In reality, time to coalescence is affected by much more than simply Ne. A range of factors including fluctuating population sizes, natural selection and immigration tend to make coalescence an extremely convoluted process. As a result, statistical and mathematical models based on coalescent theory must be wide-ranging and able to accommodate numerous demographic, evolutionary and ecological parameters. Various mathematical models have used the coalescent successfully to analyse a number of different aspects of population genetics and molecular evolution, such as effective population sizes, past bottlenecks, selection processes, divergence times among populations, migration rates and mutation rates; note that coalescent theory has applications to traditional population genetics as well as to phylogeographic analysis e.g. (Coop and Griffiths, 2004; Wilkinson-Herbots and Ettridge, 2004; Degnan and Salter, 2005).
In one study, a coalescent-based approach was used to investigate why populations of the montane grasshopper Melanoplus oregonensis in the northern Rocky Mountains are genetically differentiated from one another. By using the coalescent to identify ancestral populations it became apparent that much of the genetic divergence dated back to the last Ice Age when populations were restricted to isolated geographical areas (Knowles, 2001). This finding has leant support to the idea that Pleistocene glaciations promoted speciation when ice sheets covered vast areas and populations became separated from one another for prolonged periods by inhospitable terrain. Another study used both traditional population genetics and coalescent theory to compare the distribution of mitochondrial haplotypes among yellow warbler (Dendroica petechia) populations across North America. In this species, eastern and western populations are genetically distinct from one another. A coalescent-based evolutionary model suggested that all western haplo-types are descended from an eastern lineage, and it therefore seems likely that western yellow warbler populations were established following infrequent colonizations from the east (Milot, Gibbs and Hobson, 2000).
The previous examples were based on the application of specific coalescent-based models to phylogeographic data, but the coalescent is also relevant to some recently developed general methods of phylogenetic reconstruction. Unlike the traditional bifurcating trees, these methods allow us to depict evolutionary relationships in the form of multifurcating trees in which a single haplotype can give rise to many haplotypes, thereby creating what is more commonly known as a network.
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