Abstract
Congruence is a broadly applied notion in evolutionary biology used to justify multigene phylogeny or phylogenomics, as well as in studies of coevolution, lateral gene transfer, and as evidence for common descent. Existing methods for identifying incongruence or heterogeneity using character data were designed for data sets that are both small and expected to be rarely incongruent. At the same time, methods that assess incongruence using comparison of trees test a null hypothesis of uncorrelated tree structures, which may be inappropriate for phylogenomic studies. As such, they are ill-suited for the growing number of available genome sequences, most of which are from prokaryotes and viruses, either for phylogenomic analysis or for studies of the evolutionary forces and events that have shaped these genomes. Specifically, many existing methods scale poorly with large numbers of genes, cannot accommodate high levels of incongruence, and do not adequately model patterns of missing taxa for different markers. We propose the development of novel incongruence assessment methods suitable for the analysis of the molecular evolution of the vast majority of life and support the investigation of homogeneity of evolutionary process in cases where markers do not share identical tree structures.