We consider what effects could be produced by the long-term interaction of millennial macrotrends of the World System development and shorter-term cyclical dynamics. Among other things this will make it possible for us to demonstrate how even rather simple mathematical models of pre-industrial political-demographic cycles could help us to account for a paradox that has been encountered recently by political anthropologists.

Our research confirms that, notwithstanding recent arguments to the contrary, population density was a major determinant of warfare frequency in pre-industrial societies. However, the relationship between the two variables is dynamic, and could only be adequately described by nonlinear dynamic mod-els. Hence, we confront a rather paradoxical situation. On the one hand, we observe a millennial trend leading to the growth of both population density and warfare frequency. As a result, from a long-term perspective, we observe a very strong positive correlation between these two variables. But on the other hand, we also observe secular demographic-warfare cycles, which produce negative correlations both for individual cultures and for subsamples of cultures with similar levels of technological and/or political development. So finally, if we make a straightforward cross-cultural test of the linear rela-tionship between the two variables using a world-wide sample including cul-tures with all levels of technological and political development, we do not find any significant correlation at all. However it appears that hiding behind this "non-correlation" is the presence of an extremely strong and significant dy-namic non-linear relationship.