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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 fromthe species tree, for instance, due to incomplete lineage sorting. Second, thealigned genetic sequences at the leaves of each gene tree provide merely animperfect estimate of the topology of the gene tree. In this note, wedemonstrate formally that a basic statistical problem arises if one tries toavoid accounting for these two processes and analyses the genetic data directlyvia a concatenation approach. More precisely, we show that, under themulti-species coalescent with a standard site substitution model, maximumlikelihood estimation on sequence data that has been concatenated across genesand performed under the incorrect assumption that all sites have evolvedindependently and identically on a fixed tree is a statistically inconsistentestimator of the species tree. Our results provide a formal justification ofsimulation results described of Kubatko and Degnan (2007) and others, andcomplements recent theoretical results by DeGorgio and Degnan (2010) andChifman and Kubtako (2014).

Likelihood-based tree reconstruction on a concatenation of alignments can be positively misleading