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Various methodological approaches using molecular sequence data have been developed and applied across several fields, including phylogeography, conservation biology, virology and human evolution. The aim of these approaches is to obtain predictive estimates of population history from DNA sequence data that can then be used for hypothesis testing with empirical data. This recent work provides opportunities to evaluate hypotheses of constant population size through time, of population growth or decline, of the rate of growth or decline, and of migration and growth in subdivided populations. At the core of many of these approaches is the extraction of information from the structure of phylogenetic trees to infer the demographic history of a population, and underlying nearly all methods is coalescent theory. With the increasing availability of DNA sequence data, it is important to review the different ways in …