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
Highlights
This paper is a reformulation of the paper, Mode 1958 Evolution 12:158 - 165, which was written in terms of a deterministic paradigm, using differential equations In this paper, 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
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 be assumed to evolve as a multitype branching processes during each generation of the host
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
Summary
The genetics of pathogenicity and host resistance to flax rust, Melampsora lini (Pers) Lev., has been reported in a pioneering works by Flor (1955 and 1956). Among those researchers, who are sequencing the gnomes of host and pathogens are Dr Robert Brueggeman, Department of Plant Pathology, North Dakota State University His current focus of attention is the sequencing the genomes of barley and one of its parasites, which is a fungus called net blotch. In the paper Richards et al 2016, there is an account of the fine mapping of the barley genome 6H net blotch susceptibility locus G3 This brief review will provide the reader with some of the areas of genomic research that is currently in progress among scientists working on resistance of barley to net blotch, other plant species and pathogens
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