It is now well-established that intrinsic variations in human neural and behavioral activity tend to exhibit scaling laws in their fluctuations and distributions. The meaning of these scaling laws is an ongoing matter of debate between isolable causes versus pervasive causes. A spiking neural network model is presented that self-tunes to critical branching and, in doing so, simulates observed scaling laws as pervasive to neural and behavioral activity. These scaling laws are related to neural and cognitive functions, in that critical branching is shown to yield spiking activity with maximal memory and encoding capacities when analyzed using reservoir computing techniques. The model is also shown to account for findings of pervasive 1/f scaling in speech and cued response behaviors that are difficult to explain by isolable causes. Issues and questions raised by the model and its results are discussed from the perspectives of physics, neuroscience, computer and information sciences, and psychological and cognitive sciences. (Contains 16 figures and 1 table.)