Impact of the landscape heterogeneity on the spatial organization of a single-species population

It is common to observe in nature the emergence of collective behavior in biological populations, such as pattern formation. In this work, we are interested in characterizing the distribution of a single-species population (such as some bacteria or vegetation), based on mathematical models that describe the spatio-temporal evolution of the density, governed by elementary processes, such as dispersion, growth, and nonlocal competition by resources. Using a generalization of the FKPP equation, we study the role that a heterogeneous environment has in the spatial organization of a population. We investigate the structures that emerge near the border from one environment to the other. We found that, depending on the shape of nonlocal interaction and other model parameters, three different profiles can emerge from the interface: sustained oscillations (or spatial patterns, without amplitude decay); attenuated oscillations (with amplitude decreasing from the interface); exponential decay (without oscillations) to a flat profile. We related the wavelength and the rate of decay of oscillations with the parameters of the interaction (characteristic length and form of decay with distance). We discussed how the heterogeneities of the environment allow access to information about the biological phenomena of the system, hidden in the homogeneous case, such as those that mediate competitive interactions.