Genome-wide gene insertion and deletion rates can be modelled in a maximum likelihood framework with the additional flexibility of modelling potential missing data using the models included within. These models simultaneously estimate insertion and deletion (indel) rates of gene families and proportions of "missing" data for (multiple) taxa of interest. The likelihood framework is utilized for parameter estimation. A phylogenetic tree of the taxa and gene presence/absence patterns (with data ordered by the tips of the tree) are required. See Dang et al. (2016) <doi:10.1534/genetics.116.191973> for more details.
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