Reticulate evolution, whether due to lateral gene transfer, introgression, incomplete lineage sorting, or hybrid speciation, is a ubiquitous phenomenon, yet systematists have few tools for analyzing and summarizing the resulting genealogical discordance. Here I argue that a primary concordance tree, a tree built from clades that are true of a plurality of the genome, provides a useful summary of the dominant phylogenetic history for a group of organisms. Residual historical signals can also be extracted in the form of secondary, tertiary, etc. concordance trees, which are built from clades that are present in the genome but contradict clades on the primary concordance tree. Clades on concordance trees can be annotated with their concordance factor (CF), the proportion of the genome for which the clade is true. Concordance trees can potentially be estimated either from population histories or from multilocus molecular datasets. In the latter case one can use the recently developed Bayesian concordance analysis to obtain point estimates and credibility intervals on CF's. I argue that the concepts of concordance trees and concordance factors inform the debate on how to integrate information from multiple independent datasets and help clarify the nature of the boundary between reticulate and divergent genealogy.
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