  The log-det distance between two aligned DNA sequences was introduced as a
tool for statistically consistent inference of a gene tree under simple
non-mixture models of sequence evolution. Here we prove that the log-det
distance, coupled with a distance-based tree construction method, also permits
consistent inference of species trees under mixture models appropriate to
aligned genomic-scale sequences data. Data may include sites from many genetic
loci, which evolved on different gene trees due to incomplete lineage sorting
on an ultrametric species tree, with different time-reversible substitution
processes. The simplicity and speed of distance-based inference suggests
log-det based methods should serve as benchmarks for judging more elaborate and
computationally-intensive species trees inference methods.
