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We introduce a simple model of population dynamics which considers birth anddeath rates for every individual that depend on the number of particles in itsneighborhood. The model shows an inhomogeneous quasistationary pattern withmany different clusters of particles.  We derive the equation for the macroscopic density of particles, perform alinear stability analysis on it, and show that there is a finite-wavelengthinstability leading to pattern formation. This is the responsible for theapproximate periodicity with which the clusters of particles arrange in themicroscopic model.  In addition, we consider the population when immersed in a fluid medium andanalyze the influence of advection on global properties of the model.Comment: Some typos and some problems with the figures correcte

Clustering, advection, and patterns in a model of population dynamics with neighborhood-dependent rates