Title: Coalescent-based species tree estimation: a stochastic Farris transform,
Abstract: The reconstruction of a species phylogeny from genomic data faces two
significant hurdles: 1) the trees describing the evolution of each individual
gene--i.e., the gene trees--may differ from the species phylogeny and 2) the
molecular sequences corresponding to each gene often provide limited
information about the gene trees themselves. In this paper we consider an
approach to species tree reconstruction that addresses both these hurdles.
Specifically, we propose an algorithm for phylogeny reconstruction under the
multispecies coalescent model with a standard model of site substitution. The
multispecies coalescent is commonly used to model gene tree discordance due to
incomplete lineage sorting, a well-studied population-genetic effect.
In previous work, an information-theoretic trade-off was derived in this
context between the number of loci, $m$, needed for an accurate reconstruction
and the length of the locus sequences, $k$. It was shown that to reconstruct an
internal 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 clock
assumption, i.e., under the assumption that mutation rates (as well as
population sizes) are constant across the species phylogeny.
Here we generalize this result beyond the restrictive molecular clock
assumption, and obtain a new reconstruction algorithm that has the same data
requirement (up to log factors). Our main contribution is a novel reduction to
the molecular clock case under the multispecies coalescent. As a corollary, we
also obtain a new identifiability result of independent interest: for any
species tree with $n \geq 3$ species, the rooted species tree can be identified
from the distribution of its unrooted weighted gene trees even in the absence
of a molecular clock.