They developed a mathematical model that attributed patterns of speciation to the way that closely related species divide up their environment. According to this model, when there are few relatives around to compete for resources, such as when an environment is first colonized, species differentiate rapidly.
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This model is robust: even when the authors assumed that their phylogenetic tree contains only 25 percent of all Dendroica species, they found that their γ test was still valid, indicating that this genus experienced an explosive bout of adaptive radiation before settling down to a “more normal” rate of speciation.

This mathematical model provides an incisive tool to gain a clearer understanding of the pattern and rate of speciation for groups of closely related species, even in the absence of a fossil record, simply by analyzing their DNA.