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.