Gene-history correlation and population structure

Correlation of gene histories in the human genome determines the patterns of genetic variation ( haplotype structure) and is crucial to understanding genetic factors in common diseases. We derive closed analytical expressions for the correlation of gene histories in established demographic models for genetic evolution and show how to extend the analysis to more realistic ( but more complicated) models of demographic structure. We identify two contributions to the correlation of gene histories in divergent populations: linkage disequilibrium, and differences in the demographic history of individuals in the sample. These two factors contribute to correlations at different length scales: the former at small, and the latter at large scales. We show that recent mixing events in divergent populations limit the range of correlations and compare our findings to empirical results on the correlation of gene histories in the human genome.