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An explanation for the political processes leading to the sudden collapse of empires and states would be useful for understanding both historical and contemporary political events. We examine political disintegration across eras, cultures and geographical scale to form a simple hypothesis that can be expressed verbally yet formulated mathematically. Factions within a state make choices described by game-theory about whether to accept the political status quo, or to attempt to better their circumstances through costly rebellion. In lieu of precise data we verify our model using sensitivity analysis. We find that a small amount of dissatisfaction is typically harmless to the state, but can trigger sudden collapse when there is a sufficient buildup of political inequality. Contrary to intuition, a state is predicted to be least stable when its leadership is at the height of its political power and thus most able to exert its influence through external warfare, lavish expense or autocratic decree. [ABSTRACT FROM AUTHOR]

The advent of genome-wide dense variation data provides an opportunity to investigate ancestry in unprecedented detail, but presents new statistical challenges. We propose a novel inference framework that aims to efficiently capture information on population structure provided by patterns of haplotype similarity. Each individual in a sample is considered in turn as a recipient, whose chromosomes are reconstructed using chunks of DNA donated by the other individuals. Results of this "chromosome painting" can be summarized as a "coancestry matrix," which directly reveals key information about ancestral relationships among individuals. If markers are viewed as independent, we show that this matrix almost completely captures the information used by both standard Principal Components Analysis (PCA) and model-based approaches such as STRUCTURE in a unified manner. Furthermore, when markers are in linkage disequilibrium, the matrix combines information across successive markers to increase the ability to discern fine-scale population structure using PCA. In parallel, we have developed an efficient model-based approach to identify discrete populations using this matrix, which offers advantages over PCA in terms of interpretability and over existing clustering algorithms in terms of speed, number of separable populations, and sensitivity to subtle population structure. We analyse Human Genome Diversity Panel data for 938 individuals and 641,000 markers, and we identify 226 populations reflecting differences on continental, regional, local, and family scales. We present multiple lines of evidence that, while many methods capture similar information among strongly differentiated groups, more subtle population structure in human populations is consistently present at a much finer level than currently available geographic labels and is only captured by the haplotype-based approach. The software used for this article, ChromoPainter and fineSTRUCTURE, is available from http://www.paintmychromosomes.com/. [ABSTRACT FROM AUTHOR]