Most of the evolutionary history reconstruction approaches are based on the infinite site assumption, which is underlying the Perfect Phylogeny model and whose main consequence is that acquired mutation can never lost. This results in the clonal model used to explain cancer evolution. Some recent results gives a strong evidence that recurrent and back mutations are present in the evolutionary history of tumors, thus showing that more general models then the Perfect Phylogeny are required. We

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... pose a new approach that incorporates the possibility of losing a previously acquired mutation, extending the Persistent Phylogeny model. We exploit our model to provide an ILP formulation of the problem of reconstructing trees on mixed populations, where the input data consists of the fraction of cells in a set of samples that have a certain mutation. This is a fundamental problem in cancer genomics, where the goal is to study the evolutionary history of a tumor. An experimental analysis shows the usefulness of allowing mutation losses, by studying some real and simulated datasets where our ILP approach provides a better interpretation than the one obtained under perfect phylogeny assumption. Finally, we show how to incorporate multiple back mutations and recurrent mutations in our model.