Allocating Limited Sampling Resources for Estimating Regional Populations of Overwintering Cereal Leaf Beetles 123

Abstract

In population studies, sampling resources are often limited. To maximize the precision of the resulting estimates, it is essential to consider not only the usual statistical parameters of mean and variance, but also the specific research objectives and such distributional phenomena as stratification and spatial homogeneity. Formulae are derived for the optimal allocation of a limited number of emergence traps for estimating a regional population of overwintering cereal leaf beetles which is distributed among 5 different habitat types. With stratified sampling, a substantial increase in reliability per unit cost over simple random sampling can be obtained. Previously published estimates of the number of traps needed to obtain population estimates with a given precision are too large. It is further demonstrated that when estimates of the density of beetles in each separate habitat are wanted with equal precision, the allocation of samples among habitats is quite different from the optimal allocation for estimating the total regional population. The successful application of this last allocation is demonstrated with field results of trapping conducted for validation purposes. An analysis of variance showed that grouping traps into clusters within each habitat to reduce travel costs does not, for the case of cereal leaf beetle emergence data, result in a significant loss of information compared to a stratified random sample.