Lotka–Volterra model with Allee effect: equilibria, coexistence and size scaling of maximum and minimum abundance

Abstract

The Lotka–Volterra competition model (LVCM) is a fundamental tool for ecology, widely used to represent complex communities. The Allee effect (AE) is a phenomenon in which there is a positive correlation between population density and fitness, at low population densities. However, the interplay between the LVCM and AE has been seldom analyzed in multispecies models. Here, we analyze the mathematical properties of the LVCM + AE, investigating the coexistence of species interacting through neutral diffuse competition, their equilibria and stable points. Minimum viable population density arises as the threshold below which species go extinct, characteristic of strong Allee effects. Then, by imposing relationships of main parameters to body size, i.e. allometric scaling, we derive a general solution to the size-scaling maximum and minimum expected density under plausible scenarios. The scaling of maximum population density is consistent with the literature, but we also provide novel predictions on the scaling of the lower limit to population density, a critical value for conservation science. The resulting framework is general and yields results that increase our current understanding of how complex demographic processes can be linked to ubiquitous ecological patterns.