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Propagation systems for seedling growth play a major role in agriculture, and in notable cases (such as organic systems), are under constant threat from soil and seedborne fungal plant pathogens such as Rhizoctonia solani or Pythium spp. Yet, to date little is known that links the risk of disease invasion to the host density, which is an agronomic characteristic that can be readily controlled. We introduce here, for the first time in an agronomic system, a percolation framework to analyze the link. We set up an experiment to study the spread of the ubiquitous fungus R. solani in replicated propagation systems with different planting densities, and fit a percolation-based epidemiological model to the data using Bayesian inference methods. The estimated probability of pathogen transmission between infected and susceptible plants is used to calculate the risk of invasion. By comparing the transmission probability and the risk values obtained for different planting densities, we are able to give evidence of a nonlinear relationship between disease invasion and the inter-plant spacing, hence to demonstrate the existence of a spatial threshold for epidemic invasion. The implications and potential use of our methods for the evaluation of disease control strategies are discussed.