Forest insects and the binary power law

Hughes and Madden's binary power law was used to analyse sample data of three life stages of gypsy moth (Lymantria dispar) and adult emerald ash borer (Agrilus planipennis), both important invasive forest pests in North America. Tally thresholds were used to convert quantitative gypsy moth data to binomial, presence-absence data for binary power law analysis. Presence-absence data from two emerald ash borer surveys were analysed, an initial highly intensive and expensive survey expanding out from the point of introduction in Michigan and a second extensive survey designed to detect and track the leading edge of the beetle's expanding range. Emerald ash borer was found to be moderately aggregated in the initial survey data, but very near to random in the leading edge survey. The latter result is consistent with other findings that spatial distribution is less aggregated at range edges than near the centre of the range. Estimates of the proportion of positive observations in the initial intensive survey were found to be more precise than those obtained in the leading edge survey. Comparisons of binomial power law estimates and Taylor's power law estimates of the gypsy moth data suggest the possibility of a fundamental connection between the two power laws. A possible connection, the effect of tally thresholds and their relationship with sampling efficiency are discussed.