Efficient algorithms for the reconciliation problem with gene duplication, horizontal transfer and loss

Motivation: Gene family evolution is driven by evolutionary events such as speciation, gene duplication, horizontal gene transfer and gene loss, and inferring these events in the evolutionary history of a given gene family is a fundamental problem in comparative and evolutionary genomics with numerous important applications. Solving this problem requires the use of a reconciliation framework, where the input consists of a gene family phylogeny and the corresponding species phylogeny, and the goal is to reconcile the two by postulating speciation, gene duplication, horizontal gene transfer and gene loss events. This reconciliation problem is referred to as duplication-transfer-loss (DTL) reconciliation and has been extensively studied in the literature. Yet, even the fastest existing algorithms for DTL reconciliation are too slow for reconciling large gene families and for use in more sophisticated applications such as gene tree or species tree reconstruction. Results: We present two new algorithms for the DTL reconciliation problem that are dramatically faster than existing algorithms, both asymptotically and in practice. We also extend the standard DTL reconciliation model by considering distance-dependent transfer costs, which allow for more accurate reconciliation and give an efficient algorithm for DTL reconciliation under this extended model. We implemented our new algorithms and demonstrated up to 100 000-fold speed-up over existing methods, using both simulated and biological datasets. This dramatic improvement makes it possible to use DTL reconciliation for performing rigorous evolutionary analyses of large gene families and enables its use in advanced reconciliation-based gene and species tree reconstruction methods.