Filamentous fungi are ubiquitous and ecologically important organisms with rich and varied life histories, however, there is no consensus on how to identify or measure their fitness. In the first part of this study we adapt a general epidemiological model to identify the appropriate fitness metric for a saprophytic filamentous fungus. We find that fungal fitness is inversely proportional to the equilibrium density of uncolonized fungal resource patches which, in turn, is a function of the expected spore production of a fungus. In the second part of this study we use a simple life history model of the same fungus within a resource patch to show that a bang-bang resource allocation strategy maximizes the expected spore production, a critical fitness component. Unlike bang-bang strategies identified in other life-history studies, we find that the optimal allocation strategy for saprophytes does not entail the use of all of the resources within a patch.