A Quantitative Analysis of Reign Lengths of Pre- and Post-Taifa Periods and Taifa Kingdom Durations During the Existence of Al Andalus

Author: Harper, Tony
Almanac: History & Mathematics:Investigating Past and Future

This paper will explore the disparity in the distribution of Umayyad Caliphate reign lengths with respect to the Nasrid Sultanate reign lengths. Further resolution is given to this disparity by showing that the same disparity exists between the Taifa 1 period and the Taifa 2 period. In response to the demonstration of this disparity, a hypothetical position is put forward according to which Malthusian limits on resources did not exist until at least the Taifa 2 period. Further, a preliminary computer model is constructed to show the potential for such a non-intuitive relationship between populations of entities and their upper (Malthusian) limits.

Keywords: Zipf-Pareto size-frequency distribution, self-organization, Malthusian limits, linear, non-linear.