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THE RELATION BETWEEN THE SIZE OF PLANT AND THE SPREAD OF SYSTEMIC DISEASES: I. A DISCUSSION OF IDEAL CASES AND A NEW APPROACH TO PROBLEMS OF CONTROL
Author(s) -
Plank J. E.
Publication year - 1947
Publication title -
annals of applied biology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.677
H-Index - 80
eISSN - 1744-7348
pISSN - 0003-4746
DOI - 10.1111/j.1744-7348.1947.tb06371.x
Subject(s) - constant (computer programming) , biology , sowing , logarithm , crop , mathematics , corollary , statistics , agronomy , combinatorics , mathematical analysis , computer science , programming language
it is implicit in the concept of systemic disease that there should be a connexion between the size of the plant and the spread of infection. a first, general theorem, thought to be universally valid, is: the spread of an infectious systemic disease increases with the size of the plants, size being appropriately determined and other factors being constant. a second theorem for infections which enter a crop from without (e.g. from the soil or from another field) is: when a systemic disease enters a crop from some uniform outside source, the logarithm of the proportion of healthy plants is directly proportional to the size of the plants, other factors being constant; as an approximation, the proportion of infected plants is directly proportional to their size, provided that the proportion is small. a corollary to this theorem is that if the proportion of infected plants is small and if the size is inversely proportional to the density of planting, the number of infected plants per unit area will be approximately constant, factors other than size and number being constant. a third theorem for the spread of infection within a crop is: when a systemic disease spreads within a crop, the rate of infection is proportional to the size of the healthy plants, other factors being constant. if factors other than size, time and the proportion of infected plants are constant, the expression for the rate takes one of the three forms: dx/dt = ks (i‐ x ), (i) dx/dt = ks (i‐ x ) x , (ii) or dx/dt = ks (i‐ x ) f ( s , t , x ), (iii) in which x and 1‐ x are, respectively, the proportions of infected and healthy plants, s is the size, and k is a constant. the second part of this theorem is tentative. in these theorems we take by definition a disease to be systemic if a single effective transmission suffices to bring about maximum infection of the plant. size refers to that part of the plant which can receive infection. this definition, with the size of the receiving part having its colloquial meaning, serves for the first, general theorem. for quantitative relations, the guise but not the substance of the definition is changed: size is proportional to the probability that the plant receives infection at any instant from a uniform source in appropriate circumstances. both for general and quantitative relations there is a special case when disease is introduced into a crop by insects or other vectors. size, then, is the catchment zone of the plant for the insects. this accords with the meaning assigned to size in other circumstances; size is here a convenient fiction, the use of which gives precisely the same results as the use of numbers, which are a reality. reduction of size is discussed as a measure of control peculiar to systemic diseases.