  We analyse a maximum-likelihood approach for combining phylogenetic trees
into a larger `supertree'. This is based on a simple exponential model of
phylogenetic error, which ensures that ML supertrees have a simple
combinatorial description (as a median tree, minimising a weighted sum of
distances to the input trees). We show that this approach to ML supertree
reconstruction is statistically consistent (it converges on the true species
supertree as more input trees are combined), in contrast to the widely-used MRP
method, which we show can be statistically inconsistent under the exponential
error model. We also show that this statistical consistency extends to an ML
approach for constructing species supertrees from gene trees. In this setting,
incomplete lineage sorting (due to coalescence rates of homologous genes being
lower than speciation rates) has been shown to lead to gene trees that are
frequently different from species trees, and this can confound efforts to
reconstruct the species phylogeny correctly.
