Populations of filamentous fungus, such as Aspergillus nidulans, offer a powerful experimental system in which the evolution of drug resistance, and the emergence of mutations which compensate for drug resistance, have been well studied. Each spore in the inoculum which founds such a population produces a circular colony which grows radially at a constant rate. When a de novo beneficial mutation occurs, it produces a visible sector or wedge in the colony which grows at a faster rate. We have derived mathematical predictions for the shape of this mutant region, the expected mutant and wildtype spore counts over time, and ultimately the extinction probability for beneficial mutations. This work has been developed in tandem with experimental efforts; preliminary data will be presented.