Molecular typing methods are commonly used to study genetic relationships among bacterial isolates. Many of these methods have become standardized and produce portable data. A popular approach for analyzing such data is to construct graphs, including phylogenies. Inferences from graph representations of data assist in understanding the patterns of transmission of bacterial pathogens, and basing these graph constructs on biological models of evolution of the molecular marker helps make these inferences. Spoligotyping is a widely used method for genotyping isolates of Mycobacterium tuberculosis that exploits polymorphism in the direct repeat region. Our goal was to examine a range of models describing the evolution of spoligotypes in order to develop a visualization method to represent likely relationships among M. tuberculosis isolates.