Hall et al.: Citrus Rust Mite & the Negative Binomial 1 CITRUS RUST MITE (ACARI: ERIOPHYIDAE) COUNTS ON FRUIT AND THE NEGATIVE BINOMIAL DISTRIBUTION

Count data for the number of citrus rust mites per cm 2 on fruit across a 4-ha (10acre) area of orange trees followed the negative binomial probability distribution 79% of the time based on chi-square tests. A correlation of r = 0.993 was found between observed counts and counts projected based on the distribution. A common k of 0.149 was computed but generally appeared more suitable for mean densities of 3.0 to 55.0 than 0.5 to 3.0 citrus rust mites per cm 2 . For mean densities of from 0.5 to 55 citrus rust mites per cm 2 , the parameter k of the negative binomial was related to the mean density (x): k = 0.081 + 0.1139*(log 10 x). Estimated k -values were used to draw expected count data profiles for several mean densities ranging from 1 to 40 citrus rust mites per cm 2 . Due to the skewness of the count data, the number of mites per cm 2 expected in most individual samples was always considerably smaller than the average density. Based on the negative binomial, mean rust mite densities could be estimated from the percentage of samples with at least one mite. Results of the study provide a means to predict the relative frequency histogram of densities associated with a mean density of citrus rust mites per cm 2 across an area of trees.