  We identify a mechanism for biological spatial pattern formation arising when
the signals that mediate interactions between individuals in a population have
pulsed character. Our general population-signal framework shows that while for
a slow signal-dynamics limit no pattern formation is observed for any values of
the model parameters, for a fast limit, on the contrary, pattern formation can
occur. Furthermore, at these limits, our framework reduces, respectively, to
reaction-diffusion and spatially nonlocal models, thus bridging these
approaches.
