Pathogen Propagation Model with Superinfection in Vegetatively Propagated Plants on Lattice Space.

Many clonal plants have two reproductive patterns, seed propagation and vegetative propagation. By vegetative propagation, plants reproduce the genetically identical offspring with a low mortality, because resources are supplied from the other individuals through interconnected ramets at vegetative-propagated offspring. However, the ramets transport not only resources but also systemic pathogen. Pathogens evolve to establish and spread widely within the plant population. The superinfection, which is defined as the ability that an established pathogen spreads widely by infecting to already-infected individuals with other strains of a pathogen, is important to the evolution of pathogens. We examine the dynamics of plant reproduction and pathogen propagation considering spatial structure and the effect of superinfection on genetic diversity of pathogen by analysis of several models, 1-strain and multiple-strain models, on two-dimensional square lattice. In the analysis of 1-strain model, we derive equilibrium value by mean-field approximation and pair approximation, and its local stability by Routh-Hurwitz stability criterion. In the multiple-strain models, we analyze the dynamics by numerical simulation of mean-field approximation, pair approximation and Monte Carlo simulation. Through the analyses, we show the effect of parameter values to dynamics of models, such as transition of dominant strain of pathogen, competition between plants and pathogens and density of individuals. As a result, (i) The strain with intermediate cost becomes dominant when both superinfection rate and growth rate are low. (ii) The competition between plants and pathogens occurs in the phase of coexistence of various strains by pair approximation and Monte Carlo simulation. (iii) Too high growth rate leads to the decrease of plant population in all models. (iv) Pathogens are easy to maintain their genetic diversity with low superinfection rate. However, if they do not superinfect, the maintenance becomes difficult. (v) When growth rate of plant is low, individuals are very influenced by distant individuals.