Probability Models For Host Infection By Soilborne Fungi

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Abstract
Some theoretical models for the infection of hosts by soilborne fungi are derived. Emphasis is given to the effects of the following phenomena on the probability of infection: spatial pattern of inoculum, displacement of soil by the growth of host organs, and distance of a propagule of inoculum from the surface of the host. A binomial model, of the form P = (1-.vphi.)N, is presented for the probability (P) that a host unit, such as a root, seed, hypocotyl or (in the case of hyperparasitism) a sclerotium, should remain uninfected when exposed to soil randomly infested by N propagules of a pathogen. The probability that the host encounters a fungal propagule, and is infected by it, is given by .vphi.. The zone within which encounter and infection can occur is designated the pathozone. The relationship between the binomial model and the Poisson model is discussed. A negative binomial model, of the form P = (1 + N.vphi. k)-k, is presented for the probability that a host unit should escape infection when exposed to soil in which propagules of the pathogen of parasite are clumped; k is an index of the degree of clumping. Refinements of the models to allow for thresholds of numbers of infections required to cause disease are given and some effects of clumped and randomly dispersed inoculum on the probability of disease escape are shown. Models in which allowance is made for the displacement of soil by the host unit in estimating .vphi. are compared with those that assume no displacement. Differences in the predictions of the models are illustrated for an example of hyperparasitism of sclerotia. More complex binomial models, of the form P = (1-.theta..psi.), for the probability of a host unit escaping infection are presented, in which .theta. is the probability that a propagule occurs in the pathozone, and .psi. is the probability that the propagule can infect the host, conditional on its occurrence in the pathozone.