Summary: Split-networks are a generalization of phylogenetic trees that have proven to be a powerful tool in phylogenetics. Various ways have been developed for computing such networks, including split-decomposition, NeighborNet, QNet and FlatNJ. Some of these approaches are implemented in the user-friendly SplitsTree software package. However, to give the user the option to adjust and extend these approaches and to facilitate their integration into analysis pipelines, there is a need for robust, open-source implementations of associated data structures and algorithms. Here, we present SPECTRE, a readily available, open-source library of data structures written in Java, that comes complete with new implementations of several pre-published algorithms and a basic interactive graphical interface for visualizing planar split networks. SPECTRE also supports the use of longer running algorithms by providing command line interfaces, which can be executed on servers or in High Performance Computing environments. Availability and implementation: Full source code is available under the GPLv3 license at: https://github.com/maplesond/SPECTRE. SPECTRE's core library is available from Maven Central at: https://mvnrepository.com/artifact/uk.ac.uea.cmp.spectre/core. Documentation is available at: http://spectre-suite-of-phylogenetic-tools-for-reticulate-evolution.readthedocs.io/en/latest/. Contact: [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

Split networks are a popular tool for the analysis and visualization of complex evolutionary histories. Every collection of splits (bipartitions) of a finite set can be represented by a split network. Here we characterize which collection of splits can be represented using a planar split network. Our main theorem links these collections of splits with oriented matroids and arrangements of lines separating points in the plane. As a consequence of our main theorem, we establish a particularly simple characterization of maximal collections of these splits.