  Background.
  Models of ancestral gene order reconstruction have progressively integrated
different evolutionary patterns and processes such as unequal gene content,
gene duplications, and implicitly sequence evolution via reconciled gene trees.
In unicellular organisms, these models have so far ignored lateral gene
transfer, even though it can have an important confounding effect on such
models, as well as a rich source of information on the function of genes
through the detection of transfers of entire clusters of genes.
  Result.
  We report an algorithm together with its implementation, DeCoLT, that
reconstructs ancestral genome organization based on reconciled gene trees which
summarize information on sequence evolution, gene origination, duplication,
loss, and lateral transfer. DeCoLT finds in polynomial time the minimum number
of rearrangements, computed as the number of gains and breakages of adjacencies
between pairs of genes. We apply DeCoLT to 1099 gene families from 36
cyanobacteria genomes.
  Conclusion.
  DeCoLT is able to reconstruct adjacencies in 35 ancestral bacterial genomes
with a thousand genes families in a few hours, and detects clusters of
co-transferred genes. As there is no constraint on genome organization,
adjacencies can be generalized to any relationship between genes to reconstruct
ancestral interactions, functions or complexes with the same framework.
