Pattern formation in ecosystem with resource competition

In recent years, theoretical ecology has developed a growing interest in spatial models for population dynamics, led by the empirical evidence that spatial effects have a considerable influence on the distribution of species and on the structure of communities, affecting for instance their biodiversity levels. In such a perspective, this work aims at providing a spatial extension of the MacArthur resource-consumer model - which describes the dynamical evolution of species and resource abundances - in order to account for the emergence of spatially heterogeneous steady-state patterns from a homogeneous equilibrium solution. Following the approach adopted by Turing in his famous paper “The chemical basis of morphogenesis” (1952), a mechanism for pattern formation is investigated by adding some diffusion-like terms to the dynamical equations: the conditions for pattern initiation can then be analytically derived by studying the linearised system's instability to spatially dependent infinitesimal perturbations. Lastly, a numerical integration is performed to gain insight into the out of equilibrium behavior of the system in the nonlinear regime, thus determining the outcome of instability and the resulting patterns in the distribution of abundances.