  Motivation: The abundance of gene flow in the Tree of Life challenges the
notion that evolution can be represented with a fully bifurcating process, as
this process cannot capture important biological realities like hybridization,
introgression, or horizontal gene transfer. Coalescent-based network methods
are increasingly popular, yet not scalable for big data, because they need to
perform a heuristic search in the space of networks as well as numerical
optimization that can be NP-hard.
  Results: Here, we introduce a novel method to reconstruct phylogenetic
networks based on algebraic invariants. While there is a long tradition of
using algebraic invariants in phylogenetics, our work is the first to define
phylogenetic invariants on concordance factors (frequencies of 4-taxon splits
in the input gene trees) to identify level-1 phylogenetic networks under the
multispecies coalescent model. Our novel inference methodology is
optimization-free as it only requires the evaluation of polynomial equations,
and as such, it bypasses the traversal of network space, yielding a
computational speed at least 10 times faster than the fastest-to-date network
methods. We illustrate the accuracy and speed of our new method on a variety of
simulated scenarios as well as in the estimation of a phylogenetic network for
the genus Canis.
  Availability and Implementation: We implement our novel theory on an
open-source publicly available Julia package PhyloDiamond.jl available at
https://github.com/solislemuslab/PhyloDiamond.jl with broad applicability
within the evolutionary biology community.
  Contact<EMAIL_ADDRESS>