There exist many methods to detect recombination or mosaic structure in a s
ample of DNA sequences. But how reliable are they? Four methods were invest
igated with respect to their power to detect recombination in simulated sam
ples with different amounts of recombination and mutation. In addition, we
investigated the impact of the shape of the underlying genealogy on their p
erformances. We found that the methods detected far fewer recombinations th
an were theoretically possible and that methods based on the principle of i
ncompatibility in general had more power than methods that did not make use
of this principle explicitly. This seemed, in particular, to be the case f
or phylogenies generated under population expansion scenarios which result
in long branches at the tips and small deep branches. In addition to the re
sults obtained through simulations, a series of new theoretical results on
recombination is presented.