It is now well-established that intrinsic fluctuations in human behavior tend to exhibit long-range correlations in the form of 1/f scaling. Their meaning is an ongoing matter of debate, and some researchers argue they reflect the tendency for neural and bodily systems to poise themselves near critical states. A spiking neural network model is presented that self-tunes to a critical point in terms of its spike branching ratio (i.e. critical branching). The model is shown to exhibit 1/f scaling near critical branching, as well neural avalanches, and critical branching is associated with maximal computational capacity when assessed in terms of reservoir computing. The model provides a basis for connecting neural and behavioral activity and function via criticality.