There is increasing interest in the use of the percolation paradigm to analyse and predict the progress of disease spreading in spatially structured populations of animals and plants. The wider utility of the approach has been limited, however, by several restrictive assumptions, foremost of which is a strict requirement for simple nearest-neighbour transmission, in which the disease history of an individual is influenced only by that of its neighbours. In a recent paper, the percolation paradigm has been generalized to incorporate synergistic interactions in host infectivity and susceptibility, and the impact of these interactions on the invasive dynamics of an epidemic has been demonstrated. In the current paper, we elicit evidence that such synergistic interactions may underlie transmission dynamics in real-world systems by first formulating a model for the spread of a ubiquitous parasitic and saprotrophic fungus through replicated populations of nutrient sites and subsequently fitting and testing the model using data from experimental microcosms. Using Bayesian computational methods for model fitting, we demonstrate that synergistic interactions are necessary to explain the dynamics observed in the replicate experiments. The broader implications of this work in identifying disease-control strategies that deflect epidemics from invasive to non-invasive regimes are discussed.