imPhy: Imputing Phylogenetic Trees with Missing Information using Mathematical Programming.

Given a set of organisms, the available corresponding genetic information is often incomplete and most gene trees fail to contain all individuals. This incompleteness causes difficulties in data collection, information extraction, and gene tree inference. Outlying gene trees may represent horizontal gene transfers, gene duplications, hybridizations, but they are difficult to detect in the presence of missing data. One typical approach is to discard all individuals with missing data and focus the analysis on individuals whose information is fully available. However, this can result in a huge loss of information, especially under certain patterns of missing data. Here, we propose and design an optimization-based imputation approach to infer the missing pairwise distances between some of all possible pair of leaves in a gene tree via a mixed integer non-linear programming model. We present a new research pipeline, called imPhy, that can (i) simulate phylogenetic data with missing leaves/individuals in some gene trees, (ii) impute the pairwise distances from each missing leaf to every other leaf in all gene trees, (iii) reconstruct the gene trees using the Neighbor Joining (NJ) and Unweighted Pair Group Method with Arithmetic Mean (UPGMA) methods, and (iv) analyze and report the efficiency of the reconstruction.