  The reconstruction of a species tree from genomic data faces a double hurdle.
First, the (gene) tree describing the evolution of each gene may differ from
the species tree, for instance, due to incomplete lineage sorting. Second, the
aligned genetic sequences at the leaves of each gene tree provide merely an
imperfect estimate of the topology of the gene tree. In this note, we
demonstrate formally that a basic statistical problem arises if one tries to
avoid accounting for these two processes and analyses the genetic data directly
via a concatenation approach. More precisely, we show that, under the
multi-species coalescent with a standard site substitution model, maximum
likelihood estimation on sequence data that has been concatenated across genes
and performed under the incorrect assumption that all sites have evolved
independently and identically on a fixed tree is a statistically inconsistent
estimator of the species tree. Our results provide a formal justification of
simulation results described of Kubatko and Degnan (2007) and others, and
complements recent theoretical results by DeGorgio and Degnan (2010) and
Chifman and Kubtako (2014).
