Phylogenetic trees have often been a successful model for species evolution, but they fail to account for hybridization. A more general model is phylogenetic networks, which accommodate hybridization by permitting multiple parental species. Phylogenetic networks have been implemented in many methods which infer the predominant types of hybridization events in animals; introgression and homoploid hybrid speciation. After such events, meiotic recombination enables selection and drift to fragment and filter genes from both parental species with each generation. In plants however, a different mode of hybridization is common which results in whole genome duplication. This is known as allopolyploid hybrid speciation, where the genome of each parental species is inherited with full ploidy as a “subgenome.” In contrast to introgression and homoploid hybrid speciation, the fragmentation and filtering of subgenomes requires much longer timescales, as meiotic recombination does not occur between them. We previously developed a scalable and accurate method to infer allopolyploid hybrid speciation called “MPAllopp,” however its original implementation in “PhyloNet” assumed complete sampling of species and the absence of extinction. It also did not accommodate autopolyploidy, where multiple subgenomes originate from the same parental species. We have reimplemented MPAllopp in a new, flexible, and friendly framework for phylogenetics called “PhyNetPy,” and added support for parallel edges to accommodate incomplete sampling, extinction and autopolyploidy. We will demonstrate the importance of accounting for those phenomena, and the correct interpretation of phylogenies in their presence.