Fungal mycelia have a well-established role in nutrient cycling and are widely used as agents in biological control and in the remediation of polluted landscapes. Competition and combat between different fungal communities is common in these contexts and its outcome impacts on local biodiversity and the success of such biotechnological applications. In this investigation a mathematical model representing mycelia as a system of partial differential equations is used to simulate combat between two fungal colonies growing into a nutrient-free domain. The resultant equations are integrated numerically and the model simulates well-established outcomes of combat between fungal communities. The outcome of pairwise combat is shown to depend on numerous factors including the suppression of advancing hyphae in rivals, the degradation of a rival's established biomass and the utilization and redistribution of available nutrient resources. It is demonstrated how non-transitive hierarchies in fungal communities can be established through switching mechanisms, mirroring observations reported in experimental studies, and how specialized defensive structures can emerge through changes in the redistribution of internal resources.