Spatio-temporal pattern formation in plant communities formed by Jansen-Connell processes.

     The negative density dependences due to pathogen or herbivore are considered to be important to maintain the diversity in plant communities, so called Janzen-Connell hypothesis. Especially the effect of species-specific soil fungi on the abundance and species richness has been documented. The key component of Janzen-Connell hypothesis is the distance-dependent mortality, which expects the high mortality of seedlings near the conspecifics. It is expected to lead the low recruitment near conspecifics and to prevent the over-dominance of the common species. Although the role of Janzen-Connell hypothesis on the maintenance of diversity has been extensively studied, little is known about the effect on the spatial pattern formation of plant communities. To explore the role of activity of soil pathogen on the spatial pattern of vegetation as well as the species richness, we constructed a 2-demensional spatially explicit mathematical model which described the dynamics of plant community and species-specific soil pathogen. It was assumed that each plant species had a specialist pathogen which infected on the seedlings of focal species and kill them. The growth and spread of pathogen was described as reaction-diffusion equation. As the results, as the growth rate of soil fungi increased, each individual more sparsely distributed and higher species richness was maintained. There was an optimal value of diffusion coefficient of pathogen, in which the highest species richness was realized and the most sparsely each individual distributed. The results suggest that there is the most effective mobility of pathogen to maintain the diversity in forest ecosystems.