1. 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.
2. Tally thresholds were used to convert quantitative gypsy moth data to binomial, presence–absence data for binary power law analysis.
3. 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.
4. 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.
5. 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.
6. 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.

中文翻译：

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森林昆虫与二元幂律

1. Hughes 和 Madden 的二元幂律用于分析吉普赛蛾 ( Lymantria dispar ) 和成虫 ( Agrilus planipennis )三个生命阶段的样本数据，这两种害虫都是北美重要的入侵森林害虫。
2. 计数阈值用于将定量吉普赛蛾数据转换为二项式存在 - 不存在数据以进行二元幂律分析。
3. 分析了两次翡翠灰蛀虫调查的存在 - 不存在数据，最初的高度密集和昂贵的调查从密歇根州的引入点开始扩展，第二次广泛的调查旨在检测和跟踪甲虫扩大范围的前沿。
4. 在最初的调查数据中发现翡翠蛀虫是适度聚集的，但在前沿调查中非常接近随机。后一个结果与其他发现一致，即在范围边缘的空间分布比在范围中心附近的聚集更少。
5. 初步密集调查中积极观察比例的估计比前沿调查中获得的更精确。
6. 对吉普赛蛾数据的二项式幂律估计和泰勒幂律估计的比较表明，这两种幂律之间可能存在基本联系。讨论了可能的联系、计数阈值的影响及其与采样效率的关系。