scaling of metabolic rate, while the lower limit (β theo = -0.17) is determined by the scaling of the negative density dependence on mortality. It was established that the theoretically predicted slopes exhibited a high degree of agreement with the empirical estimations (α emp =-0.89, β emp =-0.1). Discussion The scaling of population abundance as an envelope-shaped pattern allows to define the boundaries delineating the species extinction vortex in species-rich natural communities. As a consequence, human activities that increase mortality rates (e.g., fishing or temperature changes) with respect to birth rates modify the scaling of the extinction vortex with a significant impact on the persistence of species.