The kinds of population growth differentials that I have just discussed are of course distributed across space. Sustained for centuries they can produce settlement systems with various tiers of site sizes. Typically, following the assumptions of central place theory (cf. [Haggett 1965,Johnson 1972,Johnson 1977,McAndrews et al. 1997]), these site size hierarchies are taken to indicate various types of political organization ([Anderson 1994]). Thus, a two-tier hierarchy indicates a simple chiefdom, a three-tier hierarchy a complex chiefdom, and a four-tier hierarchy a state.
This kind of mechanical correspondence between settlement configuration and political organization cannot of course be assumed. However, the fact remains that site size hierarchies are often produced by the kinds of population growth differentials that I discussed above. And if large settlements are those which house the most successful leaders, as I proposed above, then a hierarchy of leaders could in fact correspond to a hierarchy of population growth rates and therefore to a hierarchy of site sizes. This scenario is overly precise, but something similar seems to have taken place on the Taraco Basin in the Late Formative period. At any rate, I have included site size hierarchies among the measures I use to monitor settlement dynamics over time, mainly because it has become standard practice to do so.
I have made one small modification to the presentation of site size hierarchies, however. The traditional way to represent these hierarchies is with a histogram, the x axis of which represents site size intervals, and the y axis of which represents a count of sites in each category. Instead, I have used the x axis to represent intervals of the population index, and the y axis to represent a sum of the population index value for all the sites in each size class (see Figures 5.4, 6.9, and 7.6 for examples). This has the salutary effect of correcting the common problem of being unable to discern the upper tiers of the site size hierarchy due to their low count, despite the fact that they often represent the majority of the regional population.