Garden loosestrife (Lysimachia vulgaris L.), is an invasive wetland plant that is subject to management in King County, WA, USA. Large-scale management efforts are generally conducted using herbicides. In this case study, we analyzed 17 yr of monitoring and treatment data in four riparian areas in King County to estimate the rate of spread of L. vulgaris and the efficacy of herbicidal treatments against L. vulgaris populations. In each area, herbicide treatments were applied annually. In three of the areas, the area infested with L. vulgaris did not change over time, while in the fourth area populations of L. vulgaris were spreading at a rate of 0.79 m2 yr−1. There were a greater number of sampled locations infested with L. vulgaris over the 17-yr period, and because populations were either not spreading or spreading slowly, it is possible that populations were becoming more fragmented. There was no relationship between the percentage of the infested area treated with herbicides and the area infested in the following year. However, there was a negative relationship between the area treated and the percent change in the invaded area; specifically, in years when <80% of the infested area was treated, there was an increase in the percent change of the invaded area between the year of treatment and the following year. The results of this study suggest that at the current level of management effort, the spatial extent of L. vulgaris did not retract over the 17-yr study period.

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.