In this paper we distinguish between invasive and noninvasive (finite) saprotrophic spread of the soil-borne fungal plant pathogen, Rhizoctonia solani amongst discrete sites of nutrient resource. Using simple concepts of percolation theory, we predict the critical threshold distance, associated with a threshold probability, between donor (colonized) and recipient (uncolonized) nutrient sites at which R. solani can spread invasively by mycelial growth through a population of nutrient sites on a lattice. The critical distance for invasive spread is estimated from colonization profiles derived from placement experiments that summarize the probability of colonization with distance between replicated pairs of colonized and uncolonized sites. Colonization profiles were highly nonlinear, decaying sigmoidally with distance. Thresholds for invasive spread were predicted at inter-site distances of 8.1 mm and 11.8 mm for sites of low and high nutrient agar, respectively. In population experiments with inter-site distances below the predicted thresholds, the spread of the fungus was invasive in all replicates. At large distances (>10 mm for low, and >14 mm for high nutrient sites) the spread of the fungus was always finite, with the proportion of finite replicates decreasing sharply close to the percolation threshold. Invasive spread did not depend on the furthest extent of growth of the fungus but on distances predicted by the percolation thresholds. Invasive spread of the fungus is also examined in a more natural and variable, nonsterile system involving the growth and colonization of a lattice of poppy seeds over sand. The system is characterized by a decay in the probability of colonization between older poppy seeds, which effectively ‘quenches’ saprotrophic spread. Hence in the population experiments with poppy seeds all growth was ultimately finite. The threshold distance, corresponding to the critical percolation probability for invasive growth changed from 18 mm to 4 mm over 21d leading to a switch from invasive to finite growth. We conclude that percolation theory can be used to link the growth of individual mycelial colonies to the formation of patches that result from the colonization of particulate organic matter. The nonlinearity of the colonization profiles combined with the presence of a percolation threshold means that small changes in the distance between nutrient sites can result in large differences in final patch size. The rapid decay of particulate organic matter in a more natural system can have a profound effect on the dynamics of colonization, restricting saprotrophic invasion of the soil. The consequences of invasion thresholds for colony growth of saprotrophic and parasitic fungi in dynamical systems are briefly discussed.