Use of covariates in Taylor's power law for sequential sampling in pest management

In pest management, the pest density within a group of plants needs to be estimated for taking timely actions, such as spraying pesticides or releasing natural enemies. Taylor's power law is widely used for identifying the aggregation patterns of the pests and designing a sequential sampling plan to estimate the pest mean density. The conventional estimates given by Taylor's power law do not consider potential density differences due to various covariates, but focus only on the relationship between the sample means and the variances. In thisarticle, we develop a new sequential sampling stop line based on Taylor's power law by using quasi-likelihood with covariate effects. The simulation results show that the proposed estimators are better than the conventional estimators in terms of mean squared error. For validation and evaluation of the sampling stop line given by the proposed estimator, we use RVSP software in which actual observations are randomly and iteratively sampled until the total number of a pest reaches the stop line. We demonstrate both types of sequential sampling stop lines, those based on the conventional method and those based on the new method, for the population density of spider mites on glasshouse roses.