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The reconstruction of a species phylogeny from genomic data faces twosignificant hurdles: 1) the trees describing the evolution of each individualgene--i.e., the gene trees--may differ from the species phylogeny and 2) themolecular sequences corresponding to each gene often provide limitedinformation about the gene trees themselves. In this paper we consider anapproach to species tree reconstruction that addresses both these hurdles.Specifically, we propose an algorithm for phylogeny reconstruction under themultispecies coalescent model with a standard model of site substitution. Themultispecies coalescent is commonly used to model gene tree discordance due toincomplete lineage sorting, a well-studied population-genetic effect.  In previous work, an information-theoretic trade-off was derived in thiscontext between the number of loci, $m$, needed for an accurate reconstructionand the length of the locus sequences, $k$. It was shown that to reconstruct aninternal branch of length $f$, one needs $m$ to be of the order of $1/[f^{2}\sqrt{k}]$. That previous result was obtained under the molecular clockassumption, i.e., under the assumption that mutation rates (as well aspopulation sizes) are constant across the species phylogeny.  Here we generalize this result beyond the restrictive molecular clockassumption, and obtain a new reconstruction algorithm that has the same datarequirement (up to log factors). Our main contribution is a novel reduction tothe molecular clock case under the multispecies coalescent. As a corollary, wealso obtain a new identifiability result of independent interest: for anyspecies tree with $n \geq 3$ species, the rooted species tree can be identifiedfrom the distribution of its unrooted weighted gene trees even in the absenceof a molecular clock.

Coalescent-based species tree estimation: a stochastic Farris transform