Runs of Healthy and Diseased Trees in Transects Through an Infected Forest: Statistical and Computational Methods

Abstract

The order of occurrence of diseased and healthy plants on a line transect through a patchily-infected study area has been described by Pielou [1963] as a patch-gap Markov process compounded with a diseased-healthy renewal process. Gap-plants are assumed to be healthy (with probability 1) while each patch-plant has an equal and independent chance of being infected, so the process on the observable states of diseased (D) and healthy (H) is a compound of two processes. The statistical analysis of the observed D-H sequence developed by Pielou consists of first enumerating the empirical frequency distributions of diseased plant run lengths and healthy plant run lengths, then estimating the unknown parameters by a method of moments, and then testing goodness of fit to the estimated 'theoretical' frequency distributions of run length. Pielou was unable to give explicit solutions to the moment equations and did not provide standard error formulas; these shortcomings of her analysis are remedied here and, in addition, a simple recursion formula is given for calculating the estimated 'theoretical' frequency distribution of healthy plant run lengths.