The effect of spatial distribution of mycoparasites on biocontrol efficacy: a modelling approach

The spatial distribution of propagules in soil is an important factor in determining the ability of mycoparasites to control soilborne plant pathogens. The assumptions of uniform, random and aggregated propagule distribution were used to evaluate the importance of spatial distribution patterns of propagules of a mycoparasite. For the random and uniform cases explicit expressions were obtained for the average distance between propagules. Average distances among propagules are 40-50% smaller for the random compared to the uniform distribution. For the aggregated case no explicit expression is possible and numerical simulations were used to generate spatial distributions. The consequences for host inactivation by the mycoparasite were evaluated using a simple model of omnidirectional and constant growth of the mycoparasite. A random distribution of propagules gave a considerably slower rate of inactivation than the uniform distribution. Numerical simulations were made to generate comparable patterns of host inactivation for aggregated distributions in which propagule clusters were located at random in three-dimensional space and the distances between propagules with centres followed a normal distribution. The number of propagule centres and propagules/centre varied for a given inoculum density. Parameters were estimated from published data for sclerotia of Sclerotium minor inactivation at different densities of macroconidia of Sporidesmium sclerotivorum. Differences in host inactivation between the uniform and random distributions were small but both gave poor predictions of the field data at low and high densities. The aggregated distribution gave an improved fit for the higher propagule densities but no improvement at the lower. In studying the dynamics of mycoparasites it may be more significant epidemiologically to design treatments based on differences in mean distances between propagules rather than population densities. Density-dependent effects on growth rate need more attention in models and studies on mycoparasite ecology.