Population redistribution and changes in the size-density slope.

As regional population density increases territorial units tend to subdivide. For maximum societal time-efficiency the slope relating the logarithms of unit areas to those of unit densities should be -2/3. When boundaries become fixed, however, observed slopes tend to drift toward a value of zero. It was earlier hypothesized that such slope-erosion was due to increasing concentration of the population. Historical data for the primary political divisions of ten nations shows general support for the hypothesis.