Gene tree discord, simplex plots, and statistical tests under the coalescent

A bstract A simple graphical device, the simplex plot of quartet concordance factors, is introduced to aid in the exploration of a collection of gene trees on a common set of taxa. A single plot summarizes all gene tree discord, and allows for visual comparison to the expected discord from the multispecies coalescent model (MSC) of incomplete lineage sorting on a species tree. A formal statistical procedure is described that can quantify the deviation from expectation for each subset of four taxa, suggesting when the data is not in accord with the MSC, and thus either gene tree inference error is substantial or a more complex model such as that on a network may be required. If the collection of gene trees appears to be in accord with the MSC, the plots may reveal when substantial incomplete lineage sorting is present and coalescent based species tree inference is preferred over concatenation approaches. Applications to both simulated and empirical multilocus data sets illustrate the insights provided.