Topological representation of the within-species evolutionary structure of bacterial populations: the SLV graph

The representation of relationships between haplotypes in a population is performed normally through the use of trees. Frequently, the selection of a single tree implies the application of maximum parsimony principles, being prone to interpretation errors. The adoption of a graph structure, rather than a tree-like structure, avoids making simplifying assumptions leaving open the number of possible interpretations. In particular, it allows for the representation of homoplasies which can represent recombination events, frequently ignored by existing methods. Here, we propose a graph structure, denominated SLV (Single Locus Variant) graph, as an alternative to the BURST family of algorithms. This structure, connects individuals if and only if they share a single allelic difference in their MLST profile. We further explore the topological properties of such structure and propose biological interpretations for each property.