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Gene trees are evolutionary trees representing the ancestry of genes sampledfrom multiple populations. Species trees represent populations of individuals-- each with many genes -- splitting into new populations or species. Thecoalescent process, which models ancestry of gene copies within populations, isoften used to model the probability distribution of gene trees given a fixedspecies tree. This multispecies coalescent model provides a framework forphylogeneticists to infer species trees from gene trees using maximumlikelihood or Bayesian approaches. Because the coalescent models a branchingprocess over time, all trees are typically assumed to be rooted in thissetting. Often, however, gene trees inferred by traditional phylogeneticmethods are unrooted.  We investigate probabilities of unrooted gene trees under the multispeciescoalescent model. We show that when there are 4 species with one gene sampledper species, the distribution of unrooted gene tree topologies identifies theunrooted species tree topology and some, but not all, information in thespecies tree edges (branch lengths). The location of the root on the speciestree is not identifiable in this situation. However, for 5 or more species withone gene sampled per species, we show that the distribution of unrooted genetree topologies identifies the rooted species tree topology and all itsinternal branch lengths. The length of any pendent branch leading to a leaf ofthe species tree is also identifiable for any species from which more than onegene is sampled.

Identifying the Rooted Species Tree from the Distribution of Unrooted Gene Trees under the Coalescent