Estimation of the Proportion of Vectors in a Natural Population of Insects

A procedure is investigated for estimating the proportion of vectors capable of transmitting aster-yellows virus in a natural population of Macrosteles fascifrons (Stal), the six-spotted leafhopper. A straightforward method and one used in practice is to collect random samples of the population and cage insects individually with previously unexposed aster test plants. If a plant exhibits aster-yellows symptoms in a given time interval, the insect is classified as a vector, and the proportion of infected plants is an estimator of the proportion of vectors in the population. When large numbers of insects are available, this procedure requires a considerable overhead in plants and cages, and it is desirable to use several insects on each plant. If k insects are caged with each plant, the outcome is still binomial, for the experimenter can distinguish only two types of test plants; infected and non-infected. If p is the probability that a randomly selected insect is a vector, the probability that a plant is non-infected is equal to (1 p)k. Some properties of the maximum likelihood estimator of p when such a procedure is used are investigated in this paper, and a method for determining the optimum number of insects per plant for certain cost considerations is given. In general, it will be seen that the experimenter should choose k small and n large, commensurate with costs, to insure against the risk of a dangerously inefficient experiment when little or no information is available regarding p. A closely related problem is the estimation of the frequency or density ,u of a population of microorganisms when a binomial classification only of each sample is possible or desirable, but where the distribution of the number of individuals in a diluted sample is Poisson. This dilution procedure was developed by R. A. Fisher [1921], Fisher et. al. [1922], and is discussed at length by Fisher and Yates [1948], Cochran [1950], and D. J. Finney [1952]. If the population density is ,u, the samples are usually diluted or concentrated by a factor z > 0 such that the density