  Inference of species networks from genomic data under the Network
Multispecies Coalescent Model is currently severely limited by heavy
computational demands. It also remains unclear how complicated networks can be
for consistent inference to be possible. As a step toward inferring a general
species network, this work considers its tree of blobs, in which non-cut edges
are contracted to nodes, so only tree-like relationships between the taxa are
shown. An identifiability theorem, that most features of the unrooted tree of
blobs can be determined from the distribution of gene quartet topologies, is
established. This depends upon an analysis of gene quartet concordance factors
under the model, together with a new combinatorial inference rule. The
arguments for this theoretical result suggest a practical algorithm for tree of
blobs inference, to be fully developed in a subsequent work.
