Integer Linear Programming Formulation for the Unified Duplication-Loss-Coalescence Model

Abstract

The classical Duplication-Loss-Coalescence parsimony model (DLC-model) is a powerful tool when studying the complex evolutionary scenarios of simultaneous duplication-loss and deep coalescence events in evolutionary histories of gene families. However, inferring such scenarios is an intrinsically difficult problem and, therefore, prohibitive for larger gene families typically occurring in practice. To overcome this stringent limitation, we make the first step by describing a non-trivial and flexible Integer Linear Programming (ILP) formulation for inferring DLC evolutionary scenarios. To make the DLC-model more practical, we then introduce two sensibly constrained versions of the model and describe two respectively modified versions of our ILP formulation reflecting these constraints. Using a simulation study, we showcase that our constrained ILP formulation computes evolutionary scenarios that are substantially larger than the scenarios computable under our original ILP formulation and DLCPar. Further, scenarios computed under our constrained DLC-model are overall remarkably accurate when compared to corresponding scenarios under the original DLC-model.