A permutation approach for inferring species networks from gene trees in polyploid complexes by minimising deep coalescences

1. Context and purpose. Due to ubiquity of polyploid species formation in angiosperms, reconstructing the evolutionary history of polyploid complexes is at the forefront of methodological field of activity in molecular phylogenetics and systematic botany. The advent of multilocus species tree reconstruction approaches motivated by next-generation sequencing methods pave the way to species network inference methods, with which phylogenetics could accommodate to the necessity for reconstructing reticulate relationships among diploids and (allo-) polyploids in an objective manner, simultaneously taking into account gene tree incongruences caused by incomplete lineage sorting and hybridisation. 2. Methods used. The present contribution describes a relatively simple and fast workflow pipeline for the reconstruction of species networks in polyploid complexes based on multilocus gene trees. It uses a permutation strategy and a parsimony-based principle in species tree reconstruction (Minimising Deep Coalescences, MDC) for the assignment of homoeologs to parental genomes in allopolyploids, which is a crucial step in species network inference for polyploid complexes. Simulations with varying effective population sizes, different temporal scenarios for diploid or polyploid formations and different types of allopolyploid speciation (sister-species diploids, non-sister diploids or polyploidisation under participation of ancestral diploids) are used to assess the reliability of the reconstruction. 3. Main results. Simulations show that the proposed method leads to trustworthy reconstructions if effective populations sizes are not too large and divergences among ancestral taxa are not too shallow. The applicability of our method to a real data set is demonstrated by inferring the reticulate relationships among diploid, tetraploid and hexaploid representatives of the genus Leucanthemopsis (Compositae, Anthemideae) based on gene tree topologies from four nuclear single-copy genes and two plastidic intergenic spacer regions. 4. Conclusion. The proposed MDC-based method for species network reconstruction in polyploids is fast and manages to trustworthily reconstruct parentage in polyploidisation events. Concerns with and possible improvements of the described method are discussed