  Inference of network-like evolutionary relationships between species from
genomic data must address the interwoven signals from both gene flow and
incomplete lineage sorting. The heavy computational demands of standard
approaches to this problem severely limit the size of datasets that may be
analyzed, in both the number of species and the number of genetic loci. Here we
provide a theoretical pointer to more efficient methods, by showing that logDet
distances computed from genomic-scale sequences retain sufficient information
to recover network relationships in the level-1 ultrametric case. This result
is obtained under the Network Multispecies Coalescent model combined with a
mixture of General Time-Reversible sequence evolution models across individual
gene trees, but does not depend on partitioning sequences by genes. Thus under
standard stochastic models statistically justifiable inference of network
relationships from sequences can be accomplished without consideration of
individual genes or gene trees.
