Abstract

This paper is a reformulation of the paper, Mode 1958 Evolution 12:158 - 165, which was written in terms of a deterministic paradigm, using di erential equations In this paper, however, the working paradigm will be stochastic, and from the mathematical point of view, it will be a stochastic process that may be viewed as a branching process within a branching process. In particular, it will be assumed that the population of host plants will evolve as a multitype branching process, and the pathogen, which grows on the leaves of the host in every generation of the host, will also be assumed to evolve as a multitype branching processes during each generation of the host. The contents of this paper, were motivated by problems in Agriculture in which Plant Pathologists and Plant Breeders work together to control the damage inflicted by a pathogen on a growing crop of a cultivar such as flax, wheat. and many other cultivars. The focus of attention in this paper is the development of algorithms that will guide the development of software to run Monte Carol simulation experiments taking into account mutations in the host and pathogen. The writing of software to implement the algorithms developed in this paper would require a major e ort, and is, therefore, beyond the scope of this paper

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