Given a gene and a species tree, reconciliation methods attempt to retrieve the macro-evolutionary events that best explain the discrepancies between the two tree topologies. The DTL parsimonious approach searches for a most parsimonious reconciliation between a gene tree and a (dated) species tree, considering four possible macro-evolutionary events (speciation, duplication, transfer, and loss) with specific costs. Unfortunately, many events are erroneously predicted due to errors in the input trees, inappropriate input cost values or because of the existence of several equally parsimonious scenarios. It is thus crucial to provide a measure of the reliability for predicted events. It has been recently proposed that the reliability of an event can be estimated via its frequency in the set of most parsimonious reconciliations obtained using a variety of reasonable input cost vectors. To compute such a support, a straightforward but time-consuming approach is to generate the costs slightly departing from the original ones, independently compute the set of all most parsimonious reconciliations for each vector, and combine these sets a posteriori. Another proposed approach uses Pareto-optimality to partition cost values into regions which induce reconciliations with the same number of DTL events. The support of an event is then defined as its frequency in the set of regions. However, often, the number of regions is not large enough to provide reliable supports. We present here a method to compute efficiently event supports via a polynomial-sized graph, which can represent all reconciliations for several different costs. Moreover, two methods are proposed to take into account alternative input costs: either explicitly providing an input cost range or allowing a tolerance for the over cost of a reconciliation. Our methods are faster than the region based method, substantially faster than the sampling-costs approach, and have a higher event-prediction accuracy on simulated data. We propose a new approach to improve the accuracy of event supports for parsimonious reconciliation methods to account for uncertainty in the input costs. Furthermore, because of their speed, our methods can be used on large gene families. Our algorithms are implemented in the ecceTERA program, freely available from http://mbb.univ-montp2.fr/MBB/ .
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