Supplemental data from: Inference of phylogenetic networks from sequence data using composite likelihood

While phylogenies have been essential in understanding how species evolve,
they do not adequately describe some evolutionary processes. For instance,
hybridization, a common phenomenon where interbreeding between two species
leads to the formation of a new species, must be depicted by a
phylogenetic network, a structure that modifies a phylogenetic tree by
allowing two branches to merge into one, resulting in reticulation.
However, existing methods for estimating networks become computationally
expensive as the dataset size and/or topological complexity increase. The
lack of methods for scalable inference hampers phylogenetic networks from
being widely used in practice, despite accumulating evidence that
hybridization occurs frequently in nature. Here, we propose a novel
method, PhyNEST (Phylogenetic Network Estimation using SiTe patterns),
that estimates binary, level-1 phylogenetic networks with a fixed,
user-specified number of reticulations directly from sequence data. By
using the composite likelihood as the basis for inference, PhyNEST is able
to use the full genomic data in a computationally tractable manner,
eliminating the need to summarize the data as a set of gene trees prior to
network estimation. To search network space, PhyNEST implements both hill
climbing and simulated annealing algorithms. PhyNEST assumes that the data
are composed of coalescent independent sites that evolve according to the
Jukes-Cantor substitution model and that the network has a constant
effective population size. Simulation studies demonstrate that PhyNEST is
often more accurate than two existing composite likelihood summary methods
(SNaQ and PhyloNet) and that it is robust to at least one form of model
misspecification (assuming a less complex nucleotide substitution model
than the true generating model). We applied PhyNEST to reconstruct the
evolutionary relationships among Heliconius butterflies and
Papionini primates, characterized by hybrid speciation and widespread
introgression, respectively. PhyNEST is implemented in an open-source
Julia package and is publicly available at
https://github.com/sungsik-kong/PhyNEST.jl.