Multivariate control charts for ecological and environmental monitoring

Ecological and environmental monitoring has become increasingly important, with increasing threats from human disturbances. Monitoring usually involves sampling from several sites of a similar habitat at regular (or irregular) intervals through time. The purpose of monitoring is to determine where and when an impact may have occurred or, once detected, may still be occurring. Sequential statistical methods, including control charts, as developed for industrial applications, offer some promise in this regard. These provide a way of identifying when a system (e.g., in a factory) is going out of control, so as to trigger an alarm to stop the system and employ appropriate remedial measures. Such techniques clearly would be useful in the context of environmental monitoring. Traditional control charts, however, cannot be used for many ecological applications because they do not handle multivariate data, and individual counts of species abundances do not generally fulfill the necessary statistical assumptions. A distance-based multivariate control chart method is described here, with some examples of its use in monitoring coral reef fish assemblages of the Great Barrier Reef, Australia. The method is flexible, as it can be based on any dissimilarity measure of choice, and useful, as it does not require any specific assumptions regarding distributions of variables. Bootstrapping techniques are used to provide control-chart limits for an appropriate multivariate distance-based criterion through time. The method is designed to identify impacts at individual sites as quickly as possible, thus triggering an alarm bell in the context of ecological monitoring. It can also be applied at several spatial scales in hierarchical designs.