Self–organization and pattern formation represent the emergence of order in temporal and spatial processes. Self–organization in population ecology is gaining attention due to the recent advances concerning temporal fluctuations in the population size of dispersal–linked subunits. We shall report that spatially structured models of population renewal promote the emergence of a complex power law order in spatial population dynamics. We analyse a variety of population models showing that self–organization can be identified as a temporal match in population dynamics among local units, and how the synchrony changes in time. Our theoretical results are concordant with analyses of population data on the Canada lynx.