Unrooted phylogenetic networks are often used to represent evolutionary data when incompatibilities are present. Although rooted phylogenetic networks are better suited for explicitly depicting evolutionary histories that involve reticulate events, they have been rarely used in practice, due to a lack of appropriate methods for their calculation. Here we introduce PhyloFusion, a new fast and easily-applicable method for calculating rooted phylogenetic networks on sets of rooted phylogenetic trees. The algorithm can handle tens of trees on hundreds of taxa, allowing unresolved nodes (which arise when edges with low support are contracted) and missing taxa. We demonstrate how the method can be used to explore the phylogenetic relationships between different Influenza A isolates, based on gene trees built on different genome segments.