Context: The reconstruction of evolutionary scenarios for whole genomes in terms of genome rearrangements is a fundamental problem in evolutionary and comparative genomics. The DeCo algorithm, recently introduced by Bérard et al., computes parsimonious evolutionary scenarios for gene adjacencies, from pairs of reconciled gene trees. However, as for many combinatorial optimization algorithms, there can exist many co-optimal, or slightly sub-optimal, evolutionary scenarios that deserve to be considered. Contribution:We extend the DeCo algorithm to sample evolutionary scenarios from the whole solution space under the Boltzmann distribution, and also to compute Boltzmann probabilities for specific ancestral adjacencies. Results: We apply our algorithms to a dataset of mammalian gene trees and adjacencies, and observe a significant reduction of the number of syntenic conflicts observed in the resulting ancestral gene adjacencies.