Two-Dimensional Distance Class Model for Quantitative Description of Virus-Infected Plant Distribution Lattices

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Abstract
The spatial pattern of virus-infected plants arranged on a variable sized lattice is analyzed by a two-dimensional, distance-class method. The method quantitatively estimates randomness of infected plants and is tolerant of missing data. Average size of the clusters of infected plants and their relative locations on the lattice (X,Y coordinate) are presented. By using one infected plant as the origin, the distance between it and every other infected plant on the lattice is defined in horizontal (X) and vertical (Y) units. Pairs of infected plants are then categorized into two-dimensional, [X,Y], distance classes. The number of pairs of infected plants in each distance class is counted and divided by the total number of pairs in that distance class. The process is repeated using each infected plant on the lattice as the origin. Computer simulations generate expected standardized count frequencies under the assumption of random pattern on the lattice. Levels of significance for the difference between observed and expected values are generated directly during the simulations. Theoretical and empirical sampling are used to demonstrate the power of the test to describe quantitatively the spatial pattern and to compare the two-dimensional analysis with ordinary runs and doublet analysis.