Estimating densities of grasshopper (Orthoptera: Acrididae) assemblages: an extension of the binomial sampling technique

The effective range of the binomial sampling technique for determining densities of rangeland grasshopper assemblages from the proportion of samples containing grasshoppers was extended by relating the proportion of 0.1${\rm m}^{2}$samples containing at least 2, 3, 4, or 5 grasshoppers (tally thresholds, t) to grasshopper density. This was done by using the Poisson probability density function to calculate the probabilities of obtaining 0, 1, 2, 3, and 4 grasshoppers per 0.1${\rm m}^{2}$. These probabilities were then summed and subtracted from 1.0 to yield the theoretical probabilities corresponding to ≥2, 3, 4, or 5 grasshoppers per sample (binomial sampling models). Data collected throughout central and eastern Wyoming were used to evaluate the fit of these sampling models. Using tally thresholds of 2, 3, 4, and 5, and a maximum-allowable standard error to density ratio of 0.15, grasshopper densities could be reliably estimated up to 38, 63, 84, and 104 grasshoppers per${\rm m}^{2}$(32, 53, 70, and 87 per${\rm yd}^{2}$).