Dispersion Statistics and Sample Size Estimates for House Fly (Diptera: Muscidae) Larvae and Macrocheles muscaedomesticae (Acari: Macrochelidae) in Poultry Manure

The precision of the density estimate for a given population depends upon the population's density and degree of clumping and upon sampling characteristics, such as the number and surface area of the quadrats. The parameters k of the negative binomial distribution and b of Taylor's power law ( $s^2=a \bar x ^b$ ) were determined for third instars of the house fly, Musca domestica L., and for both sexes of the predaceous mite Macrocheles muscaedomesticae (Scopoli), which were sampled by random quadrats at two shallow-pit, caged-layer poultry houses. Most calculated values of k were <1, but agreement with the negative binomial distribution was found only in 4,18, and 14 of the 27 weekly samples for house fly larvae, female mites, and male mites, respectively. Taylor's power law provided the best fit for the distribution (P < 0.01 for all regression coefficients) with $s^2=9.08 \bar x$ ^1.83 (r² = 0.97) for third-instar house flies and $s^2=4.65 \bar x$ ^1.76 (r² = 0.97) for both sexes of M. muscaedomesticae. Two ecological processes, social clustering and environmental heterogeneity, were hypothesized as the mechanisms determining aggregation of house fly larvae and the macrochelid mites. Regardless of the biological model influencing their distributions, Taylor's power law provided a reliable index for measuring their degree of aggregation. Reliability defined by the coefficient of variability and Taylor's regression coefficients was used to calculate optimum sample size-density estimates for each species with coefficients of variability of 10, 15, 20, and 25%.