  We investigate distances on binary (presence/absence) data in the context of
a Dollo process, where a trait can only arise once on a phylogenetic tree but
may be lost many times. We introduce a novel distance, the Additive Dollo
Distance (ADD), which is consistent for data generated under a Dollo model, and
show that it has some useful theoretical properties including an intriguing
link to the LogDet distance. Simulations of Dollo data are used to compare a
number of binary distances including ADD, LogDet, Nei Li and some simple, but
to our knowledge previously unstudied, variations on common binary distances.
The simulations suggest that ADD outperforms other distances on Dollo data.
Interestingly, we found that the LogDet distance performs poorly in the context
of a Dollo process, which may have implications for its use in connection with
conditioned genome reconstruction. We apply the ADD to two Diversity Arrays
Technology (DArT) datasets, one that broadly covers Eucalyptus species and one
that focuses on the Eucalyptus series Adnataria. We also reanalyse gene family
presence/absence data on bacteria from the COG database and compare the results
to previous phylogenies estimated using the conditioned genome reconstruction
approach.
