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We consider the reconstruction of a phylogeny from multiple genes under themultispecies coalescent. We establish a connection with the sparse signaldetection problem, where one seeks to distinguish between a distribution and amixture of the distribution and a sparse signal. Using this connection, wederive an information-theoretic trade-off between the number of genes, $m$,needed for an accurate reconstruction and the sequence length, $k$, of thegenes. Specifically, we show that to detect a branch of length $f$, one needs$m = \Theta(1/[f^{2} \sqrt{k}])$.

Distance-based species tree estimation: information-theoretic trade-off between number of loci and sequence length under the coalescent