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, and governed by elementary processes, such as: dispersion, growth, and nonlocal competition by resources. First, using a generalization of the FKPP equation, we analyze numerically and analytically the impact of density-dependent regulatory mechanisms, both on diffusion and growth. Such mechanisms represent processes of internal feedback, which shape the system s response to population overcrowding or rarefaction. We show that, depending on the type of the response in action, some individuals can organize themselves in disconnected sub-populations (fragmentation), even in the absence of external restrictions, that is in a homogeneous landscape. We discuss the crucial role that density-dependence has in the form of patterns, particularly in fragmentation, which can have important consequences for contact processes, such as the spread of epidemics. After understanding this phenomenon in a homogeneous environment, we study the role that a heterogeneous environment has in the spatial organization of a population, which was presented as a growth rate that varies with position. 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: (i) sustained oscillations (or spatial patterns, without amplitude decay); (ii) attenuated oscillations (with amplitude decreasing from the interface); (iii) exponential decay (without oscillations) to a homogeneous 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 (hidden in the homogeneous case) about the biological phenomena of the system, such as those that mediate competitive interactions.